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ABSTRACT: Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures. The visual inspection of these maps reveals a remarkable topological picture consisting of fixed (or periodic) points embedded in so-called island chains, invariant manifolds, and regions of ergodic behavior. This paper is concerned with the effective visualization and precise topological analysis of area-preserving maps with two degrees of freedom from numerical or analytical data. Specifically, a method is presented for the automatic extraction and characterization of fixed points and the computation of their invariant manifolds, also known as separatrices, to yield a complete picture of the structures present within the scale and complexity bounds selected by the user. This general approach offers a significant improvement over the visual representations that are so far available for area-preserving maps. The technique is demonstrated on a numerical simulation of magnetic confinement in a fusion reactor.
IEEE transactions on visualization and computer graphics. 12/2011; 17(12):1765-74.
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ABSTRACT: In this technical note we show the promise of using graphic processing units (GPUs) to accelerate simulations of electrical wave propagation in cardiac tissue, one of the more demanding computational problems in cardiology. We have found that the computational speed of two-dimensional (2D) tissue simulations with a single commercially available GPU is about 30 times faster than with a single 2.0 GHz Advanced Micro Devices (AMD) Opteron processor. We have also simulated wave conduction in the three-dimensional (3D) anatomic heart with GPUs where we found the computational speed with a single GPU is 1.6 times slower than with a 32-central processing unit (CPU) Opteron cluster. However, a cluster with two or four GPUs is faster than the CPU-based cluster. These results demonstrate that a commodity personal computer is able to perform a whole heart simulation of electrical wave conduction within times that enable the investigators to interact more easily with their simulations.
Medical & Biological Engineering 09/2009; 47(9):1011-5. · 1.76 Impact Factor
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ABSTRACT: Important elements of supply and demand are starkly observable in professional athletics. Demand affects how pay varies with personal productivity, racial discrimination, the nature of factor substitutions, and player mobility. Property rights affect the supply of athletic talent, arms races and incentives to restrict competition. In sports, excess incentives to win can create negative externalities. Collective agreements such as reverse-order drafts, payroll caps and revenue sharing constrain these forces, but redistribute rents from talented players to owners because they punish success. The European approach--promoting better-performing teams and relegating those with the poorest records--punish failure.
Economic Journal. 02/2001; 111(469):47-68.
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ABSTRACT: Many interesting elements of supply and demand are starkly observable in professional athletics. Understanding institutional arrangements, competitive balance and labor-management relations requires a basic understanding of sports labor markets and the struggle for control of those markets between interest groups. In this paper we treat historical and contemporary labor issues in North America and Europe, from reserve rules and free agency, high levels of player pay and work stoppages, to the distribution of playing talents across teams. We discuss the relationship between personal productivity and pay; relative versus absolute demand; competitive and cooperative interactions across firms (teams); factor substitutions; player mobility and the Coase theorem. We briefly consider how property rights affect supply, athletic talent, arms races and restrictions on competition. The problem of (excess) incentives to compete leading to externalities and inefficiencies are noted throughout the paper. Restrictive agreements such as reverse-order drafts, payroll caps and revenue sharing may constrain these forces, but they also redistribute rents from players to owners. All of these schemes, in one way or another, punish success. The European approach -- promotion of better-performing teams and relegation of those with the poorest records -- punishes failure. It remains an interesting economic question as to which system is better.
03/2000;
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ABSTRACT: In the study of a magnetic confinement fusion device such as a tokamak, physicists need to understand the topology of the flux (or magnetic) surfaces that form within the magnetic field. Among the two distinct topological structures, we are particularly interested in the magnetic island chains which correspond to the break up of the ideal rational surfaces. Different from our previous method [12], in this work we resort to the periodicity analysis of two distinct functions to identify and characterize flux surfaces and island chains. These two functions are derived from the computation of the fieldlines and puncture points on a Poincaré section, respectively. They are the distance measure plot and the ridgeline plot. We show that the periods of these two functions are directly related to the topology of the surface via a resonance detection (i.e. period estimation and the common denomi-nators computation). In addition, we show that for an island chain the two functions possess resonance components which do not occur for a flux surface. Furthermore, by combining the periodicity analysis of these two functions, we are able to devise a heuristic yet robust and reliable approach for classifying and characterizing different magnetic surfaces in the toroidal magnetic fields.
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ABSTRACT: In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.
IEEE Transactions on Visualization and Computer Graphics 16(6):1431-40. · 2.21 Impact Factor
