Related papers: Geometric integrator for simulations in the canoni…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles…
We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some…
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…
This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum…
The existing thermodynamics of the cosmological horizon in de-Sitter spacetime is established in the micro-canonical ensemble, while thermodynamics of black hole horizons are established in the canonical ensemble. Generally in the ordinary…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…
In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and…
Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…
The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve…
Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled…
We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nos\'e-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high energy to condensed matter physics. Quantum computers may provide a way to solve this problem efficiently. Preparing a thermal state…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
Molecular dynamics simulations of a quasi-harmonic solid are conducted to elucidate the meaning of temperature fluctuations in canonical systems and validate a well-known but frequently contested equation predicting the mean square of such…
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is…