Seminars and Colloquiums
for the week of October 12, 2009
Speaker:
Dr. Diego del-Castillo-Negrete, Oak Ridge National Laboratory , Monday
Prof. Seddik Djouadi, Electrical Engineering, UTK, Monday
Elizabeth Johnson, Tuesday
Erin Bodine, Tuesday
Prof. Gilbert Weinstein, University of Alabama, Birmingham, Tuesday
Monday, October 12
PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 132
SPEAKER: Dr. Diego del-Castillo-Negrete, Oak Ridge National Laboratory
TITLE: "Fractional diffusion models: statistical basis and applications"
ABSTRACT: The statistical basis of generalized fractional diffusion models of anomalous transport is discussed in the framework of the Continuous Time Random Walk (CTRW). Starting from the CTRW for general Levy jump stochastic processes in the Levy-Khintchine representation we derive an integro-differential equation describing transport in the long-wavelength (macroscopic) limit. For the special cases of Gaussian and alpha-stable processes the equation reduces to the diffusion and the standard fractional diffusion equations respectively. However, the general equation allows the incorporation of a richer class of stochastic processes. As a specific example we consider exponentially tempered Levy processes and propose a transport model based on exponentially truncated fractional derivatives. We study the interplay of memory, long jumps, and tempering effects in the intermediate asymptotic regime. Applications to turbulent transport in fluids and plasmas and to nonlinear reaction-diffusion systems of interest to chemistry and biology are presented.
DE/APPLIED MATH & COMPUTATIONAL SCIENCE SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 112
SPEAKER: Prof. Seddik Djouadi, Electrical Engineering, UTK
TITLE: “On the Optimality of the Proper Orthogonal Decomposition and
Balanced Truncation with Application to a Nonlinear Convective Flow”
ABSTRACT: Two important model reduction methods the proper orthogonal decomposition (POD), also known as the Karhunen-Loeve decomposition or principal component analysis, and balanced truncation, are shown to be optimal in the sense of distance minimization in spaces of Hilbert- Schmidt or trace-class 2 integral operators. In particular, both POD and balanced truncation are shown to be optimal approximations by finite rank operators in the Hilbert-Schmidt norm. Optimality of balanced truncation seems to have been overlooked in the literature. Furthermore, the role of POD and balanced truncation in minimizing different n-widths of specific compact operators is discussed. The n-widths quantify inherent and representation errors due to lack of data or inaccurate measurements and loss of information. The methods are applied to a nonlinear convective flow governed by the two-dimensional Burgers' equation. This scalar equation is chosen because it has a nonlinearity that is similar to the Navier-Stokes equation, but can be accurately simulated using far fewer states. However, the number of states required is still too high for controller design purposes. The combination of POD and balanced truncation approaches results in a reduced order model that captures the dynamics of the input-output system.
Tuesday, October 14
MATH ECOLOGY SEMINAR
TIME: 9:00 – 9:50 a.m.
ROOM: NIMBioS small conference room
SPEAKER: Elizabeth Johnson
Title: “Habitat placement for the black-tailed prairie dog”
GRADUATE STUDENT FORUMS
TIME: 3:30-4:30pm
PLACE: Temple 303
SPEAKER: Erin Bodine
TITLE: "LaTeX Seminar #3 - Graphics in LaTeX"
MATHEMATICS COLLOQUIUM
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Prof. Gilbert Weinstein, University of Alabama, Birmingham
TITLE: “Mass inequalities in general relativity”
ABSTRACT: We will survey a number of results giving lower bounds on the mass of initial data in terms of other geometrical and physical quantities such as the area of the outermost horizon, and the total charge.
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Steve Wise.
Week of:
Past notices:
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year