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

A finite-element model based on the penalty function formulation of the Navier-Stokes equations governing flows of unsteady, incompressible, non-isothermal, non-Newtonian fluids in three-dimensional enclosures is presented. Power-law and Carreau constitutive relations are used, and the viscosity is assumed to be temperature dependent. The resulting non-linear equations are solved by Picard's method (i.e. direct iteration). The finite-element model is used to analyze several problems, such as flows through circular pipe, cubical cavity, and tubular and square contractions. Wherever possible, comparisons are made between present numerical solutions and available analytical or numerical solutions. The present results are in good agreement with other solutions. The finite-element model developed here can be modified to accommodate other forms of constitutive relations.

Finite-element analysis of flows of non-Newtonian fluids in three-dimensional enclosures

In this article, the equations of motion for functionally graded plates with surface-mounted piezoelectric layers, while accounting for the gradient elasticity through the modified couple stress model and linear piezoelectricity, are derived using Hamilton’s principle. The formulation includes the coupling between mechanical deformations and the charge equations of electrostatics. The mathematical model developed herein is an equivalent single layer theory for mechanical displacement field and the potential functions. The in-plane displacements are assumed to vary as cubic functions of the thickness coordinate while the transverse displacement is assumed to vary as a quadratic function of the thickness coordinate through plate thickness. The potential function is assumed as the combination of half cosine variation of electric potential and linear variation of applied voltage on outer surfaces. The approach described here is that standard plate models can be enhanced to include the coupling between...

Modeling of functionally graded smart plates with gradient elasticity effects

Two-Temperature Thermodynamics for Metal Viscoplasticity: Continuum Modeling and Numerical Experiments

On the finite element method with penalty for incompressible fluid flow problems

A finite element method based on the Eulerian velocity correction method has been used to analyse the laminar natural convection in an annular cavity. Unsteady, incompressible, axisymmetric Navier‐Stokes equations have been made use of. Different radius ratios of the annular cavity have been considered to investigate the effect of the radius of curvature on the heat transfer coefficient.

J. N. Reddy

Papers

Finite-element analysis of flows of non-Newtonian fluids in three-dimensional enclosures

Modeling of functionally graded smart plates with gradient elasticity effects

Two-Temperature Thermodynamics for Metal Viscoplasticity: Continuum Modeling and Numerical Experiments

On the finite element method with penalty for incompressible fluid flow problems

Finite element analysis of the effect of radius ratio on natural convection in an annular cavity