**November 14, 2007**

14:00-15:00, JR243

**Dr. Susana Serna**

Department of Mathematics, UCLA

**Title: High order accuracy in space for the numerical approximation of
hyperbolic conservation laws and Hamilton-Jacobi equations
**

Abstract: High order accurate shock capturing schemes are designed to
resolve complex shock dynamics with high accuracy in space and time
avoiding spurious oscillations near discontinuities. We analyze the use of
hyperbolas and parabolas as basic functions for the design of piecewise
smooth reconstruction procedures and discuss the advantage of applying
slope limiters to control the total variation growth. We propose the use
of "power" limiters to improve the behavior of the piecewise hyperbolic
method and the weighted essentially non-oscillatory (WENO) parabolic
method. We present a set of numerical experiments showing the different
approaches for Euler equations of gas dynamics. We extend the discussion
to the approximation of the viscosity solution of Hamilton-Jacobi
equations with applications to the level set reinitialization.

**October 31, 2007**

14:00-15:00, JR243

**Dr. Martin B. Short**

Department of Mathematics, UCLA

**Title: Fluids, Form, and Function: The role of fluid dynamics in the
evolution of stalactites, icicles, and aquatic
microorganisms
**

Abstract: ABSTRACT: Engineers designing such diverse objects as bicycle helmets,
automobile bodies, and ship hulls must carefully
consider how their product will interact with the fluids around it. In
fact, this unavoidable interaction often dictates
the object's form and how it will eventually function. Of course, mother
nature is not immune to this selective effect,
and the shapes and actions of many natural, everyday objects are similarly
determined by fluid dynamics. In this talk, I
will explore this phenomenon through the offbeat examples of stalactites,
icicles, and the family of Volvocalean green
algae. We shall discover how, through a synthesis of thin-film fluid
dynamics and calcium carbonate chemistry,
stalactites are all drawn toward a universal shape; how, because of
thermally buoyant boundary layers, icicles are drawn
toward this same shape; and how, through the use of their flagella,
species of Volvocalean algae were able to evolve to
ever larger sizes.

**October 10, 2007**

14:00-15:00, JR243

**Dr. Tom Chou**

Department of Biomathematics and Departmentt of Mathematics, UCLA

**Title: Simple Stochastic Problems in Biophysics**

Abstract: In this talk, two different applications of stochastic

processes in biophysics will be presented. The first will be the

development, analysis, and simulation of a simple one-dimensional

model for track-induced molecular motion. In contrast to molecular

motors that invoke a molecular conformational change to power their

biased motion, examples of track-propelled motion arise in biophysics.

Our simple model describes track-propelled motion in terms of

asymmetric nucleation of hydrolysis waves by coupling motion of a load

particle to moving domain walls. We use asymptotic analysis in a

moving frame to compute the dependence of the motor velocity as a

function of local hydrolysis rates and find a maximum velocity at

intermediate nucleation asymmetries. The second part of this talk will

a model for receptor-mediated virus adsorption and infection of cells.

Viruses are typically classified as being endocytotic or fusogenic,

with viruses that infect mammalian cells employing both entry

mechanisms. We develop the mathematics that model the stochastic

entry process as a competition between fusion and endocytosis. We find

the parameter regimes that determine which mechanism dominates.

**October 3, 2007**

14:00-15:00, JR215

**Dr. Vladislav Panferov**

Department of Mathematics, CSUN

**Title: On the Boltzmann equation in 1D in space**

Abstract: Solutions of the Boltzmann equation can be defined globally in

time using the concept of weak (renormalized) solutions. The problem of

regularity of such solutions is to a large extent still open. I will

discuss the case of solutions with one-dimensional spatial dependence

(plane waves) for which new apriori estimates are available. Such

estimates allow us to obtain strong solutions globally in time and to

describe propagation of regularity properties (derivatives, moments) in

the case of cutoff collision kernels.

**September 19, 2007**

14:00-15:00, JR215

**Dr. Jorge Balbas**

Department of Mathematics, CSUN

**Title: On the Steady State Solutions of Shallow Water Flows**

Abstract: The Saint-Venant equations, a system of PDEs commonly employed

for modeling geophysical flows, enjoys the existence of (physically

relevant) steady state solutions. A good understanding of these flows and

creating the tools for solving them will allow us to further investigate

the applications of the model and to validate existing numerical schemes

for more complex flows. In this talk I will present a summary of the

conditions that lead this type of flows, the tools we developed to compute

them (exactly), and discuss some applications. This work was conducted in

collaboration with S. Karni (U. of Michigan) and A. Wetzel (U. of

Michigan).

**September 12, 2007**

14:00-15:00, JR215

**Dr. Maria R. D'Orsogna**

Department of Mathematics, CSUN

**Title: PATTERNS, STABILITY AND COLLAPSE FOR TWO-DIMENSIONAL BIOLOGICAL**

SWARMS

Abstract: One of the most fascinating biological phenomena is the

self-organization of individual members of a species moving in unison with

one another, forming elegant and coherent aggregation patterns. Schools of

fish, flocks of birds and swarms of insects arise in response to external

stimuli or by direct interaction, and are able to fulfill tasks much more

efficiently than single agents. How do these patterns arise? What are

their properties? How are individual characteristics linked to collective

behaviors? In this talk we model a swarm as a non-linear system of self

propelled agents that interact via pairwise attractive and repulsive

potentials. We are able to predict distinct aggregation morphologies,

such as flocks and vortices, and by utilizing statistical mechanics tools,

to relate the interaction potential to the collapsing or dispersing

behavior of aggregates as the number of constituents increases. We also

discuss passage to the continuum and possible applications of this work to

the development of artificial swarming teams.

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