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

On the mathematical theory of penalty-finite elements for Navier-Stokes equations

A thermodynamic model for ionic polymer–metal composites and finite volume-finite element solution

SUMMARY

Hollow fiber membrane bioreactors (HFMB) are extensively used for the development of tissue substitutes for bones and cartilages. In an HFMB, the nutrient transport is dependent on the material properties of the porous scaffold and fiber membrane and also on the fluid flow through the hollow fiber. The difficulty in obtaining real-time data along with the presence of large number of variables in experimental studies have lead to increased application of computational models for the performance analysis of bioreactors. A major difficulty in the computational analysis of HFMB is the modeling of the interactions at the fluid and porous scaffold interfaces, which has often been neglected or incorporated using specific boundary conditions. In this study, a new FEM is developed to analyze the fluid flow in the fluid-porous region with the interface coupled directly into the FEM. Distribution of nutrients in the bioreactor is studied by coupling mass transport equations to the fluid-porous finite element framework. The new model is implemented to study the influence of permeability, cell density, and flow rate on the nutrient concentration distribution in the HFMB. The developed computational framework is an ideal tool to study fluid flow through porous-open channels and can also be used for the design of bioreactors for optimal tissue growth. Copyright © 2011 John Wiley & Sons, Ltd.

Finite element model for nutrient distribution analysis of a hollow fiber membrane bioreactor.

A computational procedure for accurate determination of interlaminar stresses in thick and thin composite laminates subjected to torsional loading is presented. A multilevel, recursively defined preconditioner in conjunction with the preconditioned conjugate gradient (PCG) algorithm is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element method. The computational procedure is used to model stress fields in thick and thin laminates in torsion using three-dimensional and quasi-three-dimensional models. Results indicate that the preconditioner developed here can be used to produce an efficient iterative solver for the determination of two- and three-dimensional stress fields in composite structures.

Study of interlaminar stresses in composite laminates subjected to torsional loading

In the present study, a finite element formulation is presented to investigate vibration response of elastic plates in contact with a fluid medium. The fluid is assumed to be incompressible and inviscid, and the impermeability condition of the plate is taken into account. The classical plate theory (CPT), first-order shear deformation plate theory (FSDT), and Reddy third-order shear deformation plate theory (RSDT) are considered for the kinematic description of the solid medium and the simplified Navier–Stokes equations are used as the governing equations for the fluid medium. For each plate theory, a coupled set of finite element equations is derived. The effect of the fluid pressure is considered as an added mass and its effect on natural frequencies and mode shapes is investigated through several numerical simulations by varying the boundary conditions.

J. N. Reddy

Papers

On the mathematical theory of penalty-finite elements for Navier-Stokes equations

A thermodynamic model for ionic polymer–metal composites and finite volume-finite element solution

Finite element model for nutrient distribution analysis of a hollow fiber membrane bioreactor.

Study of interlaminar stresses in composite laminates subjected to torsional loading

Free Vibration Analysis of Elastic Plates in Contact with an Inviscid Fluid Medium