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

This paper discusses the phase transformation of diamond cubic silicon under nano-indentation with the aid of molecular dynamics analysis using the Tersoff potential. By monitoring the positions of atoms within the model, the microstructural changes as silicon transforms from its diamond cubic structure to other phases were identified. The simulation showed that diamond cubic silicon transforms into a body-centred tetragonal form (β-silicon) upon loading of the indentor. The change of structure is accomplished by the flattening of the tetrahedron structure in diamond cubic silicon. Upon unloading, the body-centred tetragonal form transforms into an amorphous phase accompanied by the loss of long-range order of the silicon atoms. By performing a second indentation on the amorphous zone, it was found that the body-centred-tetragonal-to-amorphous phase transformation could be a reversible process.

http://iopscience.iop.org/article/10.1088/0957-4484/11/3/307/pdf

Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation

This paper aims to understand the machinability of epoxy composites reinforced by unidirectional carbon fibres when subjected to orthogonal cutting. It was found that the subsurface damage and its mechanisms of a machined component are greatly influenced by fibre orientation. The material’s bouncing back is a characteristic phenomenon associated with the cutting of a fibre-reinforced composite. Three distinct deformation zones appear, i.e., chipping, pressing and bouncing when the fibre orientation is

An experimental investigation into the orthogonal cutting of unidirectional fibre reinforced plastics

Preface Chapter 1 BASIC EQUATIONS OF ANISOTROPIC ELASTICITY: 1.1 Transformation of Strains and Stresses 1.2 Basic Equations 1.2.1 Geometric equations 1.2.2 Equations of motion 1.2.3 Constitutive equations 1.3 Boundary and Initial Conditions 1.3.1 Boundary conditions 1.3.2 Initial conditions 1.4 Thermoelasticity. Chapter 2 GENERAL SOLUTION FOR TRANSVERSELY ISOTROPIC PROBLEMS: 2.1 Governing Equations 2.1.1 Methods of solution 2.1.2 Governing equations for the displacement method 2.1.3 Equations for a mixed method - the state-space method 2.2 Displacement Method 2.2.1 General solution in Cartesian coordinates 2.2.2 General solution in cylindrical coordinates 2.3 Stress Method for Axisymmetric Problems 2.4 Displacement Method for Spherically Isotropic Bodies 2.4.1 General solution 2.4.2 Relationship between transversely isotropic and spherically isotropic solutions. Chapter 3 PROBLEMS FOR INFINITE SOLIDS: 3.1 The Unified Point Force Solution 3.1.1 A point force perpendicular to the isotropic plane 3.1.2 A point force within the isotropic plane 3.2 The Point Force Solution for an Infinite Solid Composed of two Half-Spaces 3.2. 1 A point force perpendicular to the isotropic plane 3.2.2 A point force within the isotropic plane 3.2.3 Some remarks 3.3 An Infinite Transversely Isotropic Space with an Inclusions 3.4 Spherically Isotropic Materials 3.4.1 An infinite space subjected to a point force 3.4.2 Stress concentration in neighbourhood of a spherical cavity. Chapter 4 HALF-SPACE AND LAYERED MEDIA: 4.1 Unified Solution for a Half-Space Subjected to a Surface Point Force 4.1.1 A point force normal to the half-space surface 4.1.2 A point force tangential to the half-space surface 4.2 A Half-Space Subjected to an Interior Point Force 4.2. 1 A point force normal to the half-space surface 4.2.2 A point force tangential to the half-spacesurface 4.3 General Solution by Fourier Transform 4.4 Point Force Solution of an Elastic Layer 4.5 Layered Elastic Media. Chapter 5 EQUILIBRIUM OF BODIES OF REVOLUTION: 5.1 Some Harmonic Functions 5.1.1 Harmonic polynomials 5.1.2 Harmonic functions containing ln(r I ij ) 5.1.3 Harmonic functions containing R 5.2 An Annular (Circular) Plate Subjected to Axial Tension and Radial Compression 5.3 An Annular (Circular) Plate Subjected to Pure Bending 5.4 A Simply-Supported Annular (Circular) Plate Under Uniform Transverse Loading 5.5 A Uniformly Rotating Annular (Circular) Plate 5.6 Transversely Isotropic Cones 5.6.1 Compression of a cone under an axial force 5.6.2 Bending of a cone under a transverse force 5.7 Spherically Isotropic Cones 5.7.1. Equilibrium and boundary conditions 5.7.2. A cone under tip forces 5.7.3. A cone under concentrated moments at its apex 5.7.4. Conical shells. Chapter 6 THERMAL STRESSES: 6.1 Transversely Isotropic Materials 6.2 A Different General Solution for Transversely Isotropic Thermoelasticity 6.2. 1 General solution for dynamic problems 6.2.2 General solution for static problems 6.3 Spherically Isotropic Materials. Chapter 7 FRICTIONAL CONTACT: 7.1 Two Elastic Bodies in Contact 7.1.1 Mathematical description of a contact system 7.1.2 Deformation of transversely isotropic bodies under frictionless contact 7.1.3 A half-space under point forces 7.2 Contact of a Sphere with a Half-Space 7.2.1 Contact with normal loading 7.2.2 Contact with tangential loading 7.3 Contact of a Cylindrical Punch with a Half-Space 7.3.1 Contact with normal loading 7.3.2 Contact with tangential loading 7.4 Indentation by a Cone 7.4.1 Contact with normal loading 7.4.2 Contact with tangential loading 7.5 Inclined Contact of a Cylindrical Punch with a Half-Space 7.5.1 Contact with normal loading 7.5.2 Contact with tangential loading 7.6 Discussions on Solu

Liangchi Zhang

Papers

Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation

An experimental investigation into the orthogonal cutting of unidirectional fibre reinforced plastics

Elasticity of transversely isotropic materials

Towards a deeper understanding of wear and friction on the atomic scale—a molecular dynamics analysis

Mechanical and rheological properties of carbon nanotube-reinforced polyethylene composites