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Flux

This article is about the concept of flux in natural science and mathematics. For other uses, see Flux (disambiguation).

Concept in natural science and mathematics

This article needs attention from an expert in physics. The specific problem is: confusion between flux and flux density. See the talk page for details. WikiProject Physics may be able to help recruit an expert.(September 2016)

The field lines of a vector fieldFthrough surfaces with unitnormal n, the angle from nto Fis θ. Flux is a measure of how much of the field passes through a given surface. Fis decomposed into components perpendicular (⊥) and parallel ( ‖ ) to n. Only the parallel component contributes to flux because it is the maximum extent of the field passing through the surface at a point, the perpendicular component does not contribute. Top:Three field lines through a plane surface, one normal to the surface, one parallel, and one intermediate. Bottom:Field line through a curved surface, showing the setup of the unit normal and surface element to calculate flux.
To calculate the flux of a vector field \mathbf {F} (red arrows)through a surface Sthe surface is divided into small patches dS. The flux through each patch is equal to the normal (perpendicular) component of the field, the dot productof {\displaystyle \mathbf {F} (\mathbf {x} )}with the unit normal vector {\displaystyle {\hat {\mathbf {n} }}(\mathbf {x} )}(blue arrows)at the point \mathbf {x} multiplied by the area dS. The sum of {\displaystyle \mathbf {F} \cdot {\hat {\mathbf {n} }}\,dS}for each patch on the surface is the flux through the surface

Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.[1]

Terminology[edit]

The word flux comes from Latin: fluxus means "flow", and fluere is "to flow".[2] As fluxion, this term was introduced into differential calculus by Isaac Newton.

The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena.[3] His seminal treatise Théorie analytique de la chaleur (The Analytical Theory of Heat),[4] defines fluxion as a central quantity and proceeds to derive the now well-known expressions of flux in terms of temperature differences across a slab, and then more generally in terms of temperature gradients or differentials of temperature, across other geometries. One could argue, based on the work of James Clerk Maxwell,[5] that the transport definition precedes the definition of flux used in electromagnetism. The specific quote from Maxwell is:

In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface.

— James Clerk Maxwell

According to the transport definition, flux may be a single vector, or it may be a vector field / function of position. In the latter case flux can readily be integrated over a surface. By contrast, according to the electromagnetism definition, flux is the integral over a surface; it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwell's quote only makes sense if "flux" is being used according to the transport definition (and furthermore is a vector field rather than single vector). This is ironic because Maxwell was one of the major developers of what we now call "electric flux" and "magnetic flux" according to the electromagnetism definition. Their names in accordance with the quote (and transport definition) would be "surface integral of electric flux" and "surface integral of magnetic flux", in which case "electric flux" would instead be defined as "electric field" and "magnetic flux" defined as "magnetic field". This implies that Maxwell conceived of these fields as flows/fluxes of some sort.

Given a flux according to the electromagnetism definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the transport definition. Given a current such as electric current—charge per time, current density would also be a flux according to the transport definition—charge per time per area. Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously. Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux the term corresponds to.

Flux as flow rate per unit area[edit]

In transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity]·[time]−1·[area]−1.[6] The area is of the surface the property is flowing "through" or "across". For example, the magnitude of a river's current, i.e. the amount of water that flows through a cross-section of the river each second, or the amount of sunlight energy that lands on a patch of ground each second, are kinds of flux.

General mathematical definition (transport)[edit]

Here are 3 definitions in increasing order of complexity. Each is a special case of the following. In all cases the frequent symbol j, (or J) is used for flux, q for the physical quantity that flows, t for time, and A for area. These identifiers will be written in bold when and only when they are vectors.

First, flux as a (single) scalar:

{\displaystyle j={\frac {I}{A}}}

where:

{\displaystyle I=\lim \limits _{\Delta t\rightarrow 0}{\frac {\Delta q}{\Delta t}}={\frac {\mathrm {d} q}{\mathrm {d} t}}}

In this case the surface in which flux is being measured is fixed, and has area A. The surface is assumed to be flat, and the flow is assumed to be everywhere constant with respect to position, and perpendicular to the surface.

Second, flux as a scalar field defined along a surface, i.e. a function of points on the surface:

{\displaystyle j(\mathbf {p} )={\frac {\partial I}{\partial A}}(\mathbf {p} )}
{\displaystyle I(A,\mathbf {p} )={\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} )}

As before, the surface is assumed to be flat, and the flow is assumed to be everywhere perpendicular to it. However the flow need not be constant. q is now a function of p, a point on the surface, and A, an area. Rather than measure the total flow through the surface, q measures the flow through the disk with area A centered at p along the surface.

Finally, flux as a vector field:

{\displaystyle \mathbf {j} (\mathbf {p} )={\frac {\partial \mathbf {I} }{\partial A}}(\mathbf {p} )}
{\displaystyle \mathbf {I} (A,\mathbf {p} )={\underset {\mathbf {\hat {n}} }{\operatorname {arg\,max} }}\,\mathbf {\hat {n}} _{\mathbf {p} }{\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} ,\mathbf {\hat {n}} )}

In this case, there is no fixed surface we are measuring over. q is a function of a point, an area, and a direction (given by a unit vector, \mathbf {\hat {n}} ), and measures the flow through the disk of area A perpendicular to that unit vector. I is defined picking the unit vector that maximizes the flow around the point, because the true flow is maximized across the disk that is perpendicular to it. The unit vector thus uniquely maximizes the function when it points in the "true direction" of the flow. [Strictly speaking, this is an abuse of notation because the "arg max" cannot directly compare vectors; we take the vector with the biggest norm instead.]

Properties[edit]

These direct definitions, especially the last, are rather unwieldy. For example, the argmax construction is artificial from the perspective of empirical measurements, when with a Weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway.

If the flux j passes through the area at an angle θ to the area normal \mathbf {\hat {n}} , then

\mathbf {j} \cdot \mathbf {\hat {n}} =j\cos \theta

where · is the dot product of the unit vectors. This is, the component of flux passing through the surface (i.e. normal to it) is j cos θ, while the component of flux passing tangential to the area is j sin θ, but there is no flux actually passing through the area in the tangential direction. The only component of flux passing normal to the area is the cosine component.

For vector flux, the surface integral of j over a surfaceS, gives the proper flowing per unit of time through the surface.

{\displaystyle {\frac {\mathrm {d} q}{\mathrm {d} t}}=\iint _{S}\mathbf {j} \cdot \mathbf {\hat {n}} \,{\rm {d}}A\ =\iint _{S}\mathbf {j} \cdot {\rm {d}}\mathbf {A} }

A (and its infinitesimal) is the vector area, combination of the magnitude of the area through which the property passes, A, and a unit vector normal to the area, \mathbf {\hat {n}} . The relation is \mathbf {A} =A\mathbf {\hat {n}} . Unlike in the second set of equations, the surface here need not be flat.

Finally, we can integrate again over the time duration t1 to t2, getting the total amount of the property flowing through the surface in that time (t2t1):

{\displaystyle q=\int _{t_{1}}^{t_{2}}\iint _{S}\mathbf {j} \cdot {\rm {d}}{\mathbf {A} }\,{\rm {d}}t}

Transport fluxes[edit]

Eight of the most common forms of flux from the transport phenomena literature are defined as follows:

  1. Momentum flux, the rate of transfer of momentum across a unit area (N·s·m−2·s−1). (Newton's law of viscosity)[7]
  2. Heat flux, the rate of heat flow across a unit area (J·m−2·s−1). (Fourier's law of conduction)[8] (This definition of heat flux fits Maxwell's original definition.)[5]
  3. Diffusion flux, the rate of movement of molecules across a unit area (mol·m−2·s−1). (Fick's law of diffusion)[7]
  4. Volumetric flux, the rate of volume flow across a unit area (m3·m−2·s−1). (Darcy's law of groundwater flow)
  5. Mass flux, the rate of mass flow across a unit area (kg·m−2·s−1). (Either an alternate form of Fick's law that includes the molecular mass, or an alternate form of Darcy's law that includes the density.)
  6. Radiative flux, the amount of energy transferred in the form of photons at a certain distance from the source per unit area per second (J·m−2·s−1). Used in astronomy to determine the magnitude and spectral class of a star. Also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the electromagnetic spectrum.
  7. Energy flux, the rate of transfer of energy through a unit area (J·m−2·s−1). The radiative flux and heat flux are specific cases of energy flux.
  8. Particle flux, the rate of transfer of particles through a unit area ([number of particles] m−2·s−1)

These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the divergence of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space. For incompressible flow, the divergence of the volume flux is zero.

Chemical diffusion[edit]

As mentioned above, chemical molar flux of a component A in an isothermal, isobaric system is defined in Fick's law of diffusion as:

\mathbf {J} _{A}=-D_{AB}\nabla c_{A}

where the nabla symbol ∇ denotes the gradient operator, DAB is the diffusion coefficient (m2·s−1) of component A diffusing through component B, cA is the concentration (mol/m3) of component A.[9]

This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux.[5]

For dilute gases, kinetic molecular theory relates the diffusion coefficient D to the particle density n = N/V, the molecular mass m, the collision cross section\sigma , and the absolute temperatureT by

D={\frac {2}{3n\sigma }}{\sqrt {\frac {kT}{\pi m}}}

where the second factor is the mean free path and the square root (with Boltzmann's constantk) is the mean velocity of the particles.

In turbulent flows, the transport by eddy motion can be expressed as a grossly increased diffusion coefficient.

Quantum mechanics[edit]

Main article: Probability current

In quantum mechanics, particles of mass m in the quantum stateψ(r, t) have a probability density defined as

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Sigma

Sigma.png

"There is no obligation for the universe to make sense to you."

Real Name

Siebren de Kuiper

Status

Active

Age

62

Nationality

Netherlands Dutch

Occupation

Astrophysicist

Base

The Hague, Netherlands (formerly)

Affiliation

Talon

Voice

Boris Hiestand (English)

Yann Guillemot (French)
Richard Gonlag (German)
Liu Yijia (Mandarin (China))
Huang Tian-you(Mandarin(Taiwan))
Takahiro Shimada (Japanese)
Luca Semeraro (Italian)
Luis Ferando Ríos(European Spanish)
Marcelo Pissardini (Brazilian Portuguese)

Cosmetics

Cosmetic page

Quotes

Quotation page

Role

Tank

Health

300

Shields

100

Sigma is a Tankhero in Overwatch.

Overview[]

Sigma is an eccentric astrophysicist and volatile tank who gained the power to control gravity in an orbital experiment gone wrong. Manipulated by Talon and deployed as a living weapon, Sigma’s presence on the battlefield cannot be ignored.

Abilities[]

Hero-ability-circle.svg
Abilities-sigma1.png
Aim Type
Arcing projectileArcing projectile

Sigma launches two gravitic charges, which bounce off walls and implode after a short duration, damaging enemies within a sizable radius.

Damage:

2 charges per burst, each:
55 direct damage
9 - 30 splash damage
2.25 - 7.5 self damage

Projectile speed:

50 meters per second

Max. range:

22 meters

Area of effect:

3 meter implosion radius

Rate of fire:

1 burst per 1.5 seconds

Launch two charges which implode after a short duration, dealing damage in an area.

Details:
  • Bounces off walls, floors, and ceilings.
  • Enemies hurt by the implosion will be slightly pulled towards the center.
  • The charges automatically implode after travelling 22 meters. However, the maximum reach of Hyperspheres is slightly less than 22 meters due to the fact that the charges also travel downwards.
  • Unlike other arcing projectiles like Junkrat’s grenade launcher and Torbjörn’s rivet gun, Sigma’s Hyperspheres’ downward movement is very minimal and aiming them does not require you to account for their downward movement unless enemies are near their maximum range.
Hero-ability-circle.svg
Abilities-sigma2.png

2 seconds when recalled
5 seconds if destroyed

Sigma propels a floating barrier to a location of his choosing. He can retrieve the barrier at any time.

Healing:

Regenerates 80 barrier health per second, after being down for 2 seconds

Projectile speed:

16.5 meters per second

Area of effect:

4.5 meter height; 5 meter width at the poles, curves to 7 meters in the middle

Cooldown:

2 seconds when recalled
5 seconds if destroyed

Hold to propel a floating barrier; release to stop. Press again to recall the barrier to you.

Details:
  • Upon activation, the barrier moves forward by holding down the ability key and stops when released.
  • Walls will block the barrier's path if the center of the barrier is blocked. The barrier will coast along the ground if the angle down is 45° or lower.
  • The barrier can be removed by pressing the ability key again, keeping all its remaining health. This can be done at any time, including in the middle of other abilities such as Kinetic Grasp.
  • The barrier is destroyed if it goes out of bounds.
  • The barrier immediately returns to Sigma if he is eliminated or Ability Sombra Hack.png hacked.
Hero-ability-circle.svg
Abilities-sigma3.png

12 seconds

Sigma freezes incoming projectiles in midair, converting them into shields.

Health:

60% of damage absorbed is converted to temporary shields (max. 400)

Absorb projectiles in front of you and convert them into shields.

Hero-ability-circle.svg
Abilities-sigma4.png

10 seconds

Aim Type
Arcing projectileArcing projectile

Sigma gathers a mass of debris and flings it at an enemy to knock them down.

Damage:

70 direct damage
12 - 40 splash damage
6 - 20 self damage

Projectile speed:

37.5 meters per second

Max. range:

4 meters knockback (direct)
1 - 2 meters knockback (splash)
2 meters knockback (self)

Area of effect:

2.5 meter explosion radius

Casting time:

0.65 seconds

Duration:

0.8 second knock down

Gather a mass of debris and throw it at an enemy to knock them down.

Hero-ability-circle.svg
Abilities-sigma5.png

1960 points

Aim Type
Area of effectArea of effect

Unleashing his full powers, Sigma takes flight, lifts enemies in a targeted area, and launches them into the sky before slamming them back down.

Damage:

50 damage (lift)
50% max HP (slam)

Move. speed:

7.15 meters per second

Max. range:

35 meters

Area of effect:

7 meter radius

Casting time:

0.6 seconds (intro)
1 second (lift)

Duration:

Up to 5 seconds to select the area
2 seconds (lift)
0.6 seconds (high gravity)

Ultimate cost:

1960 points

Manipulate gravity to lift enemies into the air and slam them back down.

Strategy[]

Sigma is a Tank Hero boasting both consistent offensive and defensive abilities. However, his lengthy cooldowns requires one to think ahead rather than freely using his abilities. While he is capable of high damage output, he is most useful when fighting at a distance with Accretion and Hyperspheres while making openings and defending his team with his versatile Experimental Barrier. Quick thinking and superb situational awareness is needed when using Kinetic Grasp to protect himself and his team.

Sigma's abilities can give off the perception that he is stronger than he is, which can make it tempting for players to play overly aggressive with him. While Sigma has the capability to deal a lot of damage, his lack of mobility will make any situation where you're stranded alone and surrounded by enemies a disaster. Overextending with Sigma will in most cases result in dying a swift death; likewise, if you believe your teammates are nearby but they've already fled from a fight, you're just as likely to be eliminated. With that being said, Accretion and his Hyperspheres can quickly take out a singular escaping enemy, such as Lúcio or Tracer; in these cases, finishing them off before they can flee is the correct play. Being able to distinguish when it's a good time to push forward and when it's better to stay behind your team will be instrumental to the survival of both yourself and your team.

Weapons & Abilities[]

  • Hyperspheres: Sigma's primary fire. Utilizes a two-round burst projectile fire which detonate shortly after firing, capable of damaging multiple enemies at one time and bouncing around corners to deal with heroes out of your direct view. Their detonations have a minor gravity effect similar to Orisa'sHalt!, though much weaker.
    • The projectiles' damage is moderate and consistent, though incapable of headshots. These are best utilized in close spaces, where the Hyperspheres can bounce around obstacles and deal damage to multiple enemy players or players hiding behind corners.
    • The short range of the projectiles limits their ability to fight in open areas; try to stay within an area that enemies congregate in, such as near enemy cover or in small quarters.
    • The minor gravitational effect can be utilized to slow down quick heroes such as Lucio, Soldier: 76, and Genji.
    • Though their range is limited, their moderate damage can be used to whittle away at enemy barriers without exposing yourself.
  • Experimental Barrier: A sizable barrier which can be deployed and retracted at will, and can be deployed at any area within Sigma's line of sight.
    • Experimental Barrier is able to be used in a multitude of situations to save yourself and your team, and will rely heavily on your ability to respond quickly to the situation at hand.
    • Using the speed of the barrier, you can block the usage of Ultimates from Soldier 76, Pharah, Reaper, Reinhardt, Cassidy, Ashe (B.O.B.), Bastion, Roadhog, and sometimes D.Va (although she might destroy the barrier). This can potentially deny a game-changing enemy play, and it can help contest the objective by delaying/neutralizing an enemy's ability to use their Ultimate.
    • Using your barrier, you can advance through choke-points quickly and relocate your barrier after passing through it.
    • Working with a friendly Reinhardt or Orisa can assist in absorbing a large amount of damage with your multiple barriers.
    • Experimental Barrier will best be used with another barrier Tank like Reinhardt or Orisa because it is powerful and moves quickly. You want another barrier that can cover your team's flank as you advance with Experimental Barrier.
    • A charging Reinhardt has the same speed as Experimental Barrier, so Sigma's barrier can be used to protect the Reinhardt from an otherwise deadly move.
  • Kinetic Grasp: Kinetic Grasp is similar to D.Va's Defense Matrix, though its range is shorter. Where it lacks in length, it makes up in width. It can protect not only Sigma himself, but the heroes directly besides and behind him.
    • You want to use this ability to save your teammates more than yourself, or in the event of a large amount of projectile damage coming towards the team.
    • A keen sense of situational awareness is needed for this ability, to be able to remove projectile Ultimates going on in a fight that could potentially result in game-changing plays.
    • Using this ability during Barrage can buy your team valuable time, as well as make Sigma into a physical shield to absorb the Ultimate. Combining Kinetic Grasp and Experimental Barrier can stop Barrage's damage output altogether while giving Sigma a full shield charge.
  • Accretion: Sigma's Accretion ability grants him a unique stun ability in Overwatch, given it cannot be stopped by anything other than a physical barrier. It has the ability to stun heroes for an extended period of time, while also dealing moderate damage.
    • Use this ability sparingly, as the large cooldown will leave you without the ability later in the fight when a quick pick can be achieved using it.
    • Accretion can be used to save supports being punished by either flanking Damage heroes or bruiser type tanks like D.Va by stopping them from escaping or pursuing their target.
    • Best used when a enemy hero is caught in the open by themselves, or are generally low enough to be picked off by Accretion or by some follow-up damage.
    • Tossing this ability into a hero using a channelled Ultimate ability will stop that ultimate. These include Reaper, Pharah, Roadhog, and Sigma, among others.
    • Though a high skill-gap comes with using Accretion, the ability to land long-range tosses will set your team up for an easy pick or simply disable one enemy player for 0.8 seconds for longer tosses.
  • Gravitic Flux: A powerful ability that can be used to disrupt an enemy team that is hunkering down in one location, or to end a team's contesting of the point in critical points. As powerful as the ability is it can be easy to want to use it on a few heroes at a time, try to limit its use to when the enemy is congregated together or multiple heroes are low.
    • Because of the similarities to Meteor Strike, you will want the enemy team distracted while you are using this, as they will disperse to avoid being caught in your Ultimate. Try combining your Ultimate with Earthshatter and Graviton Surge to ensure you have heroes in your Ultimate when cast.
    • Communicate with your "DPS" heroes when you are casting Gravitic Flux, as they will be able to capitalize on it with either damage output or usage of an ultimate while they are suspended in the air.
    • While this Ultimate is amazing in open areas and on objectives, don't neglect the lethality of it in enclosed spaces. Casting this Ultimate in an enclosed space can open up opportunities that aren't viable out in the open, such as RIP-Tire and Death Blossom.
    • With some practice, this ability can be used with Minefield and Self-Destruct. Timing and communication will be key, as all three Ultimates have a warm-up before they are able to deal damage.
    • Using this ability over the objective can cause Overtime to end during the suspension phase, so it is highly recommended to use this to your advantage if there is only a few heroes on point contesting to force them off or force them into the air.

General Strategies[]

  • Sigma floats like Zenyatta, meaning he makes no audible footsteps. This can be quite useful if attempting to flank, hide from enemies, or capture the objective while the enemy team is distracted.
  • Keeping distance from enemy heroes is key to playing Sigma, as Hyperspheres and Accretion both cause damage to Sigma. Being able to keep your distance and utilizing walls to bounce your Hyperspheres will prove more useful than a front-on fight.

Advanced Strategies[]

  • Sigma is best used with another tank, that comes with a defensive shield formation called the "The Roman Tortoise." This requires the main tank (Reinhardt or Orisa) to have their barrier up, usually in a choke, and Sigma has his barrier placed directly above at a roughly 45 degree angle to cover his team from explosives. This formation works best on defense, and with much practice can be used offensively with Reinhardt.
  • The Experimental Barrier can be used to mass clear mines from Wrecking Ball's ultimate ability.
  • By placing your Experimental Barrier in front of an enemy Pharah using her ultimate, it is quite likely she will eliminate herself with the splash damage. This has to be done very precisely as your shield will get melted before you know it, and the time frame is very small.
  • Barrier management is the core of Sigma’s kit. It’s recommended to play around his cool downs, using Experimental Barrier to protect your team until Kinetic grasp is ready. Then, you drop your barrier and absorb all incoming damage, which will allow you to be much more aggressive.

Tank

Hero Match-Up Team Synergy
Icon-D.Va.png
D.Va
While D.Va can block your Hyperspheres with her Defense Matrix, she won't be able to block Accretion; if D.Va is trying to shield her team from oncoming damage, feel free to hit her with a big rock. If she attempts to rush you, you can use Kinetic Grasp to block her Micro Missiles. Your Experimental Barrier can shield your team from Self-Destruct, but because it's a smaller barrier than that of most other Tanks, it may be tricky to successfully save your team in the heat of the moment.With a friendly D.Va on your team, you'll have an incredibly easy time negating incoming projectiles and covering each other's bases. That being said, you'll have a much greater difficulty against beam weapons such as the likes of Zarya and Symmetra. Play a more defensive role, as your D.Va will most likely be playing more offensively.
Icon-Orisa.png
Orisa
Orisa's rapid fire can be easily absorbed by Kinetic Grasp; when she is opening fire on you and your team, it's best to retract your Experimental Barrier to give it some downtime, absorb her fire with Kinectic Grasp, them redeploy your recovered barrier while having gained yourself some health in the process. Due to her Protective Barrier, it can be hard to land a majority of your attacks on Orisa unless either you maneuver around it or your team manages to break it. Most of the time when fighting Orisa you'll be forced to continuously lob Hyperspheres at her barrier in an attempt to crack it, but if your team is pushing onto Orisa's position, you can move past her barrier to get in her face where she's not as comfortable. Fortify will still make killing her difficult, though, as she'll be immune to the pull from your Hyperspheres as well as the stun effect from Accretion, not to mention rendering her immune to Gravitic Flux. While it's advised to save most of your abilities until Fortify is on cooldown, this is especially true for Gravitic Flux. Be careful of her Halt!, as your low mobility means you can easily be snagged by it and dropped down a pit.Working together with a friendly Orisa generally means you'll both be able to quickly put out barriers without having to dedicate yourself to staying behind them. However, while you can both move your barriers around at will, Orisa's is on the weaker side, meaning a concentrated push from the enemy could break through your barriers at once. You also need to be careful for a Sombra EMP, which can immediately demolish both of your barriers.
Icon-Reinhardt.png
Reinhardt
While you have the advantage at medium-range, at close range Reinhardt has the upper hand with his unblockable primary weapon and higher health pool. In addition, your Hyperspheres and Accretion deal self-damage at close range, making directly engaging a Reinhardt at close range very risky. However, you are still capable of nullifying some of the threat he poses. Kinetic Grasp is an excellent tool to deny Reinhardt long-range ultimate charge from his Fire Strike, giving you a small chunk of extra shield health in the process. You can fire Hyperspheres at an angle above his shield, or attempt to ricochet them around to deal damage to both him and any of his teammates close by. If he attempts to charge into your team, you can cancel it with Accretion, potentially saving any pinned teammates, and leaving Reinhardt vulnerable. Experimental Barrier and Accretion can also completely deny Earthshatter if timed properly. Having a friendly Reinhardt means running a barrier-heavy team composition. Because Reinhardt will be more planted in place, this give you a little more freedom to be aggressive, but you still shouldn't stray too far from Reinhardt so that neither of you get ambushed. If Reinhardt hits a large number of opponents with Earthshatter, you can follow up with Gravitic Flux to easy kill all of the stunned opponents. Experimental Barrier travels at the same speed as a charging Reinhardt, so consider coordinating with your allied Reinhardt to protect him during a risky charge.
Icon-Roadhog.png
Roadhog
You and Roadhog are both primarily effective at mid to close range. However, if he grabs you with his Chain Hook, he will easily gain the upper hand. It's important to keep your Experimental Barrier between yourself and Roadhog to keep him from Hooking you. Him being so large and slow makes him an easy target for your Hyperspheres as well as Accretion and Gravitic Flux. It's best to use Accretion on him when he's using Take a Breather, which will disrupt his healing and damage-reduction to render him easier to finish off. If he unleashes Whole Hog on you and your team, try to quickly cancel it out with either Kinetic Grasp or Accretion; Experimental Barrier won't do much, as his high damage with low spread will shred your barrier apart in an instant.A Roadhog being your team's second tank will force you to play a defensive, team-supporting role. Your slow mobility will also make it difficult for the two of you to flank enemies. However, so long as you keep track of each other's position, you can work well together. An enemy snagged by Roadhog's Chain Hook makes for an easy target for your Hyperspheres or Accretion if you want to stun them even longer. If Roadhog stays by your side, he can also help pull flankers off of you with his Chain Hook.
Icon-Sigma.png
Sigma
You should focus on putting pressure on an enemy Sigma's Experimental Barrier, forcing him to recall it to recharge. Your Hyperspheres can be absorbed by Kinetic Grasp, but Accretion cannot, so focus on attempting to stun Sigma out of Kinetic Grasp where possible, to deny him extra shields. You should also try to block his Accretion with your Experimental Barrier. If you know an enemy Sigma has Gravitic Flux, save your Accretion to attempt to stun him and cancel the ultimate.With Sigma's abilities such as a retractable barrier, a damaging and stunning rock, projectile absorption, and a slam. One Sigma can protect the team from behind while another from the front. Another thing you can do is one Sigma uses an ability and the other one can use that same ability while the others is on cooldown.
link=http://overwatch.gamepedia.com/Wrecking Ball
Wrecking Ball
Wrecking Ball's high mobility and knockback-based attacks can make him difficult to deal with on your own. Kinetic Grasp can block his Quad Cannons, but its damage output does not give a lot of bonus shields. Focus on attempting to hit Wrecking Ball with Accretion to stop him from plowing through your team, especially if he uses Piledriver in the middle of your group. Accretion is also a valuable tool to halt Wrecking Balls attempting to stall the point by spinning. You can use Experimental Barrier to block the damage from Piledriver to anyone behind it, as well as being able to clear a path through his Minefield, although this will probably destroy your shield.Sigma's almost non-existent mobility can make synergising with a friendly Wrecking Ball difficult. The best thing you can do to help him is to provide your Experimental Barrier to protect him, however this will leave your team short of a shield. You can also stun enemies knocked up with Piledriver with Accretion, which should be easy to hit as enemies hit by Piledriver have a locked trajectory. In addition, Gravitic Flux can be used in combination with Minefield to quickly eliminate a group of enemies.
Icon-Winston.png
Winston
Winston's Tesla Cannon damage cannot be blocked by either Experimental Barrier or Kinetic Grasp, so save both for more important sources of damage. You have a longer effective range than Winston does, and his large hitbox makes your Hyperspheres easy to hit, but his Barrier Projector can make doing damage to him difficult if he engages with it. If Winston attempts to dive directly into your team, his predictable path can make hitting him with Accretion easy, however Winston can counter it with his Barrier Projector. Instead, focus on attempting to stun Winston as he moves to disengage with Jump Pack. If you can hit him, his momentum will be cancelled, and he will be left vulnerable. Your low mobility and large hitbox makes you easy to juggle around for a Winston in Primal Rage, and his high health and lowered Jump Pack cooldown will make stunning him with Accretion largely ineffective unless your entire team is focusing him at the moment you stun, so focus on drawing an ulting Winston's attention away from your squishier teammates by shooting at him.Sigma has no notable team synergy with Winston.
Icon-Zarya.png
Zarya
At high energy, Zarya is capable of shredding your Experimental Barrier in seconds, and its beam cannot be blocked by Kinetic Grasp, however you can absorb her secondary fire projectiles. Avoid shooting into her bubbles to reduce her damage output, and wait for her to use her bubbles before casting Gravitic Flux, as they are capable of nullifying the slam damage for both her and any of her teammates that she protects, in addition to giving her a massive amount of energy. Kinetic Grasp is capable of absorbing Graviton Surge, however its short range and fairly long cooldown can make this tricky.Zarya can work with Sigma in a similar way to Reinhardt, however your smaller and weaker barrier in addition to your lower health pool makes it a less optimal duo.

Damage[]

Hero Match-Up Team Synergy
Icon-ashe.png
Ashe
You can use your Experimental Barrier to block Ashe's line of sight, but this will only momentarily faze her while she repositions. Instead, focus on using Experimental Barrier to block Dynamite, as the burn damage is a major part of Ashe's ultimate charge gain. Do not bother using Kinetic Grasp against B.O.B, as you will not gain a lot of shields, so use Experimental Barrier to block off B.O.B from doing damage.If you and a friendly Ashe time the activation of B.O.B. and Gravitic Flux just right, you can have B.O.B. crash into a team to stun them long enough to be stuck in place and grabbed by Gravitic Flux, at which point B.O.B. will have free range to gun them all down in the air.
Icon-Bastion.png
Bastion
Bastion's Sentry mode fire will demolish your Experimental Barrier extremely quickly. Only use it momentarily to block bursts of damage while your team attempts to cross an area covered by Bastion. Using Kinetic Grasp to close the gap between you and Bastion is the best move, as you will gain a massive amount of shields from Bastion's high damage output. If the Bastion has no barrier protecting him, you can use Accretion to stun him and force him out of Sentry form. Bastions in Tank mode will often play very aggressively out of cover, so you can block his rockets with Experimental Barrier and/or Kinetic Grasp, and stun him with Accretion to slow him down.If you're helping protect a friendly Bastion, you can use Kinetic Grasp to absorb a burst of attacks from the likes of Soldier: 76 or Pharah, and at all other times you can keep it safe with your Experimental Barrier.
Icon-Doomfist.png
Doomfist
(To be added)Sigma has no notable team synergy with Doomfist.
Icon-Echo.png
Echo
(To be added)(To be added)
Icon-Genji.png
Genji
With some practice, Gravitic Flux can be used effectively to counter Dragonblade (and preferrably one assisted with nano boost). First, you have to wait for the genji to pull out his blade, after which he will dash to his first target. As soon as he dashes to, for example a friendly ana, use your Gravitic flux on him while he is relatively still. The time frame here is quite small, but more than long enough to get him in the flux and finish him off. This play is always worth it, as trading 2 ults for 1 and saving many friendly's is worth it.Once you grab a large number of opponents and crash them down with Gravitic Flux, any survivors will be greatly weakened, serving as easy targets for a friendly Genji to run through with Swift Strike or Dragonblade.
Icon-Hanzo.png
Hanzo
(To be added)Sigma has no notable team synergy with Hanzo.
Icon-Junkrat.png
Junkrat
Junkrat's heavy spam damage will quickly destroy your Experimental Barrier. Close the gap with Kinetic Grasp, as the high damage output of Junkrat's explosives will give you plenty of extra shield health to work with. You can also destroy RIP-Tire with a single burst of your Hyperspheres.An enemy team lifted into the air with Gravitic Flux serves as an easy target for a friendly Junkrat to blow apart with RIP-Tire.
75px
Cassidy
(To be added)Experimental Barrier's mobility can provide good cover for a friendly Cassidy to get up close and damage enemies while giving him ample protection. If you lift the enemy team into the air with Gravitic Flux, Cassidy can easily gun them down with Deadeye. Just be careful about a lifted Reinhardt, as he'll still be able to deploy his barrier to protect any teammates floating behind him.
Icon-Mei.png
Mei
(To be added)Blizzard combos excellently with Gravitic Flux; enemies slowed to a crawl will be unable to escape Gravitic Flux's reach, and once they come crashing down, they will be quickly finished off by either your teammates or the gradual damage from Blizzard's freezing. Outside of your Ultimates, enemies frozen by Mei serve as easy targets for Hyperspheres or Accretion, while Mei can also use her Endothermic Blaster to freeze quick enemies trying to heckle you up close.
Icon-Pharah.png
Pharah
Due to her ability to constantly be hovering in the air, it will usually be easy for Pharah to hover out of your Experimental Barrier's area of protection, making it difficult to block her shots. However, a quick deployment in response to her Rocket Barrage can both save your team and cause Pharah to die from the recoil. Barring this, you can use Kinetic Grasp to absorb both her standard rocket fire as well as her Rocket Barrage. Unless Pharah is hovering extremely close to the ground, don't expect to land much damage on Pharah, if at all; focus on keeping your teammates safe so they can gun her down.Sigma has no notable team synergy with Pharah.
Icon-Reaper.png
Reaper
Out of all the shield tanks, Sigma arguably has the best match up against reaper. A good combo to remember against reaper is as follows: Hit him with hyperspheres until he uses wraith form, then use accretion and finish him off with some more hyperspheres. Do all of this after using Kinetic grasp for shield gain and while shield dancing with your Experimental Barrier to minimize the amount of damage received. Hitting your accretion and all hyperspheres is crucial, however this is very easy since reaper's combat style forces him to be up close.Sigma has no notable team synergy with Reaper.
Icon-Soldier 76.png
Soldier: 76
(To be added) Soldier 76's ultimate ability, tactical visor works very well with sigma's ultimate in open areas. By elevating everyone caught in your ultimate above any possible cover (besides barriers), you are essentially giving your friendly soldier 76 a free firing range. Use this combination of Gravitic flux + Tactical visor to pick off valuable targets in the backline, or a few isolated targets such as healers to turn the fight in your favour.
Icon-Sombra.png
Sombra
Hack will force your Experimental Barrier back to you, so make any effort you can to avoid being hacked. With quick reaction times, you can place a shield between you and Sombra to block line of sight for her Hack, and it can also block her bullets to deny her ultimate charge. You can also attempt to stun her with Accretion if your team is focusing her, to prevent her from trying to teleport away. Hack will completly cancel your Gravitic Flux, so wait for her to use it before casting your ultimate. EMP is a massive threat to you, as your Experimental Barrier will be completely destroyed by it, in addition to your shield health, and any additional shields you have gained from Kinetic Grasp. If you suspect that a Sombra has EMP, try and keep your barrier retracted to avoid it being completely obliterated.Should a friendly Sombra use EMP to neutralize an enemy team, this can render them easier targets to grab with Gravitic Flux and kill in one go.
Icon-Symmetra.png
Symmetra
Symmetra's Photon Projector beam will charge up and gain ammo from your Experimental Barrier, and can shred it in seconds if you do not manage it carefully. The beam cannot be blocked by Kinetic Grasp, which can kill you quickly at high charge, and her small frame can make her difficult to hit with your Hyperspheres, so avoid directly confronting a Symmetra if possible. You do have a slight range advantage however, so try to engage her beyond the range of her beam if possible. Kinetic Grasp can absorb her secondary fire orbs, however their low fire rate will make absorbing more than one unlikely, so only try to absorb them if they are part of additional spam. You can use Experimental Barrier to block the damage of her Sentry Turrets while you or your team destroy them, and you can ricochet Hyperspheres off surfaces to destroy hidden ones.Symmetra's teleporter can help improve your low mobility, getting you to high ground or other locations that would normally be difficult for you to reach. When she activates Photon Barrier, you'll typically want to retract your Experimental Barrier so that you can save its energy while the massive health of her barrier absorbs the brunt of enemy attacks.
Icon-Torbjörn.png
Torbjörn
(To be added)In a pinch, you can use your Experimental Barrier to keep Torbjörn's turret safe.
Icon-Tracer.png
Tracer
Tracer's erratic movement and small hitbox will make it difficult for you to hit her. You can try and stun her with Accretion, but its relatively slow cast speed will make it easy for Tracer to reactively dodge it. However, hitting one or two Hyperspheres on her will usually force a Recall out of her. You also can use Kinetic Grasp to absorb Pulse Bomb.Sigma has no notable team synergy with Tracer.
Icon-Widowmaker.png
Widowmaker
If you spot an enemy Widowmaker trying to snipe your team, you can deploy your Experimental Barrier to block off her shots by covering her sniping location, which can prove to be very annoying. Just be aware that this is a temporary solution, as the Widowmaker can eventually relocate and this act is depriving your team of a shield. Only use this tactic until a friendly flanker can approach Widowmaker and take her out, or at least disrupt her long enough that you can focus on your team again. Kinetic Grasp can absorb her shots, but she's unlikely to fire more than once, instead waiting until your ability has worn off, so be sure to be behind cover as soon as you're on cooldown.Sigma’s ultimate can allow a friendly Widowmaker to get a few headshots while enemies are in the air.

Support[]

Hero Match-Up Team Synergy
Icon-Ana.png
Ana
You can place your Experimental Barrier between Ana and her team to stop her from being able to heal them. One of the most important things you should be doing is using Experimental Barrier to block her Biotic Grenade and Sleep Dart.You're modestly powerful when Nano-Boosted by Ana; your high-powered Hyperpheres can plow through enemies, but their low range and your low mobility means that you should only be asking for Ana to hit you with her Nano-Boost in a dire situation where you need to defend an objective. Try to stick with Ana at most times; you both have low mobility, and you can protect each other from flankers.
Icon-Baptiste.png
Baptiste
While you are planning on using your ultimate ability, be very wary of Baptiste's signature ability, immortality field, as it is a very hard counter to your ultimate. Baptiste's Amplification Matrix will amplify the damage ouput of any projectiles that pass through, so absorbing the damage with Kinetic Grasp is a good idea, as you will be able to gain a massive amount of bonus shields.Sigma has no notable team synergy with Baptiste.
Icon-Brigitte.png
Brigitte
Your Hyperspheres can quickly break Brigitte's weak barrier, and your Accretion can knock down any over-zealous Brigittes. Your Experimental Barrier and Kinetic Grasp will do nothing against her melee primary, but Experimental Barrier will block Whip Shot, so try and block as many Whip Shots as possible to deny her Inspire healing.You and Brigitte lack mobility and range; if you stick together, though, you can keep each other and your team alive and allow your teammates to wreak havoc.
Icon-Lúcio.png
Lúcio
While Lúcio's speed and small size can make him obnoxious to hit, your Hyperspheres have a mild gravity effect, meaning they can slow him down just enough for you to land more shots or for your team to gun him down. An accurate Accretion hit can also grind him to a halt, letting you or your team easily finish him off. Be careful about using Gravitic Flux around Lúcio; his Sound Barrier will easily block off the damage from your Ultimate, rendering it moot. Instead, wait until he's dead, too far away to save his team, just after he uses up his Ultimate, or if you have a friendly Sombra ready with EMP to cancel his Sound Barrier.Lúcio's speed boost can help you keep up with your team. His area-of-effect healing generally means he'll want a large number of teammates to rally around, so try to focus on keeping him and your team safe so he can keep them healed.
Icon-Mercy.png
Mercy
Mercy's high mobility and self-healing can make her difficult to shoot down. One of the most important things you can do against a Mercy is cancelling her Resurrection with your Accretion. If you know a Mercy has Resurrection available, save Accretion to stun her out of it, which should be easy to hit considering Resurrection has a slow cast time and Mercy is almost completely still while using it.Mercy can boost all of your damage making you a powerful tank due to your increased damage.
Icon-Moira.png
Moira
A common strategy Moira's do on defence is throwing a biotic orb at the enemy spawn. It is always your job as Sigma to destroy this orb with your Kinetic grasp in order to deny the enemy moira any free ult charge. Sigma has no notable team synergy with Moira.
Icon-Zenyatta.png
Zenyatta
You and Zenyatta heavily lack in mobility, but a fight between you will come down to your proximity. At a distance, Zenyatta easily has the upper hand; if Zenyatta spots you from far away, put up your Experimental Barrier or block his shots with Kinetic Grasp, otherwise he can easily pick you off. He can't deploy his Orb of Discord through your barrier, so try to keep it up at all times when he's in the vicinity to deny him his Orb. Should you catch Zenyatta up-close, the fight is yours; his low mobility means it will be nearly impossible for him to avoid Accretion, and it only takes a few Hyperspheres to kill him. While it's good to dance around your Experimental Barrier to block his shots, he might take this opportunity to back off and create distance between the two of you, so be wary and don't let him back away.Sigma has no notable team synergy with Zenyatta.

Story[]

Icon-Sigma.png
"There is no obligation for the universe to make sense to you."

Fantastic astrophysicist Dr. Siebren de Kuiper's life changed forever when an experiment gone wrong gave him the ability to control gravity; now, Talon manipulates him to their own ends.[2]

De Kuiper is mentally damaged. He thinks about the universe, gravity, and physics all through the same 'prism', seeing them as being akin to music.[3] He has high regard for the work of Mei-Ling Zhou, finding it "brilliant."[4]

Background[]

Gravity... Gravity is a harness. My entire career has been devoted to this idea... to this moment. Decades! If the unifying theories are correct, we will soon be able to harness the power of a black hole! Nothing will ever be the same.
~ Dr. De Kuiper

A brilliant astrophysicist[5] Dr. Siebren de Kuiper was considered a pioneer in his field. His life's work involved devising a way to harness the power of gravity. Equally known for his groundbreaking research and eccentric personality, he conducted most of his studies from his lab in The Hague.[2] At some point he visited his good friend Dr. Harold Winston on the Horizon Lunar Colony. Winston showed him one of the gorilla test subjects.[4]

Decades of study and research led De Kuiper to the belief that "gravity is a harness;" if the unifying theories were correct, through his work mankind would soon even be able to command nature's most potent expression of gravity, a black hole, and it would change everything forever. Believing that he was close to achieving his goal, he performed his most important experiment on the International Space Station. However, something went terribly wrong. The field containing the experiment began to fail; as De Kuiper desperately tried to figure out why it was happening and how to stop it, the brief formation of a black hole was triggered. Screaming, De Kuiper was only exposed to its power for a moment, but he suffered serious psychological damage. The area around him began to experience strange fluctuations in gravity, peaking and dropping in time with his reactions. He had to be evacuated immediately.

Upon returning to Earth, De Kuiper was quarantined in a secret government facility. Between his ravings about the patterns of the universe, the psychic damage he sustained, the gravitic anomalies happening around him, and concerns for his mental wellbeing, he was deemed a danger to himself and others and detained for years under the name "Subject Sigma," with himself and his inexplicable abilities being researched. Isolated and unable to control his powers, De Kuiper retreated into his own mind. He thought he would never see the outside world again.

When Talon discovered De Kuiper's existence, they infiltrated the facility and broke him out, planning to use his brilliance and research to further their plans. In their custody, De Kuiper slowly gained control of his powers. Now, gravity moved according to his will, and he was closer than ever to achieving his life's goal. But the same experiment that had opened his mind had also fractured it, and he struggled to keep the pieces together. De Kuiper continued to develop his powers in hopes of unlocking the secrets of the universe, unaware that Talon was using both him and his research.[2] He spent most of his time working off-site in a lab Talon granted to him.[3]

Achievements[]

Trivia[]

  • Sigma is Hero 31 and the tenth new hero added to the game.
  • Sigma (Σ) is the 18th letter of the Greek alphabet, and has various uses as a symbol in science and mathematics. It is displayed on his inmate suit as "Subject Σ."
  • Sigma is currently the oldest character in the hero line-up.
  • At the beginning of Sigma's Origin Story video, there are yellow letters that appear on the screen which spell out "EM DJIRVEB." When reversed, it spells "Bevrijd me," which is Dutch for "Release me."
  • Sigma's Experimental Barrier is very similar to Symmetra's old Photon Barrier that existed prior to patch 1.25, though Sigma's is bigger, travels three times faster, can be placed anywhere, and can be recalled at any time.
  • The number 31 is the Dutch International Calling Code.
  • Although some heroes have sound effects that play in their hero selection and heroic highlight animations, Sigma is one of the few that plays music, specifically. The piano music that plays is presumably the "melody" he hears and ponders. His actions during the highlight imply he has memorized, or at least is well familiar with this precise melody.
  • Along with this, and if you listen carefully, similar piano music also plays while he unleashes his ultimate. Unlike with his highlight, the music follows no melody and becomes chaotic and sharp. With even closer attention, you can hear his echoed, crazed laughter as well.
  • Sigma's hostile ultimate voice line, "Het universum zingt voor mij!" (English: "The universe sings for me!"), was contributed by Chris Metzen, who acted as a creative consultant for the Origin Story video.[6]
  • Sigma's hero select voice line, "There is no obligation for the universe to make sense to you," is a quote from famous astrophysicist Neil deGrasse Tyson.
  • Sigma is the only hero with no Summer Games voice lines.
  • Sigma is possibly inspired in part by the Dutch scientist Gerard Kuiper.
  • Sigma's Asylum skin is heavily influenced by Hannibal Lecter as portrayed by Anthony Hopkins in The Silence of the Lambs (white suit with number during the cage scenes and the face restrainer).
  • Sigma generated some controversy with his reveal, with some claiming he was based on mental illness stereotypes. This was seen with his "asylum" look (plus, his asylum skin), including the lack of shoes. The barefoot look was chosen to "sell the ‘asylum’ look a bit more" (many psychiatric patients are not allowed to wear shoes as they might cause harm with the laces). In response to the controversy, Michael Chu stated "with the idea of the character, we never intended him to be an example of someone who’s going through mental health issues. He’s really supposed to be more focused on this very specific thing that happened to him, which is that his body and his mind were literally ripped apart by the momentary exposure to a black hole."[7]
  • In an interview at Comic-Con when Overwatch developers were talking about the development of Hammond, Hammond's original ultimate idea originally consisted of pile driving players players into the air to then have them back down to the ground to damage the players sent into the air. The developers instead changed to have a minefield as Hammond's ultimate but the idea wasn't scrapped. Later, the ultimate seems to have been transferred to Sigma.

Development[]

Blizzard began development of Hero 31 with the intent to further flesh out the Talon organization as well as to provide another barrier tank option in addition to Reinhardt and Orisa, both heavily requested by players. The creative team initially planned for Mauga to fulfill this purpose, and initially prototyped the hero dual-wielding rocket launchers, but found it difficult to convey how he would deploy his barriers with both hands occupied, and began to iterate on other concepts for his kit. In the process of developing Mauga's character for Alyssa Wong's short story, What You Left Behind, they decided that the kit being developed by Geoff Goodman and Joshua Noh no longer meshed with Mauga's violent, aggressive personality.

Rather than scrap the kit, which they found to be exceptionally fun, they pivoted and began developing a new Hero, who would become Sigma, to better reflect the more defensive and cerebral nature of the Hero's abilities. To that end, they brainstormed a physicist who would manipulate gravity, who could act as a tragic villain being manipulated by Talon without even realizing it, due to his psychological trauma, and began prototyping the character with concept artist Qiu Fang, initially using existing art. As a result of this pivoting, he was created on a tighter schedule than usual and was slightly delayed compared to previous heroes. The team consulted physics programmer Erin Catto, who holds a PhD in physics and wrote the physics engines for all of Blizzard's games, to make Sigma's physics references more scientifically accurate.

Blizzard has a campus in The Hague and as such has several Dutch employees both in Europe and North America, so they were able to consult with their employees on names and quotes, and incorporated a lot of Dutch influences into the character.[6]

Sigma was leaked four days before his official reveal on July 18th, 2019 by the Mexican blog post detailing the new role queue feature. That image was then tweeted by Team Mexico of the Overwatch World Cup.

Videos[]

Official[]

Balance Change Logs[]

For more information, see Patch Notes

11 Mar 2021

Abilities-sigma2.png Experimental Barrier

  • Cooldown reduced from 2.5 to 2.0 seconds

Developer Comment: While the previous cooldown increase for Experimental Barrier had the intended effect of opening up more counterplay, there may be a tuning value that feels less restrictive for Sigma and still achieves those goals.

12 Jan 2021

Abilities-sigma2.png Experimental Barrier

  • Redeploy cooldown increased from 1 to 2.5 seconds

Developer Comment: We're increasing the cooldown of Sigma's barrier to require a higher commitment to its placement and open up additional opportunities for counterplay.

13 Aug 2020

Abilities-sigma2.png Experimental Barrier
  • Health reduced from 900 to 700
  • Barrier health regeneration rate reduced from 120 to 80 health per second

Abilities-sigma3.png Kinetic Grasp

  • Cooldown increased from 10 to 12 seconds

29 Apr 2020

Abilities-sigma4.png Accretion
  • Knockdown duration is now a fixed 0.8 second instead of scaling with distance
  • Cast time reduced from 0.75 to 0.65 seconds

12 Mar 2020

Abilities-sigma5.png Gravitic Flux
  • Ultimate cost reduced 10%
  • Flight speed increased 30%

28 Jan 2020

Abilities-sigma5.png Gravitic Flux
  • Can now be interrupted before targets begin falling
  • Impact slow duration reduced from 0.9 to 0.6 seconds

10 Dec 2019

Abilities-sigma2.png Experimental Barrier
  • Health reduced from 1500 to 900
  • Barrier health regeneration rate reduced from 150 to 120 health per second

Abilities-sigma3.png Kinetic Grasp

  • Cooldown reduced from 13 seconds to 10 seconds
  • Damage-to-shield gain ratio increased from 40% to 60%

15 Oct 2019

Abilities-sigma3.png Kinetic Grasp
  • No longer blocks Chain Hook and Whip Shot

Abilities-sigma5.png Gravitic Flux

  • High gravity effect duration reduced from 1.2 to 0.9 seconds

Abilities-sigma2.png Experimental Barrier

  • Regeneration rate reduced from 175 to 150 per second
  • Now has a 1 second cooldown after recalling the barrier
  • Initial 0.2 second cast time removed

Developer Comment: Sigma can often feel difficult to counter since he can so quickly reposition his shield and use Kinetic Grasp to block from other directions. We’re opening up some weaknesses in these abilities to allow for more counter play from his enemies.

17 Sep 2019

Abilities-sigma1.png Hyperspheres
  • Explosion damaged reduced from 35 to 30

Abilities-sigma2.png Experimental Barrier

  • Added a toggle option for deploying Sigma’s Experimental Barrier
  • Being hacked by Sombra will now recall his barrier if it is deployed. (EMP will still destroy the barrier first if both are in range)

Abilities-sigma4.png Accretion

  • Explosion damage increased from 50 to 60

Abilities-sigma5.png Gravitic Flux

  • Intro cast time increased from 0.4 seconds to 0.6

13 Aug 2019

New Hero: Sigma (Tank)

References[]

  1. ↑Joshua Noh clarifies on Sigma's abilities.Twitch, accessed on 2019-7-24
  2. 2.02.12.2Sigma, PlayOverwatch. Accessed on 2019-09-20
  3. 3.03.12019-07-31, Blizzard explains new Overwatch hero’s design, mental health, and baby-soft feet. Polygon, accessed on 2019-08-20
  4. 4.04.1Overwatch, Sigma Quotations
  5. ↑2019-07-24, Developer Update

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U2AF1 mutation promotes tumorigenicity through facilitating autophagy flux mediated by FOXO3a activation in myelodysplastic syndromes

Abstract

Mutations in the U2 small nuclear RNA auxiliary factor 1 (U2AF1) gene are the common feature of a major subset in myelodysplastic syndromes (MDS). However, the genetic landscape and molecular pathogenesis of oncogenic U2AF1S34F mutation in MDS are not totally understood. We performed comprehensive analysis for prognostic significance of U2AF1 mutations in acute myeloid leukemia (AML) cohort based on The Cancer Genome Atlas (TCGA) database. Functional analysis of U2AF1S34F mutation was performed in vitro. Differentially expressed genes (DEGs) and significantly enriched pathways were identified by RNA sequencing. The forkhead box protein O3a (FOXO3a) was investigated to mediate the function of U2AF1S34F mutation in cell models using lentivirus. Chromatin immunoprecipitation, immunoblotting analyses, and immunofluorescence assays were also conducted. U2AF1 mutations were associated with poor prognosis in MDS and AML samples, which significantly inhibited cell proliferation and induced cellular apoptosis in cell models. Our data identified that U2AF1-mutant cell lines undergo FOXO3a-dependent apoptosis and NLRP3 inflammasome activation, which induces pyroptotic cell death. Particularly, an increase in the level of FOXO3a promoted the progression of MDS in association with restored autophagy program leading to NLRP3 inflammasome activation in response to U2AF1S34F mutation. Based on the result that U2AF1S34F mutation promoted the transcriptional activity of Bim through upregulating FOXO3a with transactivation of cell cycle regulators p21Cip1 and p27Kip1, FOXO3a, a potentially cancer-associated transcription factor, was identified as the key molecule on which these pathways converge. Overall, our studies provide new insights that U2AF1S34F mutation functions the crucial roles in mediating MDS disease progression via FOXO3a activation, and demonstrate novel targets of U2AF1 mutations to the pathogenesis of MDS.

Introduction

Myelodysplastic syndromes (MDS) are clonal hematopoietic stem cell malignancies that are characterized by inefficient hematopoiesis, progressive bone marrow (BM) dysplasia, and increased mortality due to the progression to acute myeloid leukemia (AML) [1]. Peripheral blood cytopenia can be manifested by a large proportion of MDS sufferers despite normal or hypercellular BM. Excessive cell death and cell differentiation disorder in the early stage of MDS, and abnormal hematopoietic stem and progenitor cells (HSPCs) show apoptosis resistance when the disease progresses [2]. MDS consist of a heterogeneous group, which harbor a spectrum of chromosome abnormalities and somatic gene mutations. Previous studies have shown that MDS can be initiated by genetic or epigenetic modifications to HSPCs or their functions [3]. How genetic alterations trigger the diverse MDS phenotype remains unclear.

As parts of ribonucleoprotein complexes, spliceosomes proteins are associated with the splicing of introns when pre-mRNA matures. As a small subunit of U2AF, U2 small nuclear RNA auxiliary factor 1 (U2AF1) develops the U2AF heterodimer with a larger subunit U2AF2 through combination with the 3’ AG splice acceptor dinucleotide of the pre-mRNA target intron [4]. When analyzed in relation to other genes implicated in MDS, the compiled evidence shows that U2AF1 is often the initial mutation that occurs [5, 6]. Although these studies have suggested that U2AF1 mutations are selected early during tumorigenesis, mutations in a single allele of U2AF1 that lead to a predilection for carcinogenesis and tumor progression are unexplained. The highly conserved serine at amino acid position 34 (S34F) is where U2AF1 mutations are commonly found [7]. The U2AF1S34F mutation showed altered secretion patterns of interleukin 8 (IL-8) and IL-1α in MDS, supporting the hypothesis that the inflammatory response is a driver during cancer progression [8]. In addition, NLRP3 inflammasome-dependent IL-1β and IL-18 production is reported in S34F mutant U2AF1-expressing cells, which induces HSPCs pyroptosis, a caspase-1-dependent programmed cell death [9]. However, the specificity and regulatory mechanism of the U2AF1S34F mutation in promoting NLRP3 inflammasome activation remain to be elucidated.

Here, we report that forkhead box protein O3a (FOXO3a), as a key transcription factor, is markedly increased in S34F mutant U2AF1-expressing cells. Moreover, our data strengthen the concept that the presence of a functionally active FOXO3a binding site for gene expression of cell cycle regulators induces consequent cell fate determination via FOXO3a-mediated autophagic flux and NLRP3 inflammasome activation, suggesting a potential therapeutic target in MDS and myeloid malignancies.

Results

Mutations of U2AF1 are correlated with a poor prognosis

Several sequencing studies have found that U2AF1 is frequently mutated in MDS [10, 11]. Studies on the conditional knock-in alleles of mutant U2af1 vivo models have significantly promoted the understanding of the pathogenesis of MDS despite several limitations in the presentation of clinical features [5]. Correlative analysis of U2AF1 mutations with clinical features in MDS patients suggested that patients with U2AF1 mutations had significantly lower hemoglobin percentages when compared with patients with wild-type U2AF1 (p = 0.017; Fig. 1A). We previously evaluated the prognostic value of U2AF1 mutations in MDS cohort samples, in which patients with U2AF1 mutations were found to have lower survival than patients with wild-type U2AF1 [10, 11]. The results shown in the box plots revealed that there was no difference in U2AF1 expression between mutant and wild-type samples in The Cancer Genome Atlas (TCGA) database (p > 0.05; Fig. 1B). Consistently, the survival curves of AML patients revealed a trend that U2AF1 mutations were significantly related to a shorter overall survival compared with those without a U2AF1 mutation by TCGA (p = 0.02; Fig. 1C). Taken together, these clinical data strongly associate U2AF1 mutations with a poor prognosis.

A The patients carrying the U2AF1 mutations (n = 58) revealed lower peripheral blood cell counts compared with those without a U2AF1 mutation (n = 68). B Relative expression of U2AF1 from TCGA-seq dataset. No significant differences were found for U2AF1 gene expression between mutant and wild-type samples (p > 0.05). C Kaplan–Meier survival analysis indicated that patients with U2AF1 mutations were significantly correlated with a shorter overall survival than those without the mutation (p < 0.05). Statistical significance in relative expression analysis was determined by log2(RPKM) test.

Full size image

U2AF1 mutation regulates the proliferation and apoptosis of SKM-1 and K562 cells

Mutation screening indicated that wild-type U2AF1 is expressed in K562 and SKM-1 cell lines (Supplementary Data 1). To determine whether the U2AF1 mutant plays biological roles in MDS, we constructed a recombinant lentivirus with FLAG-tagged wild-type or U2AF1 (S34F) mutant and stably transfected SKM-1 and K562 cells. The protein expression levels of U2AF1S34F and U2AF1WT compared with the levels in negative controls (NC) were confirmed by western blotting (Fig. 2A). The exogenous U2AF1S34F and U2AF1WT overexpression driven by lentiviral vectors, led to a significant increase of total U2AF1 protein levels in stably transduced cells. Nearly 95% of the cells expressing either FLAG-tagged wild-type or mutant U2AF1 were used for biological function studies. CCK-8 assays f.lux Serial Key - Crack Key For U that the U2AF1 (S34F) mutant inhibited the viability of K562 and SKM-1 cells (Fig. 2B). Moreover, colony formation assays indicated that U2AF1 (S34F) mutant-expressing cells exhibited significantly decreased proliferation capacity compared with cells expressing wild-type U2AF1 in both cell lines (Fig. 2D). We also determined the effects of the U2AF1 mutant on cellular apoptosis through Annexin V-APC/7-AAD double staining. Our data demonstrated a substantial increase in the proportion in SKM-1 in late apoptosis cells, and this trend was confirmed with K562 cells, which also showed a progressive increase in apoptosis rate (Fig. 2C). Then, U2AF1-mutant-induced apoptosis was further examined by Hoechst 33258 staining, with the results showing that the apoptotic portion constituted nearly three-fifths of the whole population (Fig. 2E). There were no significant differences between the cells expressing wild-type U2AF1 and the negative control cells. Together with these results, we concluded that the U2AF1S34F mutation could increase the apoptosis rate and suppressed cellular viability and colony formation in MDS and myeloid malignancies.

A Transfection efficiency under the fluorescence microscope. Scale bar, 50 µm. Western blotting analysis of FLAG-tagged wild-type or mutated protein level in stably transfected cells. Western blotting analysis to determine the protein expression levels of U2AF1WT or U2AF1S34F in stably transfected cells. B CCK-8 assays for investigating the proliferation capacity of WT and S34F mutant U2AF1. C Annexin V-APC/7-AAD double staining was utilized to detect cellular apoptosis by flow cytometry in both K562 and SKM-1 cell lines after wild-type and S34F mutant U2AF1 treatment for 96 h. D Colony formation ability of wild-type and S34F mutant U2AF1 in the both is shown; right histogram represents quantification analysis. Scale bar, 100 µm. E Hoechst 33258 staining of the cellular nuclei was performed to obverse apoptosis in both K562 and SKM-1 cells. Scale bar, 40 µm. The data are presented as the mean ± SD as well as the representative of no less than two single experimental processes. *p < 0.05, **p < 0.01, and ***p < 0.001. WT wild-type, NC negative controls.

Full size image

U2AF1 mutation affects gene expression profiles of SKM-1 cells

To understand how the cancer-associated U2AF1S34F mutation promotes MDS, we next compared independent RNA samples of SKM-1 cells expressing wild-type U2AF1 and S34F mutant U2AF1 using RNA sequencing (RNA-seq). A volcano plot is presented to show the expression profiles (Fig. 3A). Our RNA-seq data revealed 405 differentially expressed genes (DEGs), including 167 upregulated and 238 downregulated genes (fold changes (FC) cutoff of 1.5; P < 0.05). Through RNA-seq of three pairs of independent RNA samples from U2AF1-mutant and U2AF1-WT cell lines, we determined the transcriptome landscape and identified the potential core genes based on hierarchical clustering analysis (Fig. 3C). Among the 405 DEGs, FOXO3a (FC = 1.64 and P = 2.35E-02) and CDKN1A (p21Cip1, FC = 1.63, and P = 1.80E-02) were significantly upregulated, while c-Myc (FC = 0.09, P = 8.70E-04) was notably downregulated. These genes were further verified by qRT-PCR. Consistently, the relative mRNA f.lux Serial Key - Crack Key For U levels of FOXO3a and p21Cip1 showed a significantly increasing trend in the U2AF1 (S34F) mutant-transduced SKM-1 cells. In line with the mRNA expression data, c-Myc was transcriptionally inactivated following the overexpression of the U2AF1 mutant.

A The volcano plot indicates the distribution of DEGs based on the RNA-seq data obtained from wild-type samples as well as S34F mutant U2AF1 samples. B The pathway enrichment analysis on the upregulated DEGs of KEGG. C Hierarchical clustering plot of the fold changes (FC) of gene expressions in six samples induced by S34F mutant U2AF1 detected by RNA-seq (FC > 1.5, p-values < 0.05). The mRNA expression of FOXO3a, Bim, c-Myc, p21Cip1, and p27Kip1 in SKM-1 cells treated with wild-type and S34F mutant U2AF1 by qRT-PCR. D The altered protein levels of U2AF1S34F mutation-associated genes were validated by western blotting in SKM-1 cells. Quantitative analysis of western blotting bands from three independent experiments is shown. E Heatmap showing the enriched genes in the apoptosis pathway of GSEA results between wild-type and S34F mutant U2AF1-treated SKM-1 cells (FDR q < 0.25). F Representative bands of western blotting data showing the protein levels of p53, Cleaved caspase-3, caspase-3, Bcl-2 as well as Bax in different groups based on the GSEA results. The data represent at least two independent experiments with three samples in each group. *p < 0.05, **p < 0.01, and ***p < 0.001. WT wild-type, NC negative controls.

Full size image

We then sought to determine whether the expression of the downstream targets cooperates with FOXO3a activation during the tumorigenesis of U2AF1-mutant-expressing cells. Western blotting results revealed that the U2AF1S34F mutation was associated with substantially increased protein levels of FOXO3a, BCL2L11 (Bim), p21Cip1, and CDKN1B (p27Kip1) compared with the two controls, whereas the levels of phosphorylated FOXO3a (p-FOXO3a) and c-Myc were decreased (Fig. 3D). The results of Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis showed that these DEGs were involved in several biological pathways, including the forkhead box protein O (FOXO) and PI3K/Akt signaling pathways (Fig. 3B). Consistently, the phosphorylation levels of AKT were significantly attenuated in the U2AF1 (S34F) mutant group. Conducting GSEA of the RNA-seq data illustrated that genes related to G2/M checkpoint and apoptosis-associated pathways were statistically enriched in U2AF1 (S34F) mutant-expressing cells (FDR q < 0.25; Fig. 3E). As shown in Fig. 2F, the western blotting analyses also demonstrated altered protein levels, specifically increased expression of p53 and Bax and decreased protein levels of Bcl-2 and cleaved caspase-3 in U2AF1 (S34F) mutant-expressing cells, indicating that the U2AF1S34F mutation-induced apoptosis could be mediated by Bcl-2 family genes.

U2AF1 mutation induces G2/M cell cycle arrest mediated by FOXO3a activation

It has been shown that tumorigenesis is promoted by the upregulation of FOXO3a in AML [12]. We next performed chromatin immunoprecipitation sequencing (ChIP-seq) with FOXO3a to analyze the effect of mutant U2AF1 on the genetic landscapes and chromatin states in MDS. According to the ChIP assays, FOXO3a specifically binds to a site in the proximal promoter region. In addition, our enhancer analysis indicated that the U2AF1 (S34F) mutant increased the average FOXO3a level at the transcription start site (Fig. 4A). Recent studies have also revealed that FOXO3a could regulate Bim transcription through binding its promoter regions, mediating cell cycle distribution [13]. Above data highlighted the cell cycle regulators, p21Cip1 and p27Kip1, were transcriptionally activated following U2AF1 (S34F) mutant expression, and this effect was accompanied by upregulated FOXO3a and downregulated c-Myc expression levels. In an effort to discover the underlying molecular mechanism of U2AF1 (S34F) mutant in conjunction with an increase in the expression levels of cell cycle regulators, we performed 5-bromo-2’-deoxyuridine (BrdU) incorporation assays with SKM-1 and K562 cell lines. As shown in Fig. 4B, the expression of the U2AF1 (S34F) mutant significantly increased the proportion of BrdU-positive cells and the percentage of cells in the S-phase and significantly reduced the percentage of cells in the G2/M phase, which suggested the induction of cell cycle arrest by blocking the S/G2 checkpoint in both cell lines (Fig. 4C). Ninety-six hours after transduction with the FOXO3a-shRNA lentiviral particles, the protein expression levels of FOXO3a were significantly downregulated (Fig. 4D). Cell cycle analyses revealed that the downregulation of FOXO3a significantly attenuated a considerable portion of the U2AF1 (S34F) mutant-induced cells in S-phase and partly reversed the G2/M blockades, indicating that FOXO3a plays an important role in U2AF1 (S34F) mutant-induced SKM-1 cell cycle arrest (Fig. 4E).

A ChIP-seq for FOXO3a binding to the promoter regions. Heatmaps and average intensity curves of ChIP assay reads for FOXO3a. B The representative micrographs and quantification of BrdU-incorporating cells (red) in both K562 and SKM-1 cell lines are shown. Nuclei counterstained with DAPI. Scale bar, 50 µm. C The representative flow cytometry analysis of the cell cycle distribution after efficient transfection for 96 h in both K562 and SKM-1 cells. S34F mutant U2AF1 induced the increase in the proportion of S-phase cells and significantly reduced the percentage of cells at G2/M phase. D The knockout efficiency for FOXO3a was determined by western blotting assays in SKM-1 cells. E Gene silencing of FOXO3a rescued the G2/M blocks induced by S34F mutant U2AF1 in SKM-1 cells. The data represent all experiments in triplicate for each cell line. *p < 0.05, **p < 0.01, and ***p < 0.001. WT wild-type, NC negative controls.

Full size image

Activation of the NLRP3 inflammasome in U2AF1-mutant-expressing cells by FOXO3a

Because the altered expression of FOXO3a has been reported to influence SKM-1 cell growth [13], the effects of FoxO3a on biological functions of S34F mutant U2AF1-expressing cells were determined. As shown in Fig. 5A, the U2AF1 (S34F) mutant-positive group with shRNA- FOXO3a-expressing cells exhibited a higher proliferation rate than the group overexpressing only the U2AF1 mutant. To further investigate the effects of U2AF1S34F mutation in cell models, the apoptotic ratio was detected by Annexin V single-labeling of specific cells. Silencing FOXO3a reduced the population of Annexin V-positive cells as mediated by the U2AF1 (S34F) mutant (Fig. 5B). Consistently, colony formation assays revealed that U2AF1 (S34F) mutant-expressing cells transfected with the FOXO3a overexpression plasmid (FOXO3a-OE) showed significantly attenuated the proliferation capacity. These results confirm that the regulatory effect of U2AF1S34F mutation on cell proliferation and apoptosis was significantly reversed by silencing of FOXO3a.

A The proliferation curve of SKM-1 cells superinfected by FoxO3a-shRNA lentiviral particles at the specified time point. Then silencing of FOXO3a overcame the suppressive growth of S34F mutant U2AF1. B FOXO3a suppression abolished the induction of cellular apoptosis in S34F mutant U2AF1-expressing cells by flow cytometry using Annexin V single-staining. Overexpression of FOXO3a (FOXO3a-OE) rescued the growth capacity induced by S34F-shRNA-FoxO3a in SKM-1 cells. C, D Western blotting or qRT-PCR assays for NLRP3 inflammasome or other inflammatory biomarkers in SKM-1 or K562 cells treated with wild-type and S34F mutant U2AF1 for 96 h. E Western blotting analysis for FOXO3a and NLRP3 inflammasome markers in SKM-1 cells expressing wild-type U2AF1 and S34F mutant U2AF1 after transfection with the FOXO3a-shRNA lentiviral particles for 96 h. Band intensities represent values relative to control group. F, G Representative photomicrographs showed cells expressing S34F mutant U2AF1 containing green fluorescence protein (green) immunolabeled using the anti-FOXO3a and anti-NLRP3 antibody (red). Nuclei were stained with DAPI (blue). Scale bar, 50 µm. Magnification, ×200. Upper histogram represents quantification analysis. The data are presented as the means ± SD of multiple experiments conducted in triplicate. *p < 0.05, *p < 0.01, and ***p < 0.001. WT wild-type.

Full size image

Previous studies have illustrated that FOXO3a is critically involved in the inflammatory response mediated by the NLRP3 inflammasome in the malignant progression of tumors [14, 15]. However, the role of FOXO3a in MDS disease progression has not been reported so far. Here, we focused on the relationship between FoxO3a overexpression and NLRP3 inflammasome in U2AF1 (S34F) mutant-expressing cells. As shown in Fig. 5C, the NLRP3 mRNA levels were upregulated in both cells compared with the controls. The U2AF1 (S34F) mutant increased NLRP3 expression, and the ASC and activated caspase-1 levels were also upregulated (Fig. 5D). Moreover, western blotting analysis indicated that FOXO3a silencing significantly decreased the levels of NLRP3, ASC and active caspase-1 that were triggered by S34F mutant U2AF1 (Fig. 5E). Additionally, the expression level of Bim, an apoptosis-related FOXO3a downstream target protein, was decreased significantly after coinfection. F.lux Serial Key - Crack Key For U oxygen species (ROS) is critical for promoting the formation of NLRP3 inflammasome [9]. To further clarify the localization of FOXO3a and NLRP3, we abrogated ROS in SKM-1 and K562 cells by antioxidant N-acetylcysteine (NAC) treatment. As indicated in Fig. 5F, G, the immunostaining results using an anti-NLRP3 antibody showed that NAC effectively reduced NLRP3 inflammasome activation in the U2AF1 (S34F) mutant cells. By contrast, the number of FOXO3a-positive cells was significantly increased after treatment with the antioxidant NAC compared with that of the controls. These findings in aggregate indicate that S34F mutant U2AF1 affects NLRP3 inflammasome activation by regulating FOXO3a signaling, dependently of its apoptotic activity.

Mutant U2AF1 restores autophagy flux as a result of FOXO3a dysregulation

Previous results indicated that FOXO3a contributed to signaling pathways mediating autophagy and inflammatory responses [13]. Since the impaired autophagy program leads to NLRP3 activation [16], we wondered whether FOXO3a was capable of regulating autophagy flux in the U2AF1 (S34F) mutant cells. Gene Ontology (GO) analysis made us able to identify molecules associated with the biological process of positive regulation of reactive oxygen species-associated metabolic process and the cellular component of autophagosome lumen (Fig. 6A). We next determined the levels of autophagy-related genes by western blotting analyses. As shown in Fig. 6B, the levels of the autophagy-initiating proteins Beclin 1, ATG5, ATG12, and ATG16, as well as anti-light chain 3 (LC3)-I and LC3-II, in both the S34F-shRNA-FOXO3a and WT-shRNA-FOXO3a groups were decreased compared with those in the WT-shRNA-con group, but an increase was observed in the S34F group. The transformation of the nonlipidated LC3 form, LC3-I, to the lipidated form, LC3-II, is a general marker of autophagic activity [13, 17]. The LC3-II/LC3-I ratio in the U2AF1 (S34F) mutant-expressing cells was significantly higher than that in the WT-shRNA-con group, which is indicative of autophagy induction. Following FOXO3a silencing, the levels of both LC3-I and LC3-II were attenuated, as well as the ratio of LC3-I and LC3-II (Fig. 6C). Similar results were obtained by transmission electron microscopy of the SKM-1 cells overexpressing FOXO3a. Morphological changes in autophagosomes were observed by transmission electron micrographs (Fig. 6D). Ultrastructural analysis suggested an increase in the number and size of autophagosomes in cells expressing S34F mutant U2AF1, which was eventually enhanced by the addition of FOXO3a, indicating that FOXO3a is closely f.lux Serial Key - Crack Key For U with oxidative stress by regulating autophagic flux. Overall, the above results demonstrate that the effects of autophagy flux exerted by the U2AF1S34F mutation are achieved through FOXO3a activation.

A Biological process, molecular function, as well as cellular component are adopted to categorize GO. B, C Representative images of western blotting data. Quantitative analysis of the protein expression levels, and the LC3-II/ LC3-I ratio is demonstrated. Beclin 1, ATG5, ATG12, and ATG16 complex proteins were all up-regulated following S34F mutant U2AF1 treatment. These proteins were decreased after silencing of FOXO3a. D Representative transmission electron micrographs of autophagosomes ultrastructure. Scale bar, 5 µm. E Schematic representation of the potential role of U2AF1S34F mutation based on this study. The data represent at least two independent experiments with three samples per group in each. *p < 0.05, **p < 0.01, and ***p < 0.001. WT, wild-type, M mitochondria, AP autophagosome.

Full size image

Discussion

Mutant U2AF1, located in the highly conserved zinc fingers, facilitates increased splicing and exon skipping, disrupting the capability of U2AF1 to RNA splicing machinery [18, 19]. Abnormalities in spliceosome genes are often the initial mutation, while the remaining genetic aberrations appear gradually during the evolution of MDS [5, 6]. Nevertheless, only a single copy of the gene is mutated in malignancies, proposing the possibility that the mutations do not lead to a simple loss of function.

Because of the complexity of its cytogenetic pathogenesis, the prognostic effect of the U2AF1S34F mutation in MDS remains controversial. The present study reveals that the U2AF1S34F mutation is significantly associated with poor prognosis in patients with AML based on the TCGA database. Consistently, we previously found that patients with MDS harboring U2AF1 mutations had a shorter overall survival compared with those without a U2AF1 mutation, and patients with U2AF1 mutations usually had a higher risk of AML transformation [10]. Different phenotypes have been observed in vitro models of primary human BM CD34+ progenitor cells. U2AF1S34F mutation in human HSPCs impaired erythroid differentiation and led to the skewing of granulomonocytic differentiation towards granulocytes [20]. A defining feature of lower-risk MDS is BM failure, and excessive HSPCs apoptosis contributes toward the ineffective hematopoiesis characteristic of MDS [2]. In our study, we demonstrated that U2AF1 mutations in patients with MDS were related to lower hemoglobin percentages when compared with patients with wild-type U2AF1. Moreover, our biological assays showed that the U2AF1 (S34F) mutant suppressed K562 and SKM-1 cell proliferation by strongly inducing apoptosis and a G2/M phase blockade. How the U2AF1S34F mutation confers a clonal growth advantage in MDS is unclear.

Here, we used RNA-seq to identify 405 DEGs and found that biological processes were enriched in cytokine-mediated and FOXO signaling pathways. Among these DEGs, FOXO3a and its target molecule p21Cip1 were observed to have higher expression in the mutant cells than that in controls, as well as reduced expression of c-Myc. FOXO3a functions as a potential oncoprotein by upregulating molecules involved in the cell cycle, apoptosis, and autophagy [13]. To explore the potential regulatory mechanisms involving the FOXO signaling pathway, FOXO3a was knocked out using SKM-1 cells superinfected with FOXO3a-shRNA lentiviral particles. Our data demonstrated that the decrease in FoxO3a expression overcame the tendency toward an increased ratio of apoptotic cells as mediated by the U2AF1S34F mutation.

The FOXO transcription factor family contains four highly relevant members, namely, FOXO1, FOXO3a, FOXO4, and FOXO6, which are direct downstream targets of AKT and play important roles in cancer progression [12, 21]. Previously, it has been shown that FOXO1 belongs to positive transcription factor involved in the stress response pathway [14]. In a Gene Expression Omnibus (GEO) dataset (GSE19429) analysis of CD34+ cells of patients with MDS, FOXO1 was found to be significantly downregulated [22, 23]. Moreover, PPI network construction using STRING tools indicated FOXO1 as a core gene interacting with other genes that also have roles in apoptosis. According to RNA-seq data, apoptosis pathways were dramatically affected by the U2AF1S34F mutation, including the level of Bim, which is a proapoptotic factor in AML cells [24]. It has been reported that activated FOXO3a regulates the transcription of Bim gene by binding to the Bim promoter [25, 26]. Combining RNA-seq and ChIP-seq data, we demonstrated that FOXO3a elevation is a transcription inducer of FOXO3a-Bim axis genes in the U2AF1 (S34F) mutant samples, consistent with a previously predicted motif [27]. These results support the conclusion that FOXO3a has a strong positive impact on enhancer states and that Bim is a crucial downstream regulator of U2AF1S34F mutation-induced abnormalities in apoptosis.

Another intriguing discovery of our research is the finding that overexpression of FOXO3a mediated by the U2AF1 (S34F) mutant promotes NLRP3 inflammasome activation in SKM-1 cells. Full formation of the NLRP3 inflammasome then induces IL-1β release and caspase-1 production, hallmarks of pyroptosis [9]. Knocking down FOXO3a lowered NLRP3 activity, ASC, and active caspase-1 levels in the present study. Autophagy is a highly conserved self-digestion process that is an essential mechanism for maintaining metabolic homeostasis and energy balance in cells [17, 28]. Given the importance f.lux Serial Key - Crack Key For U NLRP3-dependent inflammatory cell death in impairing HSPCs survival in MDS, previous studies reported that impaired autophagy led to NLRP3 activation [16]. Park et al. have asserted that the U2AF1S34F mutation promoted ATG7 alternate splicing, which disrupted autophagy program [29]. Interestingly, our results showed that the autophagy flux previously induced by the U2AF1 (S34F) mutant can be partially attenuated by silencing FOXO3a. FOXO3a participates in the regulation of autophagy by inducing the expression of downstream target genes, such as Bim, p21Cip1, p27Kip1, and FasL [30]. These genes are also involved in regulating apoptosis, autophagy and ROS. In our studies, S34F mutant U2AF1 promoted the transcriptional activity of Bim through upregulating FOXO3a by depressed PI3K/AKT activity accompanied by transactivation of cell cycle regulators p21Cip1 and p27Kip1, as well as decreased c-Myc expression, leading to the activation of autophagic flux.

It is well established that tumor-promoting inflammation and genome instability are considered as the pathogenic hallmarks of cancer [31]. FOXO3a, a potentially cancer-associated transcription factor, is involved in the intersection of multiple signal pathways of oxidative stress, which causes a cascade of pathological processes by activating diverse cellular processes, including apoptosis, autophagy and immune-inflammatory responses [13]. However, the specific contribution of FOXO3a in S34F mutant U2AF1-expressing cells to MDS disease progression and the associated molecular mechanisms were not yet fully understood. Our result that FOXO3a enhanced programmed cell death activity fortifies the effect of U2AF1S34F mutation on inflammasome activation in MDS. NADPH oxidase (NOX) facilitates the production of ROS, which activates the NLRP3 inflammasome pathway when the U2AF1S34F mutation is expressed [9, 32]. Nevertheless, our data showing that FOXO3a activity remained elevated after treatment with the antioxidant NAC further supports the direct effect of FOXO3a on NLRP3 inflammasome activation in the U2AF1-mutant cell lines. More importantly, as the early events, the phenotypic changes produced by U2AF1S34F mutation might indicate the initiation of downstream oncogene mutations and diverse signaling pathways affected in the multistep development of tumor inflammatory microenvironment, and coordinately cause AML transformation [32]. Elevated ROS levels lead to increased DNA damage, which could release related inflammatory cytokines by activating the NF-κB, Wnt/β-catenin and other inflammatory response pathways, and then form a vicious cycle with the release of persistent inflammatory factors, leading to the loss of tumor suppressor factors through somatic gene mutations and chromosome rearrangement. The results are in line with these previous studies showing that the U2AF1S34F mutation is overrepresented in individuals with del (20q) and trisomy 8 [10, 18]. Although some studies show that FOXO3a acts as a tumor suppressor in cancer, we suggest that FOXO3a may play an important role in detrimental exaggeration, possibly related to the disease model. Therefore, future studies are needed to explore the role of FOXO3a in regulating MDS disease progression in vivo models.

In conclusion, our findings highlighted the functional importance of the U2AF1S34F mutation in mediating MDS disease progression by activating the NLRP3 inflammasome induced by FOXO3a-mediated autophagic flux. The identification of FOXO3a as a regulator of pyroptosis, along with the transactivating effect of FOXO3a on gene expression of cell cycle regulators, sheds light on new avenues and potential prognostic biomarkers for the therapy of patients with MDS.

Material and methods

Patients and samples

A total of 126 patients diagnosed with MDS at our department from 2018 to 2020 were enrolled in this study. Diagnosis of MDS was based on the World Health Organization (WHO) criteria [33] and the minimum diagnostic standards [34] for MDS. This research was approved by the ethics committee of the Shanghai Jiao Tong University Affiliated Sixth People’s Hospital, and informed consent was obtained from all patients for this research in accordance with the Declaration of Helsinki.

Cell line and culture

RPMI 1640 medium (Gibco, US) containing 10% heat-inactivated fetal bovine serum (Gibco, US), 100 μg/ml streptomycin, and 100 IU/ml penicillin was used to routinely culture the chronic myelogenous leukemia (CML) cell line K562 and the MDS-derived AML cell line SKM-1 (Health Science Research Resources Bank, Japan). Both K562 and SKM-1 cells were maintained at 37 °C under 5% CO2. In addition, the cell samples were recently authenticated by Short Tandem Repeat (STR) and tested for mycoplasma contamination.

Reagents and antibodies

N-acetylcysteine was obtained from Selleck (S1623). Cell Signaling Technology (Danvers, MA, USA) provided antibodies against FOXO3a (#2497), phospho-FOXO3a (#13129), BCL2L11 (#2819), CDKN1A (#2947), CDKN1B (#3686), and c-Myc (#5605). Affinity Biosciences provided the anti-GAPDH antibody (AF7021). Abcam (Cambridge, MA, USA) provided anti-FLAG (ab205606), anti-U2AF1 (ab197591), anti-NLRP3 (ab210491), anti-Caspase-1 (ab207802), anti-ASC (ab151700), anti-AKT (ab32505), anti-phospho-AKT (ab192623), anti-Bcl-2 (ab182858), anti-Bax (ab32503), and anti-Cleaved Caspase-3 (ab32042) antibodies. Autophagy Antibody Sampler Kit (#4445) was obtained from Cell Signaling Technology (Danvers, MA, USA). Sangon Biotech (Shanghai, China) provided HRP-conjugated secondary antibodies.

lentivirus infection assay

For cell transfection, wild-type and S34F mutant U2AF1 were introduced into the GV492 (Ubi-MCS-3FLAG-CBh-gcGFP-IRES-puromycin) lentiviral vectors with the open reading frame (ORF) clone of human U2AF1 (ref. ID NM_006758) and a carboxy-terminal FLAG-tag. Based on direct sequencing, this study identified the constructs overall. Plasmids were transfected with HitransG A reagent (GeneChem, Shanghai, China) at a corresponding MOI reaching 20 in accordance with the vendor’s directions when the cells reached 80% confluence. Cell samples were harvested 72 h after transfection, and in this study, stably transfected clones were transfected with 4 μg/ml puromycin and counted to determine the efficiency of green fluorescence protein (GFP). Normally, more than 80% of the cells were GFP-positive cells. By performing the western blotting assay and the flow cytometry analysis, we confirmed the transgene expression. Untransfected cells acted as negative controls. FoxO3a-shRNA (shRNA-FOXO3a) contained specific sequences targeting the FOXO3a sequence (5’-TTCCAAACTTGTACGCAGTTT-3’; 5’-AAGCTTGTCACTCCTGTTAAT-3’), and a control shRNA acted as a silencing negative control, as supplied by GeneChem Company (Shanghai, China). Cells were transfected following the manufacturer’s directions.

Quantitative real-time PCR (qRT-PCR)

In accordance with the producer’s direction, the total cellular RNA was extracted with the EZ-Press RNA purification tool based on a spin column. RNA under isolation was reverse transcribed to obtain cDNA by complying with the manufacturer’s directions. Using an ABI 7500 real-time PCR machine (Applied Biosystems, Foster, CA, USA), qRT-PCR was performed based on Real Master Mix (TaKaRa, Dalian, China). GAPDH was selected as the endogenous control gene. With the 2-△△Ct approach, the present study obtained relative expression levels of genes as fold variations. Supplementary Table S1 lists the primer sequences.

Cell cycle analysis

Cell cycle distribution was analyzed utilizing cell cycle staining solution (Beijing Solarbio Science & Technology Co., Ltd) following the vendor’s protocol. The transfected cell samples were cleaned based on cold PBS, and cold 70% ethanol was introduced in a gentle and dropwise manner to fix the samples. Cells then received the pelleting and resuspending processes in propidium iodide staining solution (50 μg/ml RNase A and 50 μg/ml propidium iodide solution), followed by incubation at 37 °C under darkness for 30 min before flow cytometry analysis. FlowJo software was used to analyze the cell cycle.

Apoptosis assay

For analysis of cellular apoptosis, the transfected cells were stained using an APC Annexin V Apoptosis Detection Kit with 7-AAD following the manufacturer’s directions. The stained cells were detected via flow cytometric analysis; all data cracked pc software analyzed with FlowJo software.

Cell proliferation assay

With Cell Counting Kit-8 (CCK-8; Dojindo, Kumamoto, Japan) assays, our study determined the cellular viability following the manufacturer’s directions. In summary, overall 5000 cells per well received the culturing process based on 96-well plates under 100 μl volume finally. Four parallel wells were seeded with the respective group of cell samples. The cell samples underwent a 4-day incubation in CO2 at 37 °C. At different time points, with the use of a microplate reading element (Thermo Scientific), 10 μl of CCK-8 solution was introduced in the respective well to measure absorbance at 450 nm. The optical density (OD) values of each well represented the viability of cells.

Colony formation assay

Colony forming tests were conducted with 500 cells per well in six-well plates. The transfected cells were resuspended in MethoCult H4434 methylcellulose medium (StemCell Technologies) with granulocyte-macrophage colony-stimulating factor (GM-CSF), stem cell factor (SCF), erythropoietin (EPO), and interleukin 3 (IL-3) and plated in triplicate wells. The cell samples were incubated for fourteen days at 37 °C to allow colony formation, and colonies covering no less than 30 cells were scored after plating.

RNA sequencing and analysis of integrative network

Cells were administered the vehicle control and S34F mutants in triplicate for 96 h, and total RNA was extracted with TRIzol reagent (Invitrogen, CA, USA) following the vendor’s process. RNA sequencing was performed on the Illumina X10 system of LC Sciences (USA). R software package was adopted for processing the DEGs. Pathway enrichment analyses of the dysregulated genes were also carried out. Our study employed the Gene Set Enrichment Analysis (GSEA) online database to identify the interactions of DEGs in the apoptosis-related cluster.

Chromatin immunoprecipitation assay

Cells were harvested, and formaldehyde was introduced to the cell samples to a final concentration of 1% for crosslinking of chromatin for 10 min at ambient temperature. Subsequently, with 125 mM glycine, formaldehyde was inactivated. Chromatin digested into fragments of 100–300 bp received preclearing and subsequently immunoprecipitation with Protein A + G magnetic beads in combination with anti-FoxO3a antibodies (ab12162, Abcam). Based on the manufacturer’s directions, high-throughput ChIP fragment sequencing was conducted with Illumina HiSeq.

Immunofluorescence assay

Cells were seeded on glass coverslips and fixed at ambient temperature for 15 min utilizing 4% paraformaldehyde. These cells were stained with anti-FOXO3a (1:200) and anti-NLRP3 (1:200) rabbit Abs and then incubated at 4 °C overnight. Next, the cell samples were incubated in fluorochrome-conjugated secondary antibodies at a 1:800 dilution for 1 h at ambient temperature under the darkness. After being cleaned, cells received the staining process with DAPI for 10 min at 37 °C. Six random immunostaining images of the specimens were captured under a fluorescence microscope; then, data were analyzed with Image-Pro Plus 6.0 software.

Western blotting

The cultured cells were harvested and then lysed for 30 min on ice in RIPA (Beyotime, China). Next, cellular protein extracts were collected with centrifugation. Twenty five micrograms of proteins were resolved under SDS-PAGE and transferred to PVDF films. In 5% fat-free milk TBST solution, films received the blocking for 1 h and then the incubation throughout the night based on each major antibody at 4 °C. After being cleaned using TBST buffer, the films were incubated for 1 h at ambient temperature with the appropriate secondary antibodies. The proteins were visualized under improved chemiluminescence (ECL). Our study confirmed the equivalent loading of samples based on immunoblotting for GAPDH. Data were analyzed using ImageJ software, and figures were cropped.

Statistical analysis

Data were presented as mean ± standard deviation (SD) based on SPSS statistics software version 23.0 from no less than two single experimental processes. Student’s t-test was used for the comparison of two conditions. One-way analysis of variance (ANOVA) was conducted for comparison of multiple conditions. Statistical significance was defined as *p < 0.05, **p < 0.01, and ***p < 0.001.

Data availability

All data analyzed in this research are available from the correspondence on reasonable request. The expression profiling data have been deposited into the NCBI Gene Expression Omnibus under GEO Accession Number GSE166798.

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Acknowledgements

Not applicable.

Funding

This work was supported by the National Natural Science Foundation of China (NO:81670121).

Author information

Affiliations

  1. Department of Hematology, Shanghai Jiao Tong University Affiliated Sixth People’s Hospital, Shanghai, China

    Yuqian Zhu, Dandan Song, Juan Guo, Jiacheng Jin, Ying Tao, Zheng Zhang, Feng Xu, Qi He, Xiao Li, Chunkang Chang & Lingyun Wu

Contributions

YQZ designed the study and performed the experiments; DDS and JCJ carried out experiments; YT and JG contributed reagents, materials, and analysis tools; CKC and XL provided patients’ sample and their clinical data; QH, FX, and ZZ reviewed and analyzed patient data; LYW analyzed and interpreted the data; LYW and YQZ wrote the manuscript.

Corresponding author

Correspondence to Lingyun Wu.

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Conflict of interest

The authors declare no competing interests.

Ethics statement

All procedures performed in studies involving human participants were approved by the ethics committee of the Shanghai Jiao Tong University Affiliated Sixth People’s Hospital, and informed consent was obtained from all patients for this research in accordance with the Declaration of Helsinki.

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Zhu, Y., Song, D., Guo, J. et al.U2AF1 mutation promotes tumorigenicity through facilitating autophagy flux mediated by FOXO3a activation in myelodysplastic syndromes. Cell Death Dis12, 655 (2021). https://doi.org/10.1038/s41419-021-03573-3

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RxJava recap

Reactor, like RxJava 2, is a fourth generation reactive library. It has been launched by Spring custodian Pivotal, and builds on the Reactive Streams specification, Java 8, and the ReactiveX vocabulary. Its design is the result of a savant mix fueled by designs and core contributors from Reactor 2 (the previous major version) and RxJava.

In previous articles in this series, "RxJava by Example" and "Testing RxJava", you learned about the basics of reactive programming: how data is conceptualized as a stream, the Observable class and its various operators, the factory methods that create Observables from static and dynamic sources.

Observable is the push source and Observer is the simple interface for consuming this source via the act of subscribing. Keep in mind that the contract of an Observable is to notify its Observer of 0 or more data items through onNext, optionally followed by either an onError or onComplete terminating event.

To test an Observable, RxJava provides awhich is a special flavor of Observer that allows you to assert events in your stream.

In this article we'll draw a parallel between Reactor and what you already learned about RxJava, and showcase the common elements as well as the differences.

Reactor's types

Reactor's two main types are the and. A Flux is the equivalent of an RxJavacapable of emitting 0 or more items, and then optionally either completing or erroring.

A Mono on the other hand can emit at most once. It corresponds to both and types on the RxJava side. Thus an asynchronous task that just wants to signal completion can use a .

This simple distinction between two types makes things easy to grasp while providing meaningful semantics in a reactive API: by just looking at the returned reactive type, one can know if a method is more of a "fire-and-forget" or "request-response" () kind of thing or is really dealing with multiple data items as a stream ().

Both Flux and Mono make use of this semantic by coercing to the relevant type when using some operators. For instance, calling on a will return awhereas concatenating two monos together using will produce a. Similarly, some operators will make no sense on a (for examplewhich produces n > 1 results), whereas other operators will only make sense on a (e.g. ).

One aspect of the Reactor design philosophy is to keep the API lean, and this separation into two reactive types is a good middle ground between expressiveness and API surface.

"Build on Rx, with Reactive Streams at every stage"

As expressed in "RxJava by Example", RxJava bears some superficial resemblance to Java 8 Streams API, in terms of concepts. Reactor on the other hand looks a lot like RxJava, but this is of course in no way a coincidence. The intention is to provide a Reactive Streams native library that exposes an Rx-conforming operator API for asynchronous logic composition. So while Reactor is rooted in Reactive Streams, it seeks general API alignment with RxJava where possible.

Reactive Libraries and Reactive Streams adoption

Reactive Streams (abbreviated RS in the remainder of this article) is "an initiative to provide a standard for asynchronous stream processing with non-blocking back pressure". It is a set of textual specifications along with a TCK and four simple interfaces (, and ), which will be integrated in Java 9.

It mainly deals with the concept of reactive-pull back-pressure (more on that later) and how to interoperate between several implementing reactive sources. It doesn't cover operators at all, focusing instead exclusively on the stream's lifecycle.

A key differentiator for Reactor is its RS first approach.Both and are implementations and conform to reactive-pull back-pressure.

In RxJava 1 only a subset of operators support back-pressure, and even though RxJava 1 has adapters to RS types, its doesn't implement these types directly. That is easily explained by the fact that RxJava 1 predates the RS specification and served as one of the foundational works during the specification's design.

That means that each time you use these adapters you are left with awhich again doesn't have any operator. In order to do anything useful from there, you'll probably want to go back to anwhich means using yet another adapter. This visual clutter can be detrimental to readability, especially when an entire framework like Spring 5 directly builds on top of .

Another difference with RxJava 1 to keep in mind when migrating to Reactor or RxJava 2 is that in the RS specification, values are not authorized. It might turn out important if your code base uses to signal some special cases.

RxJava 2 was developed after the Reactive Streams specification, and thus has a direct implementation of in its new type. But instead of focusing exclusively on RS types, RxJava 2 also keeps the "legacy" RxJava 1 types (,and )  and introduces the "RxJava Optional". Although they still provide the semantic differentiation we talked about earlier, these types have the drawback of not implementing RS interfaces. Note that unlike in RxJava 1, in RxJava 2 does not support the backpressure protocol in RxJava 2 (a feature now exclusively reserved to ). It has been kept for the purpose of providing a rich and fluent API for cases, such as user interface eventing, where backpressure is impractical or impossible. and have by design no-need for backpressure support, they will offer a rich API as well and defer any workload until subscribed.

Reactor is once again leaner in this area, sporting its and types, both implementing and both backpressure-ready. There's a relatively small overhead for to behave as abut it is mostly offsetted by other optimizations. We'll see in a later section what backpressure means for .

An API similar but not equal to RxJava's

The ReactiveX and RxJava vocabulary of operators can be overwhelming at times, and some operators can have confusing names for historical reasons. Reactor aims to have a more compact API and to deviate in some cases, e.g. in order to choose better names, but overall the two APIs look a lot alike. In f.lux Serial Key - Crack Key For U the latest iterations in RxJava 2 actually borrow some vocabulary from Reactor as well, a hint of the ongoing close collaboration between the two projects. Some operators and concepts first appear in one library or the other, but often end up in both.

For instance, has the same familiar factory method (albeit having only two just variants: one element and a vararg). Buthas been replaced by several explicit variants, most notable being. Flux also has all the usual suspects in term of operators:, …, etc.

One example of an RxJava operator name that Reactor eschewed was the puzzling operator, which has been replaced with the more appropriately named. Additionally, to introduce greater consistency in the API, has been renamed. In fact all operators now aggregate values into a specific type of collection but still produce a of said collection, while methods are reserved for type conversions that take you out of the reactive world, eg. .

One more means by which Reactor can be leaner, this time in terms of class instantiation and resource usage, is fusion: Reactor is capable of merging multiple sequential uses of certain operators (eg. calling twice) into a single use, only instantiating the operator's inner classes once (macro-fusion). That includes some data source based optimization which greatly helps offset the cost of implementing. It is also capable of sharing resources like inner queues between several compatible operators (micro-fusion). These capabilities make Reactor a fourth-generation reactive library. But that is a topic for a future article.

Let's take a closer look at a few Reactor operators. (You will notice the contrast with some of the examples in the earlier articles in our series.)

A few operator examples

(This section contains snippets of code, and we encourage you to try them and experiment further with Reactor. To that effect, you should open your IDE of choice and create a test project with Reactor as a dependency.)

To do so in Maven, add the following to the dependencies section of your pom.xml:

To do the same in Gradle, edit the dependencies section to add reactor, similarly to this:

Let's play with examples used in the previous articles in this series!

Very similarly to how you would create your first in RxJava, you can create a using the and Reactor factory methods. Remember that given a would just emit the list as one whole, single emission, while will emit each element from the iterable list:

Like in the corresponding RxJava examples, this prints

In order to output the individual letters in the fox sentence we'll also need (as we did in RxJava by Example), but in Reactor we use instead of. We then want to filter out duplicate letters and sort them using and. Finally, we want to output an index for each distinct letter, which can be done using and :

This helps us notice the s is missing as expected:

One way of fixing that is to correct the original words array, but we could also manually add the "s" value to the of letters using and a :

This adds the missing s just before we filter out duplicates and sort/count the letters:

The previous article noted the resemblance between the Rx vocabulary and the Streams API, and in fact when the data is readily available from memory, Reactor, like Java Streams, acts in simple push mode (see the backpressure section below to understand why). More complex and truly asynchronous snippets wouldn't work with this pattern of just subscribing in the main thread, primarily because control would return to the main thread and then exit the application as soon as the subscription is done. For instance:

This snippet prints "Hello", but fails to print the delayed "world" because the test terminates too early. In snippets and tests where you only sort of write a main class like this, you'll usually want to revert back to blocking behavior. To do that you could create a and call in your subscriber (both in and ). But then that's not very reactive, is it? (and what if you forget to count down, in case of error for instance?)

The second way you could solve that issue is by using one of the operators that revert back to the non-reactive world. Specifically, and will both produce a blocking instance. So let's use for our example:

As you would expect, this prints "Hello" followed by a short pause, then prints "world" and terminates.

As we mentioned above, RxJava operator has been renamed (which more clearly hints at the operator's purpose: selecting the first to emit). In the following example, we create a whose start is delayed by 450ms and a that emits its values with a 400ms pause before each value. When them together, since the first value from the comes in before the 's value, it is the that ends up being played:

This prints each part of the sentence with a short 400ms pause between each section.

At this point you might wonder, what if you're writing a test for a Flux that introduces delays of 4000ms instead of 400? You don't want to wait 4s in a unit test! Fortunately, we'll see in a later section that Reactor comes with powerful testing facilities that nicely cover this case.

But for now, we have sampled how Reactor compares for a few common operators, so let's zoom back and have a look at other differentiating aspects of the library.

A Java 8 foundation

Reactor targets Java 8 rather than previous Java versions. This is once again aligning with the goal of reducing the API surface: RxJava targets Java 6 where there is no package so classes like or can't be leveraged. Instead they had to add specific classes like, etc. In RxJava 2 these classes mirror the way Reactor 2 used to do when it still had to support Java 7.

The Reactor API also embraces types introduced in Java 8. Most of the time-related operators will be about a duration (eg.,etc.), so using the Java 8 is appropriate.

The Java 8 API and can also both be easily converted to aand vice-versa. Should we usually convert a to a though? Not really. The level of indirection added by or is a negligible cost when they decorate more costly operations like IO or memory-bound operations, but most of the time a doesn't imply that kind of latency and it is is perfectly ok to use the API directly. Note that for these use cases in RxJava 2 we'd use theas it is not backpressured and thus becomes a simple push use case once you've subscribed. But Reactor is based on Java 8, and the Stream API is expressive enough for most use cases. Note also that even though you can find and factories for literal or simple Objects, they mostly serve the purpose of being combined in higher level flows. So typically you wouldn't want to transform an accessor like "" into a "" when migrating an existing codebase to reactive patterns.

The Backpressure story

One of the main focuses (if not the main focus) of the RS specification and of Reactor itself is backpressure. The idea of backpressure is that in a push scenario where the producer is quicker than the consumer, there's value in letting the consumer signal back to the producer and say "Hey! Slow down a little, I'm overwhelmed". This gives the producer a chance to control its pace rather than having to resort to discarding data (sampling) or worse, risking a cascading failure.

You may wonder at this point where backpressure comes into the picture with : what kind of consumer could possibly be overwhelmed by a single emission? Short answer is "probably none". However, there's still a key difference between how a works and how a works. The latter is push only: if you have a reference to theit means the task processing an asynchronous result is already executing. On the other hand, what a backpressured or enables is a deferred pull-push interaction:

  1. Deferred because nothing happens before the call to
  2. Pull because at the subscription and request steps, the will send a signal upstream to the source and essentially pull the next chunk of data
  3. Push from producer to consumer from there on, within the boundary of the number of requested elements

For is the button that you press to say "I'm ready to receive my data". For Flux, this button iswhich is kind of a generalization of the former.

Realizing that is a that will usually represent a costly task (in terms of IO, latency, etc.) is critical to understanding the value of backpressure here: if you don't subscribe, you don't pay the cost of that task. Since will often be orchestrated in a reactive chain with regular backpressuredpossibly combining results from multiple asynchronous sources, the availability of this on-demand subscribe triggering is key in order to avoid blocking.

Having backpressure helps us differentiate that last use case from another broad use case: asynchronously aggregating data from a into a. Operators like and are capable of consuming each item in theaggregating some form of data about it (respectively the result of a reduce function and a boolean) and exposing that data as a. In that case, the backpressure signalled upstream iswhich lets the upstream work in a fully push fashion.

Another interesting aspect of backpressure is how it naturally limits the amount of objects held in memory by the stream. As athe source of data is most probably slow (at least slowish) at producing items, so the request from downstream can very well start beyond the number of readily available items. In this case, the whole stream naturally falls into a push pattern where new items are notified to the consumer. But when there is a production peak and the pace of production accelerates, things fall nicely back into a pull model. In both cases, at most data ( amount) is kept in memory.

You can reason about the memory used by your asynchronous processing by correlating that demand for with the number of kilobytes an item consumes, : you can then infer that at most memory will be consumed. In fact, Reactor will most of the time take advantage of knowing to apply optimizations: creating queues bounded accordingly and applying prefetching strategies where it can automatically request 75% of N every time that same ¾ amount has been received.

Finally, Reactor operators will sometimes change the backpressure signal to correlate it with the expectations and semantics they represent. One prime example of this behavior would be : for every request of from downstream, that operator would request from upstream, which represents enough data to fill the number of buffers the subscriber is ready to consume. This is called "active backpressure", and it can be put to good use by developers in order to explicitly tell Reactor how to switch from an input volume to a different output volume, in micro-batching scenarios for instance.

Relation to Spring

Reactor is the reactive foundation for the whole Spring ecosystem, and most notably Spring 5 (through Spring Web Reactive) and Spring Data "Kay" (which corresponds to spring-data-commons 2.0).

Having a reactive version for both of these projects is essential, in the sense that this enables us to write a web application that is reactive from start to finish: a request comes in, is asynchronously processed all the way down to and including the database, and results come back asynchronously as well. This allows a Spring application to be very efficient with resources, avoiding the usual pattern of dedicating a thread to a request and blocking it for I/O.

So Reactor is going to be used for the internal reactive plumbing of future Spring applications, as well as in the APIs these various Spring components expose. More generally, they'll be able to deal withbut most of the time these will happen to bebringing in the rich feature set of Reactor. Of course, you will be able to use your reactive library of choice, as the framework provides hooks for  adapting between Reactor types and RxJava types or even simpler RS types.

At the time of writing of this article, you can already experiment with Spring Web Reactive in Spring Boot by using Spring Boot and the dependency (eg. by generating such a project on start.spring.io):

This lets you write your mostly as usual, but replaces the underlying Spring MVC traditional layer with a reactive one, replacing many of the Spring MVC contracts by reactive non-blocking ones. By default, this reactive layer is based on top of Tomcat 8.5, but you can also elect to use Undertow or Netty.

Additionally, although Spring APIs are based on Reactor types, the Spring Web Reactive module lets you use various reactive types for both the request and response:

  • : as thethe request entity is asynchronously deserialized and you can chain your processing to the resulting mono afterward. As the return type, once the emits a value, the T is serialized asynchronously and sent back to the client. You can combine both approaches by augmenting the request Mono and returning that augmented chain as the resulting Mono.
  • : Used in streaming scenarios (including input streaming when used as and Server Sent Events with a return type)
  • : Same as and respectively, but switching to an RxJava implementation.
  • as a return type: Request handling completes when the Mono completes.
  • Non-reactive return types ( and ): This now implies that your controller method is synchronous, but should be non-blocking (short-lived processing). The request handling finishes once the method is executed. The f.lux Serial Key - Crack Key For U is serialized back to the client asynchronously.

Here is a quick example of a plain text @Controller using the experimental web reactive module:

The first endpoint takes a path variable, transforms it into a and that name to a greeting sentence that is returned to the client.

By doing a GET on we get "Hello Simon!" as a text/plain response.

The second endpoint is a bit more complicated: it asynchronously receives a serialized instance (a class simply made up of a and attributes) and it into a stream of the last name's letters. It then takes the first of these letters, it to upper case and enates it into a greeting sentence.

So POSTing the following JSON object to

Returns the string "Hello mister T. How are you?".

The reactive aspect of Spring Data is also currently being developed in the Kay release train, which for is the branch. There is a first Milestone out that you can get by adding the Spring Data Kay-M1 bom to your pom:

Then for this simplistic example just add the Spring Data Commons dependency in your pom (it will take the version from the BOM above):

Reactive support in Spring Data revolves around the new interface, which extends. This interface exposes CRUD methods, using Reactor input and return types. There is also an RxJava 1 based version called. For instance, in the classical blockingretrieving one entity by its id would be done using "". It becomes "" and "" in and respectively. There are even variants that take a Mono/Single as argument, to asynchronously provide the key and compose on that.

Assuming a reactive backing store (or a mock bean), the following (very naive) controller would be reactive from start to finish:

Notice how the data repository usage naturally flows into the response path: we asynchronously fetch the entity and wrap it as a usingobtaining a we can return right away. If the Spring Data repository cannot find data for this key, it will return an empty. We make that explicit by using and returning a 404.

Testing Reactor

The article "Testing RxJava" covered techniques for testing an. As we saw, RxJava comes with a that you can use with operators that accept a as a parameter, to manipulate a virtual clock on these operators. It also features a class that can be leveraged to wait for the completion of an and to make assertions about every event (number and values forhas triggered, etc.) In RxJava 2, the is an RSso you can test Reactor's and with it!

In Reactor, these two broad features are combined into the class. It can be found in the addon module from the repository. The can be initialized by creating an instance from anyusing the builder. If you want to use virtual time, you can use the builder, which takes a. The reason for this is that it will first ensure that a is created and enabled as the default Scheduler implementation to use, making the need to explicitly pass the scheduler to operators obsolete. The StepVerifier will then configure if necessary the created within the Supplier, turning timed operators into "virtually timed operator". You can then script stream expectations and time progress: what the next elements should be, should there be an error, should it move forward in time, etc. Other methods include verifying that data matches a given or even consume onNext events, allowing you to do more advanced interactions with the value (like using an assertion library). Any thrown by one of these will be reflected back in the final verification result. Finally, call to check your expectations, this will truly subscribe to the defined source via or .

Let's take a few simple examples and demonstrate how works. For these snippets, you'll want to add the following test dependencies to your pom:

First, imagine you have reactive class called that produces a few that you want to test:

The first method is intended to return the 5 letters of the alphabet following (and including) the given starting letter. The second method returns a flux that emits a given value after a given delay, in seconds.

The first test we'd like to write ensures that calling from x limits the output to x, y, z. With it would go like this:

The second test we'd like to run on is that every returned value is an alphabetical character. For that we'd like to use a rich assertion library like AssertJ:

Turns out both of these tests fail :(. Let's have a look at the output the gives us in each case to see if we can spot the bug:

and

So it looks like our method doesn't stop at z but continues emitting characters from the ASCII range. We could fix that by adding a for instance, or using the same as the second argument to range.

The last test we want to make involves virtual time manipulation: we'll test the delaying method but without actually waiting for the given amount of seconds, by using the builder:

This tests a flux that would be delayed by 30 seconds for the following scenario: an immediate subscription, followed by 3x10s where nothing happens, then an onNext("") and completion.

The output prints the actual duration the verification took, which in my latest run was 8ms :)

Note that when using the builder instead, the and methods would still be available but would actually block for the provided duration.

comes with many more methods for describing expectations and asserting state of a (and if you think about new ones, contributions and feedback are always welcome in the github repository).

Custom Hot Source

Note that the concept of hot and cold observables discussed at the end of "RxJava by Example" also applies to Reactor.

If you want to create a custom Flux, instead of the RxJava AsyncEmitter class, you'd use Reactor's. This will cover all the asynchronous corner cases for you and let you focus on emitting your values.

Use and get a in the callback that you can use to emit data via. This custom Flux can be cold, so in order to make it hot you can use publish() and connect(). Building on the example from the previous f.lux Serial Key - Crack Key For U with a feed of price ticks, we get an almost verbatim translation in Reactor:

Before connecting to the hot Flux, why not subscribe twice?  One subscription will print the detail of each tick while the other will only print the instrument:

We then connect to the hot flux and let it run for 5 seconds before our test snippet terminates:

(note that in the example repository, the feed would also terminate on its own if the method of is changed).

also lets you check if downstream has cancelled its subscription via. You can also get feedback on the outstanding requested amount viawhich is useful if you want to simply comply with backpressure. Finally, you can make sure any specific resources your source uses are released upon via .

Note that there's a backpressure implication of using FluxSink: you must provide an explicitly to let the operator deal with backpressure. This is equivalent to using operators (eg. is equivalent to using ), which kind of overrides any backpressure instructions from downstream.

Conclusion

In this article, you have learned about Reactor, a fourth-generation reactive library that builds on the Rx language but targets Java 8 and the Reactive Streams specification. We've shown how the concepts you might have learned in RxJava also apply to Reactor, despite a few API differences. We've also shown how Reactor serves as the foundation for Spring 5, and that it offers resources for testing a .

If you want to dig deeper into using Reactor, the snippets presented in this article are available in our github repository. There is also a workshop, the "Lite Rx API hands-on", that covers more operators and use cases.

Finally, you can reach the Reactor team on Gitter and provide feedback there or through github issues (and of course, pull-requests are welcomed as well).

About the Author

Simon Basle is a software development aficionado, especially interested in reactive programming, software design aspects (OOP, design patterns, software architecture), rich clients, what lies beyond code (continuous integration, (D)VCS, best practices), and also a bit of CompSci, concurrent programming. He works at Pivotal on Reactor.

This content is in the Java topic

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Источник: https://www.infoq.com/articles/reactor-by-example/

Flux

This article is about the concept of flux in natural science and mathematics. For other uses, see Flux (disambiguation).

Concept in natural science and mathematics

This article needs attention from an expert in physics. The specific problem is: confusion between flux and flux density. See the talk page for details. WikiProject Physics may be able to help recruit an expert.(September 2016)

The field lines of a vector fieldFthrough surfaces with unitnormal n, the angle from nto Fis θ. Flux is a measure of how much of the field passes through a given surface. Fis decomposed into components perpendicular (⊥) and parallel ( ‖ ) to n. Only the parallel component contributes to flux because it is the maximum extent of the field passing through the surface at a point, the perpendicular component does not contribute. Top:Three field lines through a plane surface, one normal to the surface, one parallel, and one intermediate. Bottom:Field line through a curved surface, showing the setup of the unit normal and surface element to calculate flux.
To calculate the flux of a vector field \mathbf {F} (red arrows)through a surface Sthe surface is divided into small patches dS. The flux through each patch is equal to the normal (perpendicular) component of the field, the dot productof {\displaystyle \mathbf {F} (\mathbf {x} )}with the unit normal vector {\displaystyle {\hat {\mathbf {n} }}(\mathbf {x} )}(blue arrows)at the point \mathbf {x} multiplied by the area dS. The sum of {\displaystyle \mathbf {F} \cdot {\hat {\mathbf {n} }}\,dS}for each patch on the surface is the flux through the surface

Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction f.lux Serial Key - Crack Key For U the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface.[1]

Terminology[edit]

The word flux comes from Latin: fluxus means "flow", and fluere is "to flow".[2] As fluxion, this term was introduced into differential calculus by Isaac Newton.

The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena.[3] His seminal treatise Théorie analytique de la chaleur (The Analytical Theory of Heat),[4] defines fluxion as a central quantity and proceeds to derive the now well-known expressions of flux in terms of temperature differences across a slab, and then more generally in terms of temperature gradients or differentials of temperature, across other geometries. One could argue, based on the work of James Clerk Maxwell,[5] that the transport definition precedes the definition of flux used in electromagnetism. The specific quote from Maxwell is:

In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface.

— James Clerk Maxwell

According to the transport definition, flux may be a single vector, or it may be a vector field / function of position. In the latter case flux can readily be integrated over a surface. By contrast, according to the electromagnetism definition, flux is the integral over a surface; it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwell's quote only makes sense if "flux" is being used according to the transport definition (and furthermore is a vector field rather than single vector). This is ironic because Maxwell was one of the major developers of what we now call "electric flux" and "magnetic flux" according to the electromagnetism definition. Their names in accordance with the quote (and transport definition) would be "surface integral of electric flux" and "surface integral of magnetic flux", in which case "electric flux" would instead be defined as "electric field" and "magnetic flux" defined as "magnetic field". This implies that Maxwell conceived of these fields as flows/fluxes of some sort.

Given a flux according to the electromagnetism definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the transport definition. Given a current such as electric current—charge per time, current density would also be a flux according to the transport definition—charge per time per area. Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously. Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux the term corresponds to.

Flux as flow rate per unit area[edit]

In transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity]·[time]−1·[area]−1.[6] The area is of the surface the property is flowing "through" or "across". For example, the magnitude of a river's current, i.e. the amount of water that flows through a cross-section of the river each second, or the amount of sunlight energy that lands on a patch of ground each second, are kinds of flux.

General mathematical definition (transport)[edit]

Here are 3 definitions in increasing order of complexity. Each is a special case of the following. In all cases the frequent symbol j, (or J) is used for flux, q for the physical quantity that flows, t for time, and A for area. These identifiers will be written in bold when and only when they are vectors.

First, flux as a (single) scalar:

{\displaystyle j={\frac {I}{A}}}

where:

{\displaystyle I=\lim \limits _{\Delta t\rightarrow 0}{\frac {\Delta q}{\Delta t}}={\frac {\mathrm {d} q}{\mathrm {d} t}}}

In this case the surface in which flux is being measured is fixed, and has area A. The surface is assumed to be flat, and the flow is assumed to be everywhere constant with respect to position, and perpendicular to the surface.

Second, flux as a scalar field defined along a surface, i.e. a function of points on the surface:

{\displaystyle j(\mathbf {p} )={\frac {\partial I}{\partial A}}(\mathbf {p} )}
{\displaystyle I(A,\mathbf {p} )={\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} )}

As before, the surface is assumed to be flat, and the flow is assumed to be everywhere perpendicular to it. However the flow need not be constant. q is now a function of p, a point on the surface, and A, an area. Rather than measure the total flow through the surface, q measures the flow through the disk with area A centered at p along the surface.

Finally, flux as a vector field:

{\displaystyle \mathbf {j} (\mathbf {p} )={\frac {\partial \mathbf {I} }{\partial A}}(\mathbf {p} )}
{\displaystyle \mathbf {I} (A,\mathbf {p} )={\underset {\mathbf {\hat {n}} }{\operatorname {arg\,max} }}\,\mathbf {\hat {n}} _{\mathbf {p} }{\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} ,\mathbf {\hat {n}} )}

In this case, there is no fixed surface we are measuring over. q is a function of a point, an area, and a direction (given by a unit vector, \mathbf {\hat {n}} ), and measures the flow through the disk of area A perpendicular to that unit vector. I is defined picking the unit vector that maximizes the flow around the point, because the true flow is maximized across the disk that is perpendicular to it. The unit vector thus uniquely maximizes the function when it points in the "true direction" of the flow. [Strictly speaking, this is an abuse of notation because the "arg max" cannot directly compare vectors; we take the vector with the biggest norm instead.]

Properties[edit]

These direct definitions, especially the last, are rather unwieldy. For example, the argmax construction is artificial from the perspective of empirical measurements, when with a Weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway.

If the flux j passes through the area at an angle θ to the area normal \mathbf {\hat {n}} , then

\mathbf {j} \cdot \mathbf {\hat {n}} =j\cos \theta

where · is the dot product of the unit vectors. This is, the component of flux passing through the surface (i.e. normal to it) is j cos θ, while the component of flux passing tangential to the area is j sin θ, but there is no flux actually passing through the area in the tangential direction. The only component of flux passing normal to the area is the cosine component.

For vector flux, the surface integral of j over a surfaceS, gives the proper flowing per unit of time through the surface.

{\displaystyle {\frac {\mathrm {d} q}{\mathrm {d} t}}=\iint _{S}\mathbf {j} \cdot \mathbf {\hat {n}} \,{\rm {d}}A\ =\iint _{S}\mathbf {j} \cdot {\rm {d}}\mathbf {A} }

A (and its infinitesimal) is the vector area, combination of the magnitude of the area through which the property passes, A, and a unit vector normal to the area, \mathbf {\hat {n}} . The relation is \mathbf {A} =A\mathbf {\hat {n}} . Unlike in the second set of equations, the surface here need not be flat.

Finally, we can integrate again over the time duration t1 to t2, getting the total amount of the property flowing through the surface in that time (t2t1):

{\displaystyle q=\int _{t_{1}}^{t_{2}}\iint _{S}\mathbf {j} \cdot {\rm {d}}{\mathbf {A} }\,{\rm {d}}t}

Transport fluxes[edit]

Eight of the most common forms of flux from the transport phenomena literature are defined as follows:

  1. Momentum flux, the rate of transfer of momentum across a unit area (N·s·m−2·s−1). (Newton's law of viscosity)[7]
  2. Heat flux, the rate of heat flow across a unit area (J·m−2·s−1). (Fourier's law of conduction)[8] (This definition of heat flux fits Maxwell's original definition.)[5]
  3. Diffusion flux, the rate of movement of molecules across a unit area (mol·m−2·s−1). (Fick's law of diffusion)[7]
  4. Volumetric flux, the rate of volume flow across a unit area (m3·m−2·s−1). (Darcy's law of groundwater flow)
  5. Mass flux, the rate of mass flow across a unit area (kg·m−2·s−1). (Either an alternate form of Fick's law that includes the molecular mass, or an alternate form of Darcy's law that includes the density.)
  6. Radiative flux, the amount of energy transferred in the form of photons at a certain distance from the source per unit area per second (J·m−2·s−1). Used in astronomy to determine the magnitude and spectral class of a star. Also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the electromagnetic spectrum.
  7. Energy flux, the rate of transfer of energy through a unit area (J·m−2·s−1). The radiative flux and heat flux are specific cases of energy flux.
  8. Particle flux, the rate of transfer of particles through a unit area ([number of particles] m−2·s−1)

These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the divergence of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space. For incompressible flow, the divergence of the volume flux is zero.

Chemical diffusion[edit]

As mentioned above, chemical molar flux of a component A in an isothermal, isobaric system is defined in Fick's law of diffusion as:

\mathbf {J} _{A}=-D_{AB}\nabla c_{A}

where the nabla symbol ∇ denotes the gradient operator, DAB is the diffusion coefficient (m2·s−1) of component A diffusing through component B, cA is the concentration (mol/m3) of component A.[9]

This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux.[5]

For dilute gases, kinetic molecular theory relates the diffusion coefficient D to the particle density n = N/V, the molecular mass m, the collision cross section\sigma , and the absolute temperatureT by

D={\frac {2}{3n\sigma }}{\sqrt {\frac {kT}{\pi m}}}

where the second factor is the mean free path and the square root (with Boltzmann's constantk) is the mean velocity of the particles.

In turbulent flows, the transport by eddy motion can be expressed as a grossly increased diffusion coefficient.

Quantum mechanics[edit]

Main article: Probability current

In quantum mechanics, particles of mass m in the quantum stateψ(r, t) have a probability density defined as

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