The Supposedly Stochastic Allen-Cahn Diffusion Equation

Mar 2019
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The allen cahn equation describes the stochastic diffusion of different substances in alloys. If thats the case, how can there be an equation to describe this process? This seems paradoxical.
Thanks for the help.
 
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topsquark

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Apr 2008
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On the dance floor, baby!
The allen cahn equation describes the stochastic diffusion of different substances in alloys. If thats the case, how can there be an equation to describe this process? This seems paradoxical.
Thanks for the help.
I admit that I don't know the topic but after scanning through some of the basics I could dig up on Google I see no reason why we can't pose an equation for this process. Can you tell me where you are having difficulties?

Stochastic processes can be modeled, but as in all examples of Statistical Mechanics any equation can only really describe how "bulk" properties are changing. Is this your objection?

-Dan

Edit: I have moved this thread to the Atomic and Solid State Physics Forum.
 
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Mar 2019
2
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What I fail to understand is how an equation can describe random and unpredictable behaviour.

Is there some sort of "random" variable implemented in the equation?

I really am a noob to the field of maths and physics (10th grade), but as far as what I know, one can normally break down an equation into a specific set of values, but if the diffusion of substances in alloys is never the same, how can this be.
 
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Oct 2017
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Glasgow
What I fail to understand is how an equation can describe random and unpredictable behaviour.
There is the law of large numbers, which states that when the number of trials for a given probabilistic situation is high, the result tends towards the expectation value. Another interpretation of this is that for random phenomena, the error associated with the actual state of a system versus its predicted one decreases as the system increases in size.

In physics systems this number of trials is often very high or involves many, many particles. The result is a bulk motion that is very predictable and there are equations describe the bulk motion. A good example of this is Brownian motion or diffusion. Statistics plays a big role.
 
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