I am no specialist in noise terms, either, but the \delta(\vec{r} -
\vec{r}')\delta(t - t') terms express "uncorrelated in space and time", so both
\xi_c and \xi_\eta have that property in what you attached.
Equation (1a) with the Laplacian is the appropriate conservative form for the
noise on a conserved field like composition. You get it by taking the Laplacian
of the non-conserved form of the noise. Based on some notes from ten years ago
when I wrote that term, the conserved form should not be directly affected by
the length scale (dividing the variance by the cell volume); that's taken care
of by the Laplacian, e.g.
sigmaSqrd = Mobility * kBoltzmann * Temperature / timeStep
noise = GaussianNoiseVariable(mesh=mesh, mean=mean,
variance=sigmaSqrd).faceGrad.divergence
whereas for (1b), you'll use
noise = GaussianNoiseVariable(mesh=mesh, mean=mean,
variance=sigmaSqrd / mesh.cellVolumes)
On Mar 6, 2015, at 1:14 PM, Ronghai Wu <[email protected]> wrote:
> Thanks, I am trying to install Trilinos these days in Ubuntu-12, but still
> has not been successful yet. The dependences and paths seem complicated.
> I have a new question about the noise term. I would like to have Langevin
> noise terms(please see attached picture"Langevin noise term.png"). I noticed
> it is very similar to Fipy GaussianNoiseVariable as shown in the Fipy web
> http://www.ctcms.nist.gov/fipy/fipy/generated/fipy.variables.html
> My questions are:
> (i) Since I understand little about statistical mechanics, I am not sure if
> Langevin noise term in the picture is also "uncorrelated in space and time"
> as describe in Fipy web?
> (ii) How can I implement the noise in equation (1a) in the picture? There is
> a Laplacian operator, so I guess
> sigmaSqrd must be something different.
>
>
> On 03/03/15 17:31, Daniel Wheeler wrote:
>> On Mon, Mar 2, 2015 at 4:21 PM, <[email protected]>
>> wrote:
>>
>>> Dear Fipy Developers,
>>>
>>> When I try to test the parallel running by $ mpirun -np 3 python
>>> examples/parallel.py. I got the following error massage.
>>>
>>> from PyTrilinos import Epetra
>>> ImportError: No module named PyTrilinos
>>>
>>> If I understand correctly, Trilinos is a huge package with many
>>> sub-packages(including PyTrilions and Epetra). I do not want to install
>>> all of the Trilinos. So, I am wondering if there is the list of minimum
>>> required packages for parallel running regarding the Trilinos?
>>>
>> I think Jon listed out what we normally specify for cmake when
>> installing Trilinos to work with FiPy. I don't worry about the
>> quantity of packages installed. I think the duration of the
>> installation is much more concerning and I don't believe that it is
>> that long for Trilinos anymore. Last time I installed Trilinos it
>> didn't feel that long probably less than an hour. FiPy only uses two
>> packages in Trilinos, I believe, but it really isn't worth setting up
>> the cmake script to optimize this. Something will just go wrong and
>> you'll spend hours debugging it. There are all sorts of dependencies
>> within Trilinos so there isn't much point optimizing unless you really
>> know Trilinos well IMO.
>>
>>
>
> --
> ------------------------------------------
> Ronghai Wu
>
> Institute of Materials Simulation (WW8)
> Department of Materials Science and Engineering
> University of Erlangen-Nürnberg
> Dr.-Mack-Str. 77, 90762 Fürth, Germany
>
> Tel. +49 (0)911 65078-65064
>
> <Langevin noise term.png>_______________________________________________
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