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

: In this research, the rate constitutive theories for ordered thermoviscous fluids, ordered thermoelastic solids and ordered thermoviscoelastic polymeric fluids in contra- and co-variant bases are developed. Such theories are necessitated when the mathematical models of the deforming matter are derived using the Eulerian description. In each case, the dependent variables in the rate constitutive theory and their argument tensors describing the physics of the deforming matter are identified. The dependent variables in the constitutive theory are expressed as a linear combination of the combined generators of the argument tensors. The coefficients in the linear combinations are functions of the combined invariants of the argument tensors, temperature, and density (for compressible matter; in the current configuration). The coefficients in the linear combination are determined by considering their Taylor's series expansions about the reference configuration and limiting the expansion to linear terms in the combined invariants and temperature.

Ordered Rate Constitutive Theories: Development of Rate Constitutive Equations for Solids, Liquids, and Gases

The broad focus of this paper is on developing continuum models of inelastic response of crystalline materials that include the influence of microstructure, material symmetry, and dissipation of energy accompanying the changes in the microstructure. A framework has been developed, built on the idea of natural configurations of a material, that has provisions for explicit treatment of material microstructure (slip planes, dislocations, interfaces, etc.). It is demonstrated that the developed framework is applicable to diverse phenomena such as plasticity due to slip and twinning, and martensitic phase transformations. The developed framework is used to study the inelastic behavior of crystalline silicon at elevated temperatures.

On the inelastic behavior of crystalline silicon at elevated temperatures

Nonlinear Bending of Straight Beams

The physical interaction of fluids and solids is of practical significance in engineering (e.g. flutter of aerodynamic structures, vortex induced vibrations of sub-sea pipelines and risers, inflatable dams, parachute dynamics and blood flow through arteries). In this paper, a finite element formulation is developed for determining the vibration characteristics of beams in contact with inviscid incompressible fluid. The classical, first-order and third-order shear deformation beam theories are used to model the structural response. Numerical results for vibration frequencies are presented showing the parametric effect of thickness and immersion depth on the frequency response. The results indicate that the presence of fluid interaction has significant effect on the dynamic response. The formulation presented herein is also applicable to a vast number of vibration problems related to beams under a variety of excitations.

Vibration of Elastic Beams in the Presence of an Inviscid Fluid Medium

In this paper, the mathematical models based on Navier-Stokes equations incorporating physical mechanism of viscosity and conductivity are utilized in h, p, k finite element computational framework to investigate 1-D normal shocks in air and FC70. In the case of air, shock evolution, propagation, repeated reflection and interactions are simulated using ideal gas law with constant viscosity and thermal conductivity. For FC70, numerical studies are presented for initial conditions inside the BZT zone as well as for those away from the BZT zone to investigate the possibility of compression as well as rarefaction shocks. The Van der Waals equation of state with constant transport properties is used for FC70. In all cases, “the rate of production of entropy per unit volume” is used to establish: (i) evolution of shock; (ii) sustained propagation; (iii) repeated reflections and subsequent sustained propagation; and (iv) interactions and sustained propagation of reflected shocks. In all numerical studies care is...

J. N. Reddy

Papers

Ordered Rate Constitutive Theories: Development of Rate Constitutive Equations for Solids, Liquids, and Gases

On the inelastic behavior of crystalline silicon at elevated temperatures

Nonlinear Bending of Straight Beams

Vibration of Elastic Beams in the Presence of an Inviscid Fluid Medium

Evolution, Propagation, Reflection, and Interactions of 1D-normal Shocks in Air and FC70 Using hpk Finite Element Computational Framework