# Re: Re: heat diffusion calculation

From: Jonathan Lee (jonny5_at_rice.edu)
Date: Tue Jun 19 2007 - 15:13:12 CDT

Hello all,
I've set up my system such that two ends of my rectangular box act as
my "shell" at 200K. I have periodic boundary conditions in all
directions. When I try the heat diffusion calculation from the tutorial
(with appropriate changes), I find that the temperature of my system
actually goes up. It reaches about 700-800K! I guess the langevin
dynamics help to control the system during minimization/equilibration
but are not present in the heat diffusion problem to control the
temperature. Can somebody help me troubleshoot this problem? Thanks.

Jonathan

p.s. I was having a problem during my minimization step where the
periodic cell was too small (even though I set it large enough to
contain the original configuration). I found one solution to this was
to turn on "useFlexibleCell" but is that ok?

Jonathan Lee wrote:
> All,
> Thanks everybody for your replies. I think I'm understanding it
> better now. To follow up... I'm ultimately interested in calculating
> the thermal conductivity in certain directions. For example, how well
> heat will conduct in the z-direction versus in the x- or
> y-directions. From my current understanding, the method outlined in
> the tutorial would not work for something like this. It seems that
> this method finds an isotropic diffusivity (and ultimately thermal
> conductivity). Any clues on how I could approach this problem
> (modifying the tutorial's method or otherwise)?
>
> On a side note, does anybody know how to apply periodic boundary
> conditions in only one or two directions? Realistically, what type of
> boundary conditions could I apply to the other direction(s)? If I
> were to, say, heat one end of a rectangular prism domain and observe
> the heat transfer down the length of the prism, surely I can't have
> periodic boundary conditions in that direction.
>
> (By the way, Victor, it seems like we are in fact looking at
> different versions of the tutorial. The temperature echoes appears at
> the bottom of page 56 in my version.)
>
> Thanks,
>
> Jonathan
>
>
> Victor Ovchinnikov wrote:
>> Jonathan, The page numbers that you provide correspond to the
>> calculations of the
>> temperature echos from an MD simulation (at least in the tutorial
>> version that I have)
>>
>> 1) Yes, it is a boundary condition to the diffusion equation on page 47.
>> 2) Not sure where you are; step 11 on p.55 deals with temperature echos;
>> I'm certain that the script monitors the average temp of the system
>> including the outer shell; this is an approximation, since analytically,
>> the boundary has no volume, whereas in this case, it does; perhaps
>> that's why the agreement with the theoretical plot on p.49 is not
>> perfect.
>>
>> 3) The inner radius is 22, as defined in the VMD script that populates
>> the beta column of the PDB; the simulation domain is a sphere with
>> radius 26 Angstroms; so cutting off at 22 should apply to the outer
>> layer of the water molecules, since the diameter of a water moelcule is
>> roughly 3A. So the calculation _does_ take the radius into account; for
>> a larger radius, you would have to first solvate & equilibrate the
>> protein in a larger sphere; then when you ran VMD, increase to cutoff
>> accordingly.
>> 4) Yes, the problem is that you need an analytical formula for the
>> solution of the heat equation in the rectangular domain; this should be
>> obtainable from a PDE book as a series solution (just like the spherical
>> formula) You would then need to take this solution and average over the
>> size of the box -- i.e. integrate over x,y,z & divide by the box size;
>> this would give you a an expression similar to the on p. 47
>>
>> Regarding the physics of measuring diffusion, you are correct; it is
>> easiest to fix the temp. somewhere & put a probe at another location &
>> record your temperature values; This is the lab experiment, which would
>> give you a long-time averaged quantity (the duration of the experiment
>> is of the order of seconds). However, you can only do MD for a few
>> nanoseconds -- so your statistics for a quantity at one location would
>> be extremely poor. What the method outlined in the tutorial says, is
>> that you can still extract the diffusion coefficient from averaging over
>> multiple regions -- in this case the entire domain (which will give you
>> better statistics by orders of magnitude)
>>
>> Best, Victor
>>
>>
>> On Mon, 2007-06-18 at 12:16 -0500, Jonathan Lee wrote:
>>
>>> Anybody? Thanks.
>>>
>>> Jonathan
>>>
>>>
>>> Jonathan Lee wrote:
>>>
>>>> Hello all,
>>>> I have some questions about the heat diffusion calculation in the
>>>> NAMD tutorial (page 53).
>>>>
>>>> 1) The shell is maintained at a temperature of 200, right? (As
>>>> opposed to just initialized to 200.)
>>>> 2) What is the temperature that is output (step 11, page 55)? Is
>>>> that the temperature of everything excluding the 200K shell?
>>>> 3) It seems to me that the calculation should take into account the
>>>> inner radius of the shell. If the radius is much larger, shouldn't
>>>> it take a longer time for the diffusion to occur?
>>>> 4) Can I do a similar calculation but with a rectangular prism
>>>> domain (i.e. fix the temperature at one end and calculate the heat
>>>> diffusion to the other end of the box)?
>>>>
>>>> Basically, my understanding is that the temperature should be
>>>> maintained in one region and measured in another region a finite
>>>> distance away. That distance (and the time of diffusion) should be
>>>> taken into consideration when finding the diffusivity. Am I
>>>> overlooking something? Thanks.
>>>>
>>>> Jonathan
>>>>
>>>>
>>>>
>>>>
>>>>
>>
>>
>>
>
>

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