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 <ronghai...@fau.de> 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, <ronghai...@fau.de> >> 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>_______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]