85,342 research outputs found
N-body simulations of gravitational dynamics
We describe the astrophysical and numerical basis of N-body simulations, both
of collisional stellar systems (dense star clusters and galactic centres) and
collisionless stellar dynamics (galaxies and large-scale structure). We explain
and discuss the state-of-the-art algorithms used for these quite different
regimes, attempt to give a fair critique, and point out possible directions of
future improvement and development. We briefly touch upon the history of N-body
simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu
Synchronization of stochastic hybrid oscillators driven by a common switching environment
Many systems in biology, physics and chemistry can be modeled through
ordinary differential equations, which are piecewise smooth, but switch between
different states according to a Markov jump process. In the fast switching
limit, the dynamics converges to a deterministic ODE. In this paper we suppose
that this limit ODE supports a stable limit cycle. We demonstrate that a set of
such oscillators can synchronize when they are uncoupled, but they share the
same switching Markov jump process. The latter is taken to represent the effect
of a common randomly switching environment. We determine the leading order of
the Lyapunov coefficient governing the rate of decay of the phase difference in
the fast switching limit. The analysis bears some similarities to the classical
analysis of synchronization of stochastic oscillators subject to common white
noise. However the discrete nature of the Markov jump process raises some
difficulties: in fact we find that the Lyapunov coefficient from the
quasi-steady-state approximation differs from the Lyapunov coefficient one
obtains from a second order perturbation expansion in the waiting time between
jumps. Finally, we demonstrate synchronization numerically in the radial
isochron clock model and show that the latter Lyapinov exponent is more
accurate
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