Related papers: On the probabilistic approach to the N-body proble…
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density…
We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
In this work we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal…
The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general…
Gas-poor galaxies can be modelled as composite collisionless stellar systems, with a dark matter halo and one or more stellar components, representing different stellar populations. The dynamical evolution of such composite systems is often…
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects…
We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential…
We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate…
I review recent progress from $N$-body simulations in our understanding of the secular evolution of isolated disk galaxies. I describe some of the recent controversies in the field which have been commonly attributed to numerics. The…
In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions…
The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all…
Here I propose an approximate way of simulating the outcomes of a single-experiment density measurement that is performed on a state of N bosons. The approximation is accurate if occupation of single-particle modes is macroscopic.
We present the UNIT $N$-body cosmological simulations project, designed to provide precise predictions for nonlinear statistics of the galaxy distribution. We focus on characterizing statistics relevant to emission line and luminous red…
We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let X be an isotropic random vector in R^n with a log-concave density. For a typical subspace E in R^n of dimension n^c, consider the…
We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large…
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…