相关论文: Discrete Newtonian dynamics with Nos\'{e}-Hoover t…

A recent article in J. Chem. Phys. argues that the two algorithms, the velocity-Verlet, and position-Verlet integrators, commonly used in Molecular Dynamics (MD) simulations, are different \cite{Ni2024}. But not only are the two algorithms…

Simulations of objects with classical dynamics are in fact a particular version of discrete dynamics since almost all the classical dynamics simulations in natural science are performed with the use of the simple ''Leapfrog" or ''Verlet"…

Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…

In 1687 Isaac Newton published PHILOSOPHI\AE \ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the…

For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exists a shadow Hamiltonian $\tilde{H}$ with energy $\tilde{E}(h)$, for which the discrete particle positions lie on…

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'…

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers…

The earliest molecular dynamics simulations relied on solving the Newtonian or equivalently the Hamiltonian equations of motion for a system. While pedagogically very important as the total energy is preserved in these simulations, they…

A thermostat of the Nose-Hoover type, based on relative velocities and a local definition of the temperature, is presented. The thermostat is momentum-conserving and Galilean-invariant, which should make it suitable for use in Dissipative…

A tutorial introduction to the technique of Molecular Dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is…

Classical molecular dynamics simulations are based on solving Newton's equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton's equations. We introduce…

We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods…

Thermostats are dynamic equations used to model thermodynamic variables in molecular dynamics. The applicability of thermostats is based on the ergodic hypothesis. The most commonly used thermostats are designed according to the…

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are build on our previously developed…

Molecular Dynamics is applied to Ferroelectric Perovskites in the framework of a first-principles derived effective Hamiltonian (Zhong, Vanderbilt, Rabe, Phys. Rev. Lett. {\bf 73} (1994), 1861). The degrees of freedom, that obey the Newton…

This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…

"Pedagogical derivations for Nos\'e's dynamics can be developed in two different ways, (i) by starting with a temperature-dependent Hamiltonian in which the variable $s$ scales the time or the mass, or (ii) by requiring that the equations…

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…

We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird…

Molecular dynamics is based on solving Newton's equations for many-particle systems that evolve along complex, highly fluctuating trajectories. The orbital instability and short-time complexity of Newtonian orbits is in sharp contrast to…