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Entry  Wed Jun 5 20:39:48 2013, Deep Chatterjee, Optics, General, Conventional Thermal noise (Sec V) from Liu & Thorne Thorne_thermal_noise.pngPercentage_difference.pngThorne_thermal_noise.pdfPercentage_difference.pdf
    Reply  Thu Jun 6 12:40:07 2013, Matt A., Optics, General, Conventional Thermal noise (Sec V) from Liu & Thorne Thorne_thermal_noise.pngPercentage_difference.png
Message ID: 11     Entry time: Wed Jun 5 20:39:48 2013     Reply to this: 13
Author: Deep Chatterjee 
Type: Optics 
Category: General 
Subject: Conventional Thermal noise (Sec V) from Liu & Thorne 

>The linearized PSD plots are created for the case of thermal noise in finite test mass (Sec. V) of Liu and Thorne.

S = 8*kb*T*phi*(U0 + delta_U)/omega

>The maximum energy due to stress is considered by an infinite sum here. A comparison has been made regarding the convergence of the sum.

>The two plots correspond to the cases of considering 10 and 100 terms in the sum respectively.

>The plot shows that the difference is not much and hence convergence is fast.

>The relative difference is plotted w.r.t  S_100, the PSD considering 100 terms in the sum.

Thorne_thermal_noise.png

 >The relative difference goes like abs(S_100 - S_10)/S_100, where 10 and 100 represent the number of terms considered in the sum.

Percentage_difference.png

>The algorithm used to evaluate the sum involving Bessel functions was the one by GWINC. (http://nodus.ligo.caltech.edu:8080/COMSOL/10).

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