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Seminars and Colloquiums
for the week of November 14, 2016


Ryan Jensen, UTK, Monday
Morgan Roche and Rebecca Pettit, UTK, Monday
Le Chen, University of Kansas, Tuesday
Yue Yu, Lehigh University, Wednesday
Michael Morgan Wise, UTK Thursday
Peter Perry, University of Kentucky, Thursday
Hakima Bessaih, University of Wyoming, Friday

3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401

Hosted by: ???

Monday, November 14th

TITLE: Asymptotic dimension for non-metric spaces
SPEAKER: Ryan Jensen, UTK
TIME: 2:30pm – 3:20pm
ROOM: Ayres 114
Asymptotic dimension is an important coarse property. For coarse metric spaces, there are several useful definitions, which were assembled and shown to be equivalent by G. Bell and A. Dranishnikov. In this talk, we generalize some of these definitions to non-metric coarse spaces. We begin by giving some needed background information concerning coarse spaces. Next we state a definition, originally by J. Dydak and {\v{Z}}. Virk, of asymptotic dimension suitable for non-metric spaces. Finally we extend a result of J. Dydak and {\v{Z}}. Virk, which will give another definition of asymptotic dimension for non-metric spaces.

TITLE: Discussion and Presentation of two student projects
SPEAKER: Morgan Roche and Rebecca Pettit, UTK
TIME: 2:30pm – 3:20pm
ROOM: Ayres G003

Tuesday, November 15th

TITLE: Regularity and positivity of densities for the stochastic (fractional) heat equation
SPEAKER: Le Chen, University of Kansas
TIME: 2:10pm – 3:25pm
ROOM: Ayres 114
In this talk, I will present a recent study on the density of the solution to a semilinear stochastic (fractional) heat equation (SHE), which includes the parabolic Anderson model as a special case. In the first part, we prove that the solution to a semilinear SHE with measure-valued initial data has a smooth joint density at multiple points. This result extends the work by Mueller and Nualart [EJP'08] from the density at single point to the joint density at multiple points and from function-valued initial data to more general initial data. This is achieved by proving that solutions to a related stochastic partial differential equation have negative moments of all orders. In the second part, we establish the strict positivity of the density in the interior of the support of the joint law. This result extends the known results to allow measure-valued initial data and unbounded diffusion coefficient.

This talk is based on a joint work with Yaozhong Hu and David Nualart.

Wednesday, November 16th

TITLE: Stabilized numerical methods for fluid-structure interactions with application in vascular blood flow simulations
SPEAKER: Yue Yu, Lehigh University
TIME: 3:35pm – 4:35pm
ROOM: Ayres 113
In this work, we consider the partitioned approach for fluid-structure interactions, and we develop new stabilized algorithms. There are two approaches in formulating the discrete systems in simulating fluid-structure interaction (FSI) problems: the monolithic approach, and the partitioned approach. The former is efficient for small problems but does not scale up to realistic sizes, whereas the latter suffers from numerical stability issues. In particular, in vascular blood flow simulations where the mass ratio between the structure and the fluid is relatively small, the partitioned approach gives rise to the so-called added-mass effect which renders the simulation unstable. I will present a new numerical method to handle this added-mass effect, by relaxing the exact no-slip boundary condition and introducing proper penalty terms on the fluid-structure interface, which enables the possibility of stable explicit coupling procedure. The optimal parameters are obtained via theoretical analysis, and we numerically verify that stability can be achieved irrespective of the fluid-structure mass ratio. To demonstrate the effectiveness of the proposed techniques in practical computations, I will also discuss two vascular blood flow applications in three-dimensional large scale simulations. The first application is obtained for patient-specific cerebral aneurysms. The 3D fractional-order PDEs (FPDEs) are investigated which better describe the viscoelastic behavior of cerebral arterial walls. In the second application, we apply the stabilized FSI method to heart valves, and simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions.

Thursday, November 17th

TITLE: A system of Korteweg-de Vries type equations with coupled quadratic nonlinearities: global well-posedness and stability of solitary wave solutions
SPEAKER: Michael Morgan Wise, UTK
TIME: 2:00pm – 3:00pm
ROOM: Ayres 112
In this discussion, systems
of Korteweg-de Vries (KdV) type are considered. The nonlinearities P and Q are homogeneous, quadratic polynomials in u and v with real coefficients. A condition on P and Q sufficient for global well-posedness of the initial-value problem with initial data in H^s (R)×H^s (R) for s>-3/4 will be discussed. Attention will be drawn to solitary-wave solutions of the system above and special traveling waves called proportional solitary waves will be introduced. Under the same conditions provided for global well-posedness of the initial value problem, criteria for stability of these traveling-wave solutions will be given. This talk is a summary of a paper by Bona, Cohen, and Wang (2013) and another by Bona, Chen, and Karakashian (2015).

TITLE: Where Can Graduate Study in Mathematics Take Me?
SPEAKER: Peter Perry, University of Kentucky
TIME: 3:40pm-4:30pm
ROOM: Ayres 405
Graduate study in mathematics can open up many different career possibilities in teaching, industry, and government. In this talk we'll look at some career trajectories of graduate students, how graduate school connected these students with opportunities, and how you can apply to graduate programs, evaluate offers, and make a sound decision. After a thirty-minute presentation I'll open up the floor for questions and discussion.

Note: Perry was Director of Graduate Studies at the University of Kentucky from 2012 to 2016 and directs the Graduate Scholars in Mathematics program at the University of Kentucky.

Friday, November 18th

TITLE: Homogenization of Stochastic and Heterogenous Models in Porous Media
SPEAKER: Hakima Bessaih, University of Wyoming
TIME: 3:40pm-4:30pm
ROOM: Ayres 405
We study Brinkman's equations with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by a stochastic differential equation (SDE). Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic.
We use the asymptotic properties of the SDE and the periodicity of the Brinkman’s coefficient in the space variable to prove the convergence result. The SDE has a unique invariant measure that is ergodic and strongly mixing. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics) and also by averaging the Brinkman's coefficient with respect to the space variable. Our results can be extended to more general nonlinear diffusion equations with heterogeneous coefficients.

This is a joint work with Yalchin Efendiev and Florian Maris.

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

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last updated: January 2017

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