Physics
Scientific paper
Oct 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aps..tsf.c5002a&link_type=abstract
American Physical Society, Joint Fall 2009 Meeting of the Texas Sections of the APS, AAPT, and SPS Postdeadline, October 22-24,
Physics
Scientific paper
There are open questions concerning the distribution of clusters in the expanding universe. The coupled Vlasov-Poisson equations govern the evolution of density in mu(position-velocity) space. In the comoving frame, the evolution of the μ-space density f for a one-dimensional gravitational system is governed by the Vlasov-Poisson continuity equation where a is the local acceleration: [ ft+vfx+afv=0] Here we introduce a spectral method to obtain a coupled set of ordinary differential equations governing the time dependence of the coefficients. For the bounded position space we utilize a Fourier expansion, whereas for the infinite velocity space we utilize a Hermite expansion. The resulting equations are bilinear and govern the coefficients ψm,n(t), where m represents the Fourier index and n the Hermite index. By truncating the doubly infinite series they can be integrated numerically to model and simulate the system evolution of f, in our case using a traditional fourth-order Runge-Kutta method. We will present the important derivations and preliminary results of the numerical integration.
Alvord Josh
Miller Bruce
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