Active Exterior Cloaking

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Thermal Radiation From Carbon Nanotube in Terahertz Range

The thermal radiation from an isolated finite-length carbon nanotube (CNT) is theoretically investigated both in near- and far-field zones. The formation of the discrete spectrum in metallic CNTs in the terahertz range is demonstrated due to the reflection of strongly slowed-down surface-plasmon modes from CNT ends. The effect does not appear in semiconductor CNTs. The concept of CNT as a thermal nanoantenna is proposed.Comment: 5 pages, 3 figure

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases

Source amplitudes for active exterior cloaking

The active cloak comprises a discrete set of multipole sources that destructively interfere with an incident time harmonic scalar wave to produce zero total field over a finite spatial region. For a given number of sources and their positions in two dimensions it is shown that the multipole amplitudes can be expressed as infinite sums of the coefficients of the incident wave decomposed into regular Bessel functions. The field generated by the active sources vanishes in the infinite region exterior to a set of circles defined by the relative positions of the sources. The results provide a direct solution to the inverse problem of determining the source amplitudes. They also define a broad class of non-radiating discrete sources.Comment: 21 pages, 17 figure

A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator

We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly. We propose solving the related constant coefficient Helmholtz equation with Fast Fourier Transform (FFT) based on carefully designed extensions and restrictions of the equation. The proposed Fourier method, combined with proper eigensolver, results in an efficient and clear approach for computing the Stekloff eigenvalues.Comment: 12 pages, 4 figure

Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and 3-D) because frequently the region of interest cannot be completely surrounded by the detectors, as it happens, for example, in breast imaging. We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case). Our method is based on the numerical approximation of plane waves by certain single layer potentials related to the acquisition geometry. After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform. The peformance of the method is demonstrated in several numerical examples: one can see that the algorithm produces very accurate reconstructions if the data are accurate and sufficiently well sampled, on the other hand, it is sufficiently stable with respect to noise in the data

Expansion of the Parkinson disease-associated SNCA-Rep1 allele upregulates human alpha-synuclein in transgenic mouse brain.

Alpha-synuclein (SNCA) gene has been implicated in the development of rare forms of familial Parkinson disease (PD). Recently, it was shown that an increase in SNCA copy numbers leads to elevated levels of wild-type SNCA-mRNA and protein and is sufficient to cause early-onset, familial PD. A critical question concerning the molecular pathogenesis of PD is what contributory role, if any, is played by the SNCA gene in sporadic PD. The expansion of SNCA-Rep1, an upstream, polymorphic microsatellite of the SNCA gene, is associated with elevated risk for sporadic PD. However, whether SNCA-Rep1 is the causal variant and the underlying mechanism with which its effect is mediated by remained elusive. We report here the effects of three distinct SNCA-Rep1 variants in the brains of 72 mice transgenic for the entire human SNCA locus. Human SNCA-mRNA and protein levels were increased 1.7- and 1.25-fold, respectively, in homozygotes for the expanded, PD risk-conferring allele compared with homozygotes for the shorter, protective allele. When adjusting for the total SNCA-protein concentration (endogenous mouse and transgenic human) expressed in each brain, the expanded risk allele contributed 2.6-fold more to the SNCA steady-state than the shorter allele. Furthermore, targeted deletion of Rep1 resulted in the lowest human SNCA-mRNA and protein concentrations in murine brain. In contrast, the Rep1 effect was not observed in blood lysates from the same mice. These results demonstrate that Rep1 regulates human SNCA expression by enhancing its transcription in the adult nervous system and suggest that homozygosity for the expanded Rep1 allele may mimic locus multiplication, thereby elevating PD risk

Spectral properties of the Dirichlet-to-Neumann operator for exterior Helmholtz problem and its applications to scattering theory

We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the lower half of the complex plane. We find several application of this fact in scattering by obstacles with impedance boundary conditions. In particular, we find an upper bound for the gradient of the scattering amplitude and for the total cross section. We justify numerical approximations by providing bounds on difference between theoretical and approximated solutions without using any a priory unknown constants

Plasticity of face processing in infancy

Experience plays a crucial role for the normal development of many perceptual and cognitive functions, such as speech perception. For example, between 6 and 10 months of age, the infant's ability to discriminate among native speech sounds improves, whereas the ability to discriminate among foreign speech sounds declines. However, a recent investigation suggests that some experience with nonnative languages from 9 months of age facilitates the maintenance of this ability at 12 months. Nelson has suggested that the systems underlying face processing may be similarly sculpted by experience with different kinds of faces. In the current investigation, we demonstrate that, in human infants between 6 and 9 months of age, exposure to nonnative faces, in this case, faces of Barbary macaques (Macaca sylvanus), facilitates the discrimination of monkey faces, an ability that is otherwise lost around 9 months of age. These data support, and further elucidate, the role of early experience in the development of face processing