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

The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.

American Society for Testing and Materials

A positive temperature coefficient is the term which has been used to indicate that an increase in solubility occurs as the temperature is raised, whereas a negative coefficient indicates a decrease in solubility with rise in temperature.

Effect of Temperature

Large-Scale Fabrication of Boron Nitride Nanosheets and Their Utilization in Polymeric Composites with Improved Thermal and Mechanical Properties

Bone cutting is a well know procedure in orthopedics. Large cutting force causes overstressing of the bone which may result in trauma. Control penetration of the cutting tool into bone tissue is important to avoid unnecessary damage to the bone tissue. The purpose of this study was to measure and predict cutting force using experiments and Finite Element (FE) analysis when a plane cutter passes over the bone surface in the presence of irrigation. The effect of cutting speed, tool rake angle, depth of cut and width of the cutting face on the cutting force was found. The force was found to decrease with increase in rake angle and significantly rise with increase in depth of cut and width of cutting face. The cutting force was found unaffected by the range of cutting speed used in experiment as well as in simulations. The results obtained from this study strongly recommend the use of irrigation to minimize plane cutting force or force arising from similar cutting action for safe and efficient surgical incision in bone.

In Vitro Experimental and Numerical Analysis of Forces in Plane Cutting of Cortical Bone

Finite-element models are used to estimate numerically the distribution of bone mineral density (BMD) as a result of bone remodelling process from the loads applied. However, the effect of initial BMD distribution on trabecular-bone remodelling is still unknown. In this paper, the effect of initial density distributions as an input in the finite-element model on a structural-functional relationship of trabecular bone was investigated. A multi-material model representing a realistic density distribution was used based on the grey-scale value (GV) distribution and compared with a traditional single-material model. Different trabecular morphologies with density distributions were observed for these two material models. Similar character of the occurrence of density (in terms of element and volume fraction) of trabecular bone from a femur head were found, with the same highest number of elements in the density range from 1.25 to 1.35 g/cm3. These results indicate that previous simplified models using single-material properties for trabecular bone may not lead to considerable errors.

Trabecular bone remodelling: finite-element simulation

Crack propagation in real (quasi)brittle materials possesses signs of stochasticity; a tortuous character of fracture surfaces, multiple cracking and crack branching observed in experiments are a vivid confirmation of it. Traditional approaches of fracture mechanics represent cracks as geometrically smooth objects with straight (or curved) crack fronts, thus usually neglecting morphology of real cracks. An introduction of a direct account for stochastic features of the failure process can lead to a more adequate description of real fracture processes. Numerical schemes accounting for a spatial scatter in material properties are proposed for a description of crack propagation. These schemes unify approaches of fracture mechanics with ideas of continuum damage mechanics (CDM). CDM describes a macroscopic manifestation of various failure processes developing at lower length scales. Such unification being one of the possibilities for a micromacro transition in a study of failure processes allows an analysis of non-uniform crack propagation and of multiple cracking. A necessity to describe a crack with its length changing along its front presupposes an utilisation of local stress-intensity factors. A description of complicated morphology of cracks or of a random set of cracks in a case of multiple cracking necessitates an introduction of additional quantitative parameters characterising fracture processes in heterogeneous brittle materials. This is implemented by means of scaling analyses of the crack front roughness, of the stress distribution character and of the freeenergy release. It is shown that spatial scaling parameters can be linked to the type of material’s randomness (thus being material parameters), while temporal scaling parameters are independent of it and characterise the fracture process.

Vadim V. Silberschmidt

Papers

In Vitro Experimental and Numerical Analysis of Forces in Plane Cutting of Cortical Bone

Trabecular bone remodelling: finite-element simulation

Simulation of crack propagation in heterogeneous brittle solids: scaling parameters

Performance of Cast Iron under Thermal Loading: Effect of Graphite Morphology

Numerical Modeling of the Deformation Behavior of Polymer Lattice Structures with a Density Gradient Based on Additive Technologies