Related papers: Errors, chaos and the collisionless limit
Using direct $N$-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size $N$. We find that the $N$-body chaos quantified in terms of the largest Lyapunov exponent $\Lambda_{\rm max}$…
We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the…
A database on shape evolution of direct N-body models formed out of cold, dissipationless collapse is generated using GRAPE and HARP special purpose computers. Such models are important to understand the formation of elliptical galaxies.…
In this paper, we present our conclusions from the numerical study of the collapse of a destabilized collisionless stellar system. We use both direct integration of the Vlasov-Poisson equations and an N-body tree code to obtain our results,…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective…
This paper reports on a computational study of the model error in the LANS-alpha and NS-alpha deconvolution models of homogeneous isotropic turbulence. The focus is on how well the model error may be characterized by a stochastic force.…
Inertial particles in turbulence form clusters, which strongly affect particle collisions and transport properties. Clustering models based on statistically stationary turbulence implicitly assume the instantaneous-equilibrium approximation…
What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent), multiple-scale (from 1.0E-60 to 100) numerical…
The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low…
The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in $N$-body simulations using…
This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We…
In N-body simulations of collisionless stellar systems, the forces are softened to reduce the shot noise. Softening modifies gravity at r=|x-y| smaller than softening length epsilon and the softened forces are increasingly biased for ever…
I present empirical measurements of the rate of relaxation in N-body simulations of stable spherical systems and distinguish two separate types of relaxation: energy diffusion that is largely independent of particle mass, and energy…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
We consider the error arising from the approximation of an N-particle dynamics with its description in terms of a one-particle kinetic equation. We estimate the distance between the j-marginal of the system and the factorized state,…
We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial…
We address the dynamical evolution of an isolated self--gravitating system with two stellar mass groups. We vary the individual ratio of the heavy to light bodies, $\mu$ from 1.25 to 50 and alter also the fraction of the total heavy mass…