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Macalester College Biological aggregations such as insect swarms, bird flocks, and fish schools are arguably some of the most common and least understood patterns in nature. In this talk, I will discuss recent work on swarming models, focusing on the connection between inter-organism social interactions and properties of macroscopic swarm patterns. The first model is a conservation-type partial integrodifferential equation (PIDE). Social interactions of incompressible form lead to vortex-like swarms. The second model is a high-dimensional ODE description of locust groups. The statistical-mechanical properties of the attractive-repulsive social interaction potential control whether or not individuals form a rolling migratory swarm pattern similar to those observed in nature. For the third model, we again return to a conservation-type PIDE and, via long- and short-wave analysis, determine general conditions that social interactions must satisfy for the population to asymptotically spread, contract, or reach steady state. |
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Florida A&M University TBA |
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Universität Würzburg We present a relaxation system for the Euler equations and for ideal MHD, from which one may derive approximate Riemann solvers. The solvers satisfy a discrete entropy inequality, and preserve positivity of density and pressure under a subcharacteristic condition. Next we consider the practical implementation, and derive explicit wave speed estimates satisfying the stability conditions. We put this into an astrophysical application by comparing our new positive and entropy stable approximate Riemann solver with state-of the-art algorithms for astrophysical fluid dynamics. This is joint work with F. Bouchut, W. Schmidt and K. Waagan. |
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Freie Universität Berlin TBA |
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University of Wyoming TBA |
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McGill University TBA |
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Georgia Tech TBA |
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University of Adelaide The emerging field of topological fluid kinematics is concerned with design and analysis of effective fluid mixers based on the topology of the motion of stirring apparatus and other periodic flow structures. Knowing even a small amount of flow topology often permits very powerful diagnoses, such as proving existence of chaotic dynamics and a lower bound on mixing measures based on material stretching. In this paper we present a canonical method for examining flows on surfaces of arbitrary genus given the flow topology encoded as a braid. The method may be used to study fluid mixing driven by an arbitrary number of stirrers in either bounded or spatially-periodic fluid domains. Additionally, and unlike previous techniques, the current work may also be applied to flows on manifolds of higher genus. |