Related papers: Made-to-measure N-body systems
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We first review the reasons for carrying out statistical analysis of results from large numbers of N-body simulations, including a summary of previous work. Then we describe some results about the behaviour of N-body systems which have been…
We study the orbital structure of a self-consistent N-body equilibrium configuration of a barred galaxy constructed from cosmological initial conditions. The value of its spin parameter L is near the observed value of our Galaxy L=0.22. We…
$N$-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be…
Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
The large-scale statistics of observables such as the galaxy density are chiefly determined by their dependence on the local coarse-grained matter density. This dependence can be measured directly and efficiently in N-body simulations by…
The development of numerical N -body simulations have allowed to study formation process and evolution of galaxies at different scales. This paper presents the fundamental concepts of N-body systems applied to the cosmological evolution of…
The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a…
Models of galaxy formation ultimately aim at reproducing the _observed_ properties of galaxies. We report on work in progress to predict luminosities, colours and morphologies of field objects of various masses through N-body + Smoothed…
High-resolution cosmological N-body simulations are excellent tools for modelling the formation and clustering of dark matter haloes. These simulations suggest complex physical theories of halo formation governed by a set of effective…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
This paper presents a fast, economical particle-multiple-mesh N-body code optimized for large-N modelling of collisionless dynamical processes, such as black-hole wandering or bar-halo interactions, occurring within isolated galaxies. The…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
The formation of self-gravitating systems is studied by simulating the collapse of a set of N particles which are generated from several distribution functions. We first establish that the results of such simulations depend on N for small…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…