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We propose a novel algorithm for the temporal integration of the resistive magnetohydrodynamics (MHD) equations. The approach is based on exponential Rosenbrock schemes in combination with Leja interpolation. It naturally preserves Gauss's…

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…

In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We…

A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new…

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…

Molecular dynamics (MD) simulations are useful in obtaining thermodynamic and kinetic properties of bio-molecules but are limited by the timescale barrier, i.e., we may be unable to efficiently obtain properties because we need to run…

It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…

In the previous paper [J. R. Mannouch and J. O. Richardson, J.~Chem.~Phys.~xxx, xxxxx (xxxx)] we derived a new partially linearized mapping-based classical-trajectory technique, called spin-PLDM. This method describes the dynamics…

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…

We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…

The integration time step is a critical determinant of performance in molecular dynamics simulations, governing the trade-off between speed and fidelity. Although 2 fs remains the standard in atomistic biomolecular simulations, the push for…

Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions…

In this paper we propose a dual-time stepping scheme for the Smoothed Particle Hydrodynamics (SPH) method. Dual-time stepping has been used in the context of other numerical methods for the simulation of incompressible fluid flows. Here we…

Molecular simulation technologies have afforded researchers a unique look into the nanoscale interactions driving physical processes. However, a limitation for molecular dynamics (MD) simulations is that they must be performed on…

Nonadiabatic molecular dynamics simulations aim to describe the coupled electron-nuclear dynamics of molecules in excited electronic states. These simulations have been applied to understand a plethora of photochemical and photophysical…

At a fundamental level most physical equations are time reversible. In this paper we propose an integrator that preserves this property at the discrete computational level. Our simulations can be run forward and backwards and trace the same…

The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…