Related papers: Time-Reversible, Symplectic, Angular Velocity Base…
This paper presents an analytical model and a geometric numerical integrator for a tethered spacecraft model that is composed of two rigid bodies connected by an elastic tether. This model includes important dynamic characteristics of…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are…
We propose and computationally study a method for simultaneously orienting the angular momentum of asymmetric top molecules along: 1) a laboratory-fixed direction; 2) the molecular intermediate moment of inertia axis; 3) the laser field…
We present a new technique for transferring momentum and velocity between particles and grid with Particle-In-Cell (PIC) calculations which we call Affine-Particle-In-Cell (APIC). APIC represents particle velocities as locally affine,…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
We introduce a new optical tool - a "two-dimensional optical centrifuge", capable of aligning molecules in extreme rotational states. Unlike the conventional centrifuge, which confines the molecules in the plane of their rotation, its…
A nonholonomic system is a mechanical system with velocity constraints not originating from position constraints; rolling without slipping is the typical example. A nonholonomic integrator is a numerical method specifically designed for…
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic…
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…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…
In this work, we describe various improved implementations of the mapping approach to surface hopping (MASH) for simulating nonadiabatic dynamics. These include time-reversible and piecewise-continuous integrators, which is only formally…
We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom-Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for…
An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which…
This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…
We introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…