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Saverio Spagnolie, Brown

Hydrodynamics of Self-Propulsion Near a Boundary: Construction of a Numerical and Asymptotic Toolbox

The swimming kinematics and trajectories of many microorganisms are altered by the presence of nearby boundaries, be they solid or deformable, and often in perplexing fashion. When an organism's swimming dynamics vary near such boundaries a question arises naturally: is the change in behavior fluid mechanical, biological, or perhaps due to other physical laws? We isolate the first possibility by exploring a far-field description of swimming organisms, providing a general framework for studying the fluid-mediated modifications to swimming trajectories. Using the simplified model we consider trapped/escape trajectories and equilibria for model organisms of varying shape and propulsive activity. This framework may help to explain surprising behaviors observed in the swimming of many microorganisms and synthetic micro-swimmers. Along the way, we will discuss the numerical tools constructed to analyze the problem of current interest, but which have considerable potential for more general applicability.

Ari Stern, UC San Diego

Numerical analysis beyond Flatland: semilinear PDEs and problems on manifolds


Shamgar Gurevich, UW-Madison

Channel Estimation in Wireless Communication in Linear Time

We will present the model of mobile communication, and will discuss the problem of channel estimation -- finding time-frequency shifts which a waveform undergoes while transmitted in the presence of a white noise. The digital model of the problem involves signals of length N (complex-valued vectors of length N). The current method of solving digital channel estimation problem uses O(N^2 log(N)) arithmetic operations. Using ideas from representation theory, we will present a new method of solving channel estimation problem of complexity O(N log(N)). The applications of the new method to mobile communication and GPS system will be discussed.

This is a joint work with A. Fish (Math, UW-Madison), R. Hadani (Math, UT-Austin), A. Sayeed (ECE, UW-Madison), O. Schwartz (EECS, UC Berkeley).

Mike Cullen, Met. Office, UK

Applications of optimal transport to geophysical problems

The optimal transport method can be applied to a number of important problems in geophysical fluid dynamics, including large-scale flows in the atmosphere and ocean, equatorial waves, and the one-dimensional convective adjustment problem. In this talk I go through the basic procedures. The problem to be solved has to conserve mass and energy. The mass distribution is then regarded as a probability measure, and a metric on the space of probability measures defined (usually the Wasserstein distance). This is used via the 'Otto calculus' to define derivatives of the energy with respect to changes in the mass distribution. In the problems listed above, the governing equations can be solved by finding energy minimisers in this sense. Optimal transport theory can then be used to prove existence of minimisers. If the flow evolution can now be expressed as transport of mass by a rotated gradient, then the general theory of Ambrosio and Gangbo proves that solutions exist for all times.

Ricardo Cortez, Tulane



Michael Graham, UW-Madison Engineering



Lukas Szpruch, Oxford



Dwight Barkley, Warwick



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