Computers in Physics
Volume 6, Issue 5, September 1992
Index of content:
- PEER-REVIEWED PAPERS
6(1992); http://dx.doi.org/10.1063/1.168432View Description Hide Description
The little‐known bin sort will perform more quickly than other sorting routines. With an address calculation formula that is chosen to approximate the cumulative distribution, it can readily handle cases for which it has the reputation of being ill‐suited.
6(1992); http://dx.doi.org/10.1063/1.168433View Description Hide Description
Three numerical recipes are given using Ahlberg’s algorithm for the parametric fitting by cubic splines of a set of n‐dimensional data points; subroutine SPLINE for an open curve, PSPLINE for a closed curve, and EPSPLINE for an axially symmetric surface (surface of revolution). Parametric routines are not troubled by intersections, and offer more flexibility in dealing with boundary conditions. One subroutine call is required for each data dimension. The execution speed of all programs is comparable to standard routines for an open curve.
6(1992); http://dx.doi.org/10.1063/1.168434View Description Hide Description
The distribution of conductance jumps ΔG in a Sierpinski gasket (SG) has been calculated. Using an exact renormalization scheme, the conductance jumps are obtained up to the ninth generation. It is found that the distribution of ΔG is multifractal. A comparison is also made between the SG spectrum and that of the percolation backbone of a random resistor network at the percolation threshold. Excellent agreement between the two spectra is found.
6(1992); http://dx.doi.org/10.1063/1.168435View Description Hide Description
Results are shown of methods for representing the behavior of one‐dimensional hydrogen perturbed by an electromagnetic wave. Different methods are used in classical and quantum mechanics. The quantum mechanical results appear to demonstrate the existence and overlap of resonance subspaces in Hilbert space, analogous to resonance zones in the classical phase space.
Reaction kinetic surfaces and isosurfaces of the catalytic hydrogenolysis of ethane and its self‐poisoning over Ni and Pd catalysts6(1992); http://dx.doi.org/10.1063/1.168436View Description Hide Description
The significance of three‐dimensional visualization is exhibited in the analysis of chemical reaction kinetics. The particular example used is from heterogeneous catalysis. It is also shown that this approach can be useful in exploring the mechanistic aspects of kinetics.
6(1992); http://dx.doi.org/10.1063/1.168437View Description Hide Description
A novel method for calculating and visualizing the geodesic structure of space‐time models is presented. By utilizing the symbolic computational power of M a t h e m a t i c a on a NeXT, and an IBM RS 6000 workstation, the geodesic equations are found analytically for any given metric. Once spliced into a FORTRAN program, the geodesic equations are solved numerically, on a CRAY Y‐MP supercomputer, for a given bundle of null geodesics. Here, the null geodesic structure of three singular space‐time geometries is examined: the Schwarzchild, Kerr, and Winicour space‐times. Using M a t h e m a t i c a software, the numerical data for the geodesic paths is displayed graphically, providing a picture of a given spacetime volume for each set of initial conditions. The parameter dependence of space‐time, due to a particular metric, can be observed by sequencing through various parameters, such as the mass and spin. These pictures can then be composed into a video tape which displays the range of behavior as the parameters are varied.
6(1992); http://dx.doi.org/10.1063/1.168438View Description Hide Description
This article compares both real and complex outputs from sizeable numeric computations using identical code on several computer systems. The digital signal processing technique known as the modified covariance method was used as the computational engine. It is a recursive algorithm for solving the covariance equations of a linear predictor that seeks to predict an input signal by a linear combination of past signal samples. Single precision and double precision results are presented but the study focuses primarily on differences between the VAX Fortran 4.8 and MacFortran/020 compilers. Differences in the first digit for single precision arithmetic were found and double precision differences occurred in the eighth digit. Arithmetic with complex data types was found to be less precise than with real data types. Although differences exist among various computer systems, they all show the same order of magnitude accuracy with respect to CRAY‐YMP results. The algorithm used here required a double precision implementation to obtain agreement between different computer systems.
6(1992); http://dx.doi.org/10.1063/1.168439View Description Hide Description
The quantum mechanical model of a dissipative system that is chaotic in its classical limit is solved numerically. The system is nonlinear optical second harmonic generation, and the model is the quantum optical master equation. The steady‐state of the master equation is found and compared with the classical chaotic attractor. Computational methods appropriate for vector processors and for the connection machine are described.