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

A review of shape memory alloy research, applications and opportunities

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

We survey progress over the past 25 years in the development of microscale devices for pumping fluids. We attempt to provide both a reference for micropump researchers and a resource for those outside the field who wish to identify the best micropump for a particular application. Reciprocating displacement micropumps have been the subject of extensive research in both academia and the private sector and have been produced with a wide range of actuators, valve configurations and materials. Aperiodic displacement micropumps based on mechanisms such as localized phase change have been shown to be suitable for specialized applications. Electroosmotic micropumps exhibit favorable scaling and are promising for a variety of applications requiring high flow rates and pressures. Dynamic micropumps based on electrohydrodynamic and magnetohydrodynamic effects have also been developed. Much progress has been made, but with micropumps suitable for important applications still not available, this remains a fertile area for future research.

https://microfluidics.stanford.edu/Publications/Micropumps_Cooling/Laser%20Review%20of%20Micropumps%20in%20JMM.pdf

A review of micropumps

In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed It is based on the nonlocal effects of the strain field and first gradient strain field This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational approach Two additional kinds of parameters, the higher-order nonlocal parameters and the nonlocal gradient length coefficients are introduced to account for the size-dependent characteristics of nonlocal gradient materials at nanoscale To illustrate its application values, the theory is applied for wave propagation in a nonlocal strain gradient system and the new dispersion relations derived are presented through examples for wave propagating in Euler–Bernoulli and Timoshenko nanobeams The numerical results based on the new nonlocal strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical nonlocal stress model and the contemporary strain gradient theory Thus, this higher-order nonlocal strain gradient model provides an explanation to some observations in the classical and nonlocal stress theories as well as the strain gradient theory in these aspects

A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation

In this paper, we develop a thermodynamic approach for modeling a class of viscoelastic fluids based on the notion of an `evolving natural configuration'. The material has a family of elastic (or non-dissipative) responses governed by a stored energy function that is parametrized by the `natural configurations'. Changes in the current natural configuration result in dissipative behavior that is determined by a rate of dissipation function. Specifically, we assume that the material possesses an infinity of possible natural (or stress-free) configurations. The way in which the current natural configuration changes is determined by a `maximum rate of dissipation' criterion subject to the constraint that the difference between the stress power and the rate of change of the stored energy is equal to the rate of dissipation. By choosing different forms for the stored energy function ψ and the rate of dissipation function ξ, a whole plethora of energetically consistent rate type models can be developed. We show that the choice of a neo-Hookean type stored energy function and a rate of dissipation function that is quadratic, leads to a Maxwell-like fluid response. By using this procedure with a different choice for the rate of dissipation, we also derive a model that is similar to the Oldroyd-B model. We also discuss several limiting cases, including the limit of small elastic strains, but arbitrarily large total strains, which leads to the classical upper convected Maxwell model as well as the Oldroyd-B model.

A thermodynamic frame work for rate type fluid models

Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings

This paper deals with a derivation (using a perturbation technique) of an approximation, due to Oberbeck8,9 and Boussinesq,1 to describe the thermal response of linearly viscous fluids that are mechanically incompressible but thermally compressible. The present approach uses a nondimensionalization suggested by Chandrasekhar2 and utilizing the ratio of two characteristic velocities as a measure of smallness, systematically derives the Oberbeck-Boussinesq approximation as a third-order perturbation. In the present approach, the material is subjected to the constraint that the volume change is determined solely by the temperature change in the body and uses a novel approach in deriving the thermodynamical restrictions. Consequently, it is free from the additional assumptions usually added on in earlier works in order to obtain the correct equations.

On the oberbeck-boussinesq approximation

The central idea proposed here is that, in entropy–producing processes, a specific choice from among a competing class of constitutive functions can be made so that the state variables evolve in a way that maximizes the rate of entropy production. When attention is restricted to quadratic forms for the rate of entropy production, the assumption leads to results that are fully in keeping with linear phenomenological relations that satisfy the Onsager relations. In other words, the usual linear evolution laws such as Fourier's law of heat conduction, Fick's law, Darcy's law, Newton's law of viscosity, etc., all corroborate this assumption. We clarify the difference between the maximum rate of entropy production criterion that characterizes choices among constitutive relations and the minimum entropy production theorem due to Onsager (1931) that characterizes steady states for special choices of the rate of entropy production . We then show that for other forms of entropy production that are not quadratic for which the Onsager relations and related theorems cannot be applied, we can use the procedure described here to obtain nonlinear laws. We demonstrate by means of an example that even yield–type phenomena can be accommodated within this framework, while they cannot within the framework of Onsager. We also discuss issues concerning constraints, especially in thermoelasticity within the context of our ideas.

Arun R. Srinivasa

Papers

A thermodynamic frame work for rate type fluid models

Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings

On the oberbeck-boussinesq approximation

On thermomechanical restrictions of continua

Mechanics of the inelastic behavior of materials. Part II: inelastic response