Nonlinear molecular dynamics and Monte Carlo algorithms

ABSTRACTComplimentary molecular dynamics and Metropolis Monte Carlo algorithms for the atomistic simulation of crystals at constant temperature and homogeneous tensorial pressure are summarized. The novel aspect of computational physics which unites these methods is the extension of the virial theorem to nonlinear elastic media. This guarantees the dynamical balance between the internal pressure, as determined by the interatomic potential, and effective external pressure, as determined by the applied laboratory pressure, and includes the elastic response of the material. Numerical examples are presented.

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Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals

The Journal of Chemical Physics ◽

10.1063/1.465188 ◽

1993 ◽

Vol 99 (4) ◽

pp. 2796-2808 ◽

Cited By ~ 336

Author(s):

Mark E. Tuckerman ◽

Bruce J. Berne ◽

Glenn J. Martyna ◽

Michael L. Klein

Keyword(s):

Molecular Dynamics ◽

Monte Carlo ◽

Path Integrals ◽

Hybrid Monte Carlo ◽

Monte Carlo Algorithms

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Monte Carlo Algorithms for Moments of Transition Arrays

International Astronomical Union Colloquium ◽

10.1017/s0252921100107468 ◽

1988 ◽

Vol 102 ◽

pp. 79-81

Author(s):

A. Goldberg ◽

S.D. Bloom

Keyword(s):

Monte Carlo ◽

State Vector ◽

Basis Vector ◽

Collective State ◽

Dispersion Characteristics ◽

Dipole Strength ◽

The Third ◽

Monte Carlo Algorithms ◽

Third Moment ◽

Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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Optimization of the Randomized Monte Carlo Algorithms for Solving of Problems with Random Parameters

Доклады Академии наук ◽

10.31857/s086956520003126-1 ◽

2018 ◽

Vol 482 (3) ◽

pp. 254-258

Author(s):

G. Mikhailov ◽

◽

Keyword(s):

Monte Carlo ◽

Random Parameters ◽

Monte Carlo Algorithms

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Numerical Methods for the Kinetic Theory of Fluids

10.1093/oso/9780199592357.003.0010 ◽

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.

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