Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

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A User’s Guide

Nonlinear Oscillations: Exact Solutions and their Approximations

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

A review of theories for the modeling and analysis of functionally graded plates and shells

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory

Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory

We determine the basal plane stiffness and Poisson’s ratio of single layer graphene sheets (SLGSs) in armchair and zigzag directions by using molecular mechanics simulations of their uniaxial tensile deformations with the MM3 potential, and of their axial and bending vibrations. Both approaches give the basal plane stiffness equal to ∼340 N/m which agrees well with that reported in the literature and derived from results of indentation experiments on SLGSs and from the first principle calculations. The computed value of Poisson’s ratio equals 0.21 in both armchair and zigzag directions. Assuming that the response of a SLGS is the same as that of a plate made of a linear elastic, homogeneous, and isotropic material having Poisson’s ratio = 0.21, the in-plane stiffness of ∼340 N/m and the total mass equal to that of the SLGS, the thickness of the SLGS is found to be ∼1 A. Thus Young’s modulus and the shear modulus of a SLGS equal ∼3.4 TPa and ∼1.4 TPa, respectively. It is shown that mode shapes corresponding to the several lowest frequencies of the SLGS differ noticeably from those of an equivalent thin layer made of a linear elastic isotropic material with Young’s modulus = 3.4 TPa and the shear modulus = 1.4 TPa. Furthermore, a free– free SLGS vibrates about a plane bisecting its width rather than its thickness as predicted by the Euler Bernoulli beam theory. We also investigate the effect of pretension on the natural frequencies of SLGSs using MM simulations and correlate it to that of 1 A thick linear elastic plate found by analyzing its three-dimensional deformations. These results will help design SLGS nanomechanical resonators having frequencies in the THz range.

http://www2.esm.vt.edu/~rbatra/pdfpapers/computational2010(xxx-xxx).pdf

S.S. Gupta

Papers

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory

Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory

Elastic Properties and Frequencies of Free Vibrations of Single-Layer Graphene Sheets

Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration

Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes