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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Scalable Molecular Dynamics with NAMD

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This work is concerned with the formulation of a general framework for the analysis of meshfree approximation schemes and with the convergence analysis of the Local Maximum-Entropy (LME) scheme as a particular example. We provide conditions for the convergence in Sobolev spaces of schemes that are n-consistent, in the sense of exactly reproducing polynomials of degree less or equal to n, and whose basis functions are of rapid decay. The convergence of the LME in a locally Sobolev space follows as a direct application of the general theory. The analysis shows that the convergence order is linear in h, a measure of the density of the point set. The analysis also shows how to parameterize the LME scheme for optimal convergence. Because of the convex approximation property of LME, its behavior near the boundary is singular and requires additional analysis. For the particular case of polyhedral domains we show that, away from a small singular part of the boundary, any Sobolev function can be approximated by means of the LME scheme. With the aid of a capacity argument, we further obtain approximation results with truncated LME basis functions in H1 and for spatial dimension d > 2.

Convergence Analysis of Meshfree Approximation Schemes

We present a finite element model of polydimethylsiloxane (PDMS) fluidic microvalves. A valve is fabricated by assembling two patterned layers in a two-channel crossed architecture. The valve closes as a consequence of the motion of the interlayer membrane. The membrane is deformed by the pressure of the actuation fluid, flowing in one of the two channels. By using a soft rubber material model, we setup a numerical model of the microvalve and validate it against experiments. The numerical model allows to evaluate the mechanical engagement of commonly used microvalve architectures and to analyze the performance of alternative geometries.

Numerical Analysis of Elastomeric Fluidic Microvalves

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Adaptive Goal-Oriented Data Sampling in Data-Driven Computational Mechanics

The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies in bridging across time scales to overcome the time-scale limitations of atomistics at finite temperature. To address the biggest challenge, bridging across both length and time scales, only a few techniques exist, and most of those are limited to conditions of constant temperature. Here, we present a new general strategy for the space–time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. Specifically, we evolve the statistics of an atomistic ensemble in phase space over time by applying the Liouville equation to an approximation of the ensemble’s probability distribution (which further admits a variational formulation). To this end, we approximate a crystalline solid as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites, and we investigate the resulting quasistatics and dynamics of the system. By definition, phase packets account for the dynamics of crystalline lattices at finite temperature through the statistical variances of atomic momenta and positions. We show that momentum–space correlation allows for an exchange between potential and kinetic contributions to the crystal’s Hamiltonian. Consequently, local adiabatic heating due to atomic site motion is captured. Moreover, in the quasistatic limit, the governing equations reduce to the minimization of thermodynamic potentials (similar to maximum-entropy formulation previously introduced for finite-temperature QC), and they yield the local equation of state, which we derive for isothermal, isobaric, and isentropic conditions. Since our formulation without interatomic correlations precludes irreversible heat transport, we demonstrate its combination with thermal transport models to describe realistic atomic-level processes, and we discuss opportunities for capturing atomic-level thermal transport by including interatomic correlations in the Gaussian phase packet formulation. Overall, our Gaussian phase packet approach offers a promising avenue for finite-temperature non-equilibrium quasicontinuum techniques, which may be combined with thermal transport models and extended to other approximations of the probability distribution as well as to exploit the variational structure.

Nonequilibrium thermomechanics of Gaussian phase packet crystals: Application to the quasistatic quasicontinuum method

A scaffold includes struts that intersect at nodes. In some instances, a cross section of the cores has at least one dimension less than 100 microns. The core can be a solid, liquid or a gas. In some instances one or more shell layers are positioned on the core.

Michael Ortiz

Papers

Convergence Analysis of Meshfree Approximation Schemes

Numerical Analysis of Elastomeric Fluidic Microvalves

Adaptive Goal-Oriented Data Sampling in Data-Driven Computational Mechanics

Nonequilibrium thermomechanics of Gaussian phase packet crystals: Application to the quasistatic quasicontinuum method

Design, use and fabrication of microscaffolds and nanoscaffolds