Recent content by BOAS

I thought that the conditions on the Green's function meant that for any second order linear differential operator on [a,b], y(a) = y(b) = 0.

Homework Statement I am trying to fill in the gaps of a calculation (computing the deflection potential ##\psi##) in this paper: http://adsabs.harvard.edu/abs/1994A%26A...284..285K We have the Poisson equation: ##\frac{1}{x}\frac{\partial}{\partial x} \left( x \frac{\partial \psi}{\partial...

Homework Statement Consider the density perturbation smoothed with a Gaussian of scale ##\sigma##, ##\Delta_{\sigma}(\vec x') = \int d^3 \vec x \frac{e^{- \frac{(\vec x - \vec x')^2}{2 \sigma^2}}}{(2 \pi \sigma)^{3/2}} \Delta (\vec x)## Calculate the power spectrum ##P_{\Delta_{\sigma}}## of...

My density distribution is that of a singular isothermal sphere, so ##\rho(r) = \frac{\sigma^2}{2\pi G r^2}##. I have calculated the surface mass density (which is what I will be using), ##\kappa(\theta) = \frac{\theta_E}{2 \theta}##, where ##\theta_E## is the Einstein radius for an SIS. Thank...

I believe that makes sense. So I don't actually need to compute the auto correlation function in order to find the PS of D? i.e I want to compute the FT of D, and then take it's mod-squared. Once I have done that, it is then relatively straightforward to compute it's ACF. Do you have any...

Sorry, I'm confusing things: First and foremost, I am trying to analyse the case where I have assumed a mass density distribution. I am lead to believe that this can be done analytically for the SIS profile. No data related to this step. In addition to this, I have some simulated data that I...

Thank you for your reply. I have some data that is essentially a point sampled shear field. Ideally I would like to compute the power spectrum since that is the quantity I need to calculate the variance of the aperture mass. But since they are FT pairs, I suppose I would like to calculate...

I have been reading about weak gravitational lensing and I am trying to calculate the dispersion ##\langle M_{ap}^2\rangle## of the aperture mass for a singular isothermal sphere acting as a lens for distant objects. I need some guidance on how to actually carry out the calculation of the power...

Thank you, that looks much better! I know that there are libraries for sampling from many of these distributions but I am learning a bit about different methods of doing so. The point is to generate the samples.

Hello, I am looking at different methods for generating random numbers from the beta distribution. I am a bit confused about the following statement: "It is known that if ##a, b ∈ N_{>0} = \{1, 2, 3, . . .\}##, ##Y = \frac{\sum_{i=1}^a X_i}{\sum_{j=1}^{a+b}X_k}## is ##\mathrm{Be}(a...

Thank you, I have managed to find that the second residue is indeed ##\frac{1}{Y^2}## with the help of your hint

woops - I had a latex plugin in my browser, so everything looked normal to me. Thanks for pointing it out. (I have excluded physics forums from the plugin now)

Homework Statement I have never formally studied complex analysis, but I am reading this paper: http://adsabs.harvard.edu/abs/1996MNRAS.283..837S wherein section 2.2 they make use of the residue theorem. I am trying to follow along with this (and have looked up contour integration, cauchy's...

I think I have a solution, but it depends on the photons obeying ##T = T_0(1 + z)## I say that ##da = d(1+z)^{-1} = d(T_0 / T) = - T_0 T^{-2} dT## then ##da/a = -T^{-1} dT## substituting this into my expression ##\frac{da}{dt} \frac{1}{a} = \sqrt{\frac{8\pi G}{3} \frac{g_*}{30}} \pi...

Homework Statement According to the standard assumptions, there are three species of (massless) neutrinos. In the temperature range of 1MeV < T < 100MeV, the density of the universe is believed to have been dominated by the black-body radiation of photons, electron-positron pairs, and three...