# Search Research Symposium Abstracts

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## Quasiperiodic composites: homogenization and spectral properties

A key feature of quasicrystalline microgeometry is a long-range order in the absence of periodicity. Their structures possess self-similarity on large scales and lack translational symmetry. Quasiperiodic geometries can be modeled using the cut-and-projection method that restricts or projects a periodic function in a higher dimensional space to a lower [Read More...]

**Presenter:**Elena Cherkaev, University of Utah

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 1, 2023; 9:45 am

## Herglotz-Nevanlinna function and fractional-time derivatives

The fractional-time derivatives $d^\alpha/dt$ with non-integer $\alpha$ are ubiquitous in applications where complex geometry is involved in the micro-scale, eq. diffusion in porous media with heterogeneous pore distributions. In this talk, a numerical scheme based on the Herglotz-Nevanlinna function theory will be presented for developing an efficient [Read More...]

**Presenter:**Miao-Jung Yvonne Ou, University of Delaware

**Authors:**Miao-Jung Yvonne Ou

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 1, 2023; 10:10 am

## Homogenization of a suspension of viscous fluid with magnetic particles

In this talk, the rigorous periodic homogenization for a coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid is discussed. Both one-way and two-way coupling between the fluid and particles are considered. As the size of the particles approaches zero, it is shown that the suspension’s [Read More...]

**Presenter:**Silvia Jimenez Bolanos, Colgate University

**Authors:**Thuyen Dang, Yuliya Gorb, Silvia Jiménez Bolaños

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 1, 2023; 10:35 am

## Solving two-phase Stefan problems in materials with internal heat generation in cylindrical geometry

We consider the evolution of the solid-liquid interface in a material with constant internal heat generation during melting and solidification in an infinite cylinder. The boundary of the cylinder is held either at a constant temperature or has a prescribed heat flux. The problem generalizes a classical Stefan problem by allowing heat generated internally, [Read More...]

**Presenter:**Lyudmyla Barannyk, University of Idaho

**Authors:**Lyudmyla Barannyk, John Crepeau, Sidney Williams, Alexey Sakhnov

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 1, 2023; 11:00 am

## On the Lack of Fredholm Solvability for the $L^p$ Dirichlet Problem for Weakly Elliptic Systems in the Upper Half-Space

The $L^p$ Dirichlet Problem for constant coefficient second-order systems satisfying the Legendre-Hadamard strong ellipticity condition is well posed in the upper half-space. Surprisingly, this result may fail if only weak ellipticity is assumed, and the failure manifests itself at a fundamental level through lack of Fredholm solvability. In this talk I will [Read More...]

**Presenter:**Irina Mitrea, Temple University

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 2, 2023; 8:30 am

## Analytical and Numerical Modeling of Composite Materials with Thin and Stiff Reinforcements

Emerging generations of nanomaterials and biomaterials use thin and stiff nanoplatelets or membrane sheets as reinforcements. In the talk, we will discuss the modeling methods for such materials that are based on the use of the Gurtin-Murdoch and Steigmann-Ogden material surface theories. The theories treat the reinforcement as either a membrane or a shell [Read More...]

**Presenter:**Sofia Mogilevskaya, University of Minnesota

**Authors:**Sofia G. Mogilevskaya, Anna Y. Zemlyanova, Zhilin Han

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 2, 2023; 8:55 am

## A problem for a material surface attached to the boundary of an elastic semi-plane

A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. A normal external traction is applied to a boundary of the material surface. The material surface is modeled using the Steigmann-Ogden form of surface energy. The problem is solved by using integral representations of stresses and [Read More...]

**Presenter:**Anna Zemlyanova, Kansas State University

**Authors:**Anna Zemlyanova

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 2, 2023; 9:20 am

## Homogenization of monotone operators and its application to nonlinear dielectric elastomer composites

This talk discusses the rigorous periodic homogenization of a weakly coupled electroelastic system. This system comprises a nonlinear electrostatic equation and an elastic equation enriched with electrostriction, which finds application in describing materials like dielectric elastomers or deformable (elastic) dielectrics. This project reveals that the [Read More...]

**Presenter:**Yuliya Gorb, National Science Foundation

**Authors:**Thuyen Dang, Yuliya Gorb, Silvia Jiménez Bolaños

**Symposium Year:**2023

**Session:**Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

**Presentation Time:**October 2, 2023; 9:45 am

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