Related papers: Fast calculation of the electrostatic potential in…
The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…
We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes which are either assumed to be of infinite height or slim.…
The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of…
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear…
We present a rigorous Ewald summation formula to evaluate the electrostatic interactions in two-dimensionally periodic planar interfaces of three-dimensional systems. By rewriting the Fourier part of the summation formula of the original…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic…
We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged…
Ab initio calculations of the electronic energy loss of ions moving in aluminum crystal are presented, within linear-response theory, from a realistic description of the one-electron band-structure and a full treatment of the dynamical…
We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent…
We propose a new method to accelerate the convergence of optimization algorithms. This method simply adds a power coefficient $\gamma\in[0,1)$ to the gradient during optimization. We call this the Powerball method and analyze the…
We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using the high electric polarizability of the Rydberg electronic states in combination with mutual Coulomb coupling of ions that establishes common modes of motion.…
We propose a novel methodology for drawing iid realizations from any target distribution on the Euclidean space with arbitrary dimension. No assumption of compact support is necessary for the validity of our theory and method. Our idea is…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…
We present the singular Euler--Maclaurin expansion, a new method for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. In contrast to the traditional…
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…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
Recently, Gimbutas et al derived an elegant representation for the Green's functions of Stokes flow in a half-space. We present a fast summation method for sums involving these half-space Green's functions (stokeslets, stresslets and…