Related papers: Notes on the Fast Multipole Method
The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted…
In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral…
Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external…
We reconsider the Mott transition problem in the presence of long range Coulomb interactions. Using an extended DMFT, that sums an important class of diagrams absent in ordinary DMFT, we show that in the presence of Coulomb the Mott…
We present a computational methodology to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated by moving point…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However,…
We discuss the application of the local lattice technique of Maggs and Rossetto to problems that involve the motion of objects with different dielectric constants than the background. In these systems the simulation method produces a…
In classical semi-infinite Coulomb fluids, two-point correlation functions exhibit a slow inverse-power law decay along a uniformly charged wall. In this work, we concentrate on the corresponding amplitude function which depends on the…
We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero…
Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their…
We present a new ab initio method for calculating effective onsite Coulomb interactions of itinerant and strongly correlated electron systems. The method is based on constrained local density functional theory formulated in terms of…
We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…
We introduce a direct Boltzmann inversion method to infer the interaction potential in particle systems using as input particle configurations generated at an arbitrary state point of the system. Unlike iterative Boltzmann inversion, the…
We derive a general expression for the multipole expansion of the electro-magnetic interaction in relativistic heavy-ion collisions, which can be employed in higher-order dynamical calculations of Coulomb excitation. The interaction has…
Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface…
Simulating interactions between fermions and bosons is central to understanding correlated phenomena, yet these systems are inherently difficult to treat classically. Previous quantum algorithms for fermion-boson models exhibit computation…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…
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…