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An important process for antimatter experiments is the cooling of particles in a Penning-Malmberg trap to experimentally useful temperatures. A non-neutral plasma of one species (e.g. antiprotons) can be collisionally cooled on another…
A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the appropriate canonical momenta, the model is recast into a coupled…
The earliest molecular dynamics simulations relied on solving the Newtonian or equivalently the Hamiltonian equations of motion for a system. While pedagogically very important as the total energy is preserved in these simulations, they…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More…
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an…
Based on a novel concept of multiplicative multiscale decomposition, we have derived a multiscale micromorphic molecular dynamics (MMMD)to extent the (Andersen)-Parrinello-Rahman molecular dynamics to mesoscale and macroscale. The…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows to sample high dimensional probability measures. It relies on the integration of the Hamiltonian dynamics to propose a move which is then accepted or rejected…
Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4P-Ew water models and the…
This paper proposes a hybrid learning and optimization framework for mobile manipulators for complex and physically interactive tasks. The framework exploits an admittance-type physical interface to obtain intuitive and simplified human…
A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
We study modified trigonometric integrators, which generalize the popular class of trigonometric integrators for highly oscillatory Hamiltonian systems by allowing the fast frequencies to be modified. Among all methods of this class, we…
In this paper we describe splitting methods for solving Levitron, which is motivated to simulate magnetostatic traps of neutral atoms or ion traps. The idea is to levitate a magnetic spinning top in the air repelled by a base magnet. The…
This paper proposes a variable metric splitting algorithm to solve the electrical behavior of neuromorphic circuits made of capacitors, memristive elements, and batteries. The gradient property of the memristive elements is exploited to…