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

Processing conditions play an important role in the structure-property relationship of semicrystaltine polymers. The temperature and the deformation rate history can affect the growth and nucleation rate of crystallization for a semicrystalline polymer. The flout and heat transfer during processing can be strongly coupled to the equations of material kinetics for the polymer. In this study, the effect of this coupling on the crystallization of a semicrystalline polymer is studied in a driven cavity under nonisothermal conditions. The transient analysis of the flow of a polymeric melt is modeled as a power law fluid with temperature dependent viscosity. Results are shown for the evolution of crystallinity and strain rate with time for various velocities of the moving plate and aspect ratios of the cavity for polyethylene, a fast crystallizing polymer. The importance of coupling the effects of shear-induced crystallization, flow, and temperature is shown.

Computational study of shear-induced crystallization in polymers

Abstract Conventional experimental or computational techniques are often inadequate for the analysis and development of nanocomposite-based materials as they are tedious (e.g., experimental methods) or are unsuitable to capture the properties of these novel materials (e.g., conventional computational techniques), thereby requiring multiscale computational strategies. During the last 5 years, major developments were made by the authors on the formulation and implementation of multiscale computational models, using atomistic simulation and micro-mechanics-based techniques, to study the mechanical and thermal behavior of nanocomposite-based materials. In this article, the advances made in the computational analysis of nanocomposites for tissue engineering applications (e.g., scaffolds and bioreactors) would be discussed. The material properties of the nanocomposites in the lower scales were determined using molecular dynamics, and were then transferred to the macroscale using various homogenization techniques. Also in this article, the authors discuss the development of a theory of mixture-based finite element model for nutrient flow in a hollow fiber membrane bioreactor and the use of computational tools to improve the efficiency of the bioreactor.

Recent advances in the analysis of nanotube-reinforced polymeric biomaterials

Modeling and Analysis of Carbon Nanotube Structures

Two kinds of finite-element analyses are developed for the geometrically nonlinear study of the large deformations in laminated composite structures, especially shells. The first kind of finite-element analysis utilizes the general incremental variational formulation as well as the total Lagrangian description of motion, and a three-dimensional degenerate element is adopted. The second kind of analysis employs a formulation based on deformable shell theory, and the plate-bending element is used. Numerical results for bending are presented for five plate and shell structures of isotropic as well as orthotropic composition, including an isotropic cylindrical panel with uniform loading and a laminated cylindrical panel with uniform loading. The results obtained using these analyses are found to be in good agreement with those available in the literature.

Geometrically nonlinear analysis of layered composite shells

Relationships between bending solutions (deflections and stress resultants) of the Levinson third-order plate theory are presented in terms of the solutions of the classical plate theory for sectorial plates. These relationships are algebraic in nature, and can be readily used to determine the shear deformation theory (based on the Levinson plate theory) solutions of sectorial plates without going through the process of solving the governing equations. The sectorial plates considered have simply supported radial edges while the circular curved edges may be either simply supported, clamped, or free. Numerical results are presented to illustrate the usefulness of the developed relationships.

J. N. Reddy

Papers

Computational study of shear-induced crystallization in polymers

Recent advances in the analysis of nanotube-reinforced polymeric biomaterials

Modeling and Analysis of Carbon Nanotube Structures

Geometrically nonlinear analysis of layered composite shells

Bending of sectorial Levinson plates: relationships with classical solutions