There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

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

Department of Materials Science, University of Patras, 26504 Rio Patras, Greece, Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vass. Constantinou Avenue, 116 35 Athens, Greece, Institut de Biologie Moleculaire et Cellulaire, UPR9021 CNRS, Immunologie et Chimie Therapeutiques, 67084 Strasbourg, France, and Dipartimento di Scienze Farmaceutiche, Universita di Trieste, Piazzale Europa 1, 34127 Trieste, Italy

Chemistry of Carbon Nanotubes

Carbon nanotube–polymer composites: Chemistry, processing, mechanical and electrical properties

The evaluation of critical transition loads in a wear system of metal matrix composites (MMCs) was attempted with the aid of the wear knowledge established using fuzzy rule based modelling. The model presumes that the membership function of the inputs and the rule base are proper. The membership function of the output is adjusted to minimise the error between the predicted output and the experimental results. The influencing parameters considered in this paper include particle size, composite hardness and particle volume fraction. The method shows its unique advantage to model the wear of the complex system with metal matrix composites.

Evaluation of critical wear transition loads of MMCs by rule based fuzzy modelling

Precision glass molding (PGM) can fabricate aspherical lens and irregular optical products in a single step, but its applicability is currently limited by the thermally induced residual stresses and lens shape derivation after molding. To remove this barrier, this paper develops a numerical optimization platform for PGM based on a simplex algorithm and finite element simulation. It was found that the platform can effectively reduce the residual stress in a molded lens through cooling process optimization and minimize the lens shape derivation by die shape compensation. The platform established can improve the lens quality by PMG and make molded lenses have better quality than those manufactured by ultraprecision machining processes.

Numerical optimization platform for precision glass molding by the simplex algorithm.

Material models in the libraries of commercially available finite element codes often cannot satisfy the needs of some special material property descriptions, such as those of materials under ultra-high-speed cutting. To overcome the difficulty, this paper introduces an efficient explicit algorithm to implement a generalized user-defined model of metal plasticity into the Abaqus/Explicit program. This algorithm makes the computation quite efficient by avoiding updating the tensor of elastic-plastic modulus in each increment.

An Explicit Integration Algorithm for Introducing User-Defined Thermo-Viscoplastic Constitutive Models in FE Simulations

Plasticity in Mono-Crystalline Silicon under Complex Loading Conditions

Ultra-high strain rate deformation (> 104 s−1) is common in high speed manufacturing and impact engineering. However, a general constitutive model suitable for describing the material deformation at ultra-high strain rates is still unavailable. The purpose of this study is of two-folds. The first is to systematically evaluate the performances of four typical constitutive models, Johnson-Cook (J-C), Khan-Huang-Liang (KHL), Zerilli-Armstrong (Z-A), and Gao-Zhang (G-Z), in predicting the dynamic behaviors of materials. The second is to obtain an improved constitutive model to better describe the deformation of materials under ultra-high strain rates. To this end, high strain rate tests were carried out on different crystalline structures, i.e., BCC, FCC, and HCP over a wide range of strain rate from 102 s−1 to 1.5 × 104 s−1. It was found that before the critical strain rate, around 104 s−1, all of the previous models can predict the flow stresses. When the strain rate passes a critical point, however, these models fail to predict the sudden upsurge of the flow stresses. The improved model developed in this paper, by considering the dislocation drag mechanism, can successfully characterize the dynamic behaviours of materials over the whole range of strain rates.

Liangchi Zhang

Papers

Evaluation of critical wear transition loads of MMCs by rule based fuzzy modelling

Numerical optimization platform for precision glass molding by the simplex algorithm.

An Explicit Integration Algorithm for Introducing User-Defined Thermo-Viscoplastic Constitutive Models in FE Simulations

Plasticity in Mono-Crystalline Silicon under Complex Loading Conditions

On the Constitutive Models for Ultra-High Strain Rate Deformation of Metals