Gene Cooperman

Geant4 developments and applications

Geant4 is a software toolkit for the simulation of the passage of particles through matter. It is used by a large number of experiments and projects in a variety of application domains, including high energy physics, astrophysics and space science, medical physics and radiation protection. Its functionality and modeling capabilities continue to be extended, while its performance is enhanced. An overview of recent developments in diverse areas of the toolkit is presented. These include performance optimization for complex setups; improvements for the propagation in fields; new options for event biasing; and additions and improvements in geometry, physics processes and interactive capabilities

Self‐pulsing and chaos in distributed feedback bistable optical devices

We show that the light transmitted by a nonlinear distributed feedback structure can be steady (time independent), periodic, or chaotic depending on the intensity of the input cw beam. The feasibility of an experimental demonstration of such behavior is discussed.

A New Current-Voltage Relation for Duct Precipitators Valid for Low and High Current Densities

A closed-form analytic current-voltage formula for duct electrostatic precipitators is presented. A short discussion of previous theoretical and numerical solutions is given, followed by an explanation of the theoretical formula derived here. A comparison with experimental data is then given, showing that the present formula is accurate over a wide range of conditions, including wide plate spacing.

New methods for using Cayley graphs in interconnection networks

Abstract A number of researchers have proposed Cayley graphs and Schreier coset graphs as models for interconnection networks. New algorithms are presented for generating Cayley graphs in a more time-efficient manner than was previously possible. Alternatively, a second algorithm is provided for storing Cayley graphs in a space-efficient manner (log 2 (3) bits per node), so that copies could be cheaply stored at each node of an interconnection network. The second algorithm is especially useful for providing a compact encoding of an optimal routing table (for example, a 13 kilobyte optimal table for 64,000 nodes). The algorithm relies on using a compact encoding of group elements known from computational group theory. Generalizations of all of the above are presented for Schreier coset graphs.

Close pair queries in moving object databases

Databases of moving objects are important for air traffic control, ground traffic, and battlefield configurations. We introduce the (historical and spatial) range close-pair query for moving objects as an important problem for such databases. The purpose of a range close-pair query for moving objects is to find pairs of objects that were closer than ε during time interval

STAR/MPI: binding a parallel library to interactive symbolic algebra systems

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Constructing Permutation Representations for Matrix Groups

and within spatial range R, where ε, I and R are user-specified parameters.This paper solves the range close-pair query using two components: the retrieval component and the close-pair identification component. The retrieval component breaks up long trajectories into trajectory segments, which are produced in increasing time order, without the need for sorting. The retrieval component takes advantage of a new index mechanism, the Multiple TSB-tree. The segments are then pipelined to the close-pair identification component. The identification component introduces a novel spatial sweep that sweeps by time and one spatial dimension at the same time. Extensive experimental results are provided, demonstrating the advantages of the new approach when considering close pairs.

Nearly linear time algorithms for permutation groups with a small base

Many users of symbolic algebra systems have felt the need for greater CPU power. Yet few of them have ventured into parallel programming due to the steep learning curve and the unfamiliar programming environment entailed by such an effort. In an attempt to remedy that situation, the parallel library MPI has been integrated into both GCL (GNU Common LISP) and GAP [14] (a general purpose language for mathematical group theory). These implementations are examples that extend bindings of MPI to interactive languages. (MPI already has bindings to the compiled languages C and FORTRAN.) Further, this binding to an interactive language retains the interactive environment during execution. Further, STAR/MPI represents a blueprint for binding MPI to other interactive languages besides GCL and GAP, from which comes the name STAR/MPI, or */MPI. STAR/MPI includes a simple SPMD architecture on top of this MPI binding. An important class of sequential algorithms is described that can be parallelized with little effort using STAR/MPI architecture. Since GAP is representative of systems for discrete mathematics and LISP is the basis for several symbolic algebra systems with strengths in nondiscrete mathematics, it is hoped to gain broad feedback on the issues involved. Although vendor-specific, interactive, parallel languages exist, this appears to be the first attempt at defining a binding of a vendor-independent, portable, pmallel library to arbitrary interactive languages.

TOP-C: a task-oriented parallel C interface

New techniques, both theoretical and practical, are presented for constructing permutation representations for computing with matrix groups defined over finite fields. The permutation representation is constructed on a conjugacy class of subgroups of prime order. We construct a base for the permutation representation, which in turn simplifies the computation of a strong generating set. In addition, we present an elementary test for checking the simplicity of the permutation image. The theory has been successfully tested on a representation of the sporadic simple groupLy, discovered by Lyons(1972). With noa prioriassumptions, we find a permutation representation of degree 9606125 on a conjugacy class of subgroups of order 3, find the order of the resulting permutation group, and verify simplicity. A Monte Carlo variation of the algorithm was used to achieve better space and time efficiency. The construction of the permutation representation required four CPU days on a SPARCserver 670MP with 64 MB. The permutation representation was used implicitly in the sense that the group element was stored as a matrix, and its permutation action on a “point” was determined using a pre-computed data structure. Thus, additional computations required little additional space. The algorithm has also been implemented using the MasPar MP-1 SIMD parallel computer and 8 SPARC-2s running under MPI. The results of those parallel experiments are briefly reviewed.

A unified efficiency theory for electrostatic precipitators

A base of a permutation group G is a subset B of the permutation domain such that only the identity of G fixes B pointwise. The permutation representations of important classes of groups, including all finite simple groups other than the alternating groups, admit O(log n) size bases, where n is the size of the permutation domain. Groups with very small bases dominate the work on permutation groups in much of computational group theory. A series of new combinatorial results allows us to present Monte Carlo algorithms achieving O(n log’ n) (c a constant) time and space performance for such groups with respect to the fundamental operations of finding order and testing membership. (The input is a list of generators of the group.) Previous methods have achieved similar space performance only at the expense of increased time performance. Adaptations of a ‘(cube-doubling” technique [BSZ] and a local expansion property of groups [Ba3] (cf. [Ba4]) are the key to theoretically reducing the time complexity to O(rI log’ n.). The shared principal novelty of the new ideas is in their abilitv to build and manitmlate certain chains of subsets of a grou~, which are not themselves subgroups, in order to build the point stabilizer subgroup chain. Further combinatorial ideas are used to lower the constant c. Comparative timing estimates, based on asymptotic worst-case analysis, lead us to expect a new implementation to be faster than previous implementations for groups of high degree.