A computationally tractable version of the collective model

A computationally tractable version of the Bohr-Mottelson collective model is presented which makes it possible to diagonalize realistic collective models and obtain convergent results in relatively small appropriately chosen subspaces of the collective model Hilbert space. Special features of the proposed model is that it makes use of the beta wave functions given analytically by the softened-beta version of the Wilets-Jean model, proposed by Elliott et al., and a simple algorithm for computing SO(5) > SO(3) spherical harmonics. The latter has much in common with the methods of Chacon, Moshinsky, and Sharp but is conceptually and computationally simpler. Results are presented for collective models ranging from the sherical vibrator to the Wilets-Jean and axially symmetric rotor-vibrator models.Comment: 16 pages, 9 figure

The collective computing model

The parallel computing model used in this paper, the Collective Computing Model (CCM), is a variant of the well-known Bulk Synchronous Parallel (BSP) model. The synchronicity imposed by the BSP model restricts the set of available algorithms and prevents the overlapping of computation and communication. Other models, like the LogP model, allow asynchronous computing and overlapping but depend on the use of specific libraries. The CCM describes a system exploited through a standard software platform providing facilities for group creation, collective operations and remote memory operations. Based in the BSP model, two kinds of supersteps are considered: Division supersteps and Normal supersteps. The structure of divisions produced by the Division Functions and the partnership relation among processors give place to communication patterns among processors that are topologically similar to a hypercube. We have named the resulting structures Dynamic Polytopes To illustrate these concepts, the Fast Fourier Transform Algorithm is used. Computational results prove the accuracy of the model in four different parallel computers: a Parsytec Power PC, a Cray T3E, a Silicon Graphics Origin 2000 and a Digital Alpha Server.Facultad de Informátic

Design and Evaluation of a Collective IO Model for Loosely Coupled Petascale Programming

Loosely coupled programming is a powerful paradigm for rapidly creating higher-level applications from scientific programs on petascale systems, typically using scripting languages. This paradigm is a form of many-task computing (MTC) which focuses on the passing of data between programs as ordinary files rather than messages. While it has the significant benefits of decoupling producer and consumer and allowing existing application programs to be executed in parallel with no recoding, its typical implementation using shared file systems places a high performance burden on the overall system and on the user who will analyze and consume the downstream data. Previous efforts have achieved great speedups with loosely coupled programs, but have done so with careful manual tuning of all shared file system access. In this work, we evaluate a prototype collective IO model for file-based MTC. The model enables efficient and easy distribution of input data files to computing nodes and gathering of output results from them. It eliminates the need for such manual tuning and makes the programming of large-scale clusters using a loosely coupled model easier. Our approach, inspired by in-memory approaches to collective operations for parallel programming, builds on fast local file systems to provide high-speed local file caches for parallel scripts, uses a broadcast approach to handle distribution of common input data, and uses efficient scatter/gather and caching techniques for input and output. We describe the design of the prototype model, its implementation on the Blue Gene/P supercomputer, and present preliminary measurements of its performance on synthetic benchmarks and on a large-scale molecular dynamics application.Comment: IEEE Many-Task Computing on Grids and Supercomputers (MTAGS08) 200

The SU(2) Skyrme model and anomaly

The SU(2) Skyrme model,expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. In this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure.Comment: 6 pages, Revtex. Final version to be published in Physics Letters

Cellular Automata Can Reduce Memory Requirements of Collective-State Computing

Various non-classical approaches of distributed information processing, such as neural networks, computation with Ising models, reservoir computing, vector symbolic architectures, and others, employ the principle of collective-state computing. In this type of computing, the variables relevant in a computation are superimposed into a single high-dimensional state vector, the collective-state. The variable encoding uses a fixed set of random patterns, which has to be stored and kept available during the computation. Here we show that an elementary cellular automaton with rule 90 (CA90) enables space-time tradeoff for collective-state computing models that use random dense binary representations, i.e., memory requirements can be traded off with computation running CA90. We investigate the randomization behavior of CA90, in particular, the relation between the length of the randomization period and the size of the grid, and how CA90 preserves similarity in the presence of the initialization noise. Based on these analyses we discuss how to optimize a collective-state computing model, in which CA90 expands representations on the fly from short seed patterns - rather than storing the full set of random patterns. The CA90 expansion is applied and tested in concrete scenarios using reservoir computing and vector symbolic architectures. Our experimental results show that collective-state computing with CA90 expansion performs similarly compared to traditional collective-state models, in which random patterns are generated initially by a pseudo-random number generator and then stored in a large memory.Comment: 13 pages, 11 figure

The unified Skyrmion profiles and Static Properties of Nucleons

An unified approximated solution for symmetric Skyrmions was proposed for the SU(2) Skyrme model for baryon numbers up to 8,which take the hybrid form of a kink-like solution and that given by the instanton method. The Skyrmion profiles are examined by computing lowest soliton energy as well as the static properties of nucleons within the framework of collective quantization, with a good agreement with the exact numeric results. The comparisons with the previous computations as well as the experimental data are also given.Comment: 6 pages, 3 figures, 3 tables, Created by LaTex Syste

CUDA simulations of active dumbbell suspensions

We describe and analyze CUDA simulations of hydrodynamic interactions in active dumbbell suspensions. GPU-based parallel computing enables us not only to study the time-resolved collective dynamics of up to a several hundred active dumbbell swimmers but also to test the accuracy of effective time-averaged models. Our numerical results suggest that the stroke-averaged model yields a relatively accurate description down to distances of only a few times the dumbbell's length. This is remarkable in view of the fact that the stroke-averaged model is based on a far-field expansion. Thus, our analysis confirms that stroke-averaged far-field equations of motion may provide a useful starting point for the derivation of hydrodynamic field equations.Comment: 16 pages, 4 figure