Go Back   Physics Help Forum > College/University Physics Help > Atomic and Solid State Physics

Atomic and Solid State Physics Atomic and Solid State Physics Help Forum

Like Tree1Likes
  • 1 Post By benit13
Reply
 
LinkBack Thread Tools Display Modes
Old Mar 7th 2019, 12:53 PM   #1
Junior Member
 
Join Date: Mar 2019
Posts: 2
Question The Supposedly Stochastic Allen-Cahn Diffusion Equation

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.

Last edited by Pereos; Mar 7th 2019 at 12:56 PM.
Pereos is offline   Reply With Quote
Old Mar 7th 2019, 03:23 PM   #2
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,730
Originally Posted by Pereos View Post
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.
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

Last edited by topsquark; Mar 7th 2019 at 03:27 PM.
topsquark is offline   Reply With Quote
Old Mar 8th 2019, 01:30 AM   #3
Junior Member
 
Join Date: Mar 2019
Posts: 2
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.

Last edited by Pereos; Mar 8th 2019 at 02:31 AM.
Pereos is offline   Reply With Quote
Old Mar 8th 2019, 02:54 AM   #4
Senior Member
 
Join Date: Oct 2017
Location: Glasgow
Posts: 395
Originally Posted by Pereos View Post
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.
topsquark likes this.
benit13 is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Atomic and Solid State Physics

Tags
allencahn, diffusion, equation, stochastic, supposedly



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Diffusion equation ficku1 Advanced Thermodynamics 2 Sep 25th 2017 05:56 AM
Nondimensionalization of diffusion equation DzoptiC General Physics 0 Apr 22nd 2017 04:06 PM
investigating equations of stochastic processes nsrchem Advanced Thermodynamics 0 Jul 4th 2016 11:55 PM
Supposedly Simple Volume Problem cocokat Kinematics and Dynamics 3 Aug 28th 2012 09:40 AM


Facebook Twitter Google+ RSS Feed