Seminars and Colloquiums
for the week of January 28, 2013
Speakers:
Dr. Abner Salgado, Univ of Maryland, College Park, Monday
Prof. Stefan Richter, Wednesday
Mr. Kyle Austin, Thursday
Dr. Matthew “Nick” Moore, Courant Institute, Thursday
*** Tea Time this week will be Wednesday & Friday at 3:00 pm.
Hosted this week by Parisa Fatheddin. Everyone is welcome! ***
MONDAY, JANUARY 28
COLLOQUIUM
TIME: 3:35 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Abner Salgado, Univ of Maryland, College Park
TITLE: Discrete total variation flows without regularization and applications
ABSTRACT: We propose and analyze an algorithm for the solution of the L2-subgradient flow of the total variation (TV) functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivates the use of this type of energy both in imaging and materials sciences. We derive L2 error estimates under minimal regularity assumptions, and introduce a TV-diminishing interpolation operator which yields improved error bounds. We also propose an iterative scheme for the solution of the ensuing discrete problems and analyze it. This methodology extends to the TV functional augmented with a strictly convex functional, such as a p-Laplacian term. We discuss several numerical experiments which illustrate the power and potentials of the method, and explore a model arising in materials science.
Refreshments will be available at 3:15 p.m.
WEDNESDAY, JANUARY 30
ANALYSIS SEMINAR
TIME: 3:35 – 4:30 p.m.
ROOM: Ayres 112
SPEAKER: Prof. Stefan Richter
TITLE: Weak products of spaces of analytic functions
THURSDAY, JANUARY 31
TOPOLOGY SEMINAR
TIME: 9:40 a.m. – 10:30 a.m.
ROOM: Ayres Hall B004
Speaker: Kyle Austin
Title: Partitions of Unity - 2
Abstract: The purpose of this presentation is to introduce partitions of unity and their applications to topology and analysis. This should give an interesting new point of view for normal and paracompact spaces. The presentation will follow the paper "Partitions of Unity" by Jerzy Dydak. In particular, we will use partitions of unity to prove variants of Teitze Extension Theorem which in turn will be used to prove some classical results about normal and paracompact spaces. The notion of equicontinuous partitions of arbitrary functions will be introduced. We will use this idea to create certain partitions of unity with nice properties and to give a useful characterization of when a normal space is paracompact.
COLLOQUIUM
TIME: 3:35 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Matthew “Nick” Moore, Courant Institute
TITLE: Semi-analytical models for fluids interacting with structures
ABSTRACT: Reduced models can lend unique insight into physical phenomena by stripping away all but the most essential principles. I will discuss the use of such models in the context of two fluid-structure problems. First, I will discuss motion in viscoelastic fluids. These fluids store and release elastic energy, leading to motion that is characteristically unsteady. A canonical example is the gravitational settling of body, in which terminal velocity is exceeded on a transient timescale. We have recently developed a "weak-coupling" method that gives semi-analytical solutions to this classical problem and other more complicated problems. I will discuss a biologically-inspired extension in which the body is propelled by an oscillating force, intended to mimic a swimming stroke. Secondly, I will discuss the erosion of bodies by fluid flow. Inspired by natural examples such as the formation of landforms, our study focuses on the mutual interaction between changing shape and flow. Table-top experiments of soft-clay in flowing water reveal the formation of sharp corners and facets, contrary to the common notion that erosion tends to smooth bodies. We appeal to a semi-analytical flow-model that combines an outer flow with a boundary layer flow in order to rationalize these observations and make new predictions.
Refreshments will be available at 3:15 p.m.
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 colloquium AT math DOT utk DOT edu
Past notices:
Seminars from 2011-2012 academic year
Seminars from 2010-2011 academic year
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year