Related papers: P3M algorithm for dipolar interactions
Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
Using the specific model of a bilayer of classical charged particles (bilayer Wigner crystal), we compare the predictions for energies and pair distribution functions obtained by Monte Carlo simulations using three different methods…
In this paper, a novel diffusion estimation algorithm is proposed from a probabilistic perspective by combining diffusion strategy and the probabilistic least-mean-squares (PLMS) at all agents. The proposed method diffusion probabilistic…
We present a two-dimensional (2D) Particle-Particle-Particle-Mesh (P$^3$M) algorithm with an optimized Green function and adaptive softening length for gravitational lensing studies in N-Body simulations. The analytical form of the…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results…
The outstanding progress has been made in reducing the upper bounds on EDM of several particles. Even if significant challenges must be overcome to further improve these limits, it is still one of the best chances to detect new type of…
Distributed point charge models (DCM) and their minimal variants (MDCM) have been integrated with tools widely used for condensed-phase simulations, including a virial-based barostat and a slow-growth algorithm for thermodynamic…
One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the…
The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D…
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between…
Ewald summation and physically equivalent methods such as particle-mesh Ewald, kubic-harmonic expansions, or Lekner sums are commonly used to calculate long-range electrostatic interactions in computer simulations of polar and charged…
In this note, we address some issues concerning the accurate pressure calculation of Coulomb systems with periodic boundary conditions. First, we prove that the formulas for the excess part of the pressure with Ewald summation also reduce…
Impact simulations for damage resistance analysis are computationally intensive due to contact algorithms and advanced damage models. Both methods, which are the main ingredients in an impact event, require refined meshes at the contact…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
The Ewald summation technique is generalised to power-law 1/|r|^k potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and "marginal"…