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

Advanced models of fuel droplet heating and evaporation

Special Functions and Their Applications. By N. N. Lebedev, translated by R. A. Silverman. Pp. xii, 308. 96s. 1965. (Prentice-Hall)

A chemical explosive mode analysis (CEMA) was developed as a new diagnostic to identify flame and ignition structure in complex flows. CEMA was then used to analyse the near-field structure of the stabilization region of a turbulent lifted hydrogen–air slot jet flame in a heated air coflow computed with three-dimensional direct numerical simulation. The simulation was performed with a detailed hydrogen–air mechanism and mixture-averaged transport properties at a jet Reynolds number of 11000 with over 900 million grid points. Explosive chemical modes and their characteristic time scales, as well as the species involved, were identified from the Jacobian matrix of the chemical source terms for species and temperature. An explosion index was defined for explosive modes, indicating the contribution of species and temperature in the explosion process. Radical and thermal runaway can consequently be distinguished. CEMA of the lifted flame shows the existence of two premixed flame fronts, which are difficult to detect with conventional methods. The upstream fork preceding the two flame fronts thereby identifies the stabilization point. A Damkohler number was defined based on the time scale of the chemical explosive mode and the local instantaneous scalar dissipation rate to highlight the role of auto-ignition in affecting the stabilization points in the lifted jet flame.

Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis

An algorithm for the construction of global reduced mechanisms with CSP data

The computational singular perturbation (CSP) method is employed for the solution of stiff PDEs and for the acquisition of the most important physical understanding. The usefulness of the method is demonstrated by analyzing a transient reaction-diffusion problem. It is shown that in the regions where the solution exhibits smooth spatial slopes, a simple nonstiff system of equations can be used instead of the full governing equations. From the simplified system, which is numerically provided by CSP and whose structure varies with space and time, important physical information comes to light. The relation of this method to the class of asymptotic expansion methods is explored. It is shown that the CSP results are identical to the ones obtained by the asymptotic methods. The identifications of the nondimensional parameters and the tedious manipulations needed by the asymptotic methods are performed by programmable numerical or analytic computations specified by CSP. Preliminary numerical results are presented validating the theoretical aspects of the proposed algorithm and providing a measure of its usefulness and its accuracy.

Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation

The stream function y/ for axisymmetric Stokes flow satisfies the wellknown equation E4y/ = 0. In spheroidal coordinates the equation E2y/ = 0 admits separable solutions in the form of products of Gegenbauer functions of the first and second kind, and the general solution is then represented as a series expansion in terms of these eigenfunctions. Unfortunately, this property of separability is not preserved when one seeks solutions of the equation E4i// = 0. The nonseparability of Ea >// = 0 in spheroidal coordinates has impeded considerably the development of theoretical models involving particle-fluid interactions around spheroidal objects. In the present work the complete solution for ^ in spheroidal coordinates is obtained as follows. First, the generalized 0-eigenspace of the operator E2 is investigated and a complete set of generalized eigenfunctions is given in closed form, in terms of products of Gegenbauer functions with mixed order. The general Stokes stream function is then represented as the sum of two functions: one from the 0-eigenspace and one from the generalized 0-eigenspace of the operator E . A rearrangement of the complete expansion, in such a way that the angular-type dependence enters through the Gegenbauer functions of successive order, leads to some kind of semiseparable solutions, which are given in terms of full series expansions. The proper solution subspace that provides velocity and vorticity fields, which are regular on the axis, is given explicitly. Finally, it is shown how these simple and generalized eigenfunctions reduce to the corresponding spherical eigenfunctions as the focal distance of the spheroidal system tends to zero, in which case the separability is regained. The usefulness of the method is demonstrated by solving the problem of the flow in a fluid cell contained between two confocal spheroidal surfaces with Kuwabara-type boundary conditions. Received March 18, 1992. 1991 Mathematics Subject Classification. Primary 76D07; Secondary 33A50, 33A70, 35C10, 35D99, 35J30.

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Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates

Stokes flow in spheroidal particle-in-cell models with rappel and kuwabara boundary conditions

Wrinkles in supported graphenes can be formed either by uniaxial compression or uniaxial tension beyond a certain critical load depending on the mode of loading. In the first case, the wrinkling direction is normal to the compression axis whereas in tension, wrinkles of the same pattern are formed parallel to the loading direction due to Poisson's (lateral) contraction. Herein we show by direct AFM observations that in simply-supported graphenes such instabilities appear as periodic wrinkles over existing stochastic undulations caused by the underlying-substrate-roughness. The critical strain for the generation of these wrinkles in both tension and compression is less than 1% which particularly for the former is far lower than the predicted tensile strain to fracture of suspended graphene estimated at ∼30%. Based on these findings, a constitutive model that provides the critical tensile strain for induced buckling in the lateral direction is proposed that depends only on the graphene-support interaction and not on the nature of the substrate. Understanding the wrinkling failure of graphenes under strain is of paramount importance as it leads to new threshold limits beyond which the physical-mechanical properties of graphene are impaired.

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Wrinkling formation in simply-supported graphenes under tension and compression loadings

A plane wave is scattered by two small spheres of not necessarily equal radii. Low-frequency theory reduces this scattering problem to a sequence of potential problems which can be solved iteratively. It is shown that there exists exactly one bispherical coordinate system that fits the given geometry. Then R-separation is utilized to solve analytically the potential problems governing the leading two low-frequency approximations. It is shown that the Rayleigh approximation is azimuthal independent, while the first-order approximation involves the azimuthal angle explicitly. The leading two nonvanishing approximations of the normalized scattering amplitude as well as the scattering cross-section are also provided. The Rayleigh approximations for the amplitude and for the cross-section involve only a monopole term, while their next order approximations are expressed in terms of a monopole as well as a dipole term. The dipole term disappears whenever the two spheres become equal, and this observation provide...

Maria Hadjinicolaou

Papers

Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation

Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates

Stokes flow in spheroidal particle-in-cell models with rappel and kuwabara boundary conditions

Wrinkling formation in simply-supported graphenes under tension and compression loadings

An analytic solution for low-frequency scattering by two soft spheres