Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0805.0054

Alternating Direction Implicit Method for Two-Dimensional Fokker-Planck Equation of Dense Spherical Stellar Systems

Jihye Shin·Sungsoo S. Kim
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ~2 compared to the fully implicit method, and resolves problems of numerical instability.

Explore related subjects

astro-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jihye Shin, Sungsoo S. Kim. 2008-05-01. Alternating Direction Implicit Method for Two-Dimensional Fokker-Planck Equation of Dense Spherical Stellar Systems. https://doi.org/10.5303/jkas.2007.40.4.091

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2024

Deformation procedure for scalar fields in cosmology

This work offers an extension of the deformation procedure introduced in field theory to the case of standard cosmology in the presence of real scalar field in flat space-time. The procedure is shown to work for many models, which give rise to several different cosmic scenarios, evolving under the presence of first-order differential equations which solve the corresponding equations of motion very appropriately.

astro-ph↗
arXiv2023

Dark Energy is the Cosmological Quantum Vacuum Energy of Light Particles-The Axion and the Lightest Neutrino

We uncover the general mechanism producing the dark energy(DE). This is only based on well known quantum physics and cosmology. We show that the observed DE originates from the cosmological quantum vacuum of light particles which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as log a(t) where a(t) is the scale factor, while the particle contributions dilute as 1/a^3(t), as it must be for massive particles. The DE equation of state P = w(z)H turns to be w(z)<-1 with w(z) asymptotically reaching the value -1 from below.A scalar particle can produce the observed DE through its quantum cosmological vacuum provided:(i)its mass is of the order of 10^{-3} eV = 1 meV,(ii) it is very weakly coupled and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the DE. We find that w(z=0) is slightly below -1 by an amount ranging from [-1.5 10^{-3}] to [-8 10^{-3}] and we predict the axion mass to be in the range between 4 and 5 meV. We find that the universe will expand in the future faster than the de Sitter universe, as an exponential in the square of the cosmic time. DE arises from the quantum vacua of light particles in FRW cosmological space time in an analogous way to the Casimir effect in Minkowski spacetime with non trivial boundaries.

astro-ph↗