Related papers: Symplectic algorithm for constant-pressure molecul…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
In this article we derive the effective pairwise interactions in a Langevin type united atoms model of water. The interactions are determined from the trajectories of a detailed molecular dynamics simulation of simple point charge water. A…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…
Aspects of the Nos\'e and Nos\'e-Hoover dynamics developed in 1983-1984 along with Dettmann's closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville's Theorem. Our account is pedagogical, focused…
We provide an introduction to molecular dynamics simulations in the context of the Kob-Andersen model of a glass. We introduce a complete set of tools for doing and analyzing the results of simulations at fixed NVE and NVT. The modular…
We propose a new sampler that integrates the protocol of parallel tempering with the Nos\'e-Hoover (NH) dynamics. The proposed method can efficiently draw representative samples from complex posterior distributions with multiple isolated…
The creation of a Hamiltonian in the quantum regime which has non-trivial topological features is a central goal of the cold-atom community, enabling widespread exploration of novel phases of quantum matter. A general scheme to synthesize…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for…
A very simple explicit integrator for the rotational motion of rigid linear molecules is presented which can preserve the rigidity of the molecules without requiring any constraint force. The integrator is time-reversible and symplectic,…
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
This paper studies diagonal implicit symplectic extended Runge--Kutta--Nystr\"{o}m (ERKN) methods for solving the oscillatory Hamiltonian system $H(q,p)=\dfrac{1}{2}p^{T}p+\dfrac{1}{2}q^{T}Mq+U(q)$. Based on symplectic conditions and order…
In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the…
This paper provides a rigorous derivation and analysis of accelerated optimization algorithms through the lens of High-Resolution Ordinary Differential Equations (ODEs). While classical Nesterov acceleration is well-understood via…
We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance…
A universal algorithm to derive a macroscopic dynamics from the microscopic dynamical system via the averaging process and symplecto-contact reduction was introduced by Jin-wook Lim and the second-named author in [LO23]. They apply the…
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our…