Talk:Diffusion equation

From Wikipedia, the free encyclopedia

WikiProject Physics This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
??? This article has not yet received a rating on the assessment scale. [FAQ]
??? This article has not yet received an importance rating within physics.

Help with this template Please rate this article, and then leave comments to explain the ratings and/or to identify its strengths and weaknesses.

[edit] Another form

Feynman gives the diffusion equation (Volume II 3-4) as

\frac{\partial\phi}{\partial t} = k\nabla^2\phi

Is this equivalent? Or should it be added? It is more understandable to me at a high school level.

I think we should do this too, it's much more recognizable. Isn't this:
\frac{\partial\phi}{\partial t}=\nabla\cdot D(\phi)\nabla\phi(\vec{r},t)
just the same as this:
\frac{\partial\phi}{\partial t}=D(\phi)\nabla^2\phi(\vec{r},t)
In that case, the latter form is much preferred. For example, this is how Diffusion equation at scienceworld.wolfram.com puts it.
— Sverdrup 23:50, 18 November 2005 (UTC)
They are not equivalent, since
\nabla\cdot D(\phi)\nabla\phi(\vec{r},t) = (\nabla D(\phi)) \cdot (\nabla\phi(\vec{r},t)) + D(\phi)\nabla^2\phi(\vec{r},t).
However, if the diffusion coefficient D is a constant, say k, then we do get the equation
\frac{\partial\phi}{\partial t} = k\nabla^2\phi.
The latter equation is treated at heat equation.
In fact, the case where D is constant (or at least independent of φ) is very common. So it might be better to redirect diffusion equation to heat equation and move this article to nonlinear diffusion equation. -- Jitse Niesen (talk) 20:39, 20 November 2005 (UTC)

[edit] Missing \cdot

Dear Sir

In the first equation after: "The equation is usually written as: ....

is missing a dot after the nabla: "...= nabla . ( D( ..."

"Nabla dot" is the divergency.

The italian version for "Diffusion equation" is correct. It has the "dot".

150.163.46.38 23:25, 25 May 2007 (UTC) Ivan J.Kantor

You are completely right. Thanks for bringing this to our notice. I now fixed it. -- Jitse Niesen (talk) 05:10, 27 May 2007 (UTC)

[edit] Merge with Fick's second law

As far as I can see Fick's second law and the diffusion equation are the same equation, therefore shouldn't the articles be merged? Eraserhead1 15:27, 12 July 2007 (UTC)