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| 10:00 - 10:45 |
Gunther Uhlmann (University of Washington)
We will survey recent developments on making objects invisible, or almost invisible, to different types of waves using transformations. |
| 10:45 - 11:00 | Coffee break |
| 11:00 - 11:45 |
Michael Vogelius (Rutgers University)
In this talk I shall discuss estimates of the electromagnetic boundary effects of small internal inhomogeneities. In particular I shall focus on cases where these estimates assert that the boundary effects tend to zero, uniformly with respect to the material properties of the inhomogeneities, as the "volume" of the inhomogeneities tends to zero. Such uniform estimates for small inhomogeneities have important implications as far as "cloaking" is concerned. In particular these estimates permit (by a mapping technique) the construction of non-singular "near cloaks" with very precise information about the degree of approximate invisibility. |
| 11:45 - 12:30 |
Naoshi Nishimura (Kyoto University)
In this talk we present an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell's equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. After verifying the proposed method by solving simple problems with known analytic solutions, we apply it to various scattering problems for periodic two dimensional arrays of dielectric objects. We then discuss applications of the proposed method in problems related to photonic crystals. This talk also includes discussions on the performance of the proposed method near the so called Wood's anomalies, where the solutions of the problems change drastically for a small change in the frequency or incident angle. |
| 12:30 - 14:00 | Lunch |
| 14:00 - 14:45 |
Yves Capdeboscq (Oxford University)
Biological tissues have different electrical properties that change with cell concentration, cellular structure, and molecular composition. Such changes of electrical properties are the manifestations of structural, functional, metabolic, and pathological conditions of tissues, and thus provide valuable diagnostic information. Since all the present EIT technologies are only practically applicable in feature extraction of anomalies, improving EIT calls for innovative measurement techniques that incorporate structural information. The core idea of the approach presented in this talk is to extract more information about the conductivity from data that has been enriched by coupling the electric measurements to localized elastic perturbations. This is a joint work with H. Ammari, E. Bonnetier, M. Tanter, and M. Fink |
| 14:45 - 15:30 |
Eric Bonnetier (Université Joseph Fourier,
Grenoble) |
| 15:30 - 16:00 | Coffee break |
| 16:00 - 16:45 |
Victor Isakov (Wichita State University)
We describe recent results on uniqueness, stability and reconstruction methods for an important characteristic of semiconductor devices from physically realistic measurements. We use adjoint problem and some asymptotic simplifications to design a simple identification method. We will discuss similar problems for more general drift-diffusion equations arising in secondary oil search and mathematical biology. |
| 16:45 - 17:30 |
George Dassios (University of Cambridge)
Neuronal currents within the brain act as sources for every electric and magnetic activity that is measured outside the head. A long standing mathematical question concerns the existence of overlapping information, about the current, that is recorded during Electroencephalography (EEG) and Magnetoencephalography (MEG). In the present talk, we demonstrate that this ambiguity depends on the assumptions we make about the geometry of the conductive medium representing the cerebral tissue. We show that complementary information about the current holds only for the spherical model, while in any other geometry a part of the current is encoded in both EEG and MEG measurements |
| 17:30 - 18:15 |
Roman Novikov (CNRS & Université de Nantes) We present a method for monochromatic inverse scattering in three dimensions of [R.Novikov 2005] and implemented numerically in [Alekseenko, Burov, Rumyantseva 2008]. This method is obtained as a development of the d-bar- approach to inverse scattering at fixed energy in dimension d >= 3 of [Beals, Coifman 1985] and [Henkin, R.Novikov 1987] and involves, in particular, some results of [Faddeev, 1965, 1974] and some ideas of the soliton theory (in particular, some ideas going back to [Manakov 1976] and [Dubrovin, Krichever, S.Novikov 1976]. Our studies go back also, in particular, to [Regge 1959]. |
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| 10:00 - 10:45 |
Graeme W. Milton (University of Utah)
The Dirichlet and Thompson energy minimization variational principles for electrical conductivity are well known, as are the analogous variational principles for elasticity. Less well known is the result of Cherkaev and Gibiansky that these variational principles can be extended to allow for complex conductivity tensors, and complex elasticity tensors, corresponding to the quasistatic limit where the wavelength is much larger than the body. Here we show that these variational principles can be extended to acoustics, elastodynamics and electromagnetism at any fixed frequency. This is joint work with Guy Bouchitte and Pierre Seppecher. |
| 10:45 - 11:00 | Coffee break |
| 11:00 - 11:45 |
Gang Bao (Michigan State University)
Consider time-harmonic electromagnetic plane wave incident on microscopic semiconductor. Inside the medium, at any given frequency, more than one polariton mode can arise with the same frequency but different wave numbers due to the presence of excitons. Besides Maxwell boundary conditions, additional boundary conditions are required to handle the multi-mode polariton. In order to model the confinement effect of excitons in the microscopic semiconductor, Maxwell's equations and the Schronger equation are coupled to characterize the polarization in terms of the quantum description. In the weak confinement regime, multiscale approach has been developed to analyze and compute the optical linear response of the exciton in both one-dimensional and two-dimensional confinements. The speaker will also discuss related inverse problems. |
| 11:45 - 12:30 |
Michael Weinstein (Columbia University)
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| 12:30 - 14:00 | Lunch |
| 14:00 - 14:45 |
Hyundae Lee (Ecole Polytechnique)
Our aim is to find the asymptotic formulas of eigenvalues of Laplacian (or Lame system) in the following situations: one under variation of domains and the other due to presence of inclusions. For this we will combine the layer potentials techniques with the elegant theory of Ghoberg and Sigal on meromorphic operator-valued functions. This leads to the general and systematic method to attack the eigenvalue perturbation problems. Our exposition is accompanied by many new applications of our asymptotic theory: imaging of small inclusions, analysis of photonic (phononic) crystals with high contrast, and optimal design. |
| 14:45 - 15:30 |
Darko Volkov (Worcester Polytechnic Institute)
Earth science is seeking to understand the physics involved in seismic activity. It has established that most earthquakes occur near faults. It has been speculated that measurements of Earth's surface displacements in the vicinity of faults could in theory, signal the possible imminence of earthquakes. The goal of this research project is to process measurements of surface displacements in such a way to use them as data for the inverse problem consisting of locating faults and portraying their geometry. Our research is also aiming at determining whether a measured displacement field on the surface is indicative of the onset of a destabilization phase. We have already entirely solved a two dimensional problem associated to the strike slip model, which essentially reduces displacement fields to two dimensional scalar fields. Deriving the inversion method involved a rigorous mathematical eigenvalue asymptotic analysis, leading to closed form inversion formulas. Those formulas were then tested for robustness in numerical simulations. As the strike slip model is limited in scope (it captures only one of the textbook examples of faults), we have worked on extending our results to fully three dimensional fault problems. In this much more difficult case, we have already obtained very promising closed form formulas (valid for the dominant part of the asymptotic behavior), and we have tested their use on numerical data. This is joint work with I. R. Ionescu, with the support of NSF grant DMS 0707421. |
| 15:30 - 16:00 | Coffee break |
| 16:00 - 16:45 |
Mikyoung Lim (Colorado State University)
We derive high-order terms in the asymptotic expansions of the boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with C2-boundary. Numerical experiments based on the expansion will be presented. We also consider the problem of determining the boundary of scatterers from electric or acoustic far-field measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relation between the far-field data and the shape of the object. This relation is used to find the Fourier coefficients of the perturbation of the shape. |
| 16:45 - 17:30 |
Elena Beretta (University of Rome I)
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| 17:30 - 18:15 |
Vladimir Sharafutdinov (Sobolev Institute of Mathematics)
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| 9:15 -10:00 |
Rémi Carminati (Ecole Supérieure de Physique
et Chimie Industrielles de la ville de Paris) The development of near-field optics, both on the technical and fundamental aspects, has made possible the detection and control of single-molecule fluorescence at the nanometer scale. A single emitter behaves as a small dipole antenna, whose emission properties strongly depend on the environment. It can be used as an optical probe at the nanometer scale. We will review the mechanisms inducing changes in the fluorescence emission, in particular the interaction with metallic nanostructures (particles, tips, plasmonic slabs). We will discuss the connection between the fluorescence decay rate and the local density of states, a fundamental quantity in terms of optical characterization of micro and nanostructures. Finally, we will show that fluorescence decay rate (or lifetime) statistics carry information on the local structure of complex disordered systems. Acknowledgements : Part of this work has been performed by Luis Froufe and C  ric Vandenbem (post-doctoral fellows). |
| 10:00 - 10:45 |
Mathias Fink (Uinversité de Paris VII)
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| 10:45 - 11:00 | Coffee break |
| 11:00 - 11:45 |
John C. Schotland (University of
Pennsylvania) The inverse problem of optical tomography is to reconstruct the optical properties of a highly-scattering medium from boundary measurements. I will review recent work on associated inverse scattering problems for the radiative transport equation. Our results will be illustrated by numerical simulations and experiments in model systems. |
| 11:45 - 12:30 |
David Holcman (Ecole Normale Supérieure de
Paris) |
| 12:30 - 14:00 | Lunch |
| 14:00 - 14:45 |
Martin Hanke (Johannes Gutenberg University,
Mainz) We consider the reconstruction of an anomaly within a homogeneous body from electrostatic measurements on its boundary. Our aim is to gather as much information as possible about the anomaly using only one pair of current/voltage measurements from the entire boundary. Two different approaches will be considered. The first one adapts the convex scattering support developed by Kusiak and Sylvester to our particular problem: We reconstruct a convex domain within the body that is known to be part of the convex hull of the anomalies. In our second approach we reinvestigate a method suggested by Kwon, Seo, and Yoon, which determines a single point in order to locate the (approximate) position of the anomaly. We will compare their results with a novel approach which we call the effective dipole method. We plan to demonstrate that the effective dipole method yields a good approximation of the center of mass of the anomaly. This is joint work with Nuutti Hyvönen and Steffi Reusswig. |
| 14:45 - 15:30 |
Dominique Lesselier (L2S Supélec)
Fast, non-iterative, single-frequency imaging of a collection of small 3-D bounded inclusions buried within homogeneous or stratified linear isotropic media via electromagnetic means, using the least amount of (vector field) data is studied herein. The framework is the one of small-scatterer asymptotic formulations derived from the full 3D Maxwell equations and involving the pertinent Green dyads. They in particular call for polarization tensors in specific coordinate systems (spherical, bispherical) yielded by low-frequency scattering theory. Algorithms of the MUltiple SIgnal Classification type (MUSIC) are proposed to achieve the above imaging from the Multi-Static Response matrix which is assumed to be available in dipole array configurations. Inverse-crime asymptotic data as well as exact ones (with discretization), noise added, are computed and pros and cons of the imaging method in a variety of configurations is investigated from them. Potential applications and necessary extensions are briefly browsed through. |
| 15:30 - 16:00 | Coffee break |
| 16:00 - 16:45 |
Elisa Francini (University of Florence)
We present some results concerning the determination of thin inclusions in an isotropic elastic medium from boundary measurements. |
| 16:45 - 17:30 |
Jin Keun Seo (Yonsei University)
We propose a new nondestructive evaluation method for detecting cracks, voids, and other hidden defects inside the concrete structure, called frequency differential electrical impedance scanning (fdEIS). The primary benefit of fdEIS over the conventional nondestructive methods is that it is possible to determine the thickness of the voids. In fdEIS, we inject a sequence of electrical currents with various frequencies through the tested concrete wall by applying sinusoidal voltage difference between a surface electrode and a scan probe, which are placed on surface of the wall. Through the probe, we measure the derivative of exit currents (Neumann data) with respect to the angular frequency variable. We found the fundamental concept in fdEIS relating the thickness of the voids to the derivative of exit currents and derives an approximation formula for estimating the thickness of the voids. We demonstrate the performance of our method in numerical simulations. This is joint work with Sungwhan Kim (Division of Liberal art, Hanbat National University, Korea) and Teayoung Ha (National Institute for Mathematical Sciences, Korea). |
| 17:30 - 19:00 | Reception |