Related papers: Time-Reversible, Symplectic, Angular Velocity Base…

The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…

For a separable Hamiltonian, there are two fundamental, time-symmetric, second-order velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators. Similarly, there are two VV and PV version of exact energy conserving algorithms for…

We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i)…

Cytoskeletal filaments are capable of self-assembly in the absence of externally supplied chemical energy, but the rapid turnover rates essential for their biological function require a constant flux of ATP or GTP hydrolysis. The same is…

Accurate computer simulations of the rotational dynamics of linear molecules solvated in He clusters indicate that the large-size (nano-droplet) regime is attained quickly for light rotors (HCN, CO) and slowly for heavy ones (OCS, N$_2$O,…

Angular momentum has recently been defined as a surface integral involving an axial vector and a twist 1-form, which measures the twisting around of space-time due to a rotating mass. The axial vector is chosen to be a transverse,…

Using calculations and mathematical modeling, we demonstrate the feasibility of constructing a synchrotron storage ring for neutral polar molecules. The lattice is a racetrack type 3.6 m in circumference consisting of two of 180-degree…

We computationally demonstrate a new method for coherently controlling the rotation-axis direction in asymmetric top molecules with an optical centrifuge. Appropriately chosen electric-field strengths and the centrifuge's acceleration rate…

Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack…

We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a time-reversal symmetric version of the Wold decomposition that singles…

We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps…

Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…

Rigid particles suspended on a micropolar fluid provide microstructure that coexists and interacts with the local rotation of the fluid given by the vorticity. In this work we prove that the particles' angular velocity and the vorticity…

We suggest a protocol for the sympathetic cooling of a molecular asymmetric top rotor co-trapped with laser-cooled atomic ions, based on resonant coupling between the molecular ion's electric dipole moment and a common normal mode of the…

The Sllod equations of motion enable modeling of homogeneous flow at the atomic scale, and are commonly used to predict fluid properties such as viscosity. However, few publicly available codes support such simulations, and those that do…

Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators…

We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…

This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate…

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…