## Computational and Applied Mathematics Seminar

**Spring 2019**

**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.

Archive of previous CAM seminars

4/22

**Title: Single-ion and two-ion magnetocrystalline anisotropy using a Green's function method**

** Liqin Ke **

Ames Laboratory-USDOE

**ABSTRACT:** Developing and improving magnetic materials is of great interest for both basic sciences and practical applications. Trial-and-error investigations are often slow, partly because of the wide range of materials and processing options available; making it advantageous to combine computational and experimental approaches in a synergistic approach to accelerate discovery.
In this talk, I discuss computational methods we used in investigating intrinsic magnetic properties with a focus on magnetocrystalline anisotropy energy (MAE).
I discuss the computation of single-ion and two-ion MAE in second-order perturbation theory using a Green's function method. Both analytical and numerical methods are used to compute the MAE values and illustrate the nature of MAE in various systems.
Results are compared to available experimental data.

4/29

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5/06

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1/14

**Title: Moving Mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems**

**Yufei Yu **

University of Kansas

**ABSTRACT:** Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections that model micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial differential equation and the contact events occur in this system as finite time singularities. In this talk, I will talk about an adaptive moving mesh strategy, which is developed based on a moving mesh partial differential equation that dynamically relocates a fixed number of mesh points to increase density where the singularities take place. To complement this computational tool, a singular perturbation analysis is used to develop a geometric theory for predicting the possible contact sets. Numerical results that demonstrate the validity of these two approaches will be presented.

1/21

**University holiday**

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1/28

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2/04

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2/11

**Title: Nonconvexity and Compact Containment of Mean Value Sets for General Elliptic Operators**

** Niles Armstrong **

Kansas State University

**ABSTRACT: ** In his Fermi Lectures on the obstacle problem, Caffarelli stated a mean value theorem for second order uniformly elliptic divergence form operators with the form $L:=D_i a^{ij}(x) D_j.$ This theorem is a clear analog to the standard mean value theorem for Euclidean balls for the Laplacian, with the only difference being the sets over which the averages are taken. I will discuss the initial regularity results that were known for these sets, show a new compact containment result, and finally give an example of an operator with smooth coefficients and nonconvex mean value sets.

2/18

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2/25

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3/04

**Title: Recent Results for the 3D Quasi-Geostrophic System: Boundary Conditions and Non-Uniqueness**

**Matthew Novack **

University of Texas, Austin

**ABSTRACT:** The 3D Quasi-Geostrophic system is a set of equations used in meteorology to describe the evolution of the atmosphere. The surface quasi-geostrophic equation (2D SQG) is a well-studied special case where the atmosphere above the earth is at rest. In this talk, we will discuss a pair of recent results, the first of which derives the physical boundary conditions for the 3D model and constructs global in time weak solutions. The second result shows the non-uniqueness of weak solutions to the 3D model via a convex integration argument.

3/11

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3/18

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3/25

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4/01

**Title: Applied Topology and Data Science**

** Michael Catanzaro **

Iowa State University

**ABSTRACT:** In the past 30 years, there have been an abundance of applications of algebraic topology to other fields, including mathematical physics, statistics, and physical chemistry. In this talk, we will describe another application of how ideas from algebraic topology can be used to study problems arising in data science. We focus on theoretical and practical aspects of applied algebraic topology in statistics and in visualization of complex data. We will work through several examples of how these tools can be used, and assume no background in algebraic topology.

4/08

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4/15

**Title: Quadrature-Based Moment Methods for Multiphase Flow Simulations **

** Bo Kong **

Ames Laboratory-USDOE

**ABSTRACT:** Kinetic theory is a useful theoretical framework for developing multiphase flow models, which account for complex physics (e.g., particle trajectory crossings, particle size distributions, etc.). Due to the high-dimensionality of the phase space, direct solution of the kinetic equation is intractable for most applications. Therefore, the key challenge is to reduce the dimensionality of the problem without losing the underlying essential physics. A reduced description for multiphase flow systems must be numerically tractable and possess the favorable attributes of the original kinetic equation (e.g. hyperbolic, conservation of mass/momentum, etc.). In this seminar, I will present our efforts of developing such a description, a general closure approximation referred to as quadrature-based moment methods (QBMM). The basic idea behind these methods is to use the local (in space and time) values of the moments to reconstruct a well-defined local distribution function (i.e. non-negative, compact support, etc.). The reconstructed distribution function is then used to close the moment transport equations (e.g. spatial fluxes, nonlinear source terms, etc.). First, I will introduce the underlying theoretical and numerical background of QBMM. Then, I will describe the some of our recent developments, such as validation against Euler-Lagrangian simulation, extension to dense flow regimes, and dealing with polydispersity in multiphase flows. Finally, I will discuss some of our ongoing efforts on QBMM development.