In highly concentrated surfactant solutions the surfactant molecules self-assemble into long flexible "wormy" structures. Properties of these wormlike micellar solutions make them ideal for use in oil recovery and in body care products (shampoo). These properties depend strongly on temperature and concentration conditions.   In solution the "worms" entangle, forming a network, but also continuously break and reform, thus earning the name ‘living polymers’. In flow these fluids exhibit spatial inhomogeneities,  shear-banding, and dynamic elastic recoil. In this talk a rheological equation of state that is capable of describing these fluids is described   The resultant governing  macroscale equations consist of a coupled nonlinear partial differential equation system.  Model predictions are presented, contrasted with experimental results, and contrasted with predictions of other existing models.  Generalizations of the model to allow the capturing of  behaviors under changing concentration or temperature conditions, namely power law and stretched exponential relaxation as opposed to exponential relaxation, will be discussed and  particularly a mesoscale stochastic simulation network model will be presented.  

One general approach to random number generation is to take a uniformly distributed (0,1) random variable and then invert the cumulative distribution function (CDF) to generate samples from another distribution.  This talk follows this approach, approximating the inverse CDF for the Poisson distribution in a way which is particularly efficient for vector execution on NVIDIA GPUs.

I shall show that for every conjugacy class O in a connected semisimple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice S to the set of conjugacy classes in G such that O intersects S and dim O=codim S. The construction of the slice utilizes some new combinatorics related to invariant planes for the action of Weyl group elements in the reflection representation. The condition dim O=codim S is checked using some new mysterious results by Lusztig on intersection of conjugacy classes in algebraic groups with Bruhat cells.