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Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
A representation of the static MHD equilibrium system in coordinates connected with magnetic surfaces is suggested. It is used for producing families of non-trivial 3D exact solutions of isotropic and anisotropic plasma equilibria in…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
Monoclonal antibodies are among the most promising therapeutic agents in modern medicine, yet their formulation into high-concentration solutions for subcutaneous self-administration poses a major challenge. A key obstacle is the marked…
We propose a new method to sum up electrostatic interactions in 2D slab geometries. It consists of a combination of two recently proposed methods, the 3D Ewald variant of Yeh and Berkowitz, J. Chem. Phys. 111 (1999) 3155, and the purely 2D…
In this article we introduce a novel coupled algorithm for massively parallel direct numerical simulations of electrophoresis in microfluidic flows. This multiphysics algorithm employs an Eulerian description of fluid and ions, combined…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of…
A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…
Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
We present teraflop-scale calculations of biomolecular electrostatics enabled by the combination of algorithmic and hardware acceleration. The algorithmic acceleration is achieved with the fast multipole method (FMM) in conjunction with a…
We develop an efficient Ewald method of molecular dynamics simulation for calculating the electrostatic interactions among charged and polar particles between parallel metallic plates, where we may apply an electric field with an arbitrary…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…