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Message ID: 25     Entry time: Thu Jun 20 12:41:01 2013
Author: Deep Chatterjee 
Type: General 
Category: General 
Subject: The expression for the "work dissipated" in the TE and TR noise calculations 

While discussing TE noise with Yanbei Chen, it was realized that the expression for the work dissipated W_diss was derivable from the inhomogenous Heat equation with a source term.
The exercise was tried out to some success and can be found in the attachment. The attachment describes the steps roughly.
The important point to note is the fact that while Liu and Thorne considered stresses developed in the material by means of the heat balance equation, they have ultimately resorted to the
expression for W_diss = 1/T * integral{ kappa * grad(T)^2 rdr } to calculate the dissipation. They have used an expression whch relates the expansion, Theta, to the gradient of temperature.

It is suspected that the fundamental approach is to consider a source of heat and evaluating the dissipation. However, Liu and Thorne considered applying pressure probably because of the
physical scenario of the fluctuations in the mirror face.

Discussion over the same would be helpful.

Attachment 1: dissipated_work.pdf  91 kB  Uploaded Thu Jun 20 13:53:05 2013  | Hide | Hide all
dissipated_work.pdf dissipated_work.pdf
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