Showing papers in "Computers in Physics in 1994"
1,731 citations
236 citations
TL;DR: It is found that a proposed random number generator ran2 is a good one, but a number of generators are presented that are at least as good and are simpler, much faster, and with periods ‘‘billions and billions’’ of times longer.
Abstract: It is found that a proposed random number generator ran2, recently presented in the Numerical Recipes column [W. H. Press and S. A. Teukolsky, Comput. Phys. 6, 521–524 (1992)], is a good one, but a number of generators are presented that are at least as good and are simpler, much faster, and with periods ‘‘billions and billions’’ of times longer. They are presented not necessarily to supplant ran2, but to put it in perspective. Any serious user of Monte Carlo methods should have a variety of random number generators from which to choose. In addition to two specific programs, one in Fortran and one in C, a framework is offered within which the readers can easily fashion their own generators with periods ranging from 1027–10101.
75 citations
TL;DR: This paper presents a meta-modelling architecture for the Numerical Integration of Ordinary Differential Equations using a model based on the model developed in [Bouchut-Boyaval, M3AS, 2013].
Abstract: The Nature of Dynamic Systems. Basic Concepts in the Numerical Integration of Ordinary Differential Equations. Accuracy in the Numerical Integration of Ordinary Differential Equations. Stability in the Numerical Integration of Ordinary Differential Equations. Systems Modeled by Ordinary Differential Equations. Systems Modeled by First Order Partial Differential Equations. Systems Modeled by Second Order Partial Differential Equations. Systems Modeled by First/Second Order, Multidimensional andMultidomain Partial Differential Equations. Appendices 1-9. Index.
63 citations
TL;DR: Exploring the advantages of extending the powerful spreadsheet style of computation to multiple sets of images and organizing image processing tasks is the objective of the Interactive Image SpreadSheet project at Goddard Space Flight Center.
Abstract: New methods are needed for visualizing, interpreting, comparing, organizing, and analyzing immense multispectral satellite datasets. The traditional numerical spreadsheet paradigm has been extended to develop a new scientific visualization approach for processing multisensor image datasets interactively. Exploring the advantages of extending the powerful spreadsheet style of computation to multiple sets of images and organizing image processing tasks is the objective of the Interactive Image SpreadSheet (IISS) project at Goddard Space Flight Center. In the IISS each cell can display any portion of an original or calculated image, a projection of a multidimensional dataset such as a 3‐D surface, a glyph (graphic symbol) representing an image, digitized maps, digital terrain models, graphs, or vector drawings. The term image is used in a general sense to refer to any 2‐D multisource dataset. The IISS typically contains an array of image cells of arbitrary size each of which can contain one or more frames (images). The user can scroll or page through this multidimensional cube of frames along any dimension. The IISS emphasizes an immediate visual approach to interacting with data. A unique capability that the IISS provides are the highly interactive browsing tools, accessible through a graphical user interface, for effectively inspecting large sets of image arrays using synchronized cell level operations such as zoom, roam, animation, and function execution. The IISS combines the quantitative aspects of a numerical spreadsheet with powerful visualization tools to enable an investigator to easily experiment with various combinations of multispectral image data using a library of standard algorithms and to interactively develop custom algorithms. Remotely sensed datasets from multispectral instruments on satellites such as GOES, NOAA, Nimbus, DMSP, and Landsat have been used to develop and evaluate the functionality of the IISS. Formula expressions for creating color composites, implementing image enhancements, calculating vegetation indices, viewing perspective and stereo imagery have been developed using multispectral data. The IISS can also be used in a variety of imaging disciplines that routinely need to organize and manipulate large volumes of visual data including numerical simulation data, observational field data, astronomical imaging, biomedical imaging, computer vision and manufacturing robotics, business document imaging, and multimedia. The practical realization of the computationally challenging IISS project relies on the fact that personal superworkstations have become inexpensive enough that one can extend the interactive scalar spreadsheet concept to the image processing field. The hardware features that make this possible include multiple processors, large amounts of general purpose memory, high‐performance data buses, large mass storage, and pipelined or other advanced architectures for graphics and image operations. The need for increasingly more interactive imaging and visualization applications using high definition displays in collaborative environments will continue to drive the demand for more powerful hardware features and information network capabilities that are widely accessible.
54 citations
47 citations
TL;DR: The performance of C++ in solving physics problems is discussed and its ability to translate physics concepts into computer instructions may lead to fewer programming errors and greater productivity.
Abstract: The performance of C++ in solving physics problems is discussed. One of the attractive features of using C++ language is its ability to translate physics concepts into computer instructions. This may lead to fewer programming errors and greater productivity. (AIP)
43 citations
39 citations
TL;DR: The crystal field (CF) package applicable to orthorhombic or higher symmetry has been extended to enable calculations of energy levels and ligand field states for 3d N ions in crystals at arbitrary symmetry sites by taking into account the contributions of the ‘‘imaginary’’ CF terms.
Abstract: The crystal field (CF) package applicable to orthorhombic or higher symmetry has been extended to enable calculations of energy levels and ligand field states for 3d N ions in crystals at arbitrary symmetry sites by taking into account the contributions of the ‘‘imaginary’’ CF terms. The full Hamiltonian matrix, including the electrostatic terms, Trees correction, the spin–orbit interaction, and the ligand field terms, is diagonalized within the whole 3d N configuration. Several techniques based on the transformation properties of the crystal field Hamiltonian have been devised to test the package for internal consistency. The package is especially suitable for analysis of the low symmetry effects for transition metal ions at sites with the tetragonal and trigonal symmetry involving the imaginary CF terms as well as monoclinic and triclinic symmetry. It can be useful in analyzing the electron paramagnetic resonance spectra of 3d N ions and in correlating the ligand field parameters with the spin Hamiltonian parameters.
37 citations
TL;DR: It is argued that the rigorous use of expert systems and abstract data types for quantum chemical calculations can lead to a more open, more flexible program, which is easier for a novice to use but also, through the possibility of rapid prototyping and symbolic manipulation, for an expert to exploit as an important working tool.
Abstract: The case is argued that the rigorous use of expert systems and abstract data types for quantum chemical calculations can lead to a more open, more flexible program, which is easier for a novice to use but also, through the possibility of rapid prototyping and symbolic manipulation, for an expert to exploit as an important working tool. The ideas behind this program are, however, quite general and apply equally to many other scientific areas where experience and different numerical techniques have to be combined in a flexible way to produce useful results.
35 citations
TL;DR: In this article, an unconditionally stable, accurate, and efficient algorithm was proposed to solve the time-dependent Schrodinger equation for a particle moving in an inhomogeneous magnetic field.
Abstract: This paper introduces an unconditionally stable, accurate, and efficient algorithm to solve the time‐dependent Schrodinger equation for a particle moving in an inhomogeneous magnetic field. The algorithm is used to simulate a fundamental thought experiment of quantum mechanics: the magnetic Aharonov–Bohm effect. The calculations demonstrate that the Aharonov–Bohm prediction of the phase shift holds with great precision, even when the dimensions of the interferometer are comparable to the de Broglie wavelength of the particle.
TL;DR: In this article, a second-order finite-difference time domain (FDTD) algorithm was proposed to solve the wave equation on a coarse grid with a solution error less than 10−4 that of the conventional one.
Abstract: We introduce a new second‐order finite‐difference time‐domain (FDTD) algorithm to solve the wave equation on a coarse grid with a solution error less than 10−4 that of the conventional one. Although the computational load per time step is greater, it is more than offset by a large reduction in the number of grid points needed, while maintaining high accuracy, as well as by a reduction in the number of iterations. In addition, boundaries can be more accurately characterized at the subgrid level. This algorithm is based on a second‐order finite‐difference Laplacian that is nearly isotropic with respect to the wave propagation direction. Although optimum performance is achieved at a fixed frequency, the accuracy is still much higher than that of a conventional FDTD algorithm over ‘‘moderate’’ bandwidths.
TL;DR: The package TTC (Tools of Tensor Calculus) implements the majority of the basic tools of tensor and exterior calculus in a differentiable manifold using the point‐of‐view of the modern differential geometry (DG).
Abstract: The package TTC (Tools of Tensor Calculus) implements the majority of the basic tools of tensor and exterior calculus in a differentiable manifold using the point‐of‐view of the modern differential geometry (DG). It can be of interest to any physicist using DG, for research or teaching purposes, in relativity theory, mechanics, electromagnetism, thermodynamics, Hamiltonian theory, fluid dynamics, elementary particle physics, etc. It is written in the computer algebra language Mathematica, which gives the user a powerful environment. Emphasis has been put on using the full expression of tensors, on defining objects with no restrictions at all, and on using a close‐to‐textbook notation.
TL;DR: The implementation of the Lattice–Boltzmann method, a relatively new technique for computational fluid dynamics, on the IBM SP1 Scalable Parallel processor is discussed and sustained rates of almost 4 Gflops on high‐resolution simulations with up to nearly 800 million of degrees of freedom are demonstrated.
Abstract: We discuss the implementation of the Lattice–Boltzmann method, a relatively new technique for computational fluid dynamics, on the IBM SP1 Scalable Parallel processor. Sustained rates of almost 4 Gflops on high‐resolution simulations with up to nearly 800 million of degrees of freedom are demonstrated.
TL;DR: In this article, the authors investigated the sources for the nucleation coercivity and wall motion coercivity in magneto-optical recording thin films based on Connection Machine simulations and found that the wall motion is mostly caused by the fluctuation in the exchange stiffness constant and the patch-to-patch variations of the easy-axis orientation.
Abstract: The sources for the nucleation coercivity and wall motion coercivity in magneto‐optical recording thin films are investigated based on the Connection Machine simulations. It was assumed that the thin films consist of nanoscale patches which are magnetic structure other than columnar structure or crystal grains. The postulated inhomogeneities have not been observed directly, but we believe that magnetic structure must exist in view of the fact that the media suitable for practical applications do not have columnar structure and crystal grains, yet they exhibit coercivity phenomena which can only be caused by nanoscale inhomogeneities. The nucleation and wall motion processes were simulated in the patchy films with different types of inhomogeneities and with the average patch size ranging from 60 to 200 A. The simulation results show that the nucleation coercivity depends sensitively on the patch size characterizing the fluctuation of the anisotropy constant, but weakly on the exchange at the patch borders and the fluctuation of easy‐axis orientation. To account for the observed nucleation coercivity in magneto‐optical thin films the average patch size should be on the order of 100 A. In contrast, the wall motion coercivity is mostly caused by the fluctuation in the exchange stiffness constant and the patch‐to‐patch variations of the easy‐axis orientation. It was found that the domain wall, when encountering a high anisotropy region, first encircles it and then reverses its magnetization due to the domain wall force. This suggests a scenario other than thermal fluctuation by which a wall can go over a local energy barrier.
TL;DR: In this article, the Schrodinger equation is used to solve the problem of computing the potential energy surfaces of the H3 electronic structure of a triatomic system, focusing on the interaction potentials.
Abstract: The solution of the complete Schrodinger equation for scattering and electronic structure calculations is the objective of this work, focusing on the triatomic systems. The mathematical difficulties of solving the Schrodinger equation are analyzed, what can be done easily and what needs large scale computational work. An overview of basic atomic and molecular quantum mechanics is given, including how adiabatic and diabatic approximations are used in calculating scattering cross sections. Effective interaction potentials are discussed in detail, how to compute them and what they look like. Besides describing how computers have opened the door to real computation of the full spatial behavior of these multicomponent systems, some simple graphical images significantly aid the development of intuition of how the system actually behaves. The graphical representation focuses on the potential energy surfaces of the H3 electronic structure.
TL;DR: In this paper, the G and Γ function expansions of the solution of a perturbed linear system of ordinary differential equations are presented and implemented as the recursion relation for a one-step integrator.
Abstract: In this article we present in detail the G and Γ function expansions of the solution of a perturbed linear system of ordinary differential equations, and its implementation as the recursion relation for a one‐step integrator. The two first terms of this expansion offer an exact solution to the unperturbed system, a fact which makes the corresponding error for the solution of the perturbed system proportional to the strength of the perturbation. This contrasts with what is offered by popular algorithms, which is a flat response of the error with the perturbation strength. Accordingly, the scheme presented here provides a substantial gain in accuracy when it comes to detailed monitoring of very small deviations from the unperturbed orbit. Finally, we brush over its generalization to linear multistep algorithms.
TL;DR: The program RELAX3D is useful for the solution of the three‐dimensional, second‐order, elliptic partial differential equation, ∇2V(x,y,z)=F (x, y,z), which includes Laplace's equation and Poisson’s equation, and uses the finite‐difference algorithm known as symmetric successive over‐relaxation.
Abstract: The program RELAX3D is useful for the solution of the three‐dimensional, second‐order, elliptic partial differential equation, ∇2V(x,y,z)=F(x,y,z), which includes Laplace’s equation and Poisson’s equation. It uses the finite‐difference algorithm known as symmetric successive over‐relaxation. After a brief survey of other solution techniques, the program is described in detail and several examples of its actual use are given. The program is interactive and accurately solves for V according to the function F and the arbitrary boundary conditions, both supplied via the user‐encoded subroutine ‘‘BND.’’ The functions V and F are defined on grids of two or three dimensions, in Cartesian, cylindrical, or polar coordinates. To improve the efficiency of the repetitive five‐point or seven‐point relaxation iterations on the grid, conventional fortran array addressing is replaced by a fast hard‐coded addressing method. In the inner loop where the program spends most of its time, references to the V and F arrays are a...
TL;DR: RelLab, a computer‐based Relativity Laboratory designed to lead high school or introductory college physics students to a qualitative understanding of Special Relativity is described, and students demonstrated a level of qualitativeUnderstanding of relativity superior to that of the graduate students used in a previous study.
Abstract: RelLab, a computer‐based Relativity Laboratory designed to lead high school or introductory college physics students to a qualitative understanding of Special Relativity is described. RelLab is an open‐ended ‘‘construction kit’’ for building a wide variety of gedanken experiments. Students are posed problems by the teacher, usually in the form of paradoxes. They break into small groups to discuss the paradox, construct a gedanken experiment to try to understand and solve it, and then come together as a class to discuss their results. The effectiveness of the software and the pedagogical approach are evaluated by giving high school students a test problem drawn from the physics education literature. The students demonstrated a level of qualitative understanding of relativity superior to that of the graduate students used in a previous study.
TL;DR: This article used lattice gas cellular automata to study a buoyant mixture of hot and cold bubbles and found that, depending on the volume fraction of bubbles, the model can exhibit either a coarsening instability familiar from studies of sedimentation, or a convective instability similar to the large-scale flows of Rayleigh-Benard convection.
Abstract: Multiphase fluid mixtures present not only fascinating examples of nonequilibrium pattern formation, but also illustrate rather general questions concerning new emergent levels of organization. To illustrate these issues, we use lattice‐gas cellular automata to study a buoyant mixture of hot and cold bubbles. We find that, depending on the volume fraction of bubbles, the model can exhibit either a coarsening instability familiar from studies of sedimentation, or a convective instability similar to the large‐scale flows of Rayleigh–Benard convection.
TL;DR: The hardware and software of a 64‐node transputer‐based parallel processor used to study the photophysics and photochemistry of the image‐recording process in silver‐halide microcrystals in a film coating are described.
Abstract: Monte Carlo simulations are used to study the photophysics and photochemistry of the image‐recording process in silver‐halide microcrystals in a film coating. Because the microcrystals are independent of each other during exposure to light, the simulation is ideally suited to a parallel processor in which each processor represents a microcrystal in the film coating. This paper describes the hardware and software of a 64‐node transputer‐based parallel processor. Emphasis is placed on the O C C A M code used to distribute the simulation software over the transputer array and on how communications and computations are balanced in a multiprocessor system. Benchmarking results and preliminary data are also included.
TL;DR: It was found that graphics answer representations can be used to measure student understanding: students with correct graphics answers provide correct explanations and conversely.
Abstract: A computer program that presents and grades physics problems is described. The reliability of the grading is discussed in the context of diagnostic tests. The concept of computerized testing in physics is shown to be feasible. It was found that graphics answer representations can be used to measure student understanding: students with correct graphics answers provide correct explanations and conversely. The sample problem studied did not produce any false negative results; the only false positive results were caused by incomplete explanations which are easily caught by keyword checking.
TL;DR: A new, operator‐based algorithm for the calculation of Clebsch–Gordon coefficients for the group SU 3 is introduced, and an A N S I C program for its implementation is described.
Abstract: A new, operator‐based algorithm for the calculation of Clebsch–Gordon coefficients for the group SU 3 is introduced, and an A N S I C program for its implementation is described. The algorithm involves the use of raising and lowering operators in analogy to a standard pedagogical approach to the more familiar SU 2 Clebsch–Gordon coefficients. The nature of the approach makes the sign conventions utilized and the rules for resolution of the outer degeneracy explicit, and therefore allows straightforward changes to adapt the program to other choices. The program is written to allow its execution on personal computers of modest memory size, but also to take advantage of available memory allowing more complex results to be obtained on larger computing systems.