Some New Directions in Science on Computers

The following sections a included:

• Preface

• Contents

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on bodyfitted structured meshes. An efficient multigrid implicit scheme is incorporated for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Numerical computations using Langevin, lattice Boltzmann and finite volume methods have provided a means to investigate the dynamics of phase separation in models of fluids. They have been important in testing predictions from phenemonlogical theories. We review recent results on growth kinetics obtained using these methods.

In this survey we describe the constructions of modern shock capturing methods for the computation of discontinuous solutions in nonlinear systems of conservation laws. A typical such method consists of three steps: reconstruction, evolution and averaging. We study in detail several reconstruction and evolution strategies. The aim is to provide a global view on the development in this exciting field and to show how these methods may be used to solve problems in fluid dynamics.

Implementing molecular dynamics on the IBM SP parallel computer, we have studied the fracture of two and three dimensional notched solids under tension using in excess of one hundred million atoms. Many recent laboratory findings occur in our simulation experiments. For rapid brittle fracture, one of the most intriguing phenomena is the dynamic instability of the crack tip as it approaches a fraction of the Rayleigh sound speed. A detailed comparison between laboratory and two dimensional computer experiments is presented, and microscopic processes are identified. In particular, an explanation for the limiting velocity of the crack being significantly less than the theoretical limit is provided. For three dimensions, we discover a similar dynamical instability, but now the instability is immediately followed by an unexpected brittle-to-ductile transition giving rise to a proliferation of loop dislocations and the arrest of the crack.

The symbiotic relationship between modeling the underlying physics in semiconductors and modeling small semiconductor devices is discussed. Both modeling activities depend on large scale computing in an intrinsic way, with progress tied to the continued growth in raw computing power. Modeling the underlying physics in semiconductors involves the numerical evaluation of electronic material properties from detailed physical theories, e.g., bandstructure, scattering rates and conductivity. Device modeling takes the results of these materials calculations and incorporates them into a device context, i.e., computational domains representing a device geometry complete with doping profiles, contacts, and external electrical and/or optical excitations. The mutual benefit between these disciplines is obvious: predictive device modeling benefits from the physics modeling, since improved physical models yield more predictive device models; physics modeling often needs a device context to allow the theory to be directly compared with experimental data derived from device measurements. This chapter reviews our work in both of these areas.

Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales.

Simulations using simple cellular automata algorithms can be used to study various abstract polymer problems. We describe the two-space algorithm where interactions of a monomer are only with monomers in the other space. It is a particularly efficient algorithm for polymer simulation that is easy to implement and generalize. Three applications: 2-D melts, gel-electrophoresis and polymer collapse, are described. Simulations of high density melts in 2-D show that contrary to expectations polymers do not completely segregate at high density -- there is significant interpenetration. Preliminary simulations of gel-electrophoresis show its behavior in the diffusive regime and demonstrate the use of Cellular Automaton Machines (CAMs). Polymer collapse is studied in the regime of large departures from good solvent conditions. In this regime kinetics plays a significant role. Collapse is found to be dominated (nucleated) by migration of the chain ends. The kinetic process of collapse can systematically and reproducibly restrict the possible conformations that are explored during protein folding. This suggests that the kinetics of collapse may help lead to the desired folded conformation.

Although unconstrained DNA under physiological conditions occurs entirely in the B-form duplex conformation, local separations of its two strands can be induced at susceptible sites by processes which provide the energy needed to drive them. This local duplex opening has been shown to occur in response to imposed stresses, such as those that occur in vivo. It is an essential step in important DNA functions, including the initiation of gene expression and of replication. The duplex separation behavior of a stressed DNA molecule is determined by a competitive interaction involving all its base pairs. This paper describes a computational method to analyze this phenomenon. Its application to the analysis of diverse genomic DNA sequences shows that sites of predicted duplex destabilization are closely associated with regions regulating DNA transcription, replication, and other processes.

Two types of collective neuronal behaviors can be produced experimentally in brain slices that contain only thousands of neurons: events resembling epileptic seizures in vivo, and events resembling fast EEG waves in the gamma frequency range (> 20 Hz). Computer simulations of single neurons, and of networks of neurons, have contributed to our understanding of the physiological principles that underlie both types of collective behavior.

Computer modelling can be a valuable adjunct in immunological research. It can be used both as a theoretical tool to explore and understand the behavior of immunological processes as well as in a mode to provide an additional experimental tool, experiments in machina, experiments in the computer. Cellular automata are particularly useful in this regard since they can easily handle the complexities and special cases inherent in the immune system. We describe a generalized cellular automaton that has been designed to model the humoral component of the immune system.

Over the past twenty years N-body simulations have provided astrophysics with a wealth of information concerning the formation of structure on large-scales in the universe. The goal of such simulations is to understand the initial conditions and physical processes that lead to the observed structure. In this article we review the state of the art in N-body simulations in cosmology and then discuss the application of the Minimal Spanning Tree to the resulting simulations.

Ocean circulation models fall into two classes: level models that solve the pertinent equations on a 3-dimensional grid fixed in space, and layer models that keep grid points fixed horizontally but allow them to be carried up and down by the moving fluid. Layer models have certain numerical properties that make them attractive for long-term climate simulations, but they are more complicated to build than level models. This article describes recent attempts to simulate, in a layer model, the 3-dimensional global ocean circulation as it evolves over time in response to atmospheric wind, moisture, and heat input. By using a massively parallel supercomputer for this simulation, we were able to reduce the horizontal mesh size below the threshold where hydrodynamic instabilities of ocean currents show up in the numerical solutions; these instabilities give rise to current meanders and eddies that compare favorably to observations. Given the intended use of this model in coupled ocean-atmosphere simulations, the thermohaline circulation - the global overturning motion driven by heat exchange with the atmosphere as well as precipitation and evaporation - is analyzed in considerable detail. Results are compared to results obtained with a far more economical, coarse-mesh version of the same model.