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We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
In condensed matter physics, particularly in perovskite materials, the rotational motion of molecules and ions is associated with important issues such as ion conduction mechanism. Constrained Molecular Dynamics (MD) simulations offer a…
The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
Kinematics of rigid bodies can be analyzed in many different ways. The advantage of using Euler parameters is that the resulting equations are polynomials and hence computational algebra, in particular Gr\"obner bases, can be used to study…
In recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly correlated phases and complex phenomena in solid-state systems. Here we reveal their potential as quantum…
This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in…
We study the question of lack of reversibility and the chaotic nature of the equations of motion in numerical simulations of lattice QCD.
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
A method for time-reversible numerical integration of the deterministic Landau-Lifshitz Gilbert equation by means of a second order Suzuki-Trotter decomposition is presented and tested against commonly used second order predictor-corrector…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…
Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical…
We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the…
We present several implementations of the Metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The Metropolis technique…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical…