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

The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.

/pdf/a-finite-element-solver-for-3-d-compressible-viscous-flows-1ku2un8ifg.pdf

A finite element solver for 3-D compressible viscous flows

Treated herein is the elastic buckling of circular plates based on the Reddy plate theory. This plate theory extends the Kirchhoff (or the classical thin) plate theory to allow for the effect of transverse shear deformation. Unlike the Mindlin's shear deformation plate theory, there is no need for a shear correction factor in the Reddy plate theory. In this paper, exact buckling solutions are derived for circular plates whose edges are simply supported and elastically restrained against rotation as well. This general edge condition includes the classical simply supported and clamped edges at the limiting, values of the elastic rotational restraint constant. The buckling solutions are expressed in terms of the well-known Kichhoff buckling solutions. A comparison of buckling loads between the Mindlin, Reddy and three-dimensional elasticity plates is also given.

Buckling of circular plates based on Reddy plate theory

In this work, we propose an automatic mesh generation algorithm, FlowMesher, which can be used to generate unstructured meshes for mesh domains in any shape with minimum (or even no) user intervention. The approach can generate high-quality simplex meshes directly from scanned images in OBJ format in 2D and 3D or just from a line drawing in 2-D. Mesh grading can be easily controlled also. The FlowMesher is robust and easy to be implemented and is useful for a variety of applications including surgical simulators. 
The core idea of the FlowMesher is that a mesh domain is considered as an "airtight container" into which fluid particles are "injected" at one or multiple selected interior points. The particles repel each other and occupy the whole domain somewhat like blowing up a balloon. When the container is full of fluid particles and the flow is stopped, a Delaunay triangulation algorithm is employed to link the fluid particles together to generate an unstructured mesh (which is then optimized using a combination of automated mesh smoothing and element removal in 3D). The performance of the FlowMesher is demonstrated by generating meshes for several 2D and 3D mesh domains including a scanned image of a bone.

FlowMesher: An automatic unstructured mesh generation algorithm with applications from finite element analysis to medical simulations.

Bioreactors play important role in tissue engineering, as they simulate physiological environment required for the development of tissue substitutes. The significant parameters involved in the efficient working of a bioreactor are the transfer of nutrients and removal of wastes. Use of carbon nanotube polymeric scaffolds for tissue engineering applications has gained recent attention, primarily due to the enhanced mechanical properties of carbon nanotubes. In this study, a hierarchical approach to determine the atomistic properties of carbon nanotube based polymers using molecular dynamics and coupling between the scales through complex multi‐scale mathematical homogenization models is discussed. A new computational methodology for the analysis of tissue‐fluid interaction problem based on a biphasic representation of fluid and tissue domain is also presented. The significance of this work lies in the use of a multi‐physical modelling of complex material geometry as well as physical processes that represent different physiological systems, leading to an efficient multiscale‐multi‐physical computational algorithm.

Multiscale Analysis and Nutrient Transport in Carbon Nanotube Reinforced Nanofiber Bioreactor

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governi...

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0674

J. N. Reddy

Papers

A finite element solver for 3-D compressible viscous flows

Buckling of circular plates based on Reddy plate theory

FlowMesher: An automatic unstructured mesh generation algorithm with applications from finite element analysis to medical simulations.

Multiscale Analysis and Nutrient Transport in Carbon Nanotube Reinforced Nanofiber Bioreactor

Variational formulation for dissipative continua and an incremental J-integral