# Re: Re: heat diffusion calculation

From: Jonathan Lee (jonny5_at_rice.edu)
Date: Mon Jun 18 2007 - 16:13:00 CDT

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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