Numerical Methods for Stochastic Molecular Dynamics

2015 ◽  
pp. 261-328 ◽  
Author(s):  
Ben Leimkuhler ◽  
Charles Matthews
Keyword(s):  
Molecular Dynamics ◽  
Numerical Methods

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

scholarly journals Parallel reactive molecular dynamics: Numerical methods and algorithmic techniques

2012 ◽  
Vol 38 (4-5) ◽  
pp. 245-259 ◽  
Author(s):  
H.M. Aktulga ◽  
J.C. Fogarty ◽  
S.A. Pandit ◽  
A.Y. Grama
Keyword(s):  
Molecular Dynamics ◽  
Numerical Methods ◽  
Reactive Molecular Dynamics ◽  
Algorithmic Techniques

scholarly journals Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques

2012 ◽  
Vol 34 (1) ◽  
pp. C1-C23 ◽  
Author(s):  
Hasan Metin Aktulga ◽  
Sagar A. Pandit ◽  
Adri C. T. van Duin ◽  
Ananth Y. Grama
Keyword(s):  
Molecular Dynamics ◽  
Numerical Methods ◽  
Reactive Molecular Dynamics ◽  
Algorithmic Techniques

CHAOTIC SCATTERING IN CLASSICAL TRIATOMIC MOLECULAR DYNAMICS

1993 ◽  
Vol 03 (04) ◽  
pp. 999-1012 ◽  
Author(s):  
B. BRUHN ◽  
B. P. KOCH
Keyword(s):  
Molecular Dynamics ◽  
Fixed Point ◽  
Numerical Methods ◽  
Periodic Orbits ◽  
Invariant Manifolds ◽  
Melnikov Method ◽  
Numerical Results ◽  
Scattering Function ◽  
Chaotic Scattering ◽  
Type Transformation

The classical scattering dynamics of two coupled Morse systems is investigated by analytical and numerical methods. If a McGehee type transformation and the Melnikov method are applied to the invariant manifolds of a nonhyperbolic fixed point at infinity, a proof of the appearance of chaotic scattering is obtained. Furthermore, we study the occurrence of hyperbolic and elliptic periodic orbits under perturbation using the subharmonic Melnikov approach. The analytical predictions regarding the range of the scattering function where chaotic scattering appears are compared with numerical results. Moreover, we investigate the threshold for channel transitions and discuss some mechanisms for this transition.

An Investigation on New Numerical Methods for Molecular Dynamics Simulation

2007 ◽  
Author(s):  
Nick Schafer ◽  
Radu Serban ◽  
Dan Negrut
Keyword(s):  
Molecular Dynamics ◽  
Numerical Methods ◽  
Large Time ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Md Simulations ◽  
Dynamics Simulation ◽  
Benchmark Problems ◽  
Implicit Methods ◽  
Efficient Simulation

Explicit integrators have found common use in Molecular Dynamics (MD) simulations because they are easy to implement and work well under many conditions. However, in other classical mechanics applications that require the numerical solution of the equations of motion for complex systems, explicit methods have encountered major difficulties. In these cases, the state of the art relies on implicit methods, which are stable under large time steps and therefore can be used to decrease the number of integration steps necessay for a simulation. This in turn results in an overall reduction of CPU time that opens the door to an increase in the dimension of the problem that can be considered. The premise of this work is that numerical methods that are suitable for efficient simulation of mechanical systems will lead to significant gains when used in MD. The goal of the proposed work is to investigate this assumption by comparing in terms of accuracy and efficiency the Hilber-Hughes-Taylor (HHT) integrator against current explicit MD integrators for a set of two benchmark problems.

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