## 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.

_________________________________________________________________________________________________________

4/24

**Exact controllability of some PDE involving internal point masses**

**Scott Hansen **

Iowa State University

**Abstract: **It is known that a 1-d wave equation with an internal point mass subject to boundary control at one end is exactly controllable on an asymmetric Sobolev space which differs by one Sobolev order across the point mass. In the case of a Schr ̈odinger equation the description of the EC spaces is more complex as the spaces can be symmetric, asymmetric or a combination, depending upon coefficients and boundary conditions. I’ll present a characterization of the spaces for the case of Dirichlet control at one end for the Schodinger equation and describe related results for Euler-Bernoulli equation and Heat Equation with an internal point mass.

___________________________________

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.

4/10

** Bound-preserving discontinuous Galerkin method for compressible miscible displacements in porous media**

Yang Yang

Michigan Tech.

**Abstract:** In this talk, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the ith component of the fluid mixture, c_i, should be between 0 and 1. However, c_i does not satisfy the maximum-principle due to the existence of the source terms. Therefore, the numerical techniques introduced in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. The main idea is to apply the positivity-preserving techniques to both c_1 and c_2, respectively and enforce c_1+c_2=1 simultaneously to obtain physically relevant approximations. By doing so, we have to treat the time derivative of the pressure dp/dt as a source in the concentration equation. Moreover, c_i's are not the conservative variables, as a result, the classical bound-preserving limiter in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. Therefore, another limiter will be introduced. Numerical experiments will be given to demonstrate the good performance of the numerical technique.

April 19 (Wednesday, 4:10pm, Carver 294)

This is a special CAM seminar, joint with Math Colloquium

**Modularity clustering, random geometric graphs, and Kelvin's tiling problem**

**Sunder Sethuraman**

University of Arizona

**Abstract:** Given a graph, the popular `modularity' clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this talk, we will discuss scaling limits, or `consistency' properties, of this method with respect to random geometric graphs constructed from n points, X_1, X_2, . . . ,X_n, drawn independently according to a probability measure supported on a bounded domain in R^d, edges being placed between vertices X_i and X_j only if they are within \epsilon distance of each other. A main result is the following: Suppose the number of clusters, or partitioning sets of V_n, is bounded above by a fixed level, then we show that the discrete optimal modularity partitions converge, as n grows, in a specific sense to a continuum partition of the underlying domain, characterized as the solution of a `soap bubble', or `Kelvin'-type shape optimization problem.

Ref: Dr **Sunder Sethuraman** was a member of mathamical faculty at Iowa state Univeristy from 1998-2011. His speciality is Probability, both applied and theoretical.

4/24

**Exact controllability of some PDE involving internal point masses**

**Scott Hansen **

Iowa State University

**Abstract: **It is known that a 1-d wave equation with an internal point mass subject to boundary control at one end is exactly controllable on an asymmetric Sobolev space which differs by one Sobolev order across the point mass. In the case of a Schr ̈odinger equation the description of the EC spaces is more complex as the spaces can be symmetric, asymmetric or a combination, depending upon coefficients and boundary conditions. I’ll present a characterization of the spaces for the case of Dirichlet control at one end for the Schodinger equation and describe related results for Euler-Bernoulli equation and Heat Equation with an internal point mass.