Related papers: Optimized Parallelization of Boundary Integral Poi…
This work investigates the convergence of a domain decomposition method for the Poisson-Boltzmann model that can be formulated as an interior-exterior transmission problem. To study its convergence, we introduce an interior-exterior…
Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing…
Furthering our understanding of many of today's interesting problems in plasma physics---including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects---requires large-scale kinetic…
Chemical space is so large that brute force searches for new interesting molecules are infeasible. High-throughput virtual screening via computer cluster simulations can speed up the discovery process by collecting very large amounts of…
A solver for the Poisson equation for 1D, 2D and 3D regular grids is presented. The solver applies the convolution theorem in order to efficiently solve the Poisson equation in spectral space over a rectangular computational domain.…
Molecular dynamics models materials by simulating each individual particle's trajectory. Many-body potentials lead to a more accurate trajectory simulation, and are used in materials science and computational chemistry. We present…
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…
A solution to the linear Boltzmann equation satisfies an energy bound, which reflects a natural fact: The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the…
Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of…
The Poisson-Boltzmann equation (PBE) models the electrostatic interactions of charged bodies such as molecules and proteins in an electrolyte solvent. The PBE is a challenging equation to solve numerically due to the presence of…
Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances in computing devices…
When the planar circular restricted 3-body problem (PCRTBP) is periodically perturbed, as occurs in many useful astrodynamics models, most unstable periodic orbits persist as whiskered tori. Intersections between stable and unstable…
The Poisson-Boltzmann equation (PBE) is a fundamental implicit solvent continuum model for calculating the electrostatic potential of large ionic solvated biomolecules. However, its numerical solution encounters severe challenges arising…
In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for…
Thermodynamic properties of charge-stabilised colloidal suspensions are commonly modeled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together…
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…