Bulletin of the American Physical Society
2007 APS Four Corners Section/SPS Zone 16 Joint Fall Meeting
Volume 52, Number 14
Friday–Saturday, October 19–20, 2007; Flagstaff, Arizona
Session G4: Nonlinearity and Complexity |
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Chair: David Neilsen, Brigham Young University Room: Physical Sciences (Bldg. 19) Room 321 |
Saturday, October 20, 2007 8:15AM - 8:27AM |
G4.00001: Does it matter if I exercise? What can ``cardiophysics" tell us? Gus Hart, Benjamin Wilson, Allen Parcell Lower heart rates are often associated with better cardiovascular health. But there's a lot more to cardiac rhythms than just the average heart rate. Fractal analysis of inter-beat intervals shows a surprising ability to discriminate between healthy and unhealthy, young and old groups. Are the fluctuations in the heartbeat of a healthy heart random, small, periodic, or chaotic? Does exercise make a difference? We discuss our analysis of the cardiac data of two groups of individuals, those that were physically active and those that were sedentary. [Preview Abstract] |
Saturday, October 20, 2007 8:27AM - 8:39AM |
G4.00002: Fractal Hearts are Healthy Hearts---Are Fractal Companies Healthy Companies? Bronson Argyle, Gus Hart Fractal analyses of cardiac rhythms have implied that healthy individuals have complex cardiac behavior whereas aged or unhealthy individuals show either more random or more periodic behavior. Does this marker of ``complexity = health'' show up elsewhere? Can this technique be used in other fields as well? Particularly in the field of finance, can we use a similar approach to assess a corporation's financial health? It may be possible to find a similar relationship between a corporation's volatility and future share price, that is, between past corporate markers and future value-related indicators. Such an analysis may provide for more accurate risk aversion and allow us to predict future corporate health. [Preview Abstract] |
Saturday, October 20, 2007 8:39AM - 8:51AM |
G4.00003: Self-Organized Dynamic Flocking Behavior from a Simple Deterministic Map Wesley Krueger Coherent motion exhibiting large-scale order, such as flocking, swarming, and schooling behavior in animals, can arise from simple rules applied to an initial random array of self-driven particles. We present a completely deterministic dynamic map that exhibits emergent, collective, complex motion for a group of particles. Each individual particle is driven with a constant speed in two dimensions adopting the average direction of a fixed set of non-spatially related partners. In addition, the particle changes direction by $\pi$ as it reaches a circular boundary. The dynamical patterns arising from these rules range from simple circular-type convective motion to highly sophisticated, complex, collective behavior which can be easily interpreted as flocking, schooling, or swarming depending on the chosen parameters. We present the results as a series of short movies and we also explore possible order parameters and correlation functions capable of quantifying the resulting coherence. [Preview Abstract] |
Saturday, October 20, 2007 8:51AM - 9:03AM |
G4.00004: Nonlinear Differential Equation Reconstruction and Takens' Embedding Theorem Keith Warnick, Charles Tolle, John James In the study of nonlinear systems, creating an adequate model of the dynamics is a central and often difficult task. A trajectory method published by Perona et al. for generating systems of nonlinear differential equations modelling times series data has been developed into a MATLAB-based software application. Given a user-defined set of nonlinear basis functions, a system of equations is formed from linear combinations of these functions through an iterative optimization process. The trajectory method is demonstrated to be capable of accurately reconstructing several multidimensional and nonlinear systems using only time series data. The effects of noise on the reconstructed dynamics are investigated. Furthermore, how this method might be used to explore possible ways of identifying diffeormorphisms between time series and time-embedding representations of a dynamical system, which are guaranteed to exist by Takens' Embedding Theorem, will be discussed. [Preview Abstract] |
Saturday, October 20, 2007 9:03AM - 9:15AM |
G4.00005: Correlations of Couples Logistic Maps John Harrison Most systems in the world around us are non-linear and often chaotic. Moreover, many systems influence or are influenced by other physical systems. Understanding the behavior of coupled chaotic systems is essential to understanding the many facets of the physical world of our everyday experience. The simplest chaotic system, the logistic map, shows unusual correlations when coupled to second logistic map. We use a Master--Slave coupling, where the first map influences the second, but not the other way. We observe two forms of correlation between the master and slave due to coupling strength. With low coupling the correlations are complex and very interesting. With higher values of coupling the two maps ``lock'', becoming synchronized. I intend to discuss some of the intricacies of the correlations at low couplings. [Preview Abstract] |
Saturday, October 20, 2007 9:15AM - 9:27AM |
G4.00006: First order post-Newtonian analysis of a chaotic three-body problem. J.J. Campbell, Miriam Neubauer, David Tanner, David Neilsen In classical Newtonian gravity, the three-body problem is known to be chaotic for general initial data. We investigate the existence of chaos for the three-body problem in general relativity using the first post-Newtonian approximation. We examine the scattering of a third object from a binary pair, discuss solution methods, and present results suggestive of general relativistic chaos. [Preview Abstract] |
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