相关论文: Minimum relaxation n-body simulations using orthog…
An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly…
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…
By numerical integration, we study the relaxation dynamics of degenerate harmonic oscillator modes dispersively coupled to particle positions. Depending on whether the effective inertial potential induced by the oscillators keep the…
In N-body simulations the force calculated between particles representing a given mass distribution is usually softened, to diminish the effect of graininess. In this paper we study the effect of such a smoothing, with the aim of finding an…
I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on…
Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2 kT, but, when inter-particle forces are an inverse cubic…
Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
The Successive Over-Relaxation (SOR) method is a useful method for solving the sparse system of linear equations which arises from finite-difference discretization of the Poisson equation. Knowing the optimal value of the relaxation…
Cosmological N-body simulations aim to calculate the non-linear gravitational growth of structures via particle dynamics. A crucial problem concerns the setting-up of the initial particle distribution, as standard theories of galaxy…
A criterion for the choice of optimal softening length $\epsilon$ and time-step $dt$ for $N$-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to follow how changes in various…
We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\pm 1$)…
With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex OPF problem. Recently, "moment-based" relaxations from the Lasserre hierarchy for polynomial optimization have…
A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in…
Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…
In self-consistent N-body simulations of collisionless systems, gravitational interactions are modified on small scales to remove singularities and simplify the task of numerically integrating the equations of motion. This `gravitational…
A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…
The local relaxation algorithm is promising for fast solution of Poisson's equations, which computes the electric field distribution in a stepwise manner via local curl-free updates while strictly enforcing Gauss's law. We propose a novel…
Estimating a binary vector from noisy linear measurements is a prototypical problem for MIMO systems. A popular algorithm, called the box-relaxation decoder, estimates the target signal by solving a least squares problem with convex…
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…