**From:** \ (*jonathan_at_ibt.unam.mx*)

**Date:** Sun Jul 17 2005 - 12:09:41 CDT

**Next message:**xiaojing gong: "pressure control in config file"**Previous message:**Mauricio Carrillo Tripp: "Re: Runnig same config file many times"**In reply to:**Blake Charlebois: "Random forces in Langevin temperature control -- three questions"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hello.

I am not familiar with Langevin Dynamics, so I can only answer question two.

The only thing you missed here is that the Dirac delta does have dimensions, and

they are inverse to the ones of its variable.

This is easy to notice from the function's particular property that

Integral(DiracDelta(x-x0)*dx)=1 if x runs along an interval that contains x0.

Through dimensional analysis, we see that the right side is adimensional. On the

left side there is a "sum of products", so the dimensions are those of the

products. That is, each of the products DiracDelta(x-x0)*dx must be adimensional

(like 1 on the right hand). We know that dx has the dimensions of x, so the

dimensions of the delta must the inverse of these.

Thus, in this case, DiracDelta(t-t') has dimensions of (time)^(-1), so the

dimensions of 2*m*gamma*kB*T*delta(t-t') are

(mass)*(time)^(-1)*(force)*(distance)*(time)^(-1) or (force)^2.

Hope you get the rest of the answers.

J. Valencia

Quoting Blake Charlebois <bdc_at_mie.utoronto.ca>:

*> QUESTION TWO:
*

*> It seems to me that the dimensions of the left- and right-hand sides
*

*> of
*

*> <R(t)*R(t')> = 2*m*gamma*kB*T*delta(t-t') do not agree. What blunder am
*

*> I
*

*> making here?
*

*>
*

*> The dimensions of gamma are (time)^(-1).
*

*>
*

*> The dimensions of 2*m*gamma*kB*T*delta(t-t') are
*

*> (mass)*(time)^(-1)*(force)*(distance) or (force)^2*(time).
*

*>
*

*> The dimensions of <R(t)*R(t')> are (force)^2.
*

**Next message:**xiaojing gong: "pressure control in config file"**Previous message:**Mauricio Carrillo Tripp: "Re: Runnig same config file many times"**In reply to:**Blake Charlebois: "Random forces in Langevin temperature control -- three questions"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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