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

Scale invariance in stochastic fracture of rocks

The theory of dynamic three-point bending tests under high-loading rates is developed for the first time with account for structural vibration. Analytical solutions for dynamic normal (flexural) and shear stresses are derived. To study the dynamic effect, dynamic factors for both types of stresses are defined and investigated by employing a dimensionless characteristic time and a strain rate. It is found that both dynamic factors attenuate with respect to the characteristic time and, therefore, the quasi-static time thresholds and loading conditions are obtained. In addition, the dominant failure mode is studied for potential application in brittle materials in terms of normal-to-shear stress ratio, which is oscillatory in contrast to the quasi-static case. The developed theory is verified with a split Hopkinson bar test together combined with digital image correlation as well as finite-element simulations. The findings of this study can provide a guideline for test design, such as selection of specimen geometry and loading rate. As the theory provides a modal decomposition of dynamic normal and shear stresses, it can also be used in the field of structural health monitoring. 

Dynamic three-point bending tests under high loading rates

The ability to manufacture complex geometries with additive manufacturing (AM) has led to a significant increase in research in this field. Thermoplastic polymer-matrix composites are mostly fabricated using fused deposition modelling, and the addition of fibres demonstrated a considerable increase in strength and stiffness of resultant composites. Dynamic deformation and fracture of AM structures are investigated to optimise architectures for biomedical, industrial, and civil applications. This study focuses on the dynamic-fracture behaviour of AM continuous-carbon-fibre-reinforced composites with nylon polymer-matrix under ballistic impact. The mechanical behaviour of these composites exhibits brittle fracture under tension and ductile deformation under compression. Compared to short-carbon-fibre-reinforced AM composites with similar carbon content, the continuous-fibre composite had higher tensile and compressive moduli. Although the tensile strength was also found to be significantly higher than that of composites with short fibres, the elongation at break in tension and the compressive strength was lower. A ballistic test on a solid unidirectional plate was carried out using a 9 mm steel bullet at 100 – 120 m s−1. Complete perforation was achieved, with a circular hole at the front of the target and a delaminated damaged area at the back. The impact boundary conditions were replicated in finite-element simulations at 100 m s−1. The material's linear elastic behaviour was modelled based on in-house mechanical characterisation tests, and a VUMAT of Hashin damage model was used for the description of impact damage with cohesive-surface modelling of the delamination failure. The simulation showed a good agreement with the experimentally observed damaged areas at the front and the back of the plate, indicating that traditional composite-material and damage models can be used to predict the dynamic impact fracture of AM composites. 

Dynamic fracture of additively manufactured continuous-fibre composites under ballistic impact: experimental and numerical study

A prosthesis is loaded by forces and torques exerted by its wearer, the amputee, and should withstand instances of peak loads without failure. Traditionally, strong prosthetic sockets were made using a composite with a variety of reinforcing fibres, such as glass, carbon, and Kevlar. Amputees in less-resourced nations can lack access to composite prosthetic sockets due to their unavailability or prohibitive cost. Therefore, this study investigates the feasibility of polyethylene terephthalate (PET) fibre-reinforced composites as a low-cost sustainable composite for producing functional lower-limb prosthetic sockets. Two types of these composites were manufactured using woven and knitted fabric with a vacuum-assisted resin transfer moulding (VARTM) process. For direct comparison purposes, traditional prosthetic-socket materials were also manufactured from laminated composite (glass-fibre-reinforced (GFRP)), monolithic thermoplastic (polypropylene (PP) and high-density polyethylene (HDPE)) were also manufactured. Dog-bone-shaped specimens were cut from flat laminates and monolithic thermoplastic to evaluate their mechanical properties following ASTM standards. The mechanical properties of PET-woven and PET-knitted composites were found to have demonstrated to be considerably superior to those of traditional socket materials, such as PP and HDPE. All the materials were also tested in the socket form using a bespoke test rig reproducing forefoot loading according to the ISO standard 10328. The static structural test of sockets revealed that all met the target load-bearing capacity of 125 kg. Like GFRP, the PETW and PETK sockets demonstrated higher deformation and stiffness resistance than their monolithic counterparts made from PP and HDPE. As a result, it was concluded that the PET-based composite could replace monolithic socket materials in producing durable and affordable prostheses.

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Strength Assessment of PET Composite Prosthetic Sockets

The dynamic energy release rate (ERR) of a stationary crack in a double cantilever beam (DCB) under a constant applied opening rate at the free end
is derived using beam dynamics, and completely analytical formulae are obtained. It is discovered that the dispersive propagation of flexural waves must be
considered otherwise the contributions to the dynamic ERR from the higher-order vibration modes cannot be correctly captured. In addition, it is shown that the
intact part of the DCB (ahead of the crack tip) can be replaced with a single vertical spring and a rotation constraint at the crack tip to significantly simplify the
analytical modeling. The dynamic ERR is accurately captured in comparison to
finite element method (FEM) simulations, including the higher-order vibration
modes.

Vadim V. Silberschmidt

Papers

Scale invariance in stochastic fracture of rocks

Dynamic three-point bending tests under high loading rates

Dynamic fracture of additively manufactured continuous-fibre composites under ballistic impact: experimental and numerical study

Strength Assessment of PET Composite Prosthetic Sockets

Dynamic interfacial fracture with higher-order vibration modes