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

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

From the Publisher:
This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.

Robot dynamics and control

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A Simple Higher-Order Theory for Laminated Composite Plates

EQUATIONS OF HEAT TRANSFER AND FLUID MECHANICS Present Study Governing Equations of a Continuum Governing Equations in Terms of Primitive Variables Porous Flow Equations Auxiliary Transport Equations sChemically Reacting Systems Boundary Conditions sChange of Phase Enclosure Radiation Summary of Equations THE FINITE ELEMENT METHOD: AN OVERVIEW Model Differential Equation Finite Element Approximation Weighted-Integral Statements and Weak Forms Finite Element Model Interpolation Functions Assembly of Elements Time-Dependent Problems Axisymmetric Problems Convective Boundary Conditions Library of Finite Elements Numerical Integration Modeling Considerations Illustrative Examples 3D CONDUCTION HEAT TRANSFER Semidiscrete Finite Element Model Interpolation Functions Numerical Integration Computation of Surface Fluxes Semidiscrete Finite Element Model Solution of Nonlinear Equations Radiation Solution Algorithms Variable Properties sPost-Processing Operations sAdvanced Topics in Conduction sExamples of Diffusion Problems VISCOUS INCOMPRESSIBLE FLOWS Mixed Finite Element Model Penalty Finite Element Models Finite Element Models of Porous Flow Computational Considerations Solution of Nonlinear Equations Time-Approximation Schemes sStabilized Methods Post-Processing sAdvanced Topics Advanced Topics - Turbulence Numerical Examples CONVECTIVE HEAT TRANSFER Mixed Finite Element Model Penalty Finite Element Model Finite Element Models of Porous Flow Solution Methods Convection with Change of Phase Convection with Enclosure Radiation Post-Computation of Heat Flux Advanced Topics - Turbulent Heat Transfer Advanced Topics - Chemically Reacting Systems Numerical Examples sNON-NEWTONIAN FLUIDS Governing Equations of Inelastic Fluids Finite Element Models of Inelastic Fluids Solution Methods for Inelastic Fluids Governing Equations of Viscoelastic Fluids Finite Element Model of Differential Form Finite Element Model of Integral Form Unresolved Problems Numerical Examples sCOUPLED PROBLEMS Coupled Boundary Value Problems Fluid Mechanics and Heat Transfer Solid Mechanics Electromagnetics Coupled Problems in Mechanics Implementation of Coupled Algorithms Numerical Examples sADVANCED TOPICS Parallel Processing Other Topics Note: Chapters also include an Introduction, Exercises, and References APPENDIX A: COMPUTER PROGRAM--HEATFLOW Heat Transfer and Related Problems Flows of Viscous Incompressible Fluids Description of the Input Data A Source Listings of Selective Subroutines Reference sAPPENDIX B: SOLUTION OF LINEAR EQUATIONS Introduction Direct Methods Iterative Methods References for Additional Reading sAPPENDIX C: FIXED POINT METHODS AND CONTRACTION MAPPINGS Fixed Point Theorem Chord Method Newton's Method The Newton-Raphson Method Descent Methods References for Additional Reading

The Finite Element Method in Heat Transfer and Fluid Dynamics

Vibration of functionally graded cylindrical shells

A refined nonlinear theory of plates with transverse shear deformation

On Engineering By J T Oden J N Reddy ONLINE SHOPPING FOR NUMBER INTRODUCTION AN INTRODUCTION. MATHEMATICAL LEARNING THEORY R C ATKINSON. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF FINITE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF THE NAVIER. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF VIBRATIONS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. INTRODUCTION MATHEMATICAL THEORY FINITE ELEMENTS ABEBOOKS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE

An introduction to the mathematical theory of finite elements

A general two-dimensional shear deformation theory of laminated composite plates is presented. The theory account for a desired degree of approximation of the displacements through the laminate thickness. As special cases, the classical, first-order (Reissner–Mindlin) and other shear deformation theories available in the literature can be deduced from the present theory.

J. N. Reddy

Papers

The Finite Element Method in Heat Transfer and Fluid Dynamics

Vibration of functionally graded cylindrical shells

A refined nonlinear theory of plates with transverse shear deformation

An introduction to the mathematical theory of finite elements

A generalization of two-dimensional theories of laminated composite plates†