Curvature Fields, Topology, and the Dynamics of Spatiotemporal Chaos

The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.Comment: 5 pages, 5 figure

Transient spatiotemporal chaos on complex networks

Thesis (M.S.) University of Alaska Fairbanks, 2004Some of today's most important questions regard complex dynamical systems with many interacting components. Network models provide a means to gain insight into such systems. This thesis focuses on a network model based upon the Gray-Scott cubic autocatalytic reaction-diffusion system that manifests transient spatiotemporal chaos. Motivated by recent studies on the small-world topology discovered by Watts and Strogatz, the network's original regular ring topology was modified by the addition of a few irregular connections. The effects of these added connections on the system's transience as well on the dynamics local to the added connections were examined. It was found that the addition of a single connection can significantly effect the transient time of spatiotemporal chaos and that the addition of two connections can transform the system's spatiotemporal chaos from transient to asymptotic. These findings suggest that small modifications to a network's topology can greatly affect its behavior.Introduction -- Background -- Transient spatiotemporal chaos in the presence of one shortcut -- Local dynamics in the vicinity of a shortcut -- Conclusion -- Bibliography

This elusive objective existence

Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of objective existence in two ways. The elimination of these prejudices makes it possible to recognize the quantum formalism's ontological implications - the relative and contingent reality of spatiotemporal distinctions and the extrinsic and finite spatiotemporal differentiation of the physical world - which in turn makes it possible to arrive at an unqualified objective existence. Contrary to a widespread misconception, viewing the quantum formalism as being fundamentally a probability algorithm does not imply that quantum mechanics is concerned with states of knowledge rather than states of Nature. On the contrary, it makes possible a complete and strongly objective description of the physical world that requires no reference to observers. What objectively exists, in a sense that requires no qualification, is the trajectories of macroscopic objects, whose fuzziness is empirically irrelevant, the properties and values of whose possession these trajectories provide indelible records, and the fuzzy and temporally undifferentiated states of affairs that obtain between measurements and are described by counterfactual probability assignments.Comment: To appear in IJQI; 21 pages, LaTe

Basic gestures as spatiotemporal reference frames for repetitive dance/music patterns in samba and charleston

THE GOAL OF THE PRESENT STUDY IS TO GAIN BETTER insight into how dancers establish, through dancing, a spatiotemporal reference frame in synchrony with musical cues. With the aim of achieving this, repetitive dance patterns of samba and Charleston were recorded using a three-dimensional motion capture system. Geometric patterns then were extracted from each joint of the dancer's body. The method uses a body-centered reference frame and decomposes the movement into non-orthogonal periodicities that match periods of the musical meter. Musical cues (such as meter and loudness) as well as action-based cues (such as velocity) can be projected onto the patterns, thus providing spatiotemporal reference frames, or 'basic gestures,' for action-perception couplings. Conceptually speaking, the spatiotemporal reference frames control minimum effort points in action-perception couplings. They reside as memory patterns in the mental and/or motor domains, ready to be dynamically transformed in dance movements. The present study raises a number of hypotheses related to spatial cognition that may serve as guiding principles for future dance/music studies