Mathematics Department Seminar

 
 

Computational and Applied Mathematics Seminar

Spring 2017

Mondays at 4:10 p.m. in 401 Carver

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

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3/27/2017

Self-Organized Hydrodynamic models for nematic alignment and the application to myxobacteria


Hui Yu

RWTH Aachen University

Abstract: A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or antiparallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to myxobacteria is presented.

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2/13

Calderón-Zygmund estimates for parabolic equations

Pablo Raúl Stinga
Iowa State University

Abstract: We show how to use the language of semigroups in combination with the general Calderón—Zygmund theory on spaces of homogeneous type to obtain (weighted) Sobolev estimates for parabolic equations. One of the main features of this point of view is that it avoids the heavy use of the symmetries of the Fourier transform. Instead, our method takes advantage of semigroup kernel estimates. In this way we can prove novel estimates for non-translation invariant equations as well as for equations with bounded measurable time-dependent coefficients. We finally present some new (weighted) mixed-norm Sobolev estimates in the spirit of N. V. Krylov

2/20

Identification of an inclusion in multifrequency electrical impedance tomography

Faouzi Triki
University of Grenoble, Alpes


Abstract: In the talk I will present recent results on multifrequency electrical impedance tomography. The inverse problem consists in identifying a conductivity inclusion inside a homogeneous background medium by injecting one current. I will use an original spectral decomposition of the solution of the forward conductivity problem to retrieve the Cauchy data corresponding to the extreme case of perfect conductor. Considering results based on the unique continuation I will then prove the uniqueness of the multifrequency electrical impedance tomography and obtain rigorous stability estimates. Finally, I will present numerical results inspired by the developed theoretical approach. This work has been done in collaboration with Habib Ammari (ETH Zürich,Switzerland) and Chun-Hsiang Tsou (Grenoble Alpes University)

 

2/27

On a nonlocal selection-mutation model with a gradient flow structure

Hailiang Liu

Iowa State University

 

3/6 There are two talks:


Carver 401, 2:10pm--3:00pm

Oscillatory traveling wave solutions to an attractive chemotaxis system


Tong Li

University of Iowa

Abstract: We investigate global existence and long time behavior of solutions for PDE models of chemotaxis. In particular, we study oscillatory traveling wave solutions to an attractive chemotaxis system. The convective part of this system is of mixed-type.
The oscillatory nature of the traveling wave comes from the fact that one far-field state is in the elliptic region and another in the hyperbolic region. Such traveling wave solutions are shown to be linearly unstable.
This is a joint work with Hailiang Liu and Lihe Wang.

 

Carver 401, 4:10pm--5:00pm

Estimates and Scales for Elliptic Equations

Lihe Wang

University of Iowa

Abstract: We will talk about the key ideas of scaling and its applications to elliptic equations, with lower order terms and critical nonlinearlities.

 

3/23-25, 2017

KI-Net Conference:

Kinetic Descriptions of Chemical and Biological Systems: Models, Analysis and Numerics

March 23-25, 2017, Iowa State University, Ames, IA.

For more information regarding the conference and the process for applying to participate, please click on the link below:Inal

KI-Net Conference Announcement

 

KI-Net Conference Schedule - March 23-25, 2017 Includes speakers, titles and schedule.

 

More detailed KI-Net Conference Program - March 23-25, 2017 Includes abstracts of all talks.

 

3/27

Self-Organized Hydrodynamic models for nematic alignment and the application to myxobacteria


Hui Yu

RWTH Aachen University

Abstract: A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or antiparallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to myxobacteria is presented.