Related papers: Energy-momentum conserving integration schemes for…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which…
We propose new algorithms for numerical integration of the equations of motion for classical spin systems with fixed spatial site positions. The algorithms are derived on the basis of a mid-point scheme in conjunction with the multiple time…
In this paper, we present different types of integrators for electro-magnetic particle-in-cell (PIC) methods. While the integrator is an important tool of the PIC methods, it is necessary to characterize the different conservation…
We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
Constrained molecular dynamics(CoMD) model, previously introduced for nuclear dynamics, has been extended to the atomic structure and collision calculations. Quantum effects corresponding to the Pauli and Heisenberg principle are enforced…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
-Molecular simulations allow the study of properties and interactions of molecular systems. This article presents an improved version of the Adaptive Resolution Scheme that links two systems having atomistic (also called fine-grained) and…
A basic leapfrog integrator and its energy-preserving and variational / symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The…
A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical…
We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and enforce the continuity of velocities at system…
We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…
Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional…
The quantum dynamics of electron-nuclear systems is analyzed from the perspective of the exact factorization of the wavefunction, with the aim of defining gauge invariant equations of motion for both the nuclei and the electrons. For pure…