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We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an…
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential…
We propose a matrix-free algorithm for evaluating linear combinations of $\varphi$-function actions, $w_i := \sum_{j=0}^{p} \alpha_i^{\,j}\,\varphi_j(t_i A)v_j$ for $i=1\colon r$, arising in exponential integrators. The method combines the…
We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear helical part and a perturbation consisting of a…
It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincar\'e…
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle…
This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution…
The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors of the matrices, which need to be solved numerically. We propose and analyze a…
We present an innovative robotic device designed to provide controlled motion for studying active matter. Motion is driven by an internal vibrator powered by a small rechargeable battery. The system integrates acoustic and magnetic sensors…
We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
An explicit second-order numerical method to integrate the isokinetic equations of motion is derived by fitting circular arcs through every three consecutive points of the discretized trajectory, so that the tangent and the curvature…
Recently, it has been shown that entropy can be used to sort Brownian particles according to their size. In particular, a combination of a static and a time-dependent force applied on differently sized particles which are confined in an…