40 MS08 Abstracts CP1 oretical results such as the Lifshitz-Slyozov growth law; the Percolation of Conductivity for Carbon Nanotubes effect of adjusting the interaction length scale is also de- scribed. The problem of the percolation of conductivity that oc- curs from the suspension of carbon nanotubes in a non- David J. Horntrop conductive polymer matrix is of considerable interest for Dept of Mathematical Sciences, Center for Applied Math applications in the development of electronic devices at the New Jersey Institute of Technology nanoscale. The onset of conductivity awaits accurate pre- [email protected] diction. This talk will examine models (Schramm-Loewner evolution [SLE], lattice-path walks, moduli space integra- tion) that attempt to present this behavior. The advan- CP2 tages and disadvantages of these approaches will be dis- Mathematical Modeling of Heat-Shrinkable Thin cussed. Films Joseph P. Brennan We present a mathematical model for simulating the be- Department of Mathematics and Nanoscience Technology havior of thin films that undergo an irreversible deforma- Center tion upon applying heat to their surface. We derive an University of Central Florida asymptotic model, compare and relate to results obtained [email protected] by using Γ-convergence techniques, and present numerical results. The problem is motivated by industrial attempts Qun Huo to deform originally flat, thin protective layers into shapes Department of Chemistry and Nanoscience Technology that can be easily applied onto car windshields. A typical Center material used in the simulations is PET. University of Central Florida Pavel Belik [email protected] Department of Mathematics University of St. Thomas Aihua Li [email protected] Department of Mathematical Sciences Montclair State University Cristina Thomas, Bob Jennings [email protected] 3M [email protected], [email protected] CP1 Facet Evolution on Supported Nanostructures: the Mikhail M. Shvartsman Effect of Finite Height University of St. Thomas [email protected] Nanostructures relaxing on a substrate consist of a finite number of steps and therefore have a finite height. We show that finite height effects play an important role in CP2 the structure’s macroscopic evolution: for axisymmetric New PDEs from Polycrystal Plasticity nanostructures relaxing under elastic/entropic repulsions and step line tension, we demonstrate a switch in the time Several highly degenerate nonlinear PDE arising as Arons- 1/4 son equations associated to variational principles for mod- behavior of the facet’s radius from O(t )toO(t). els in Polycrystal Plasticity obtained via Γ-convergence are Pak-Wing Fok introduced. Caltech Marian Bocea [email protected] North Dakota State University [email protected] Rodolfo R. Rosales Massachusetts Inst of Tech Department of Mathematics CP2 [email protected] High Contrast Homogenization in Dimension 2: Conduction Vs. Elasticity Dionisios Margetis University of Maryland, College Park We study the asymptotic behaviour of two-dimensional lin- [email protected] ear elasticity problems with equicoercive elasticity tensors. Assuming the L1-boundedness of the sequence of tensors, we obtain a compactness result extending to the elasticity CP1 setting the divcurl approach of M. Briane and J. Casado- Simulation of Self-Organization in Surface Pro- Daz for the conduction. We also show there is a gap, in the cesses limit behaviour, between the very stiff problems of elastic- ity and those of conduction described by M. Briane and J. Self-organization of components of two phase mixtures Casado-Daz. through diffusion is known as Ostwald ripening. This mul- tiscale phenomenon is can be studied using mesoscopic Mohamed Camar-Eddine models which are stochastic partial differential equations INSA de Rennes & IRMAR that have been derived directly from the underlying micro- Centre de Math´ematiques physics. In this talk, results from simulations using spec- [email protected] tral schemes for stochastic partial differential equations are described. These simulation results are compared with the- Marc Briane MS08 Abstracts 41 INSA de Rennes & IRMAR Applications to Soft Materials and Bio-Materials [email protected] In this work we study how the fine-scale geometry of a 2- dimensional network of deformable fibers affects the sym- CP2 metry properties of the elastic and bending energy of the Variational Estimates for the Effective Conductiv- material. We focus on textiles that can be modelled as ity of 3D Nonlinear Polycrystals 2-dimensional networks of inextensible fibers, with a view to applications to biological tissues. For networks made Bounds and estimates for the effective conductivity of non- by two families of fibers, four types of fine-scale structures linear polycrystalline aggregates with isotropic crystallo- are possible, corresponding to the simplest weave patterns graphic texture and two-point statistics are obtained by in textiles as defined by the angle between the fibers and means of the ”variational linear comparison” method of their material properties. The symmetry properties of the deBotton and Ponte Castaeda (1995). Use is made of pattern determine the material symmetry group of the net- the Hashin-Shtrikman (HS) bounds and of the ”effective work, under which the deformation energy is invariant. medium approximation” (EMA) for certain, suitably cho- In this work we derive representations for the elastic and sen classes of ”linear comparison composites” to gener- bending energy of such materials, that are invariant under ate corresponding estimates for the nonlinear polycrystals. the symmetry group of the network. We also discuss the The new results are compared with the bounds of Gar- relation of these invariants with classical models in which roni and Kohn (2003) for isotropic nonlinear polycrystals. the deformation energy depends from the shear and the As expected, it is found that the HS bound improves on curvature of the fibers only. the translation Garroni-Kohn bound for weakly anisotropic crystals, but is much weaker for strongly anisotropic crys- Giuliana Indelicato tals. However, surprisingly, it was found that the HS bound Department of Mathematics could be sharper than the linear comparison Garroni-Kohn University of Torino, Italy bound, generated by making use of the linear conductiv- [email protected] ity bounds of Avellaneda et al. (1988), even for strongly anisotropic crystals (in some special situations). In addi- tion, the linear comparison EMA estimates, not only satis- CP3 fies all the bounds, including the translation Garroni-Kohn A Model for Particle Size Segregation in Granular bound, but exhibits a scaling law that is strictly sharper Flow under Nonuniform Shear than that predicted by the translation bound. The impli- cations of these observations for the variational linear com- A hyperbolic conservation law in one space variable and parison methods, and for nonlinear homogenization, more time describes particle size segregation in the presence of generally, will be discussed. nonuniform shear. This PDE generalizes the Savage-Lun (1988) and Gray-Thornton (2005) models of segregation in Pedro Ponte Castaneda granular avalanches, which assume uniform shear. Size seg- Dept Mech. Engng regation is observed in a Couette cell experiment in which & Appl. Mech a bidisperse mixture of spherical glass beads is sheared by University of Pennsylvania rotating the bottom boundary. Experimental results are [email protected] compared to analysis of the PDE model. Lindsay May, Karen Daniels, Kasey Phillips Vikranth Racherla North Carolina State University Departement de Mecanique [email protected], karen [email protected], Ecole Polytechnique [email protected] [email protected] Michael Shearer CP3 North Carolina State Univ. Complex Fluids in Microfluidic Devices: Purely [email protected] Elastic Instabilities and Drop Breakup Fluids with mesoscopic structure (e.g. polymeric liquids CP4 and DNA suspensions) often exhibit complex rheologi- Inverse Elastic Electron Scattering with Adaptive cal behavior, particularly in response to applied external Regularization and Meshes forces. Two examples are discussed here. First, we inves- tigate the flow of viscoelastic polymeric fluids in an ex- To recover nanoscale material properties from the trans- tensional flow, in which two flow instabilities are found. mission electron microscope, inverse scattering is consid- Next, the effects of elasticity on filament thinning and drop ered. Basically an accelerated electron considered as a breakup in microchannels are investigated, in which the fil- plane wave propagates in empty space before interacting ament thinning shows two distinct temporal regimes: flow- with a sample potential that is looked for. The mea- and capillary-driven. sured and computed waves at the sample exit plane depend on this potential. Adaptive meshing methods regularizes Paulo E. Arratia the inverse scattering problem for both direct and adjoint Mechanical Engineering and Applied Mechanics states. Error estimators iteratively drive the refinement of University of Pennsylvania, Philadelphia. the potential discretization. [email protected] Denis Aubry Ecole Centrale Paris CP3 [email protected] Symmetry Properties of the Elastic and Bending Energy of a 2-Dimensional Fibered Network, with Ann-Lenaig Hamon, Guillaume Puel 42 MS08 Abstracts MSSMat as how to choose the size of the patches and the boundary Ecole Centrale Paris conditions and the simulated microscopic time. We present