Related papers: Time-Reversible, Symplectic, Angular Velocity Base…
In the absence of inertia, a reciprocal swimmer achieves no net motion in a viscous Newtonian fluid. Here, we investigate the ability of a reciprocally actuated particle to translate through a complex fluid that possesses a network using…
The Kelvin circulation is the kinematical Hermitian observable that measures the true character of nuclear rotation. For the anisotropic oscillator, mean field solutions with fixed angular momentum and Kelvin circulation are derived in…
Thermal radiative transfer models physical phenomena ranging from supernovas in astrophysics to radiation from a hohlraum striking a fusion target in plasma physics. Transport and absorption of particles in radiative transfer at different…
We present a set of second-order, time-reversible algorithms for the isothermal (NVT) molecular-dynamics (MD) simulation of systems with mixed hard-core/continuous potentials. The methods are generated by combining real-time Nose'…
We consider symplectic time integrators in numerical General Relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard…
We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in [Ricketson & Chac\'on, JCP, 2020] to include finite Larmor-radius (FLR) effects in the presence of electric-field…
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 develop a mathematically simple yet accurate model for the single-pulse non-resonant impulsive alignment of thermal ensembles of linear molecules. We find that our molecular alignment model not only provides a simplification for…
This paper presents an analytical model and a geometric numerical integrator for a system of rigid bodies connected by ball joints, immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in…
Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In a companion paper [S. Choi and J. Van\'{\i}\v{c}ek, 2019], we presented numerical integrators of arbitrary-order of accuracy that…
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…
Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid particles per unit cell, in a two-dimensional Stokes fluid…
A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework…
The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment…
The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this…
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
An analogy between asymmetric rotor molecules and anisotropic cosmology can be used to calculate new centrifugal distortion terms in the effective potential of asymmetric rotor molecules which have no internal 3-fold symmetry. The torsional…