# Reception and Poster Session

Thursday, September 13, 2012 - 4:30pm - 5:45pm

Lind 400

**Compressive sensing: A new paradigm for model**

building

Gus Hart (Brigham Young University)**Mathematical Modeling of The Interstitial Space**

Carme Calderer (University of Minnesota, Twin Cities)Carlos Garavito-Garzon (University of Minnesota, Twin Cities)Yoichiro Mori

The interstitial space is the region that surrounds the cells of a given tissue.

It plays an important role in the control of fluid volume

in the human body. The interstitial space contains about one sixth

of total fluid volume in the body. The goal of this

project is to provide mathematical insights into the fluid distribution of the interstitial space.

Also with S. Lyu**Closed-form solutions to the effective properties of**

magnetoelectric composites

Liping Liu (Rutgers, The State University Of New Jersey )

Magnetoelectric coupling is of interest for a variety of applications,

but is weak in natural materials. Strain-coupled fibrous composites of

piezoelectric and piezomagnetic materials are an attractive way of

obtaining enhanced effective magnetoelectricity. This paper studies the effective magnetoelectric behaviors of two-phase multiferroic composites with periodic array of inhomogeneities. For a class of microstructures called periodic E-inclusions, we obtain a rigorous closed-form formula of the

effective magnetoelectric coupling coefficient in terms of the shape

matrix and volume fraction of the periodic E-inclusion. Based on the closed form formula, we find the optimal volume fractions of the fiber phase for maximum magnetoelectric coupling and correlate the maximum magnetoelectric

coupling with the material properties of the constituent phases. Based

on these results, useful design principles are proposed for

engineering magnetoelectric composites.**Virtual Testing of Composite Materials**

Timothy Breitzman (US Air Force Research Laboratory)

The qualification of new materials and certification of new structures is a major hurdle in the deployment of new material systems. Virtual testing may provide a way to decrease the long lead time associated with maturing new materials. This area is a problem rich field, including effect of defects, variability of the material and structure, load control/testing apparatus, and many more.**New and unique materials from dewetting of pulsed-laser melted, multilayer metallic films at the nanoscale: experiments and modeling**

Mikhail Khenner (Western Kentucky University)

Self-organized nanoparticle arrays from pulsed laser-induced

dewetting of ultra-thin (used to manufacture complex multifunctional surfaces that can be

applied to existing technologies such as surface Raman sensing or

magnetic data storage devices, but can also enable a host of new

applications that are generally based on sensing, detecting or

manipulating charge, electromagnetic signals, and magnetization.

This poster describes the basic nonlinear PDE model of self-organization

in bilayer films. In experiments, pulsed irradiation by

thousands of pulses with pulse width around 10 ns results in film

dewetting into nanoparticle arrays with well-defined length scales,

composition, and intricate morphologies. We used stability analyses

and computations of film height dynamics to determine dependencies

of these quantities on physical and process parameters. The combined

experimental/theoretical exploration is a step toward predictively

manufacture scalable multifunctional surfaces in new systems.**Use of the String Method to Find Minimal Energy Paths and Energy Barriers of Droplets on Superhydrophobic Surfaces**

Kellen Petersen (New York University)

Interest in superhydrophobic surfaces has increased due to a number of interesting advances in science and engineering. Here we use a diffuse interface model for droplets on topographically and chemically patterned surfaces in the regime where gravity is negligible. We then apply the constrained string method to examine the transition of droplets between different metastable/stable states. The string method finds the minimal energy paths (MEPs) which correspond to the most probable transition pathways between the metastable/stable states in the configuration space. In the case of a hydrophobic surface with posts of variable height and separation, we determine the MEP corresponding to the transition between the Cassie-Baxter and Wenzel states. Additionally, we realize critical droplet morphologies along the MEP associated with saddle points of the free-energy potential and the energy barrier of the free energy. We analyze and compare the MEPs and free-energy barriers for a variety of surface geometries, droplets sizes, and static contact angles ranging from partial wetting to complete wetting. We also introduce an unbiased double well potential in the diffuse interface model by introducing a chemical potential that is fixed for a given simulation. We find that the energy barrier shifts toward the Wenzel state along the MEP as the height of the pillars increases in the topographically patterned case while a shorter energy barrier exists and is more centered along the MEP for pillars of shorter height. More importantly, we demonstrate the string method as a useful tool in the study of droplets on superhydrophobic surfaces by presenting a numerical study that finds MEPs in configuration space, critical droplet morphologies and free-energy barriers which in turn give us a greater understanding of the free-energy landscape.**A Dynamic Model of Polyelectrolyte Gels**

Haoran Chen (University of Minnesota, Twin Cities)

Volume phase transition is a very important phenomenon of many polyelectrolyte gels. It is widely used in artificial devices, however, mathematically not much has been studied yet. In this poster, we give a dynamic model of polyelectrolyte gels, including governing equations and boundary conditions at the interface, which satisfies free energy dissipation identity. We analyze the 1-D linear stability for nonionic case and two ionic cases. We also show numerical simulations for the nonionic model. When using backward Euler method, there is a certain way that a discretized version of free energy dissipation identity can hold.**A weak compatibility condition of Widmanstatten structure: the 'Materials Genome' of Sb2Te3 in PbTe**

Richard James (University of Minnesota, Twin Cities)

We propose a weak condition of compatibility between phases applicable to cases exhibiting full or partial coherence and Widmanstatten microstructure. The condition is applied to the study of Sb2Te3 precipitates in a PbTe matrix in a thermoelectric alloy. The weak condition of compatibility predicts elongated precipitates lying on a cone determined by a transformation stretch tensor. Comparison of this cone with the long directions of precipitates revealing by FIB/SEM shows good agreement between theory and experiment.**Multiscale computational modeling of complex materials systems**

Maria Emelianenko (George Mason University)

This poster gives an overview of the computational issues underpinning

mathematical modeling of polycrystalline materials on multiple spatial

and temporal scales and calculation of phase diagrams for advancing

materials design and engineering. There is a number of challenges to

be faced, including the development of fast yet reliable simulation

techniques for prediction of microcracking and irreversible damage in

materials caused

by environmental factors, as well as the design of efficient methods

for analyzing vast

amounts of 3-d imaging data recently made available by advances in

experimental design

and instrumentation.