International Journal of Modern Physics C

The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques. A set of tools is developed for determining gauge choices, setting boundary and initial conditions, handling spacetime singularities, etc. As required by the special physical and mathematical properties of general relativity, such techniques are indispensable for the numerical evolutions of spacetime. (3) Coding. The optimal use of parallel processing is crucial for many problems in numerical relativity, due to the intrinsic complexity of the theory. (4) Visualization. Numerical relativity is about the evolutions of 3-dimensional geometric structures. There are special demands on visualization. (5) Interpretation and Understanding. The integration of numerical data in relativity into a consistent physical picture is complicated by gauge and coordinate degrees of freedoms and other difficulties. We give a brief overview of the progress made in these areas.

Symmetry breaking occurs in the discretizations of the partial differential equations of fluid dynamics, both advertently and inadvertently. Although it can occur even in one-dimensional steady flow algorithms, we have found its consequences to be more pronounced in two and three space dimensions and in the computation of time dependent flows. This has led us to some interesting new computational schemes.

Through numerical simulations over the past decade we have made significant progress toward solving quantum chromodynamics (QCD), the widely accepted theory of the strong interactions. Quantitatively respectable results are beginning to emerge. We are also gaining new qualitative insights into the workings of the theory that will assist in the design and analysis of experiment. I give a few examples of recent progress in lattice QCD and discuss goals and prospects for computations using the coming generation of teraflops-scale supercomputers.

A computational model has been used to determine the terms in the dynamical equations which are responsible for the formation of a certain horizontal circulation seen in a simply connected, differentially heated rotating fluid annulus. Experiments with a differentially heated rotating fluid annulus that is fully blocked by a thin, rigid, vertical radial barrier at rotation rates of up to 5 rad.sec⁻¹ and with an externally applied radial temperature difference of 4 or 10 °C show two principal circulations. This paper is concerned with the mechanism for one of those circulations, which occurs in a horizontal plane. Computer modelling shows that this circulation is caused by small radial temperature gradients in the fluid, rather than centrifugal effects.

Two-dimensional incompressible turbulent boundary layer flows over a flat plate were predicted using turbulent boundary layer equations. Reynolds stresses were calculated using Cebeci-Smith, Baldwin-Lomax, and Johnson-King eddy viscosity models. Computational results of mean-flow properties based on Cebeci-Smith model and Baldwin-Lomax model are in excellent agreement with experimental data, and, those based on Johnson-King model are not as accurate as the other two models.

We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

In this study a three-dimensional transient dynamic contact problem is solved, and a theorem relating the contact stress and displacement over an elliptic region is proved. Numerical results for the contact displacement-time variation clearly demonstrate the effect of inertia induced by the dynamic stress.

This paper presents a simple model on the fracture of a laminated strip. Based on the method of complex variable function for solving plane elasticity and the confomal mapping technique, a closed form solution for the simplified model is constructed. The most important physical quantity for fracture analysis—the stress intensity factor—includes analytically the effects of structure geometry and the material constants. The analysis is very easily extended to solve the problem of material nonlinear behaviour and the problem of any 2n+1 layers with n+1 different materials. These may provide useful insight into the field of interlaminar fracture of composite materials.

This paper reviews the need for reduced chemistry modeling for hypersonic reactive flows, and describes the method of computational singular perturbation which can computationally derive reduced chemistry models for a massively complex reaction system.

The renewed interest in hypersonic flows has created a large demand for physicochemical models for air flow computations around reentry bodies. It is obvious, that besides the improvement of mathematical algorithms for solving the Euler or Navier-Stokes equations detailed physico-chemical models for air in chemical and thermal nonequilibrium are needed for a realistic prediction of hypersonic flowfields. In this paper we present a model, based on elementary physico-chemical processes, for a detailed description of the chemical nonequilibrium together with the excitation of internal degrees of freedom. Results show the strong influence of thermal nonequilibrium on the flowfields.

The kinetic theory of gases can be used to accurately calculate the transport properties of gases based on knowledge of the intermolecular potential between the interacting atoms, molecules or ions. This approach has been especially useful at high temperatures where experimental transport data are either sparse or unavailable. In recent years, increasingly accurate potentials for atom-atom and atom-ion interactions have become available for such calculations, and approaches for applying these potentials to calculate the high temperature thermophysical properties of gases are described.

Parametric studies using the plane Couette flow as a simple model for shear flows to test different physico-chemical aspects of the very complex high-temperature chemically reacting flows occurring in hypersonic flow configurations are under way. Some typical results on the dissociation/recombination reactions of diatomic gases as to the effects of the choice of transport coefficient modelling and reaction rate coefficient data on the practically relevant quantitites such as heat transfer and skin friction at the solid walls are discussed.

Molecular dynamics simulations of supercooled fluid mixtures of soft-spheres and of Lennard-Jones particles have revealed the existence of a kinetic transition that occurs above the glass transition temperature. This transition appears to be thermodynamic in origin. It is associated with a change in the local mobility of the particles. The basis for these conclusions is discussed.

I briefly review new analytical formulas for the correlation length and interface tension of two-dimensional q-state Potts models and compare them with numerical results from recent Monte Carlo simulation studies.

The Heisenberg antiferromagnetic chain of spin 1 with the most general single ion anisotropy is numerically analyzed. Chains of length up to 22 sites are studied by a Lanczös method and up to 32 sites with a quantum Monte Carlo. Gaps, magnetic excitations, dynamical properties and magnetic field behaviour are obtained. The recent neutron scattering experiments on the quasi one-dimensional antiferromagnet NENP are fully explained by our results.

We study the 3d Edwards-Anderson Ising spin glass on finite lattices by multicanonical ensemble. Performing simulations of this ensemble enables to generate large numbers of groundstate configurations in thermal equilibrium.

To study the role of topological defects in the three-dimensional classical Heisenberg model we have simulated this model on simple cubic lattices of size up to 80³, using the single-cluster Monte Carlo update. Analysing the specific-heat data of these simulations, we obtain a very accurate estimate for the ratio of the specific-heat exponent with the correlation-length exponent, α/ν, from a usual finite-size scaling analysis at the critical coupling K_c. Moreover, by fitting the energy at K_c, we reduce the error estimates by another factor of two, and get a value of α/ν, which is comparable in accuracy to best field theoretic estimates.

Applications of the multicanonical ensemble for the protein folding problem are presented. Performing simulations of this ensemble alleviates the multiple-minima problem and allows to calculate thermodynamical quantities at any temperature from only one Monte Carlo run.

To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

Efficient parallel molecular dynamics (MD) algorithm based on the multiple-time-step (MTS) approach is developed. The MTS-MD algorithm is used to study structural correlations in porous silica at densities 2.2 g/cm³ to 1.6 g/cm³. Nature of phonons and effects of hydrostatic pressure in solid C₆₀ is studied using the tight-binding MD method within a unified interaction model which includes intermolecular and intra-molecular interactions.

New developments in the self-consistent Green’s function (SCGF) method as applied to nuclear systems are discussed. Results for high-momentum components in the single-particle spectral function of ¹⁶O reveal that their observation is only feasible at a correspondingly high excitation energy in the (e, e′p) reaction. The consequences of the non-mean-field character of nucleons in the nuclear medium are further explored in the context of the nuclear matter saturation problem.

A method to reduce the CPU time required for molecular dynamics computer simulations of nonequilibrium phenomena in physics has been developed. At each time step in the simulation of a solid system, a force calculation is performed on only those atoms that satisfy at least one of three criteria: (i) its distance moved, (ii) its acceleration, (iii) its change in acceleration. A fourth criteria on the time interval since the forces on all atoms were updated is also employed. For a gas system, forces of the atoms which fly freely in a certain time interval are not updated until these atoms move in a distance that is greater than a predetermined value. A savings in CPU time greater than a factor of two is obtained with negligible loss in accuracy.

A new parallel algorithm suitable for molecular dynamics simulations of organic systems is presented. It reduces the communication cost and memory requirements of other commonly-used parallel algorithms by a factor of where P is the number of processors. The algorithm has been implemented in a CHARMM-like molecular dynamics model and its performance on 1024-processor nCUBE 2 and Intel Paragon machines is discussed.

Based on cluster model, we have calculated the fundamental vibrational frequencies of rutile by combining ab initio method and Wilson’s GF-matrix method. In the calculation, we have introduced the concept of environment factor α to correct the force field of the cluster model. The results of calculation are in good agreement to the experimental data and the normal modes give us clear physical picture of the crystal vibration.

It has been shown by Maradudin and Flinn¹ (1963) that, in weak anharmonic crystals, the lowest order anharmonic contributions to the Debye-Waller factor are of 0(λ²), where λ is the Van Hove² (1961) ordering parameter. There are four such terms, two of them are of (where is the scattering wave-vector) and are known as the normal terms. Other two terms are of and are known as the anomalous terms. These four terms are of significant complexity. In this present work, a computation of these four terms will be reported for sodium metal and the results will be compared with experimentally determined values.

This paper explores some basic representational and implementation issues arising from the premise that cortical circuits operate on probability density functions to reason about analog quantities. Some insight is provided into why neurobiological systems can appear messy, while at the same time provide a rich and robust computational environment.

Although it is generally agreed that neural networks with graded input neurons may correspond more closely with biological reality, there are some severe problems associated with such networks. When using multi-state neurons, it has recently been shown, that the information capacity falls off like 1/Q², if Q is the number of neuron states. Why this is so, will be discussed here along with a first-order solution to this problem. The solution lends itself quite naturally to implementation on a parallel computer.

A network of coupled maps is introduced to model the evolution of the genetic sequence of the HIV1 AIDS virus. Within a space of RNA chemical composition, short range interactions correspond to mutations. Ecological constraints generate long range couplings. The resulting equations are of a reaction-diffusion type. Quasi-species with an error threshold emerge from the model dynamics. Predictions relating chemical composition regularity properties with the variability of the HIV RNA sequence agree with a statistical analysis from gene data banks. The model suggests a clue for an alternative therapeutical treatment.

We discuss two proposals for a non-perturbative formulation of chiral gauge theories on the lattice. In both cases gauge symmetry is broken by the regularization. We aim at a dynamical restoration of symmetry. If the gauge symmetry breaking is not too severe this procedure could lead in the continuum limit to the desired chiral gauge theory.

We will discuss here an indirect lattice evaluation of the baryon axial singlet current matrix element. This quantity may be related to the fraction of nucleon spin carried by the quarks. The appropriate structure function has recently been measured (EMC experiment). As in this experiment, we find that the quarks do not appear to carry a large component of the nucleon spin.

We study glueball and meson scattering in compact QED₂₊₁ gauge theory in a Hamiltonian formulation on a momentum lattice. We compute S-matrix elements and scattering cross sections and compare our results with strong coupling perturbation theory

The investigation of topological properties of the gauge field in a two-dimensional Higgs model can help in understanding anomalous fermion number violation.

We study the Coulomb-Higgs phase transition of the U(1)-Higgs model.

A single magnetic monopole in pure SU(2) gauge theory is simulated on the lattice and its mass is computed in the full quantum theory. The results are relevant for our proposed realization of the dual superconductor hypothesis of confinement.

We summarize our lattice investigation of the Nambu-Jona-Lasinio model¹.

We give a 1993 update of non-compact lattice QED, in particular the chiral condensate, finite size effects and meson mass ratios. We compare descriptions of the phase transition. Our previous conclusions remain valid.

Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagomé lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.

We present the results of a high statistics study of a model for four dimensional euclidean quantum gravity based on summing over triangulations.

We apply improved Langevin methods with Fourier acceleration to SU(N)×SU(N)/SU(N) spin models in two dimensions for N=3, 4 & 6. We discuss the effect of fourier acceleration and operator improvement techniques, measure the fundamental correlation length on lattices upto 128² and observe asymptotic scaling in a physical scheme. Bound state masses are also measured and evidence is found for excited states in all channels. Our results are found to be in good agreement with theory.

We discuss the strength of the first order thermal phase transition of the SU(2) Higgs model appearing in a lattice study. Based on block-spinning, an order parameter for Higgs condensation is proposed.

According to the electroweak baryogenesis scenario the matter-antimatter asymmetry of the Universe was created shortly after the Big Bang, during the electroweak phase transition. This process depends strongly on the detailed nature of the electroweak phase transition. For realistic Higgs particle masses, the standard perturbative analysis indicates that the transition is at most only weakly first order. We have studied the transition with non-perturbative lattice Monte Carlo simulations. We found large non-perturbative effects; in particular, the phase transition is a strongly first order one, at least up to Higgs mass of about 85 GeV. This makes electroweak baryogenesis a viable scenario with a Higgs mass not exceeding 85 GeV.

Evidence indicating that quarks are not confined inside mesons above the chiral transition is presented.

The charge density around a static charge is investigated within finite temperature QCD and compact QED both in the chirally broken and symmetric phase. We display the functional behavior of the charge polarization for various masses of the sea particles and for static sources in higher representations. The total induced charge is found to be consistent with the results from the MILC Collaboration.

We present the QCD-TARO program of calculations for lattice Quantum Chromo-dynamics which uses the parallel computer AP1000 of Fujitsu.

Hamiltonian integration schemes for the Nonlinear Schroedinger Equation are examined. The efficiency with respect to accuracy and integration time of an integrable scheme, a standard conservative scheme, and a symplectic method is compared.

Polarization decorrelation in single-mode fibers with randomly varying birefringence is studied. We find that polarization decorrelation length is minimized for a given beat length if the autocorrelation length of the internal birefringence fluctuation is close to the average beat length. Implications for both soliton and linear communication systems are discussed

In this paper two numerical schemes for the numerical simulation of the nonlinear partial differential equation u_t+6αuu_x+6βu²u_x+u_xxx=0 are implemented by the method of lines (MOL). The first scheme is based on the inverse scattering transform (IST), and the second scheme is a combination of the IST schemes for the Korteweg-de Vries (KdV) and modified KdV (MKdV) equations. The only difference between the two schemes is in the discretization of the nonlinear terms. Numerical experiments have shown that the first scheme is significantly more accurate than the second one. This demonstrates the importance of a proper discretization of nonlinear terms when a numerical method is designed for solving a nonlinear differential equation.

The fluid equations for a plasma are numerically integrated to obtain soliton solutions in a bounded one—dimensional system. This contrasts with KdV and modified KdV approaches which are approximations generally valid for small amplitudes only.

The main objective of this work is to present a survey of the most recently developed parallel multivariate integration routines for various architectures (MIMDDM, MIMD-SM, Network of workstations). Applications to computational physics problems is also provided.

Measure of algorithmic complexity c(n) which has been suggested by Lempel and Ziv is one of important quantities for characterizing properties of nonlinear dynamical systems. The temporal variation of c(n) is investigated for time series generated by some physical processes. The relationship between algorithmic complexity and other characteristics of nonlinear systems is discussed.

We present a method for determining optimum quantization tables for use in image compression systems which conform to the ISO/CCITT standard for Image Compression, also known as the Joint Photographic Experts Group (JPEG) standard¹. An algorithm based on simulated annealing² compresses and decompresses any collection of 8 by 8 pixel blocks, while searching the space of 8 by 8 quantization tables for optimum fidelity according to some chosen measure. A composite cost function maintains a predefined compression ratio while minimizing the RMS error in the decoded image compared to the original. The process can be carried out on a raw image, or greater weight can be given to a selected range of DCT coefficients on the basis of psychophysical considerations³. The results of applying the methods to the intensity (y) components of three JPEG test images are presented. In all cases improved fidelity as measured by RMS error is obtained compared to the quantization table suggested in the JPEG standard. Significantly, the quantization tables obtained for one image most often provide smaller error when applied to other images than does the table suggested with the JPEG standard. An unexpected result when using pre-emphasized images suggests that the psychophysical assumptions underlying the suggested JPEG table may be oversimplified. By applying the method to blocks selected from a variety of images, improved quantization tables can be found for images in general, including color.