Related papers: Errors, chaos and the collisionless limit
N-Body simulations are a very important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of galaxy formation and comparison with observations would not have been possible without…
We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
We consider the space-time scaling limit of the particle mass in zero-range particle systems on a $1$D discrete torus $\mathbb{Z}/N\mathbb{Z}$ with a finite number of defects. We focus on two classes of increasing jump rates $g$, when…
Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof,…
We study the dynamics of small inhomogeneities in an expanding universe collapsing to form bound structures using full solutions of the Einstein-Vlasov (N-body) equations. We compare these to standard Newtonian N-body solutions using…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics…
We use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude greater than in previous experiments. For the first time, a clear ~ln N-dependence of…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can…
We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases…
We develop a discrete-event modeling framework that captures the progression of geophysical systems toward catastrophic failure through sequences of distinct damage events. By representing system evolution as a succession of temporally…
To study the effect of slow heat conduction during phase separation, we discuss the relaxation properties of an $O(N)$ symmetric model with Phase field type dynamics, where a non conserved order parameter field couples bilinearly to a…
We perform direct numerical simulation (DNS) and large eddy simulation (LES) of an initially spherical region of turbulence evolving in free space. The computations are performed with a lattice Green's function method, which allows the…
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the…
We analyse the asymptotic growth of the error for Hamiltonian flows due to small random perturbations. We compare the forward error with the reversibility error, showing their equivalence for linear flows on a compact phase space. The…
Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important…
Models of faults incorporating slip rate- and state-dependent friction have reproduced phenomena from spontaneous slow, aseismic slip to earthquake-generating dynamic rupture. Numerical explorations of model parameter space regularly show…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…