Related papers: Discrete Molecular Dynamics
In molecular dynamics (MD), systems are molecules made up of atoms, and the aim is to determine their evolution over time. MD is based on a numerical resolution algorithm, whose role is to apply the forces generated by the various…
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…
In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…
A Molecular Dynamics (MD) study of static and dynamic properties of molten and glassy germanium dioxide is presented. The interactions between the atoms are modelled by the classical pair potential proposed by Oeffner and Elliott (OE)…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The algorithm is under various names ("Verlet, leap-frog,...") the most used algorithm in simulations of complex…
A Molecular Dynamics (MD) parallel to the Control Volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood, J. Chem. Phys. 18, 817 (1950) over a finite cubic volume of molecular dimensions.…
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…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Molecular Dynamics method is based on solution of Newtonian differential equations of motion. A new very accurate and efficient time-reversible explicit integrator was derived on the basis of second order Tailor expansion of force. There is…
Soliton models are used in elementary particle physics and nuclear physics to model extended objects such as nucleons, using effective field theories derived from more fundamental theories such as QCD. Computer simulation requires some sort…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Ab-initio molecular dynamics (AIMD) is a powerful tool to simulate physical movements of molecules for investigating properties of materials. While AIMD is successful in some applications, circumventing its high computational costs is…
The dynamics of galaxies in an expanding universe is often determined for gravitational and dark matter in an Einstein-de Sitter universe, or alternatively by modifying the gravitational long-range attractions in the Newtonian dynamics…
The powerful molecular dynamics (MD) simulation is basically based on a picture that the atoms experience classical-like trajectories under the exertion of classical force field determined by the quantum mechanically solved electronic…
The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…