# Registered Data

## [00164] Recent Advances in Direct and Inverse Problems in Mathematical Materials Science

**Session Date & Time**:- 00164 (1/3) : 2C (Aug.22, 13:20-15:00)
- 00164 (2/3) : 2D (Aug.22, 15:30-17:10)
- 00164 (3/3) : 2E (Aug.22, 17:40-19:20)

**Type**: Proposal of Minisymposium**Abstract**: In recent years, there has been a tremendous growth of activity in developing methods for materials-related phenomena occurring over multiple scales in time and space. This minisymposium focuses on multiscale modeling, analysis, and simulation of the problems arising in composites and other heterogeneous media. In particular, topics that will be discussed include but are not limited to asymptotic analysis such as homogenization, modeling of new materials, inverse problems, and computational tools. The purpose of this minisymposium is to encourage the exchange of ideas and networking among researchers working on the topics mentioned above.**Organizer(s)**: Lyudmyla Barannyk, Silvia Jimenez Bolanos, Yvonne Ou**Sponsor**: This session is sponsored by the SIAM Activity Group on Mathematical Aspects of Materials Science.**Classification**:__35Qxx__,__74Qxx__,__74Rxx__,__80Axx__,__78Mxx__**Speakers Info**:**Lyudmyla Barannyk**(University of Idaho)- Alexander Panchenko (Washington State University)
- Yvonne Ou (University of Delaware)
- Elena Cherkaev (University of Utah)
- Petr Plechac (University of Delaware)
- Ken Golden (University of Utah)
- Silvia Jimenez Bolanos (Colgate University)
- Yuliya Gorb (National Science Foundation)
- Robert Lipton (Louisiana State University)
- Shari Moskow (Drexel University)
- Anna Zemlyanova (Kansas State University)
- Yuri Godin (University of North Carolina at Charlotte)

**Talks in Minisymposium**:**[00473] Bloch Waves in High Contrast Electromagnetic Crystals****Author(s)**:**Silvia Jimenez Bolanos**(Colgate University)- Robert Lipton (Louisiana State University)
- Robert Viator (Swarthmore College)
- Abiti Adili (University of Massachusetts Lowell)

**Abstract**: In this talk, we present the derivation of analytic representation formulas and power series describing the band structure inside non-magnetic periodic photonic crystals, made from high dielectric contrast inclusions. We identify a resonance spectrum for quasi-periodic source-free modes, which are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high-contrast media. A convergent power series for the Bloch wave spectrum is obtained from the representation formulas and explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum.

**[00483] An axisymmetric problem for a nano-sized material surface on a boundary of an elastic semi-space****Author(s)**:**Anna Zemlyanova**(Kansas State University)

**Abstract**: An axisymmetric problem for a nano-sized penny-shaped material surface attached to the boundary of an elastic isotropic semi-space is considered. The surface is modeled using the Steigmann-Ogden form of surface energy. The problem is solved by using the Boussinesq potentials and Hankel transforms. The problem can be reduced to a system of two singular integral equations. This is a joint work with Lauren M. White.

**[00569] Clusters of Bloch waves in three-dimensional periodic media****Author(s)**:**Yuri Godin**(University of North Carolina at Charlotte)

**Abstract**: We consider acoustic wave propagation through a periodic array of small inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion relation for general frequencies and show that there are exceptional frequencies for which the solution is a cluster of waves propagating in different directions with different frequencies so that the dispersion relation cannot be defined uniquely. The results are illustrated by an example of a medium with a simple cubic lattice of spherical inclusions where we derived the dispersion relation, determine the parameters of the effective medium, and provided examples of some clusters. This is joint work with B. Vainberg.

**[00588] Modeling sea ice as a multiscale composite material****Author(s)**:**Kenneth Morgan Golden**(University of Utah)

**Abstract**: Sea ice exhibits composite structure on length scales ranging over many orders of magnitude. Forward and inverse homogenization are central to modeling sea ice and its role in climate and ecosystems. We’ll tour recent advances, from the fractal geometry of millimeter-scale brine inclusions and meter-scale melt ponds, to the homogenized dynamics of the marginal ice zone on the scale of the Arctic Ocean. We’ll also explore spectral representations for effective parameters in several contexts.

**[00596] Forward and inverse homogenization for quasiperiodic composites****Author(s)**:**Elena Cherkaev**(University of Utah)- Sébastien Guenneau (Imperial College London)
- Niklas Wellander (Swedish Defence Research Agency )

**Abstract**: From quasicrystalline alloys to twisted bilayer graphene, materials with a quasiperiodic structure exhibit unusual properties that drastically differ from those with periodic structures. Quasiperiodic geometries can be modeled using the cut-and-projection method restricting a periodic function in a higher-dimensional space to a lower-dimensional subspace cut at an irrational projection angle. The talk will discuss the homogenized equations for quasiperiodic materials and an inverse problem of recovering information about microstructural parameters from known effective properties.

**[00609] Studying Stefan problems with internal heat generation using sharp interface models****Author(s)**:**Lyudmyla L. Barannyk**(University of Idaho)- John C. Crepeau (University of Idaho)
- Patrick Paulus (University of Idaho)
- Alexey Sakhnov (Kutateladze Institute of Thermophysics SB RAS)
- Sidney D. V. Williams (Georgia Institute of Technology)

**Abstract**: We study the evolution of the solid-liquid interface during melting and solidification of a material with constant internal heat generation with prescribed temperature and heat flux conditions at the boundary of an infinite cylinder. We derive a nonlinear differential equation for the motion of the interface, which involves Fourier-Bessel series. The problem is also solved numerically by the front catching into a space grid node method as well as the enthalpy-porosity method to validate results.

**[00623] Capturing Quasistatic Fracture Evolution with Nonlocal Models****Author(s)**:**Robert Lipton**(Louisiana State University)- Debdeep Bhattacharya (Louisiana State University)

**Abstract**: Nonllocal quasistatic fracture evolution for interacting cracks is developed. The approach is implicit and based on local stationarity and fixed point methods. It is proved that the fracture evolution decreases the stored elastic energy with each load step; provided the load increments are taken sufficiently small. Existence theory for the fracture evolution is proved rigorously. Numerical examples include capturing the crack path propagating inside an L-shaped domain, and two offset inward propagating cracks.

**[00631] The Lippmann Schwinger Lanczos algorithm for inverse scattering problems****Author(s)**:**Shari Moskow**(Drexel University)- Vladimir Druskin (WPI)
- Mikhail Zaslavsky (Southern Methodist University)

**Abstract**: We combine data-driven reduced order models with the Lippmann- Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced. This internal solution is then used in the Lippmann-Schwinger equation, in a direct or iterative framework. The approach also allows us to process more general transfer functions, i.e., to remove the main limitation of the earlier versions of the ROM based inversion algorithms. We also describe how the generation of internal solutions simplifies in the time domain and give examples of its use given mono static data, targeting synthetic aperture radar.

**[00647] Uncertainty quantification for stochastic models of damage mechanics****Author(s)**:**Petr Plechac**(University of Delaware)- Gideon Simpson (l University)
- Jerome R Troy (University of Delaware)

**Abstract**: We study models used for describing brittle materials which exhibit linear elastic behavior until an applied load reaches a critical yield stress at which point a damage/fracture occurs . The underlying visco-elasto dynamics PDEs are characterized by a non-monotone stress-strain relation with a non-linearity linked to the critical yield stress. We study these equations in the presence of random yield stress field. The developed computational techniques will be demonstrated in numerical examples.

**[00649] On the governing equations of poro-piezoelectric composite materials****Author(s)**:**Miao-Jung Yvonne Ou**(University of Delaware)

**Abstract**: Materials such as quartz, cortical bones and cancellous bones exhibit piezo-electric behaviors, for which a mechanical wave such as ultrasound can trigger electro-magnetic waves. In this talk, we consider a porous material made of piezo-electric solid with pores saturated with conducting fluid, a model mimicking in vivo bones. The focus is to understand how the microstructure is encoded in the effective piezoelectric properties of these porous composites by using the two-scale convergence homogenization approach.

**[01237] Homogenization of a suspension of viscous fluid with magnetic particles****Author(s)**:**Yuliya Gorb**(NSF)- Thuyen Dang (University of Chicago)
- Silvia Jimenez Bolanos (Colgate University)

**Abstract**: 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 behavior is governed by a generalized homogenized magnetohydrodynamic system, whose parameters are explicitly derived. The two-scale convergence is utilized to justify obtained homogenized behavior of the original heterogeneous system.

**[05177] Energy-efficient flocking of particle systems****Author(s)**:**Alexander Panchenko**(Washington State University)

**Abstract**: The talk explores the problem of achieving flocking in multi-agent systems using minimal amount of on-board energy. We also assume that censor capacity is limited. Starting from a model reminiscent of Dissipative Particle Dynamics augmented with self-propulsion forces, we prove existence of an attractor for certain non-dissipative systems. Computer simulations show that velocity alignment is more energy efficient than formation control.