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| 10:00 - 10:45 |
Gunther Uhlmann
(University of Washington)
Invisibility and transformation media
Invisibility and transformation media
We will survey recent developments on making objects invisible, or almost invisible, to
different types of waves using transformations.
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| 10:45 - 11:00 |
Coffee break
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| 11:00 - 11:45 |
Michael Vogelius
(Rutgers University)
Uniform estimates of the effects of small inhomogeneities, and their implications
for electromagnetic "cloaking"
Uniform estimates of the effects of small inhomogeneities, and their implications
for electromagnetic "cloaking"
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.
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| 11:00 - 11:45 |
Naoshi Nishimura
(Kyoto University)
A fast multipole method for three dimensional periodic boundary value problems
for Maxwell's equations
A fast multipole method for three dimensional periodic boundary value problems
for Maxwell's equations
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.
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| 12:30 - 14:00 |
Lunch
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| 14:00 - 14:45 |
Yves Capdeboscq
(Oxford University)
A zero-Laplacian approach to impedance imaging
A zero-Laplacian approach to impedance imaging
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
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| 14:45 - 15:30 |
Eric Bonnetier
(Université Joseph Fourier, Grenoble)
Asymptotics in the presence of inclusions of small volume for a conduction
equation: a case with a non-smooth reference potential
Asymptotics in the presence of inclusions of small volume for a conduction
equation: a case with a non-smooth reference potential
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| 15:30 - 16:00 |
Coffee break
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| 16:00 - 16:45 |
Victor Isakov
(Wichita State University)
Inverse doping profile problem
Inverse doping profile problem
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.
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| 16:45 - 17:30 |
George Dassios
(University of Cambridge)
On the character of neuronal currents as sources for EEG and MEG fields
On the character of neuronal currents as sources for EEG and MEG fields
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
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| 17:30 - 18:15 |
Roman Novikov
(CNRS & Universit de Nantes)
The d-bar-approach to monochromatic inverse scattering in three demensions
The d-bar-approach to monochromatic inverse scattering in three demensions
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 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)
Variational principles for acoustics, elastodynamics and electromagnetism
Variational principles for acoustics, elastodynamics and electromagnetism
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.
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| 10:45 - 11:00 |
Coffee break
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| 11:00 - 11:45 |
Gang Bao
(Michigan State University)
Computational modeling of optical response from excitons in a nano optical medium
Computational modeling of optical response from excitons in a nano optical medium
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.
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| 11:45 - 12:30 |
Rémi Carminati
(Ecole Supériuere de Physique et Chimie Industrielles de la ville de Paris)
Single-molecule fluorescence in near-field optics
Single-molecule fluorescence in near-field optics
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).
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| 12:30 - 14:00 |
Lunch
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| 14:00 - 14:45 |
Hyundae Lee
(Ecole Polytechnique)
Asymptotic spectral analysis and its applications
Asymptotic spectral analysis and its applications
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.
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| 14:45 - 15:30 |
Michael Weinstein
(Columbia University)
Resonance problems for microstructures in linear and nonlinear photonics
Resonance problems for microstructures in linear and nonlinear photonics
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| 15:30 - 16:00 |
Coffee break
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| 16:00 - 16:45 |
Mikyoung Lim
(Colorado State University)
Reconstructing small perturbations of an interface
Reconstructing small perturbations of an interface
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.
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| 16:45 - 17:35 |
Elena Beretta
(University of Rome I)
Vibration testing for detection of small perturbation of an interface
Vibration testing for detection of small perturbation of an interface
We present some results concerning the detection of a small perturbation of an interface from modal parameters measured on the boundary of the body.
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| 10:00 - 10:45 |
Mathias Fink
(Uinversité de Paris VII)
Time Reversal of Electromagnetic waves
Time Reversal of Electromagnetic waves
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| 10:45 - 11:00 |
Coffee break
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| 11:00 - 11:45 |
John C. Schotland
(University of Pennsylvania)
Image reconstruction in optical tomography
Image reconstruction in optical tomography
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.
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| 11:45 - 12:30 |
David Holcman
(Ecole Normale Superiéure, Paris)
The degenerated geometry of the synaptic cleft and its consequence for synaptic
transmission
The degenerated geometry of the synaptic cleft and its consequence for synaptic
transmission
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| 12:30 - 14:00 |
Lunch
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| 14:00 - 14:45 |
Martin Hanke
(Johannes Gutenberg University, Mainz)
Electric impedance tomography with only one pair of measurements
Electric impedance tomography with only one pair of measurements
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.
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| 14:45 - 15:30 |
Dominique Lesselier
(L2S Supélec)
MUSIC-Type imaging of 3-D inclusions from asymptotic formulations within the framework of the full Maxwell system
MUSIC-Type imaging of 3-D inclusions from asymptotic formulations within the framework of the full Maxwell system
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.
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| 15:30 - 16:00 |
Coffee break
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| 16:00 - 16:45 |
Elisa Francini
(University of Florence)
Detection of linear cracks in an elastic material
Detection of linear cracks in an elastic material
We present some results concerning the determination of thin inclusions in an isotropic
elastic medium from boundary measurements.
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| 16:45 - 17:30 |
Jin Keun Seo
(Yonsei University)
A new nondestructive evaluation method of crack: frequency differential electrical impedance scanning
A new nondestructive evaluation method of crack: frequency differential electrical impedance scanning
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).
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| 17:30 - 19:00 |
Reception
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