The analytical expressions for thermal noise, as calculated by Liu & Thorne and Levin, was plotted as a function of frequency in a log  log plot using Matlab.
The value of the parameters were used from Levin's paper on thermal noise.
phi = 1*10^{7} (loss angle)
r0 = 1.56*10^{2 }(beam radius)
T = 300 K (temperature)
E0 = 7.18*10^{10 } (Young's modulus)
sigma = 0.16 (Poisson ratio)
The value of S_{x}(100) that given in Levin's paper (8.7*10^{40} m^{2} /Hz) while the LiuThorne value is 9.1*10^{40} m^{2} /Hz.
