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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Physical Review B

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the energy associated with these atoms will, in general, be different from that of the atoms in the bulk. The excess energy associated with surface atoms is called surface free energy. In traditional continuum mechanics, such surface free energy is typically neglected because it is associated with only a few layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume of material of interest is extremely small. However, for nano-size particles, wires and films, the surface to volume ratio becomes significant, and so does the effect of surface free energy. In this paper, a framework is developed to incorporate the surface free energy into the continuum theory of mechanics. Based on this approach, it is demonstrated that the overall elastic behavior of structural elements (such as particles, wires, films) is size-dependent. Although such size-dependency is negligible for conventional structural elements, it becomes significant when at least one of the dimensions of the element shrinks to nanometers. Numerical examples are given in the paper to illustrate quantitatively the effects of surface free energy on the elastic properties of nano-size particles, wires and films.

Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films

This paper reports on the application of guided waves techniques to nondestructively determine the structural integrity of engineering components. Specifically, this research uses a commercial finite element (FE) code to study the propagation characteristics of ultrasonic waves in annular structures. In order to demonstrate the accuracy of the proposed FE technique, the propagation of guided waves in a flat plate is examined first. Next, the propagation of guided waves in thick ring structures is investigated. Finally, these FE results are compared to analytical and experimental results. The results of this study clearly illustrate the effectiveness of using the FE method to model guided wave propagation problems and demonstrate the potential of the FE method for problems when an analytical solution is not possible because of “complicated” component geometry.

Modeling elastic wave propagation in waveguides with the finite element method

This research develops a robust experimental procedure to track the evolution of fatigue damage in a nickel-base superalloy with the acoustic nonlinearity parameter, β, and demonstrates its effectiveness by making repeatable measurements of β in multiple specimens, subjected to both high- and low-cycle fatigue. The measurement procedure developed in this research is robust in that it is based on conventional piezoelectric contact transducers, which are readily available off the shelf, and it offers the potential for field applications. In addition, the measurement procedure enables the user to isolate sample nonlinearity from measurement system nonlinearity. The experimental results show that there is a significant increase in β linked to the high plasticity of low-cycle fatigue, and illustrate how these nonlinear ultrasonic measurements quantitatively characterize the damage state of a specimen in the early stages of fatigue. The high-cycle fatigue results are less definitive (the increase in β is not as...

Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves

Preface. 1 Introduction. 1.1 Background and Motivation. 1.2 Objectives. 1.3 Organization of Book. 1.4 Notation Conventions. References. 2 Basic Equations of Continuum Mechanics. 2.1 Displacement and Deformation. 2.2 Stresses and Equilibrium. 2.3 Energy, Work, and Thermodynamic Potentials. 2.4 Constitutive Laws. 2.5 Boundary Value Problems for Small-Strain Linear Elasticity. 2.6 Integral Representations of Elasticity Solutions. Problems. Appendix 2.A. Appendix 2.B. Appendix 2.C. References. Suggested Readings. 3 Eigenstrains. 3.1 Definition of Eigenstrains. 3.2 Some Examples of Eigenstrains. 3.3 General Solutions of Eigenstrain Problems. 3.4 Examples. Problems. Appendix 3.A. Appendix 3.B. References. Suggested Readings. 4 Inclusions and Inhomogeneities. 4.1 Definitions of Inclusions and Inhomogeneities. 4.2 Interface Conditions. 4.3 Ellipsoidal Inclusion with Uniform Eigenstrains (Eshelby Solution). 4.4 Ellipsoidal Inhomogeneities. 4.5 Inhomogeneous Inhomogeneities. Problems. Appendix 4.A. Appendix 4.B. Suggested Readings. 5 Definitions of Effective Moduli of Heterogeneous Materials. 5.1 Heterogeneity and Length Scales. 5.2 Representative Volume Element. 5.3 Random Media. 5.4 Macroscopic Averages. 5.5 Hill's Lemma. 5.6 Definitions of Effective Modulus of Heterogeneous Media. 5.7 Concentration Tensors and Effective Properties. Problems. Suggested Readings. 6 Bounds for Effective Moduli. 6.1 Classical Variational Theorems in Linear Elasticity. 6.2 Voigt Upper Bound and Reuss Lower Bound. 6.3 Extensions of Classical Variational Principles. 6.4 Hashin-Shtrikman Bounds. Problems. Appendix 6.A. References. Suggested Readings. 7 Determination of Effective Moduli. 7.1 Basic Ideas of Micromechanics for Effective Properties. 7.2 Eshelby Method. 7.3 Mori-Tanaka Method. 7.4 Self-Consistent Methods for Composite Materials. 7.5 Self-Consistent Methods for Polycrystalline Materials. 7.6 Differential Schemes. 7.7 Comparison of Different Methods. Problems. Suggested Readings. 8 Determination of the Effective Moduli-Multiinclusion Approaches. 8.1 Composite-Sphere Model. 8.2 Three-Phase Model. 8.3 Four-Phase Model. 8.4 Multicoated Inclusion Problem. Problems. Appendix 8.A. Appendix 8.B. Appendix 8.C. References. Suggested Readings. 9 Effective Properties of Fiber-Reinforced Composite Laminates. 9.1 Unidirectional Fiber-Reinforced Composites. 9.2 Effective Properties of Multilayer Composites. 9.3 Effective Properties of a Lamina. 9.4 Effective Properties of a Laminated Composite Plate. Problems. Appendix 9.A. References. Suggested Readings. 10 Brittle Damage and Failure of Engineering Composites. 10.1 Imperfect Interfaces. 10.2 Fiber Bridging. 10.3 Transverse Matrix Cracks. Problems. Appendix 10.A. References. Suggested Readings. 11 Mean Field Theory for Nonlinear Behavior. 11.1 Eshelby's Solution and Kro..ner's Model. 11.2 Applications. 11.3 Time-Dependent Behavior of Polycrystalline Materials: Secant Approach. Problems. References. 12 Nonlinear Properties of Composites Materials: Thermodynamic Approaches. 12.1 Nonlinear Behavior of Constituents. 12.2 Effective Potentials. 12.3 The Secant Approach. Problems. Suggested Readings. 13 Micromechanics of Martensitic Transformation in Solids. 13.1 Phase Transformation Mechanisms at Different Scales. 13.2 Application: Thermodynamic Forces and Constitutive Equations for Single Crystals. 13.3 Overall Behavior of Polycrystalline Materials with Phase Transformation. Problems. References. Suggested Readings. Index.

Fundamentals of Micromechanics of Solids

This paper reports the development of a new stress-dependent chemical potential for solid state diffusion under multiple driving forces including mechanical stresses. The new stress-dependent chemical potential accounts for nonlinear, inelastic, and finite deformation. By using this stress-dependent chemical potential, insertion and extraction of lithium ions into a silicon particle is investigated. The distribution and evolution of diffusion-induced stress during the insertion/extraction processes are numerically calculated. Critical particle size is obtained as a function of the charging/discharging rates. It is also found that when plastic deformation occurs, the hoop stresses on the particle surface, contrary to intuition, can become positive even during the charging process, which may explain some of the recent experimental observations.

Jianmin Qu

Papers

Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films

Modeling elastic wave propagation in waveguides with the finite element method

Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves

Fundamentals of Micromechanics of Solids

A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries