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   \LARGE {\bf CMDS13 Conference Abstracts} \\ \relax
    [alphabetical by author name]
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\begin{enumerate}

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\item \textbf{Nathan Albin, \texttt{albin@math.ksu.edu}}\\
 \papertitle{Modulus of Path Families: Continuous and Discrete}

The modulus of a family of paths in a metric space provides a
quantitative assessment of the ``richness'' of the family: large families of short
paths have larger modulus than small families of long paths.  In Euclidean space,
the concept of modulus is closely related to the concept of capacity and to certain
energy minimization problems over gradient vector fields. In the discrete setting,
the concept of modulus can be linked to several graph-theoretic quantities including
shortest path, minimum cut, and effective resistance. This talk will present
connections among these concepts, suggest possible applications, and introduce a new
numerical algorithm for computing the modulus of path families on discrete grids and
on graphs in general.

\item \textbf{Andrea Alu, \texttt{alu@mail.utexas.edu}}\\
\textbf{Co-authors:} Dimitrios Sounas, Romain Fleury\\
\papertitle{Parity-time symmetric metasurfaces and metamaterials}

Metamaterials are artificially
structured materials possessing exotic electromagnetic or acoustic properties that
are not readily available in nature, for instance synthesizing negative, zero, or
very large index of refraction. Their exotic features are typically associated with
narrow bandwidths and losses. In this talk, we introduce the concept and theoretical modeling of parity-time (PT)
symmetric metasurface pairs and metamaterials, which offer a unique solution to
these issues, realizing loss-compensated, broadband wave manipulation, including
negative refraction, cloaking and planar focusing. We discuss the largely uncharted
scattering properties of PT-symmetric metamaterials and metasurfaces, with an
emphasis on the exciting mathematical and physical aspects involved in these
problems.

\item \textbf{Ali Rana Atilgan, \texttt{atilgan@sabanciuniv.edu}} \\
\textbf{Co-authors:} Canan Atilgan\\
\papertitle{Multiscale Interactions and Dynamical Systems Theme}

Non-synonymous single nucleotide polymorphisms within the coding
regions of genes giving rise to amino acid substitutions have shown to
alter drastically biological function of proteins. We have developed
methods to simply, yet efficiently, characterize the effects of those
substitutions on the conformational changes and, therefore, on the
dynamics and function of biological macromolecules [Annual Review of
Biophysics, 41, 205 (2012)]. By changing the residue's
physical--chemical characteristics, such as its charge distribution
[Journal of Physical Chemistry B, 116, 7145 (2012)], or playing with
the residue and its neighboring micro-environment [Journal of Chemical
Physics, 135, 155102 (2011)], or altering the temperature of the
surrounding water body [Journal of Chemical Physics, 133, 85101
(2010)], we have effectively demonstrated and confirmed with
experimental studies that the turnover rate of an enzyme, or the time
scale of ligand release may be altered in a controlled manner.

Bacteria continuously adapt to their environment, and while doing
that, they carry mutations that take place at critical locations to
their function. Random mutations taking place at the gene level may be
expressed on proteins that are vital for the survival of the organism;
with natural selection (``natural'' referring to the current environment
that may actually be extreme for normal life) these may become
permanent. In this talk we formulate the ways to decipher the
structural and dynamical changes induced on a given protein, by
mutants that let the organism carry its normal function while
conferring resistance, under the selection pressure induced by a given
antibiotic.

\item \textbf{Katayun Barmak, \texttt{kb2612@columbia.edu}}\\
\papertitle{Grain Growth and Grain Growth Stagnation in Metallic Films}

Polycrystalline metallic films play an important role in the
advance of many modern technologies such as integrated circuits, information storage
systems, displays, sensors and coatings. In integrated circuit technology, the
transistors on the semiconductor chip are interconnected via narrow, thin metallic
lines. Metallic films are also used as the magnetic information storage layer in
hard disk drives, and as antenna and reflector elements in in optical applications.
The physical behavior of metals in thin film form is often remarkably different from
that of the corresponding bulk metallic material so it is important to study their
structure and properties. The polycrystalline structure of the films forms during
deposition and evolves during post-deposition processing via, for example, grain
coarsening, more commonly termed grain growth.  This talk focuses on the comparison
of experiments and simulations of grain growth in metallic films. Experimental grain
growth characteristics are examined by bringing together a large body of grain size
data for Al and Cu films, in addition to data for the distribution of grain sides
and other topology and topology-geometry metrics. The experimental data is used to
evidence stagnation of grain growth and to arrive at a universal experimental grain
size distribution. This universal distribution deviates from the distribution
obtained in two-dimensional simulations of grain growth with isotropic boundary
energy in two notable regions termed the ``ear'' and the ``tail''. In seeking the cause
of the observed differences between experiment and simulation, the impact of surface
and elastic strain energy, anisotropy of grain boundary energy, grain boundary
grooving, impurity drag, and triple junction drag is examined.  Recent work on
comparison of experiments and simulations of the phase field crystal model of grain
growth will also be discussed.

\item \textbf{Yakov Benveniste, \texttt{benben@eng.tau.ac.il}}\\
\papertitle{Exact results for the local fields and the effective moduli of fibrous composites
with thickly coated fibers}\\


Fibrous composites that consist of thickly coated cylindrical fibers embedded in a
matrix are considered [1]. All of the three phases of the composite are assumed to be
transversely isotropic. The study consists of three parts. In the first part exact relations
are derived for the influence functions that connect applied uniform overall fields to
the induced local fields in piezomagnetoelectric systems. We consider the case of coated fibers with a
concentrically circular cross section, and contrast the derived relations with the more limited ones that
could be obtained in the case of coated fiberswith an arbitrary cross section. The derivation is
based on the ability to create uniform strain, electric and magnetic fields in the composite by the application of
certain mechanical, electric, magnetic and thermal loadings. In the second part of the study, exact microstructure independent
connections are derived for a subgroup of the effective moduli of the homogenized piezomagnetoelectric composite which exhibits
overall transverse isotropy. The first and second parts become a generalization of some of the contents of [2] to the above
described coated-fiber composite. In the third part of the study, the derived exact connections between the effective moduli are
reduced to the setting of thermoelasticity; letting the coating to be thin and highly
stiff or highly compliant, we make contact with the exact connections derived in [3] and [4] for two-phase fibrous thermoelastic
composites with surface-stress-type and spring-type imperfect interfaces. \\




{\bf References}
\\ \relax
[1] Benveniste, Y., 2014. Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers.  Submitted for publication.
\\ \relax
[2] Benveniste, Y., 1995. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys. Rev. B 51, 16424-16427.
\\ \relax
[3] Chen, T., Dvorak, G. J., 2006. Fibrous nanocomposites with interface stress: Hill's and Levin's connections for effective moduli. Appl. Phys. Let. 88, 211912.
\\ \relax
[4] Duan, H. L., Karihaloo, B. L., 2007. Thermo--elastic properties of heterogeneous materials with imperfect interfaces--generalized Levin's formula and Hill's connections. J. Mech. Phys. Solids 55, 1036-1052.
\\ \relax



\item \textbf{Viktor Berdichevsky, \texttt{vberd@eng.wayne.edu}}\\
\papertitle{Homogenization of random structures in probabilistic terms}

Studying of materials with evolving random microstructures requires the knowledge of probabilistic characteristics of local
fields because the path of the microstructure evolution is determined by the local
fields. The mathematical problem for determining the probabilistic characteristic
was formulated as a minimization problem for energy with the respect to
probabilistic measure long ago (Berdichevsky, 1987). This variational problem
contains an infinite chain of constraints for probability distributions. It remained
unclear how to properly truncate this infinite chain. In this talk a way of
truncation is suggested. The corresponding probability distributions are found for
two-phase composites. As a by-product, one gets also the dependencies of the
effective coefficients on the parameters of microstructures. Other issues that will
be discussed are: formulation of Hashin--Shtrikman results in probabilistic terms, a
universal extension of the Hashin--Shtrikman bounds, the law of decrease of
microstructure entropy.

\item \textbf{David J. Bergman, \texttt{bergman@post.tau.ac.il}}\\
\textbf{Co-authors:} Asaf Farhi\\
\papertitle{Exact analysis of a Veselago lens in the quasi-static regime}

The resolution of conventional optical lenses
is limited by the wavelength. Materials with negative refractive index have been
shown to enable the generation of an enhanced resolution image where both
propagating and non-propagating waves are employed. We analyze such a Veselago lens
by exploiting some exact one dimensional integral expressions for the quasi-static
electric potential of a point charge in that system. Those were recently obtained by
expanding that potential in the quasi-static eigenfunctions of a three-flat-slabs
composite structure. Numerical evaluations of those integrals, using realistic
values for physical parameters like the electric permittivities of the constituent
slabs and their thicknesses, reveal some surprising effects: E.g., the maximum
concentration of the electric field occurs not at the geometric optics foci but at
the interfaces between the negative permittivity slab and the positive permittivity
slabs. The analysis provides simple computational guides for designing such
structures in order to achieve enhanced resolution of an optical image.

\item \textbf{Liliana Borcea, \texttt{borcea@umich.edu}}\\
\papertitle{Imaging in complex environments}

The talk is concerned with the application of sensor array imaging in
complex environments. The goal of imaging is to estimate the support
of remote sources or strong reflectors using time resolved
measurements of waves at a collection of sensors (the array). This is
a challenging problem when the imaging environment is complex, due to
numerous small scale inhomogeneities and/or rough boundaries that
scatter the waves. Mathematically we model such complexity (which is
necessarily uncertain in applications) using random processes, and
thus study imaging in random media. I will focus attention on the
application of imaging in random waveguides, which exhibits all the
challenges of imaging in random media. I will present a quantitative
study of cumulative scattering effects in such waveguides and then
explain how we can use such a study to design high fidelity imaging
methods.

\item \textbf{Rebecca Brannon, \texttt{Rebecca.Brannon@utah.edu}}\\
\textbf{Co-authors:} Farah Huq, Lori Graham-Brady\\
\papertitle{Initialization of Discrete Statistical Crack Properties in Continuum-Scale Domains}

 Aleatory uncertainty in continuum damage models is a direct result of
variability in the number, size, and orientation of flaws within a finite-element.
Each discrete flaw in a structural ceramic may be modeled explicitly only if the
finite element is extremely small ($< 0.1$mm across). Beyond a few millimeters (as
needed in engineering applications), homogenization of discrete expectation
summations is needed to estimate ensemble effects of many flaws. It is not
computationally tractable to evaluate expectation summations over each of the
millions or trillions of flaws in these larger elements, but they still are not
large enough to justify replacing the discrete flaw realizations with a continuous
approximation. In fact, it is proved that the finite elements would need to be of
``planetary'' size in order for the discrepancy between a discrete and continuous
expectation to fall below numerical round-off. To address this difficulty, mapping
principles of the Material Point Method are applied to obtain a novel and flexible
flaw binning scheme. At initialization, the original Poisson-process realization of
the number of cracks is mapped to a background grid, and then discarded. The Dirac
deltas in the original (exact) discrete joint PDF for crack size and orientation are
thus mapped (in probability reference space) to a grid-based continuous delta-like
approximate field. Gauss locations and weights for averages over this field provide
bin properties, after which the grid is also discarded, leaving only a much smaller
set of equivalent cracks for subsequent crack evolution calculations. The approach
rigorously converges to the original discrete PDF as the grid is refined, and it
easily handles any number of random variables for each flaw (size, orientation,
planarity, etc.).  Judicious grid zooming to favor larger cracks (because of their
greater influence on stiffness and strength) provides high accuracy of the binned
approximation of the original expectation integrals at a fraction of the
computational cost.

\item \textbf{Nathan Briggs, \texttt{\texttt{nathancbriggs@gmail.com}}}\\
\papertitle{A Look at the Numerical Results of the Optimal Design of Multiphase Elastic Structures}

The optimal
design problem is considered: It is required to lay out two elastic materials and
void in the design domain in order to minimize the elastic energy stored in the
domain plus the total cost. It is assumed that the cost of each material is known:
the strong material is expensive, the weak material is cheap. The loading and
supports are fixed. The problem of optimal three material composite as formulated
and solved in [1], optimal microstructures were defined for various loading
conditions. Mathematically, this problem is a multivariable nonconvex minimization
problem: determination of the quasiconvex envelope of a multiwell Lagrangian, where
the wells represent materials' energies plus their costs; the quasiconvex envelope
represents the energy and the cost of an optimal composite [2].
The main focus of the talk is to investigate the problem of finding the optimal
design of a macrostructure consisting of the previously discussed microstructures.
The compliance of a macrostructure is minimized with respect to both microstructure
and volume fraction for a given state of stress, several examples are computed and
discussed.  The found optimal structures explain the role of each material in the
optimal design. The results are compared with two-material optimal designs.

[1] A. Cherkaev and G. Dzierzanowski. Three-phase plane composites of minimal
elastic stress energy: High-porosity structures. International Journal of Solids and
Structures, 50, 25-26, pp. 4145-4160, 2013.\\ \relax

[2] A. Cherkaev. Variational Methods for Structural Optimization. Springer\\ \relax

[3] N. Briggs, A. Cherkaev and G. Dzierzanowski. 2013. Note of Optimal design from
three materials. Submitted to Int. J. of Structural Optimization.

\item \textbf{Michele Brun, \texttt{mbrun@unica.it}}\\
\textbf{Co-authors:} Daniel Colquitt, Massimiliano Gei, Alexander B. Movchan, Natasha V.
Movchan, Ian S. Jones\\
\papertitle{Transformation cloaking for flexural waves in elastic plates}

Cloaking transformation for flexural waves in plates are
considered. For the Kirchhoff-Love problem governed by a fourth-order partial
differential equation it is shown that the equation governing the problem is not
invariant with respect to cloaking transformation as opposed to the Helmholtz
operator. The transformed equation finds a consistent physical interpretation
as a inhomogeneous orthotropic flexural plates in the presence of pre-stress and
in-plane external forces. Additionally, an asymptotic derivation from
three-dimensional continuum elasticity provides a rigorous link between the model in
question and elastic wave propagation in thin solids, showing connection with
non-symmetric formulation in vector elasticity studied in earlier works. Example on
a regularized push-out transformation show the broadband cloaking effect within the
plate Kirchhoff-Love plate theory. The proposed physical interpretation of the
transformed equation may lead to a refinement of the experimental implementations.


\item \textbf{Blaise Bourdin, \texttt{bourdin@lsu.edu}}\\
\papertitle{Multiscale Problems in Brittle Fracture}

The Variational Approach to Fracture has now emerged as a versatile
yet rigorous
model of fracture in brittle materials. Its natural ability to handle crack
propagation along complex unknown geometry in two and three dimensions is allowing
unprecedented numerical investigations of problems involving very complex fracture
systems. I will focus on two such situations: the morphogenesis of complex cracks induced by
thermal shocks, and fracture of heterogeneous materials. In the first situation, we
will show how the regularized fracture energies used in the numerical simulations
can be seen as ad-hoc graduent damage models in order to faithfully reproduce crack
nucleation then propagation over many order of magnitude in scale. In the later one,
we will show how the intuitive concept of ``effective toughness'' of an
heterogeneous material may be inappropriate. We present a new formalism based on
a ``surfing experiment'' for the determination and numerical computation of this
effective toughness.

\item \textbf{Xian Chen, \texttt{chen1561@umn.edu}}\\
\textbf{Co-authors:} Yintao Song, Richard D. James\\
\papertitle{From compatibility conditions to stress-free microstructure for martensitic transformation}
The
cofactor conditions (CC) are the conditions of super compatibility between phases
for martensitic transformation. By satisfying CC, austenite and variants of
martensite can fit together without elastic transition layers for any twinning
volume fraction between 0 and 1. Here we discuss different forms of CC in Type I/II,
Compound twins and domains, followed by the prediction of their possible
microstructures. Then we calculate the geometric linear case of CC. Finally, we show
real examples whose lattice parameters were tuned to satisfy CC closely for both
Type I and II twin system.

Materials undergoing reversible phase transformations are desirable for applications
in medical devices, microelectronics and energy conversion devices [1]. The
conditions of elastic compatibility of the phase-transforming materials have
profound impact on these applications. Because they dominate the hysteresis, the
reversibility and the resistance to functional degradation upon cyclic operation [2,
3]. It has been proven experimentally that the degree of hysteresis and the cycling
ability of the materials can be optimized [4] by making the lattice parameters
satisfy a set of geometric compatibility conditions
\begin{eqnarray}
&\lambda_2 = 1 \\
&\mathbf a \cdot \mathbf U \text{cof}(\mathbf U^2 - \mathbf I)\mathbf n = 0\\
&\text{tr}\mathbf U^2 - \det \mathbf U^2 - \frac{|\mathbf a||\mathbf n|}{4} \geq 2
\end{eqnarray}
where $\lambda_2$ is the middle eigenvalue of the transformation stretch tensor
$\mathbf U$, the vector $\mathbf a$, $\mathbf n$ are the twinning parameters.
Microscopically, the satisfaction of these conditions means a perfect lattice points
match at the interface between the initial and final phase, which results in
stress-free microstructure in the material. Therefore, it allows for materials
transforming back and forth freely without paying internal elastic penalty. This is
why the materials satisfying CC exhibit tremendous reversibility.

\item \textbf{Andrej Cherkaev, \texttt{cherk@math.utah.edu}}\\
\papertitle{Optimal multimaterial composites: Bounds and structures}

The paper suggests a method for funding exact bounds for the
effective conductivity moduli of  multimaterial composites. These bounds expand and
refine Hashin--Shtrikman and Nesi bounds.  We prove that  the fields in the materials
within optimal structures vary in restricted domains and take this  into account,
obtaining more restricted bounds. The new bounds are solutions of a formulated
relaxed finite-dimensional constrained optimization problem.
For two-dimensional conducting three-material composites, bounds for effective
conductivity are explicitly computed. These bounds are exact: Three-material
isotropic microstructures of extremal conductivity are found that realize the bounds
for all values of parameters. The optimal structures are laminates of a finite rank,
their parameters vary with the volume fractions and they experience two topological
transitions: For large values of material of minimal conductivity, its subdomain
percolates (is connected), for intermediate values of that fraction, no material
forms a connected domain, and for small values of that fraction, the domain of
intermediate material percolates. Another type of isotropic optimal three--material
structures is the ``wheel assemblages'' that replaces the Hashin--Shtrikman coated
circles.

\item \textbf{Elena Cherkaev, \texttt{elena@math.utah.edu}}\\
\papertitle{Spectral representation in forward and inverse homogenization problems for composite materials}

The talk discusses
spectral representation of the effective properties of composites and inverse
homogenization problem which is a problem of
deriving information about the microgeometry of the composite
from given effective properties. The approach is based on the spectral measure of a
self-adjoint operator that depends on the geometry
of composite. Stieltjes analytic representation of the effective property
relates the n-point correlation functions of the microstructure to the moments
of the spectral measure, which contains all information about the microgeometry.
I show that the problem of identification of the spectral function
from effective measurements known in an interval of frequency, has a unique
solution. In particular, the volume fractions of materials in the
composite and an inclusion separation parameter, as well as the spectral
gaps at the ends of the spectral interval, can be uniquely recovered.
I will discuss reconstruction of microstructural parameters
from electromagnetic and viscoelastic effective measurements, application to
coupling of different effective properties, and show an extension to
nonlinear and multi-component composites.

\item \textbf{Alexander Chudnovsky, \texttt{achudnov@uic.edu}}\\
\papertitle{Scale Effect in Brittle Fracture}

Heterogeneous morphology and a hierarchy of defects from grain size level up to a large-scale network of cracks are typical for most of engineering materials. It create a challenge for determining macroscopic properties of materials, particularly the scale dependent ones such as strength, toughness and other brittle fracture characteristics. The most pictorial manifestation of material heterogeneity are highly irregular and random fracture surfaces. Modeling of brittle fracture of micro-heterogeneous materials calls for a synthesis of fracture mechanics with probability and stochastic calculus. This work present a brief overview of Statistical Fracture Mechanics that addresses the statistical aspects of fracture. It is illustrated by studies of concrete brittle fracture and includes determination of a scaling rule for fracture toughness. Complex interaction between a macroscopic crack and an array of pre-existing micro-defects results in highly tortuous, stochastic fracture paths and in large scatter of all fracture-related parameters. Results of application of Statistical Fracture mechanics and related experimental studies are reported in this presentation.

\item \textbf{Daniel Colquitt, \texttt{d.colquitt@imperial.ac.uk}}\\
\textbf{Co-authors:} RV Craster, T Antonakakis, S Guenneau\\
\papertitle{In-plane Rayleigh-Bloch waves for elastic diffraction gratings}

Despite being extensively studied in scalar wave systems, Rayleigh--Bloch
waves in elasticity appear to have received very little attention.
Given the significance of Rayleigh--Bloch waves in applications and the pervasive
nature of diffraction gratings, there has been no investigation of whether such
waves occurs within elastic diffraction gratings for the in-plane vector elastic
system. In the present work, we demonstrate that Rayleigh--Bloch waves do exist for elastic
diffraction gratings and identify the boundary conditions that support such waves.
In parallel, an asymptotic procedure is developed that allows the diffraction
grating to be replaced by an homogenised continuum at all frequencies, whilst
retaining the essential features of the Rayleigh--Bloch waves.
Numerical simulations demonstrate the efficacy of the asymptotic scheme.

\item \textbf{Shankar Prasad Das, \texttt{shankar0359@yahoo.com}} \\
\textbf{Co-authors:} Nita Bidhoodi, Madhu Priya\\
\papertitle{Qualitatively different collective and single particle dynamics in a supercooled liquid}

The dense supercooled liquid develops finite shear
modulus below a
characteristic temperature though crystallization of the system in
to a structurally ordered state has not occurred. The process of
formation of the amorphous solid or the mechanism of glass formation
remains an unsolved problem. In this work we demonstrate that the
nature of the dynamics of a single tagged particle in the
supercooled liquid is qualitatively different, having finite self
diffusion constant even when the system has developed solid like
properties at macroscopic length scales. Our analysis is based on
the microscopic model of mode coupling theory (MCT) used for
understanding slow dynamics in liquids. In its simplest form MCT
predicts an ergodicity-nonergodicity (ENE) transition at a critical
density $n_c$. The correlation function $\phi(q,t)$ of collective
density fluctuations at wave vector $q$ and time separation $t$ is
$f(q)\ne{0}$ at the transition. We show that maintaining consistency
with the basic conservation laws of the system requires that even
beyond the ENE transition, the self-diffusion constant $D_s$ of a
tagged particle remains finite. Only if the mode coupling effects
are evaluated in the so called adiabatic approximation which
violates momentum conservation, $D_s$ goes to zero at the ENE
transition.

\item \textbf{ Grzegorz Dzierzanowski, \texttt{gd@il.pw.edu.pl}} \\
\textbf{Co-authors:} Nathan Briggs, Andrej Cherkaev\\
\papertitle{Optimal structures made of two elastic materials and void}

In this research we use the
framework of theory of elasticity to describe the exact solution in optimal design
of three-phase structures of minimal compliance, or equivalently, maximal stiffness.
Our problem is formulated as follows: lay out two elastic materials and void in a
given two-dimensional design domain $\Omega$, loaded at its boundary
$\partial\Omega$, so that the structural compliance achieves its minimal value. It
turns out that optimal layout of phases is determined on two levels: macro and
microscopic. On the macrolevel, the design domain is divided into subdomains filled
with pure phases or their mixtures (composites) with optimal microgeometries. The
main aim of the talk is to discuss the case when optimal macroscopic distribution of
phases is not unique.

\item \textbf{Yekaterina Epshteyn, \texttt{epshteyn@math.utah.edu}}\\
\textbf{Co-authors:} K. Barmak, E. Eggeling, M. Emelianenko,
D.Kinderlehrer, R. Sharp, S. Ta'asan and P. Bardsley\\
\papertitle{A Theory and Challenges for Coarsening in Microstructure}

Cellular networks are
ubiquitous in nature. Most technologically useful materials arise as polycrystalline
microstructures, composed of a myriad of small crystallites, or grains, separated by
interfaces, or grain boundaries. The energetics and connectivity of the grain
boundaries network plays a crucial role in determining the properties of a material
across a wide range of scales. Coarsening, or growth process is influenced mainly by
the effort of the system to decrease the interfacial energy subject to spatial
constraints. The recently discovered Grain Boundary Character Distribution (GBCD)
indicates that the boundary network of a cellular structure, and, more generally,
material texture has a natural order.
In this talk we will present and discuss a theory for the evolution of this
statistic which leads to many interesting and challenging questions.

\item \textbf{Alexander Figotin, \texttt{afigotin@uci.edu}}\\
\textbf{Co-authors:} Guillermo Reyes\\
\papertitle{Multi-transmission-line-beam interactive system}

We construct a Lagrangian field formulation for a system
consisting of an electron beam interacting with a slow-wave structure modeled by a
possibly non-uniform multiple transmission line (MTL). In the case of  a single line
we recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce. Since
a properly chosen MTL can approximate a real waveguide structure with any desired
accuracy, the proposed model can be used in particular for design optimization.
Furthermore, the Lagrangian formulation provides for: (i) a clear identification of
the mathematical source of amplification, (ii) exact expressions for the conserved
energy and its flux distributions obtained from the Noether theorem. In the case of
uniform MTLs we carry out an exhaustive analysis of eigenmodes and find sharp
conditions on the parameters of the system to provide for amplifying regimes.

\item \textbf{Alexander Freidin, \texttt{alexander.freidin@gmail.com}}\\
\textbf{Co-authors:} Elena Vilchevskaya\\
\papertitle{Chemical affinity tensor in mechanochemistry of deformable solids}

Chemical affinity is
one of the basic notions in physical chemistry since its value determines a chemical
reaction rate. In the case of liquid and gas constituents the chemical affinity is a
scalar equal to the combination of chemical potentials of the constituents. Recently
it was shown that the chemical affinity is a tensor in the case of solid
constituents. An expression of the chemical affinity tensor was derived as a
consequence of the mass, momentum and energy balances and entropy inequality written
down for an open system ``solid--gas'' in which a chemical reaction took place
between gas and solid with arbitrary constitutive equations. In a quasi-static case
the chemical affinity tensor takes the form of the combination of chemical
potentials tensors of the solid constituents (equal to the Eshelby stress-tensors
divided by the reference mass densities) and the chemical potential of the gas
constituent. Having the expression of the chemical affinity tensor, we formulate a
kinetic equation for the reaction rate at the oriented surface element in a form of
the dependence on the normal component of the chemical affinity tensor. Then we
study the role of the invariants of the chemical affinity tensor. We specify the
expressions for the case of linear elastic solid constituents. We find the
orientation of the surface elements at which the reaction rate is maximal using the
formalism developed earlier for interfaces in the case of phase transformations. We
formulate boundary value problems of mechanochemistry and study a planar chemical
reaction front propagation and solve axially-symmetric and spherically-symmetric
problems of mechanochemistry. Finally we consider inelastic solid constituents and
incorporate the relaxation of stresses produced by chemical transformation strain.

\item \textbf{Joe Goddard, \texttt{jgoddard@ucsd.edu}}\\
\papertitle{Continuum modeling of granular media}

This
talk summarizes a recent survey [1] of the  interesting phenomenology  and the
prominent r\'egimes of granular flow which also offers a unified mathematical
synthesis of  continuum modeling. The unification is based on ``parametric'' viscoelasticity
and hypoplasticity  involving elastic and inelastic potentials. Fully non-linear,
anisotropic visco-elastoplastic models are achieved  by expressing the potentials as
functions of the joint isotropic invariants  of kinematic and  structural tensors.
These  take on the role of evolutionary parameters or internal variables,  whose
evolution equations  are derived from the internal balance of generalized forces.
The resulting continuum models
encompass most of the mechanical constitutive equations currently employed for
granular media. Moreover, these models are readily modified to include Cosserat and
other multipolar effects. Several outstanding questions are  identified  as to the
contribution of parameter evolution to dissipation, the distinction between
quasi-elastic and inelastic models of material instability, and the role of
multipolar effects in material instability, dense rapid flow and particle migration
phenomena. \\

\noindent [1] J. Goddard, {\it Appl. Mech. Rev.} {\bf 64}:5, 2014.

\item \textbf{Yury Grabovsky, \texttt{yury@temple.edu}}\\
\papertitle{A complete list of exact relations for effective elastic tensors of fiber-reinforced composites}

Microstructure-independent relations for effective tensors of
composites have been attracting the attention of materials scientists
throughout the history of the subject. In the context of fiber-reinforced
elastic composites, the confluence of fully 3-dimensional elastic tensors with
an inherently 2D microstructure yields an enormous number of exact relations
ranging from physically obvious to bewildering. Invariably, these relations
can be represented by unexpectedly elegant formulas. I will describe a long
and exciting journey starting from the general theory, through the efforts of
Ph.D. and undergraduate students, to the complete list of exact relations.

\item \textbf{Fernando Guevera Vasquez,  \texttt{fguevara@math.utah.edu}}\\
\textbf{Co-authors:} Liliana Borcea, Alexander V. Mamonov\\
\papertitle{A network based inversion method for the Schr\``odinger problem}

Consider the inverse problem of finding the Schr\''odinger potential
$q(x)$ from measurements of the Dirichlet to Neumann map of the
Schr\``odinger differential operator $u \to \Delta u + qu$. We present a
method for solving this problem in 2D that is based on an analogous of
the Liouville transform on resistor networks. The continuum Liouville
transform maps an operator of the form $v \to \nabla \cdot [\sigma
\nabla v]$, with $\sigma>0$ to a Schr\''odinger differential operator.
The discrete Liouville transform on a network maps a Laplacian on the
network to another Laplacian plus a diagonal perturbation which can be
thought as a discrete Schr\``odinger potential. The first step in the
inversion is to find a resistor network that fits the data. In the
second step, a discrete Liouville transform is applied to get a diagonal
perturbation of a discrete Laplacian. The final step is to interpret the
discrete Laplacian and its diagonal perturbation as a finite volumes
discretization of the Schr\''odinger differential operator. This gives a
cheap reconstruction of the continuum Schr\``odinger potential from the
discrete one. The method needs to be calibrated by data for two known
constant Schr\''odinger potentials.

\item \textbf{Klaus Hackl, klaus.\texttt{hackl@rub.de}}\\
\textbf{Co-authors:} Muhammad Sabeel Khan\\
\papertitle{Modeling of microstructures in a Cosserat continuum using relaxed energies}

A continuum model for granular materials exhibiting microstructures is presented using the concept of
energy relaxation. In the framework of Cosserat continuum theory the free energy of
the material is enriched with an interaction energy potential taking into account
the counter rotations of the particles. The total energy thus becomes
non-quasiconvex, giving rise to the development of microstructures. Relaxation
theory is then applied to compute its exact quasiconvex envelope. It is worth
mentioning that there are no further assumptions necessary here. The computed
relaxed energy yields all possible field fluctuations of displacements and
micro-rotations as minimizers. We show that the material behavior can be divided
into three different regimes. Two of the material phases are exhibiting
microstructures in rotational and translational motion of the particles,
respectively, and the third one is corresponding to the case where there is no
internal structure of the deformation field. The properties of the proposed model
are demonstrated by carrying out numerical computations. The obtained results
exhibit a number of unexpected features, for example the transition between
distributed and localized microstructures.

\item \textbf{Yilong Han, \texttt{yilong@ust.hk} } \\
\textbf{Co-authors:} Yi Peng, Feng Wang\\
\papertitle{Nucleation in solid-solid transitions of colloidal crystals}


Solid-solid phase transitions between different
crystalline structures are ubiquitous in nature, but their kinetic pathways and
mechanisms present formidable challenges for theory, simulation and experiment. Here
we directly imaged the solid-solid transitions in colloidal thin films composed of
diameter-tunable NIPAM microspheres with single-particle resolution by video
microscopy. We discover a surprising two-step diffusive nucleation behavior for
transitions from square- to triangular-lattices with an intermediate liquid stage.
The observations and resulting theoretical analysis suggest that, provided
solid-liquid interfacial energies are sufficiently small, s-s transitions in most
traditional metals and alloys should follow this two-step nucleation with
intermediate liquid stage, and should generally arise in 2D, 3D and thin-film single
crystals and polycrystals.  The nucleation precursors are particle-swapping loops
rather than structural defects, which, in turn, provide a new relaxation mode that
makes s-s transitions easier and faster. This new kinetic factor controlling the s-s
transition rate has never been considered and should be incorporated in future s-s
transition theories.

Applying a small anisotropic strain can reduces the liquid nucleus size. Above a
threshold of the applied strain, the intermediate liquid nuclei vanished. Instead, a
few pairs of dislocations were first generated from the square lattices as
nucleation precursors, which triggered tens of particles to collectively transform
to a triangular-lattice nucleus and then grew diffusively. This martensitic
transformation at the early stage and the diffusive nucleation at the later stage is
another novel type of kinetic pathway in solid-solid transition.

In addition, we observed that the coherent and incoherent facets of the evolving
nuclei exhibit different energies and growth rates which can dramatically alter
nucleation kinetics. The coalescence of two crystalline nuclei exhibits different
behaviors for different lattice angles.

\item \textbf{Alex Hansen, Alex.\texttt{Hansen@ntnu.no}} \\
\papertitle{Crack front propagation using the fiber bundle model}

Disentangling the dynamics of a crack moving along a weak plane is
along--standing problem that has interested the statistical physics community for
nearly twenty years.  The advancing crack front has been shown experimentally to
exhibit all the signatures of a dynamical critical phenomenon. The theoretical
approach to this problem has been a top--down one where one uses LEFM as a starting
point. We take here an opposite view and approach the problem bottom-up. By using
the fiber bundle model, we are able to connect with the LEFM--based approach
explaining a number of open question on the way.

\item \textbf{Davit Harutyunyan, \texttt{davith@math.utah.edu}}\\
\textbf{Co-authors:} Graeme W.Milton\\
\papertitle{Examples of extremal quasiconvex quadratic forms that are not polyconvex}

We prove that if the associated fourth order tensor of a quadratic form has a linear elastic cubic
symmetry then it is a quasiconvex form if and
only if it is polyconvex, i.e., a sum of convex and null--Lagrangian quadratic forms.
We prove that allowing for slightly less symmetry, namely only cyclic and
axis--reflection symmetry,
gives rise to a class of extremal quasiconvex quadratic forms, that also turn out to
be non--polyconvex.

\item \textbf{Hisao Hayakawa, \texttt{hisao@yukawa.kyoto-u.ac.jp}} \\
\textbf{Co-authors:} Koshiro Suzuki\\
\papertitle{Theory on rheology of dense granular flow}

In this talk, I will discuss on possible
theoretical approaches on dense granular flows. The systems I will discuss are both
plane shear and pulling a tracer particle in a granular medium. The main part of
this talk will be focused on the first topic.
 In the first part, I will summarize some identities of granular flows, known as the
fluctuation theorem and the generalized Green-Kubo formula. These identities are
basis of the analysis of granular flows.
 In the second part, I will explain the formulation to describe the granular flows,
where I have adopted the mode coupling theory (MCT) to get a closure.
 In the third part, I apply MCT to the sheared granular flow. Thanks to the coupling
between the density correlation function and the cross correlation function of
density-current, the plateau of the density correlation function is suppressed. MCT
also can predict the viscosity if the density shift is adopted. Nevertheless, MCT
cannot be used to describe the jamming transition as it is. I will also discuss the
possible extension of MCT how to describe the jamming transition.
 In the fourth part, I apply MCT to the drag problem of a pulling tracer particle in
a granular medium. This can be regarded as one of problems on microrheology.

\item \textbf{Gengkai Hu, \texttt{hugeng@bit.edu.cn}}\\
\textbf{Co-authors:} Xiaoning Liu, Yi Chen, Guoliang Huang\\
\papertitle{Elastic metamaterials with chiral microstructure}

 By carefully designing
microstructures of composites to promote internal resonances under wave loading,
elastic metamaterials with negative material parameters (density, bulk and shear
modulus) can be obtained over a certain frequency. This property may have a great
potential to control low-frequency elastic waves. In the first part of the talk, we
will explain how to realize elastic metamaterials with chiral microstructure to
trigger rotational resonance. Chiral lattice with embedded resonators and thin plate
with chiral microstructure are designed and the both are demonstrated to have
simultaneous negative effective mass density and bulk modulus over certain
frequency, negative refraction of the latter is also verified experimentally by a
transient elastic wave tests. In the second part of the talk, we will present a
homogenization method for planar chiral lattices such as tetrachiral lattices
(isotropic chiral lattice as a special case), a bi--dimensional orthotropic chiral
micropolar model is developed based on the theory of irreducible orthogonal tensor
decomposition. The material constants of the continuum model are analytically
derived by a homogenization process. By comparing with discrete lattices, the
proposed continuum model is shown to be able to characterize correctly the wave
properties of the chiral lattices.

\item \textbf{Lee Hyundae, \texttt{hdlee@inha.ac.kr}}\\
\textbf{Co-authors:} Hyeonbae Kang, Kyoungsun Kim, Xiaofei Li, Graeme W. Milton\\
\papertitle{ Size estimate in complex conductivity using translation method}

The size estimation problem in electrical impedance tomography is
considered when the conductivity is a complex number and the body is
two-dimensional. Upper and lower bounds on the volume fraction of the unknown
inclusion embedded in the body are derived in terms of two pairs of voltage and
current data measured on the boundary of the body. These bounds are derived using
the translation method. We then show by numerical examples that these bounds are
quite tight and stable under measurement noise.


\item \textbf{Dominique Jeulin, dominique.\texttt{jeulin@mines-paristech.fr}}\\
\papertitle{On the statistical RVE of some long range random media}

It is usual to estimate the variance of local
averages by means of the
integral range (or integral of the centered normalized correlation function).
This procedure is followed to estimate the representative volume elements
(RVE) of the microstructure for numerical homogenization of effective
properties on simulations. Long fibers or stratified media show very long range correlations, inducing an
infinite integral range. This media can be simulated by models of Boolean
random varieties. \ For these models non standard scaling power laws exist for
the decrease of the variance of local averages, like the volume fraction, with
the volume of domains $K$ . In $R^{n}$, the asymptotic expression of the variance $D_{Z}^{2}(K)$ of the
local fraction $Z=\frac{\mu_{n}(A\cap K)}{\mu_{n}(K)}$ ($\mu_{n}(K)$ being the
Lebesgue measure of $K$) of a Boolean model built on isotropic Poisson
varieties of dimension $k$ ($k=0,1,...,n-1$) $V_{k}$, is expressed by [1]:
\[
D_{Z}^{2}(K)=p(1-p)\left(  \frac{A_{k}}{\mu_{n}(K)}\right)  ^{\frac{n-k}{n}}%
\]
The exponent $\gamma=$ $^{\frac{n-k}{n}}$ is equal to $\frac{2}{3}$ for
Boolean fibers in 3D, and $\frac{1}{3}$ \ for Boolean strata in 3D. When
working in 2D, the scaling exponent of Boolean fibers is equal to $\frac{1}%
{2}$. This reflects a much lower decrease of fluctuations with respect to the
volume of observations, as compared to media with a finite integral range,
where $\gamma=1$. As a result, very large domains have to be simulated to
obtain statistical RVE of the microstructure for numerical homogenization.
This behaviour was checked in the case of the estimation of elastic moduli and
thermal conductivity of simulations of various fiber systems.\\

[1] Jeulin D. (2011) Variance scaling of Boolean varieties, Paris School of
Mines internal report N/10/11/MM (2011), hal-00618967, version 1.

\item \textbf{Ken Karmin, \texttt{kkamrin@mit.edu}} \\
\textbf{Co-authors:} David Henann, Georg Koval\\
\papertitle{Nonlocal continuum modeling of dry granular flow}

 Despite the ubiquity of granular matter in the
world around us, the challenge of predicting the motion of a collection of flowing
grains has proven to be a difficult one, from both computational and theoretical
perspectives. In this talk, we begin by presenting a number of the ``unusual''
behaviors exhibited by dry granular media, which have posed hurdles from the
perspective of developing a continuum model.  These behaviors include: steady-flow
fields that do not obey any local flow rheology, flow onset and stoppage phenomena
that do not abide by a standard yield stress, and the motion-induced ``quicksand''
effect whereby far-away motion changes the flow resistance everywhere.  Herein we
present a non-local constitutive relation for granular matter, and demonstrate that
it correctly captures each of these unusual phenomena. This is achieved by
corroborating the model's predictions against hundreds of existing experimental data
sets, which elucidate the aforementioned behaviors.

\item \textbf{Robert V. Kohn, \texttt{kohn@cims.nyu.edu}} \\
\textbf{Co-authors:} Benedikt Wirth\\
\papertitle{Optimal design revisited: The leading order effect of perimeter regularization}

We consider a 2D shape
optimization problem involving a structure loaded in shear. When the goal is to
minimize compliance, optimality requires microstructure and a 2nd rank laminate is
known to suffice. We ask the question: what happens when the goal is to minimize
compliance plus epsilon times perimeter? Our main accomplishment is to identify the
leading-order effect of the perimeter regularization. This entails proving upper and
lower bounds that match (with respect to scaling). The construction associated with
the upper bound resembles a second-rank laminate, but uses branching rather than
approximate interfaces. The ansatz-free lower bound uses the Hashin--Shtrikman
variational principle, and therefore works mainly in Fourier space

\item \textbf{Michal Kordy, \texttt{kordy@math.utah.edu}}\\
\textbf{Co-authors:} Elena Cherkaev, Phil Wannamaker\\
\papertitle{Forward and inverse multi--frequency problem for Maxwell's equations using adaptive model order reduction}

This work develops a model order
reduction method for numerical solution of forward and inverse multi--frequency eddy
current problem. Using Helmholz decomposition, we extend previously developed
technique to the case when the operator has a non-empty null space. In the case of
Finite Element discretization of Maxwell's equations with edge elements, the
discrete Helmholtz decomposition is accomplished by solving a Poisson equation on
nodal elements of the same grid. Exploiting analyticity of the electromagnetic
field, we use Pade interpolation in the complex frequency plane; this allows us to
approximate the forward solution as well as the frequency-dependent jacobian in the
inversion procedure. To adaptively choose interpolating frequencies, we propose to
minimize the maximal approximation error. We discuss several error estimates and
propose a fast method of calculating the residual across a range of frequencies. The
efficiency of the developed approach is demonstrated by applying it to the forward
and inverse magnetotelluric problem, which is a geophysical electromagnetic remote
sensing method used in mineral, geothermal, and groundwater exploration. Numerical
tests show excellent performance of the proposed methods characterized by
significant reduction of computational time without loss of accuracy.

\item \textbf{Slava Krylov, \texttt{vadis@eng.tau.ac.il}} \\
\textbf{Co-authors:} Stella Lulinsky, Bojan R. Ilic, Inbar Schneider\\
\papertitle{Dynamics of Arrays of Parametrically Excited Electrostatically Coupled Micro Oscillators}

In this work we investigate collective dynamics of an array of
mechanically and electrostatically coupled micro cantilevers interacting through
electrostatic forces. The motivation of the work is twofold. On the one hand, arrays
of individually addressed elements could be used as  sensors and the knowledge of
their properties is necessary for the implementation of these devices in
applications. On the other hand, large arrays of micro oscillators interacting by
typically nonlinear and often tunable electrostatic forces exhibit rich dynamic
behavior. In this prospective micro technology can be viewed as a convenient and
versatile platform for the theoretical and experimental exploration of this kind of
systems. The device considered in this work is composed of two sets of partially
interdigitated flexible cantilevers. The coupling between the adjacent beams is a
combination of a mechanical coupling appearing due to the clamping compliances and
the electrostatic interaction through voltage-dependent electrostatic force. In the
framework of the reduced order model built using the Galerkin decomposition the
array is considered as an assembly of single degree of freedom oscillators. The
mechanical coupling matrix is extracted using the full scale finite element analysis
of the array.  Collective dynamics of the array under linear kinematic and
parametric electrostatic excitation are investigated numerically and experimentally.
In the long wave quasi continuum limit the dynamics of the system are described by a
nonlinear Klein-Gordon type equation and the array is equivalent to a string resting
on an elastic foundation and pulled by a nonlinear voltage-dependent force.  We show
that large amplitude collective vibrations of the array can be achieved using
parametric excitation while the dynamic properties of the array such as the width of
the propagation band as well as the modal patterns can be efficiently tuned by the
applied voltage.

\item \textbf{Rod Lakes, \texttt{lakes@engr.wisc.edu}} \\
\papertitle{Extreme elastic, viscoelastic and piezoelectric properties in structured materials}

Materials with extremely high, even
singular values of physical properties, are developed. Materials with designed
heterogeneity including inclusions of negative compressibility can exhibit extremely
high values of viscoelastic damping approaching a singularity, high Young's modulus
(even greater than that of diamond) or piezoelectric sensitivity. Such behavior
exceeds the usual theoretical bounds. The reason is that assumptions made in
deriving the bounds can be relaxed in certain materials and microstructures. We
consider toughness in the context of Cosserat elasticity in which there are
characteristic lengths as additional engineering elastic constants. There are a
total of six independent elastic constants in an isotropic Cosserat solid.
Experimental work discloses a variety of cellular and fibrous materials to exhibit
such freedom, and the characteristic lengths have been measured. In selected
isotropic cellular solids all six of the Cosserat elastic constants have been
measured. Several of these constants have been verified by further experiments in
geometries different from those used in the original measurements. Holographic
studies show that strain can spill over into regions which are classically
forbidden, specifically the corners of a square cross-section prism in torsion.

\item \textbf{Khanh Chau Le,  \texttt{chau.le@rub.de}} \\
\papertitle{Dislocations and formation of microstructures in single crystals}

The present paper develops nonlinear continuum dislocation
theory (CDT) to describe formation of microstructure in ductile single crystals. The
key quantity distinguishing this theory from the strain gradient plasticity is the
dislocation density being expressed in terms of the gradient of the plastic slip. We
propose the thermodynamic framework of the CDT in which the elastic strain and the
dislocation density are chosen as state variables. We specify the energy and
dissipation in terms of these state variables and derive the governing equations and
boundary conditions from the corresponding variational principles. We apply CDT to
three problems: i) formation of lamellar structure in TWIP-alloys by deformation
twinning, ii) formation of subgrain mictrostructure in bent single crystal beam by
the process of polygonization, iii) formation of shear bands in micropillars under
compression. We show that these processes are energy driven and compare the obtained
results with experimental data. The excellent agreement justifies CDT.

\item \textbf{Mikyoung Lim, mikyoung.\texttt{lim@gmail.com}} \\
\textbf{Co-authors:} Sanghyeon Yu\\
\papertitle{Asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions}

We consider the conductivity problem in the presence of adjacent circular inclusions
having arbitrary constant conductivity. When two
inclusions get closer and their conductivities degenerate to zero or infinity, the
gradient of the solution can be arbitrary large. We characterize the gradient
blow-up by deriving an explicit formula for the singular term of the solution in
terms of the Lerch transcendent function. This derivation is valid for inclusions
having arbitrary constant conductivity. We illustrate our results with numerical
calculations.

\item \textbf{Liping Liu, liu.\texttt{liping@gmail.com}} \\
\papertitle{Attainability of Hashin--Shtrikman's bounds for multiphase composites}

We address the
attainability of the Hashin--Shtrikman (HS) bounds for multiphase composite
materials. We demonstrate that the HS bounds are
not always attainable and give new restrictions on the attainable HS
bounds in terms of the conductivities and volume fractions of the
constituent phases. New optimal microstructures are also constructed to
attain the HS bounds. Combined together, these results allow for precise
characterization of the set of effective properties for a wide range of
composite materials.

\item \textbf{Konstantin Lurie, \texttt{klurie@wpi.edu}} \\
\papertitle{On Material Optimization in Continuum Dynamics}

The talk is aimed to discuss reasonable statement of the typical
problems of optimal material optimization in continuum dynamics. Most of such
problems are originally ill-posed and therefore require relaxation. In statics, such
relaxation is achieved due to a material scaling accompanied by homogenization.
Unlike that, in dynamics relaxation may be achieved through the involvement of
dynamic materials - material formations with properties variable in space and time.
The paper introduces some scenarios for such relaxation; in the absence of any
general existence theorems, such scenarios are prompted by a suitable physical
insight. Homogenization applies only in some of these scenarios.


\item \textbf{Fred MacKintosh, \texttt{fcmack@gmail.com}} \\
 \papertitle{"Elasticity on the edge of stability: soft matter inspired by the cell}
 
Much like the bones in our bodies, the
cytoskeleton consisting of stiff protein biopolymers determines the mechanical
stability and response of cells. Unlike passive materials, however, living cells are
kept far out of equilibrium by metabolic processes and energy-consuming molecular
motors that generate forces to drive the machinery behind various cellular
processes. Inspired by such networks, we describe recent theoretical and
experimental advances in our understanding of fiber networks in vitro and in vivo.
We show that these exhibit a unique state of highly responsive matter near the
isostatic point first studied by Maxwell [1,2]. For fiber networks, this represents
a marginal state of matter with exceptional mechanical properties, including a
strongly nonlinear elastic response and zero-temperature critical behavior [3].
Moreover, the introduction of molecular motor activity can dramatically affect the
stability of such systems [4,5].\\


[1] JC Maxwell, Philos Mag, 27 294 (1864).\\ \relax
[2] CP Broedersz, X Mao, TC Lubensky, and FC MacKintosh, Nat Phys, 7 983 (2011).\\ \relax
[3] M Dennison, M Sheinman, C Storm, FC MacKintosh, Phys Rev Lett, 111 095503 (2013).\\ \relax
[4] M Sheinman, CP Broedersz and FC MacKintosh, Phys Rev Lett, 109 238101 (2012).\\ \relax
[5] J Alvarado, M Sheinman, A Sharma, FC MacKintosh, GH Koenderink, Nat Phys, 9 591 (2013).\\ \relax



\item \textbf{Alexander Mamonov, \texttt{mamonov@gmail.com}} \\
\textbf{Co-authors:} Vladimir Druskin, Mikhail Zaslavsky\\
\papertitle{Krein--Gelfand--Levitan algorithm for inverse hyperbolic problems via spectrally matched finite-difference grids}

We present a method for the
numerical solution of inverse problems for coefficients of hyperbolic PDEs based on
the spectrally matched finite-difference grids (a.k.a. Gaussian quadrature rules or
optimal grids). The method is built around an algorithm for interpolation of the
measured time domain data. Once an interpolant is obtained, it can be expressed in
terms of Stieltjes continued fraction or its matrix generalization. The use of
S-fraction coefficients in inversion is twofold. First, they can be used to
reformulate the traditional optimization-based approaches to drastically improve the
objective functional, which addresses issues such as the abundance of local minima
and slow convergence. Second, the coefficients provide a way to obtain direct,
non-iterative reconstructions on the spectrally matched grids. We supplement the
theoretical considerations with the numerical results.

\item \textbf{Ross McPhedran, \texttt{ross@physics.usyd.edu.au}} \\
\textbf{Co-authors:} J. O'Neill, O. Selsil, A.B. Movchan and N.V. Movchan\\
\papertitle{A Platonic View of Active Cloaking}

We consider active
cloaking of flexural waves in a Kirchhoff plate, where the objective is to minimise
the far-field scattering signature of a rigid, clamped inclusion. The method relies
on placing control sources at small distances from the scatterer and choosing their
strengths to eliminate propagating orders of the scattered wave, thus reconstructing
the incident wave.
We use six control sources to obtain an effective configuration for cloaking the
circular inclusion. Finally, we successfully cloak an arbitrarily shaped scatterer
by deriving a semi-analytical, asymptotic algorithm.
For further details, see  arXiv:1403.0816

\item \textbf{Graeme W. Milton, \texttt{milton@math.utah.edu}} \\
\papertitle{Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots}

A complete characterization is given of the possible macroscopic
deformations of periodic nonlinear affine unimode metamaterials constructed from
rigid bars and pivots. The materials are affine in the sense that their macroscopic
deformations can only be affine deformations: on a local level the deformation may
vary from cell to cell. Unimode means that macroscopically the material can only
deform along a one dimensional trajectory in the six dimensional space of invariants
describing the deformation (excluding translations and rotations). We show by
explicit construction that any continuous trajectory is realizable to an arbitrarily
high degree of approximation provided at all points along the trajectory the
geometry does not collapse to a lower dimensional one. In particular, we present two
and three dimensional dilational materials having an arbitrarily large flexibility
window. These are perfect auxetic materials for which a dilation is the only easy
mode of deformation. They are free to dilate to arbitrarily large strain with zero
bulk modulus.

\item \textbf{Sebastien Motsch, \texttt{smotsch@asu.edu}}\\
\textbf{Co-authors:} Pierre Degond, Irene Gamba, Jeff Haack, Laurent Navoret\\
\papertitle{Emergence of macroscopic behavior in complex systems}

In a human crowd
or in a shoal of fish, thousands of individuals interact and form large scale
structures. Although the interaction among individuals might be simple, the
resulting dynamics is quite complex. Modeling is an essential tool to understand
such dynamics. For instance, Agent-based models, also referred to as microscopic
models, are widely developed to analyze various dynamics such as swarming and
opinion formations. In this talk, we investigate the emergence of macroscopic behavior for such models.
The challenge is to link ``microscopic models'' describing each agent with
``macroscopic models'' describing the evolution of a fluid. To achieve this
transition, we present a novel approach based on kinetic theory and asymptotic
analysis. Numerical simulations are also presented to illustrate the results.

\item \textbf{Benjamin N. Murphy, \texttt{nbmurphy@math.uci.edu}} \\
\papertitle{Random Matrix Universality, Spectral Measures, and Composite Media}

We consider composite media with a broad range of
scales, whose effective properties are important in materials science, biophysics,
and climate modeling. Examples include random resistor networks, polycrystalline
media, porous bone, the brine microstructure of sea ice, ocean eddies, melt ponds on
the surface of Arctic sea ice, and the polar ice packs themselves. The analytic
continuation method provides a rigorous approach to treating the effective
properties of such systems. At the heart of this method is a random matrix which
depends only on the composite geometry. In this lecture we will discuss computations
of the spectral measures of this operator which yield effective properties, as well
as statistical measures of its eigenvalues. In particular, the effective behavior of
these systems often exhibits large changes associated with transitions in the
connectedness or percolation properties of a particular phase. We demonstrate that
an onset of connectedness gives rise to transitional behavior in the eigenvalue
correlations of the random matrix, which is captured by a one-parameter universality
class of random matrix ensembles. This, in turn, gives rise to transitional behavior
in the spectral measures, leading to observed critical behavior in the bulk
transport properties.

\item \textbf{Akio Nakahara, \texttt{nakahara@phys.ge.cst.nihon-u.ac.jp}}\\
\textbf{Co-authors:} Hiroshi Nakayama, Yousuke Matsuo, Ooshida Takeshi\\
\papertitle{Control of desiccation crack patterns using memory effects of paste and Faraday waves}

 A densely packed colloidal suspension, called paste,
remembers the direction of horizontal vibration and flow it experienced, and the
memory of such motion can be visualized as a morphology of crack patterns which
appear when the paste is dried. When the paste remember the direction of the
horizontal vibration, desiccation
cracks run in the perpendicular to the direction of the initial vibration. On the
other hand, when the paste remembers the direction of the flow, desiccation cracks
run in the direction parallel to the flow direction. Even if we had found a method
to control the direction of crack propagation using memory effect of paste, it was
difficult to control the position where cracks will appear. Here we find a method to
control the position of crack formation by using both the memory effects and the
Faraday waves which will appear when the paste is vibrated vertically. The
experiments show that cracks tend to appear in the node zones of the Faraday waves,
where the paste is vibrated locally and strongly in horizontal direction. We also
succeed in making square lattice crack patterns using square lattice Faraday waves.

 \item \textbf{Hoai-Minh Nguyen,  \texttt{hoai-minh.nguyen@epfl.ch}} \\
\papertitle{Cloaking and Superlensing using complementary media}

 Negative index material (NIM) is an artificial structure where the
 refractive index has a negative value over some frequency range.
NIMs were first investigated theoretically by Veselago in 1964 and were innovated by
Nicorovici et al. in 1994 and Pendry in 2000.
The existence of such materials was confirmed by Shelby et al. in 2001.  NIMs has
many interesting applications such as  cloaking suggested by Lai et al. in 2009,
superlensing proposed by Veselago in 1964, Nicorovici et al. in 1994 and Pendry in
2000, and cloaking by anomalous localized resonance by Milton et al. in 2006.
An important class of NIMs related to these phenomena are complementary media.  In
this talk, I will present the ideas of cloaking and superlensing using complementary
media and discuss their rigorous proofs. If time permits, cloaking by anomalous localized
resonance is also discussed.

\item \textbf{Andrew Norris, \texttt{norris@rutgers.edu}} \\
\papertitle{Static and dynamic elastic homogenization of periodic  structures}

The talk considers  (i) static homogenization of lattice
structures modeled by thin beam members and (ii) a  procedure for dynamic
homogenization of general periodic elastic media.   The seemingly disparate topics
are motivated by a need to understand the static and dynamic behavior of lattice
structures which have been proposed as candidates for pentamode materials.  Our main
result for {\it static} properties of a lattice structure  with coordination number
$Z$  is that the   effective moduli  can be expressed in  Kelvin-like form
$ {\bf C} =   \sum_{i, j=1}^{N}  P_{ij}  {\bf U}_i\otimes {\bf U}_j
$ where  $N = \frac 12 Z(Z+1)$,  $ {\bf U}_i $ are  second order tensors, and
$P_{ij}  $ are elements of a $N\times N$ projection matrix ${\bf P} $ of rank $N-d$,
in $d=2$ or $3$ dimensions.  The $N$ second order tensors $\{ {\bf U}_i  \}$  split
into $Z$ stretch dominated and $N-Z$ bending dominated elements.  The latter
contribute little to the stiffness in the limit of very thin members, in which case
the elastic stiffness is, at most,  of rank $Z-d$.    ${\bf C}$ is rank one if
$Z=d+1$, corresponding to pentamode materials.
Part (ii) describes a general procedure for defining and calculating {\it dynamic}
effective  properties of periodic media.   The dynamic homogenization yields
constitutive relations for  the effective medium  of the so-called Willis type which
couples stress with  velocity,  and momentum to strain.    It turns out that there
is then  a unique system of equations governing the  effective field variables
defined according to
$h^{\text{eff}}(\mathbf{x},t)=\langle h\rangle \,e^{i(\mathbf{k}\cdot
\mathbf{x}-\omega t)} $
for each field variable (displacement, stress, etc.) where   $\langle h\rangle$ is
the spatial average of the periodic part of $h$.  The  effective dynamic parameters
yield the exact dispersion relation for Bloch waves.  Implications of the dynamic
homogenization scheme for lattice networks will be discussed and compared with the
static effective moduli.

\item \textbf{ Braxton Osting, \texttt{braxton@math.ucla.edu}}\\
\textbf{Co-authors:} Jeremy Marzuola\\
\papertitle{Concentrated density of states and the triangular lattice}

Motivated by a problem in
solar cell design, we consider a spectral optimization problem for a weighted graph
Laplacian on a geometric configuration of points, where the edge weights are
dependent on pairwise distances. We seek finite (infinite) configurations of points
whose associated Laplacian has eigenvalues (density of states) concentrated at a
particular value. The challenge of this problem stems from the geometric constraints
on the point configuration. Preliminary results show that for the two-dimensional
periodic problem, the triangular lattice is a robust optimizer of this and several
other spectral properties. This is joint work with Jeremy Marzuola.

\item \textbf{Alexander Panchenko, \texttt{anpanchenko@gmail.com}} \\
\papertitle{Non-local continuum models of particle systems}

The main question addressed in the
talk is how to obtain continuum equations for spatial averages from the ODEs of
classical particle dynamics. Balance equations for the average density, linear momentum, and energy were derived
by Irving and Kirkwood, Noll, Hardy, Murdoch and others. These equations are exact,
but not in closed form since fluxes are given as functions of particle positions and
velocities. Evaluating the exact fluxes requires solving the full ODE system which
can be prohibitively expensive. We present a closure approximation that leads to
continuum models in the true sense of the word. The fluxes in these models are given
by operators acting on the average density and velocity. The closure construction is
based on the use of regularized deconvolution. In the discrete setting,
characterized by a finite non-improvable resolution, the error associated with
deconvolution closure can be further reduced by incorporating a priori knowledge of
empirical statistics of fluctuations.  At the end of the talk we briefly discuss
connections with large eddy simulation and quasi-continuum method. Results of
numerical experiments and partial error estimates are presented as well

\item \textbf{Mikhail Raikh, \texttt{raikh@physics.utah.edu }} \\
\textbf{Co-authors:} R. C. Roundy\\
\papertitle{Spin dynamics of a diffusively moving electron in a random hyperfine field}

We study the dynamics,
$\langle S_z(t)\rangle$, of the average spin of electron hopping over sites which
host random hyperfine magnetic fields. If the typical waiting time for a hop is
$\tau$ and the typical magnetic fields is $b_{s_0}$, then the typical
spin-precession angle on a given site is $\delta \phi \sim b_0\tau \ll 1$. Then the
Markovian theory predicts that the spin, initially oriented along the $z$-axis
decays, on average, as  $\langle S_z(t)\rangle=\exp(-t/\tau_s)$, where
$\tau_s=1/b_0^2\tau$ is the spin-relaxation time.
We find that in low dimensions, $d=1,2$,  the  decay, $\langle S_z(t)\rangle$, is
non-exponential at all times. The origin of the effect is that for $d=1,2$ a typical
random-walk trajectory exhibits numerous self-intersections. Multiple visits of the
carrier to the same site accelerates the relaxation since the corresponding partial
rotations, $\delta \phi$,  of spin during these visits add up. As a result, the
Markovian description does not apply.  For one-dimensional diffusion of electron
over sites, the average,  $\langle S_z(t)\rangle$, is the universal function of
$t^{3/2}/\tau^{1/2}\tau_s$, so that the characteristic decay time is
$\tau^{1/3}\tau_s^{2/3}$ is much shorter than $\tau_s$. Moreover, when the random
magnetic fields are located in the $(x,y)$ plane, the decay of  $\langle
S_z(t)\rangle$ to zero is preceded by a {\em reversal} of $\langle S_z(t)\rangle$ to
the value $\langle S_z\rangle =-0.16$ at intermediate times. We develop an
analytical self-consistent description of the spin dynamics which explains this
reversal. Another consequence of self-intersections of the random-walk trajectories is that,
in all dimensions, the average,   $\langle S_z(t)\rangle$, becomes sensitive to a
weak external magnetic field directed along $z$.
Our analytical predictions are complemented by the numerical simulations of
$\langle S_z(t)\rangle$.


\item \textbf{Gregory Rodin, \texttt{gjrodin@gmail.com}} \\
\textbf{Co-authors:} George J. Weng\\
\papertitle{On reflected interactions in elastic solids containing inhomogeneities}

Interactions in
linear elastic solids containing inhomogeneities are examined using integral
equations. Direct and reflected interactions are identified. Direct interactions
occur simply because elastic fields emitted by inhomogeneities affect each other.
Reflected interactions occur because elastic fields emitted by inhomogeneities are
reflected by the specimen boundary back  to the individual inhomogeneities. It is
shown that the reflected interactions are of critical importance to analysis of
representative volume elements. Further, the reflected interactions are expressed in
simple terms, so that one can obtain explicit approximate expressions  for the
effective stiffness tensor for linear elastic solids containing ellipsoidal and
non-ellipsoidal inhomogeneities. For ellipsoidal inhomogeneities, the new
approximation is closely  related to that of Mori and Tanaka. In general,  the new
approximation can be used to recover Ponte-Casta$\tilde{\rm n}$eda-Willis' and
Kanaun-Levin's approximations. Connections with Maxwell's approximation are
established.

\item \textbf{Massimo Ruzzene, \texttt{ruzzene@gatech.edu}} \\
\textbf{Co-authors:} Marshall Schaeffer\\
\papertitle{Wave Propagation in Multistable Magneto-Elastic Lattices}

The paper discusses the wave
propagation characteristics of two-dimensional (2D) magneto-elastic meta-structures.
 These structures demonstrate the ability to undergo large topological and stiffness
changes, which allows for dramatic changes in wave propagation characteristics.
The analysis is conducted using a lumped mass system of magnetic particles.
Instabilities caused by the magnetic interactions are exploited in combination with
particle contact to produce topological changes leading to stiffness changes and
corresponding variations in wave propagation patterns.  The propagation of plane
waves is predicted by applying Bloch theorem to linearized unit cells, and
subsequently evaluated through direct numerical simulations of the fully nonlinear
governing equations. Changes in mechanical properties are also assessed through
homogenization procedures relying on the long-wavelength approximation of the
discrete equations of motion and the formulation of equivalent continua.


\item \textbf{Gal Shmuel, \texttt{galshm@caltech.edu}} \\
\textbf{Co-authors:} Adam Thor Thorgeirsson, Kaushik Bhattacharya \\
\papertitle{Wavelet Analysis of Microscale Strains}

Recent experiments and numerical
simulations provide numerous observations on the microstructure and deformation of
polycrystals. These show how confined bands of deformation percolate in a complex
way across various grains. Such information is represented as samples on grids, and,
in turn, creates huge data sets. The extensive size of data in this form renders
identifying key features difficult, and the cost of digital storage expensive. To
represent, analyze, and predict strain fields with localized features, we use
wavelets: multiresolution functions, which are localized both in frequency and real
domains. By way of example, we focus on pseudo-elastic polycrystals, capable of
recovering strains beyond an apparent elastic limit. We will show how wavelets
efficiently represent experimental and simulated strains of Ni-Ti, while reducing
data size by two orders of magnitude. More importantly, We will show how the compact
wavelet representation captures the essential physics within.


% \item \textbf{Ole Sigmund, \texttt{sigmund@mek.dtu.dk}} \\
% \papertitle{Topology optimization for material and optical surface design}

% The topology optimization approach is a numerical technique
% based on alternating finite element analyses, analytical gradient computations and
% math--programming--base design updates. Although originally developed for structural
% optimization, the methods has with great success been applied to inverse problems in
% material design, such as the design of negative Poisson's ratio, negative thermal
% expansion, acoustic, elastic and optical band gaps as well as for reflecting or
% transmitting surface design. The presentation will discuss recent advances in systematic material and surface
% design by density-based topology optimization. The applications include: extremal
% elastic materials for finite deformations, design for manufacturability of 3D
% elastic structures as well as systematic design of nano-surfaces for structural
% color generation

\item \textbf{Alexey Stepanov, \texttt{alex314@umd.edu}}  \\
\textbf{Co-authors:} Stuart S. Antman\\
\papertitle{Equilibrium States of Nonlinearly Elastic Annuli and Spherical Shells}

Within the linear theory of
elasticity, the problems for the
equilibria of circular annuli and spherical shells composed of homogeneous,
transversely isotropic materials were solved by Gabriel Lam\'e. The radially symmetric
equilibria of an isotropic nonlinearly elastic disk or ball is elementary. If,
however, the disk or ball is aeolotropic, even for a homogeneous linearly elastic
material, the solution can exhibit a rich range of singular behavior at the origin.
We show that BVPs for the equilibria of circular annuli and spherical shells
composed of transversely isotropic nonlinearly elastic materials are far from
elementary within the framework of geometrically exact theories. We employ a variety
of mathematical approaches, discussing the virtues and idiosyncracies of each.

\item \textbf{Tuomas Tallinen, tuomas.\texttt{tallinen@jyu.fi }} \\
\papertitle{Hyperelastic modeling of morphogenesis}

Soft tissues in developing embryos exhibit complex mechanics with
characteristics between those of fluid and solid. Elastic behavior of the tissues at
short time scales is followed by inelastic deformation and flow, and interesting
open questions are related to the underlying cellular dynamics. For example, tissue
fluidity may result either from flow of cells or from nonuniform cell proliferation.
We model growing soft tissues by continuum mechanics, starting from a hyperelastic
model, with extensions to inelasticity and flow. In particular, we first focus on
the development of the gut and its patterning through mechanical instabilities. Even
though the endoderm and mesenchyme tissue layers are just few cells thick, a minimal
elastic continuum model provides a reasonable description of the mechanical
behavior. We also consider the folding of the brain and how its neuronal and axonal
growth may be mapped to a large strain visoelastic model producing folding patterns
consistent with observations on a wide range of brains.

\item \textbf{Andrew Thaler, \texttt{thaler@math.utah.edu}} \\
\textbf{Co-authors:} Graeme Milton\\
\papertitle{Bounds on the volume fraction of an inclusion in a body with complex conductivities}

In this talk, I
will present some recent work concerning the derivation of bounds on the volume
fraction occupied by an inclusion in a body (or one of the phases in a two-phase
composite). We assume that both the inclusion and the body are isotropic and homogeneous with complex-valued
conductivities.  The bounds we derive correlate the average electric
field, average current field, and volume fractions of the phases;
practically, the average electric field and average current field can
be measured in terms of boundary measurements of the complex potential and electric
current flux.  These bounds could have potential
applications in nondestructive testing and medicine, such as in the
screening of organs prior to transplantation.


\item \textbf{Andrejs Treibergs, \texttt{treiberg@math.utah.edu}} \\
\textbf{Co-authors:} Marc Briane, Graeme W. Milton\\
\papertitle{On the Realizability of Electric Fields in Conducting Materials}

Given an
electric field $\nabla u$ in $\mathbf R^d$, we discuss whether  it is realizable in
the sense that there is a conductivity matrix function  $\sigma$ such that the
current field given by Ohm's law, $\sigma\nabla u$, satisfies conductivity equation
$$
\operatorname{div}(\sigma \nabla u) = 0.
$$
For application we focus on periodic fields.
In the isotropic case the conductivity, given by a scalar $\sigma=fI$, may be found
by solving a first order partial differential equation. A smooth, non-vanishing,
electric field may be isotropically realized locally. Assuming that the vector field
is periodic or satisfies a geometric condition such as having a transverse
hyperplane, it may be realized globally. If the electric field is not smooth, it may
not not be realized. If the electric field is periodic it may not be realizable by a
periodic conductivity. In two dimensions, if a periodic field is realized by a
periodic conductivity, then the field does not vanish. This fails in three
dimensions.
In two dimensions we characterize the periodic gradient fields  which are realized
by a periodic symmetric positive definite matrix valued function $\sigma$.
We consider also vector valued potentials and their matrix valued fields $DU$.
Positivity of the determinant is sufficient  for a smooth  potentials with periodic
$DU$ to be anisotropically realizable. The condition is necessary in dimension two.
Analogously, laminate electric fields are anisotropically realizable if they have
constant sign determinants.
[{\it v.}, ``Which electric fields are realizable in conducting materials?,'' {\it
ESAIM: Mathematical Modeling and Numerical Analysis 2013/89: Special Issue 2014:
Multiscale Problems and Techniques}, Archive {\tt http://arxiv.org/abs/1301.1613.}]

\item \textbf{Lev Truskinovsky, \texttt{trusk@lms.polytechnique.fr}} \\
\papertitle{Passive mechanical behavior of skeletal muscles}

In contrast to inert matter, distributed biological systems
are
characterized by hierarchical network architecture with domineering
long-range interactions.
Even in the absence of metabolic fuel  this leads to a highly
cooperative passive mechanical behavior. Collective effects are usually
associated with conformational changes which can be  interpreted as
folding-unfolding  transitions. In the presence of  long-range interactions  systems
with
internal unfolding  exhibit coherent macroscopic hopping  between folded and
unfolded configurations  resisting the destabilizing effect of finite
temperatures. A  minimal mechanical system exemplifying such behavior is  a parallel
bundle of  bi-stable units linked by two shared backbones and its most well known
biological  prototype is  the collective  power-stroke in sarcomeric acto-myosin
networks.  In this talk we review  the mechanics of this mean-field type
model at zero and finite temperatures.  We show that at  zero temperature the
ground states always correspond to coherent configurations.   The
relaxed potential, representing the global minimum of the energy, is  convex in a
soft  device but is only convex-concave in a hard device.  Such ensemble
non-equivalence and the meta-material  response, which persist in the continuum
limit, is a result of non-additivity:  each element is linked with all other
elements and  the whole is not a sum of the parts. An important  feature of the
finite  temperature behavior in this system is the appearance of a critical
point  of Curie-Weiss type separating the correlated  hopping at low temperatures
from the uncorrelated fluctuations at high temperatures. We show that the actual
skeletal muscles  appear to be functioning very close to this critical point.




\item \textbf{Anna Vainchtein, \texttt{aav4@pitt.edu}} \\
\papertitle{The discrete charm of nonlinearity: solitary waves in non-integrable lattices}

The interplay between discreteness and
nonlinearity in many physical systems leads to the formation of solitary waves. For
example, such waves were experimentally observed in granular materials, electrical
transmission lines and optical fibers. Much of the interest in these nonlinear waves
was triggered by the pioneering study by Fermi, Pasta and Ulam (1955). The
subsequent work of Zabusky and Kruskal (1965) has revolutionized the nonlinear
science by connecting the FPU problem to its quasicontinuum near-sonic limit
described by the KdV equation. In integrable systems solitary waves, known as
solitons, are now well understood, with one-dimensional Toda lattice being the most
prominent example that has an exact solution covering a broad range of behaviors
from delocalized low-energy waves in the KdV limit to highly localized high-energy
waves. Most discrete systems, however, are non-integrable. In this case understanding the
transition from the KdV limit to the strongly discrete waves has mostly relied on
numerical and quasicontinuum approximations. In this talk I will review some of
these results and describe recent work with Lev Truskinovsky on a non-integrable FPU
problem with piecewise quadratic potential. We construct an exact solitary wave
solution that captures the entire crossover velocity range between the low-energy
limit and strongly localized waves that involve only one particle moving at a time.
The solution is expressed in the form of an infinite series. A truncation of the
series involving progressively smaller characteristic wavelengths produces a nested
set of approximate solutions. Even the simplest solution of this type that accounts
only for the longest wave lengths provides a better overall approximation of
solitary waves than some conventional quasicontinuum models. Some related open
problems will also be discussed.

\item \textbf{Valy Vardeny, \texttt{val@physics.utah.edu}} \\
\textbf{Co-authors:} R. C. Polson\\
\papertitle{Advances in Organic Random Lasers}

Systems which produce laser emission that contain sharp coherent resonant
alines, but without an engineered cavity are grouped under the term `random lasers'
(RL). There are many examples of RL systems such as: powders of laser crystals, dye
and scatterers in suspension, clusters of nanoparticles,
$\pi$-conjugated polymer, etc.; here we focus on RL organic gain media. This
includes thin films, dye-infiltrated opals, and dye infiltrated human tissues.
Usually RL emission spectra contain numerous narrow lines (say $> 20$) on top of a
broader background of amplified spontaneous emission. Since there are so many
resonant lines, subsequent analysis of the RL emission spectrum is rather
complicated; however it has been relatively easy to explain RL spectra by several
different theoretical models that produce a variety of lines, which typically are
not correlated one to the other. This type of theoretical view misses an important
experimental discovery, namely that the average Fourier transform (FT) of RL spectra
over different locations on the organic gain medium film does not average out to a
smooth line, but instead contains regular Fourier components that are typical to the
material studied and the excitation intensity. We show that this phenomenon stems
from the existence of naturally formed microcavities in the gain medium films, which
can be effectively mapped using a novel optical technique. We also show that the FT
spectrum of RL emission from dye infiltrated human tissues can be used for cancer
diagnosis and mapping.

% \item \textbf{Fengven Wang, \texttt{fwan@mek.dtu.dk}} \\
% \textbf{Co-authors:} Ole Sigmund, Jakob S. Jensen\\
% \papertitle{Topology optimization of finitely deformable multifunctional materials}

% Based on the homogenization method, topology optimization has been
% demonstrated to be an effective approach to design novel materials for small
% deformations with extreme properties, such as auxetic materials (i.e. negative
% Poisson's ratio materials) and high damping materials. However, under large
% deformation material properties vary with strain and recently, 2D auxetic materials
% have been designed using topology optimization to achieve constant negative
% Poisson's ratios under large deformation. Auxetic foams have been reported to
% exhibit high damping factor, but systematic studies have received little attention
% previously to design materials with focus on the damping properties under large
% deformation. In this study, we aim to design novel materials with prescribed multifunctional
% properties under large deformation, e.g., negative Poisson's ratio and high loss
% factor. The geometrically nonlinear behavior of the periodic microstructure is
% simulated using a total Lagrangian finite element formation, and solved by a
% Newton--Raphson algorithm. Numerical instabilities due to excessive element
% deformations are avoided using an energy interpolation scheme. In the first part, we
% aim at designing 2D and 3D materials with different prescribed Poisson's ratio
% profiles. The optimization problem is formulated to minimize the errors between the
% actual and prescribed Poisson's ratio profiles in a given strain range. In the
% second part, we aim at designing high damping materials under large deformation
% while retaining material stiffness. The damping properties of materials are
% evaluated in the quasi-static frequency domain. The corresponding optimization
% problem is to maximize loss factors in a given strain range subjected to stiffness
% constraint, including effects of material constituents with different bulk and shear
% loss factors.

\item \textbf{Martin Wegener, \texttt{martin.wegener@kit.edu}}\\
\papertitle{Experiments on Elastic and Thermodynamic Cloaking}

We review our recently published as well as unpublished
experiments on cloaking in optics, mechanics, and thermodynamics. This includes
broadband cloaking of flexural waves in thin elastic plates based on coordinate
transformations, three-dimensional core-shell elastostatic cloaks based on pentamode
metamaterials, transient thermal cloaks based on coordinate transformations, and
three-dimensional cylindrical as well as spherical core-shell invisibility cloaks
for diffusive light that work throughout the entire visible spectral range.

\item \textbf{Niklas Wellander,  \texttt{niklas.wellander@hotmail.com, niklas.wellander@foi.se}} \\
\textbf{Co-authors:} Gerhard Kristensson\\
\papertitle{A priori estimates of solutions to the Maxwell equations}

We present a collection of a priori
estimates of the electromagnetic field scattered by a general bounded domain. The
constitutive relations of the scatterer are in general anisotropic. Surface averages
are investigated and several results on the decay of these averages are presented.
The norm of the exterior Calder\'on operator for a sphere is investigated and
depicted as a function of the frequency.

\item \textbf{Anna Zemlyanova,  \texttt{azem@math.ksu.edu}} \\
\papertitle{Curvature-dependent surface tension in modelling of fracture}

A new model of fracture mechanics
which takes into account interfacial effects due to a curvature-dependent surface
tension will be considered. This model is based on a physically valid assumption
that the behavior of molecules near a surface of a material is significantly
different from those in the bulk and depends on the local curvature of the material
surface. The theory will be presented through several examples: a curvilinear
non-interface and interface crack, and contact problems for a rigid stamp
indentation into an elastic half-plane. It will be shown that the incorporation of
surface effects on the crack boundary eliminates the power and oscillating
singularities at the crack tips which are predicted by linear elastic fracture
mechanics. The mechanical problems will be reduced to the systems of singular
integro-differential equations. The regularization and numerical solution of these
systems will be addressed and numerical examples will be presented. Potential
direction for future research and connections with experimental results will be
discussed.
\end{enumerate}

\end{document}
