Creon Levit

A tool for visualizing the topology of three-dimensional vector fields

A description is given of a software system, TOPO, that numerically analyzes and graphically displays topological aspects of a three-dimensional vector field, v, to produce a single, relatively simple picture that characterizes v. The topology of v considered consists of its critical points (where v=0), their invariant manifolds, and the integral curves connecting these invariant manifolds. The field in the neighborhood of each critical point is approximated by the Taylor expansion. The coefficients of the first nonzero term of the Taylor expansion around a critical point are the 3*3 matrix Delta v. Critical points are classified by examining Delta vs eigenvalues. The eigenvectors of Delta v span the invariant manifolds of the linearized field around a critical point. Curves integrated from initial points on the eigenvectors a small distance from a critical point connect with other critical points (or the boundary) to complete the topology. One class of critical surfaces that is important in computational fluid dynamics is analyzed.<<ETX>>

The virtual windtunnel-an environment for the exploration of three-dimensional unsteady flows

A recently completed implementation of a virtual environment for exploring numerically generated three-dimensional unsteady flowfields is described. A boom-mounted six-degree-of-freedom head-position-sensitive stereo CRT system is used for viewing. A hand-position-sensitive glove controller is used for injecting various tracers (e.g. smoke) into the virtual flowfield. A multiprocessor graphics workstation is used for computation and rendering. The techniques for visualizing unsteady flows are described, and the computer requirements for a variety of visualization techniques are discussed. These techniques generalize to visualization of other 3D vector fields.<<ETX>>

The virtual wind tunnel

The design and implementation of a virtual environment linked to a graphics workstation for the visualization of complex fluid flows are described. The system user wears a stereo head-tracked display, which effectively displays 3-D information, and an instrumented glove to intuitively position flow-visualization tools. The visualization structures and their interfaces in the virtual environment and the implementation hardware and software are described. The performance of the virtual wind tunnel is reviewed using the flow past a tapered cylinder as an example. Performance issues and future directions for the system are discussed.<<ETX>>

Feature extraction of separation and attachment lines

Separation and attachment lines are topologically significant curves that exist on 2D surfaces in 3D vector fields. Two algorithms are presented, one point-based and one element-based, that extract separation and attachment lines using eigenvalue analysis of a locally linear function. Unlike prior techniques based on piecewise numerical integration, these algorithms use robust analytical tests that can be applied independently to any point in a vector field. The feature extraction is fully automatic and suited to the analysis of large-scale numerical simulations. The strengths and weaknesses of the two algorithms are evaluated using analytic vector fields and also results from computational fluid dynamics (CFD) simulations. We show that both algorithms detect open separation lines-a type of separation that is not captured by conventional vector field topology algorithms.

Numerical Simulation of Flow Past a Tapered Cylinder

The unsteady three-dimensional low Reynolds number flow past a tapered cylinder is computed. The spanwise variation in natural shedding frequency results in interesting three-dimensional flow phenomena. The computed hot-wire and spectral data are very similar to experimental results. The computation was done on the Connection Machine, a massively parallel computer; highlights of the capabilities of the Connection Machine for computation and visualization of three-dimensional unsteady flow fields are shown.

Machine phase fullerene nanotechnology

Recent advances in fullerene science and technology suggest that it may be possible, in the distant future, to design and build atomically precise programmable machines composed largely of functionalized fullerenes. Large numbers of such machines with appropriate interconnections could conceivably create a material able to react to the environment and repair itself. This paper reviews some of the experimental and theoretical work relating to these materials, sometimes called machine phase, including the fullerene gears and high-density memory recently designed and simulated in our laboratory.

Are the Bader Laplacian and the Bohm quantum potential equivalent

Abstract The de Broglie–Bohm ontological interpretation of quantum theory clarifies the understanding of many otherwise counter-intuitive quantum mechanical phenomena. We report here on an application of Bohms quantum potential to the bonding and reactivity of small molecules. In quantum chemistry, Bader has shown that the topology of the Laplacian of the electronic charge density characterizes many features of molecular structure and reactivity. Examination of ab initio solutions for several small molecules suggests that the Laplacian of Bader and the quantum potential of Bohm are morphologically equivalent.

EXPLICIT AND IMPLICIT SOLUTION OF THE NAVIER–STOKES EQUATIONS ON A MASSIVELY PARALLEL COMPUTER

Abstract We describe the design, implementation and performance of a two-dimensional time-accurate Navier-Stokes solver for the Connection Machine (tin) model CM2. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The entire flow solver is written in starlisp, a set of parallel extensions to common-lisp, developed by Thinking Machines Corporation. Our code is based on ARC2D, and we are attempting to emulate its functionality. Thus, we can check our Connection Machine results against those of a mature, well-vectorized Cray 2 program, both for correctness and performance. We find the code to be correct and the performance in some cases to be up to several times that of the Cray 2.

Implementation of a Distributed Interactive Graphics System

The design, implementation, and performance of a distributed interactive graphics software system are described. The software is distributed between two machines with very different ca pabilities, a supercomputer (CRAY-2) and a graphics workstation (Silicon Graphics Iris). Both machines run the same operating system (UNIX) and are programmed by the user. Three-dimen sional graphical transformations, display updates, the user interface, and related operations are handled by the graphics workstation, while computationally intensive operations and some graphics are performed by the supercomputer. Three versions of this distributed graphics system are described; one builds display lists on the supercomputer, one builds them on the workstation, and one does not build them at all. Communication between the two machines con sists of a remote graphics protocol built on TCP/ IP. The performance of two distributed graphics programs—a test case and an application from computational fluid dynamics—is reported, and the timing results are analyzed.

Multimedia environments for scientists

This paper addresses the question of how the work of the scientist will change in the new multimedia environments. Scenarios for the process of simulating and analyzing data in such environments are constructed, and some of the underlying models used in their construction are examined.<<ETX>>