76 DS07 Abstracts CP1 exist in the neighbourhood of linear instability threshold A Note on the use of Lagrangian-Averaged Navier- for strongly non-Newtonian mud flows. Many bifurcation Stokes-Alpha Model for Wind-Driven Surface scenarios exhibited by the permanent wave equation ob- Waves tained at the second order approximation for film flows with moderate surface tension are identified, examined and The Lagrangian-averaged Navier-Stokes-α model was in- delineated in the parameter space and compared with the troduced in 1998. Since then, some developments have Newtonian results(R. Usha and B. Uma, Physics of Fluids, been made in mathematical and computational analysis of Vol 16, 2679-2696, 2004) the α-model. There, however, are few examples of the use of the model for real fluid problems. One of the obstacles R Usha is in the fact that the α-model is a system of fourth-order Professor, Department of Mathematics partial differential equations and needs additional bound- Indian Institute of Technology Madras, Chennai-36, India ary conditions for the well-posedness. We apply the α-
[email protected] model to the generation of sea surface waves by winds and illustrate that such conditions might not be feasible, when I. Mohammed Rizwan Sadiq the regularizing parameter α is constant. We try to consol- Research Scholar, Department of Mathematics idate the Lagrangian-averaging modeling concept and look Indian Institute of Technology Madras, Chennai 36, India for possible alternatives.
[email protected] Bong-Sik Kim Department of Mathematics and Statistics CP2 Arizona State University Drift-Diffusion Models for the Dynamics of Deci-
[email protected] sion Making Behavioral and neural data from humans and animals at- CP1 tempting to identify randomly-presented stimuli can be de- Resonant Surface Waves scribed by a simple stochastic differential equation: the drift-diffusion (DD) process.