Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet\u2013 Neumann map. We extend here the stability result obtained by Alessandrini and Vessella (Alessandrini G and Vessella S 2005 Lipschitz stability for the inverse conductivity problem Adv. Appl. Math. 35 207\u2013241), where the authors considered the piecewise constant isotropic case

Solar Reector Design

The design of solar panels is investigated. Different aspects of this problem are presented. A formula averaging the solar energy received on a given location is derived rst. The energy received by the collecting solar panel is then calculated using a specially designed algorithm. The geometry of the device collecting the energy may then be optimised using different algorithms. The results show that for a given depth, devices of smaller width are more energy efficient than those of wider dimensions. This leads to a more economically efficient design

Aberration-free ultra-thin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces

The concept of optical phase discontinuities is applied to the design and demonstration of aberration-free planar lenses and axicons, comprising a phased array of ultrathin subwavelength spaced optical antennas. The lenses and axicons consist of radial distributions of V-shaped nanoantennas that generate respectively spherical wavefronts and non-diffracting Bessel beams at telecom wavelengths. Simulations are also presented to show that our aberration-free designs are applicable to high numerical aperture lenses such as flat microscope objectives

Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy

The manipulation of light by conventional optical components such as a lenses, prisms and wave plates involves engineering of the wavefront as it propagates through an optically-thick medium. A new class of ultra-flat optical components with high functionality can be designed by introducing abrupt phase shifts into the optical path, utilizing the resonant response of arrays of scatters with deeply-subwavelength thickness. As an application of this concept, we report a theoretical and experimental study of birefringent arrays of two-dimensional (V- and Y-shaped) optical antennas which support two orthogonal charge-oscillation modes and serve as broadband, anisotropic optical elements that can be used to locally tailor the amplitude, phase, and polarization of light. The degree of optical anisotropy can be designed by controlling the interference between the light scattered by the antenna modes; in particular, we observe a striking effect in which the anisotropy disappears as a result of destructive interference. These properties are captured by a simple, physical model in which the antenna modes are treated as independent, orthogonally-oriented harmonic oscillators

Enhanced Fear Expression in a Psychopathological Mouse Model of Trait Anxiety: Pharmacological Interventions

The propensity to develop an anxiety disorder is thought to be determined by genetic and environmental factors. Here we investigated the relationship between a genetic predisposition to trait anxiety and experience-based learned fear in a psychopathological mouse model. Male CD-1 mice selectively bred for either high (HAB), or normal (NAB) anxiety-related behaviour on the elevated plus maze were subjected to classical fear conditioning. During conditioning both mouse lines showed increased fear responses as assessed by freezing behaviour. However, 24 h later, HAB mice displayed more pronounced conditioned responses to both a contextual or cued stimulus when compared with NAB mice. Interestingly, 6 h and already 1 h after fear conditioning, freezing levels were high in HAB mice but not in NAB mice. These results suggest that trait anxiety determines stronger fear memory and/or a weaker ability to inhibit fear responses in the HAB line. The enhanced fear response of HAB mice was attenuated by treatment with either the α2,3,5-subunit selective benzodiazepine partial agonist L-838,417, corticosterone or the selective neurokinin-1 receptor antagonist L-822,429. Overall, the HAB mouse line may represent an interesting model (i) for identifying biological factors underlying misguided conditioned fear responses and (ii) for studying novel anxiolytic pharmacotherapies for patients with fear-associated disorders, including post-traumatic stress disorder and phobias

Determining the absorption in anisotropic media

The problem in Optical Tomography of determining the spacially dependent absorption coefficient in an anisotropic medium with a-priori known strong scattering is considered. The problem is modelled by the diffusion approximation of the Radiative Transfer Equation and the time-harmonic case is studied. In this particular situation the diffusion approximation leads to an elliptic second order partial differential equation with complex variable coefficients which allows to treat the problem equivalently to the inverse conductivity problem in Electrical Impedance Tomography (EIT). Results of uniqueness and stability for the absorption coefficient are proven by using the approach of the work in SIAM J. Math. Anal. 33 (2001), no. 1, 153–171 for the inverse conductivity problem in EI

Recovering Riemannian metrics in monotone families from boundary data

We discuss the inverse problem of determining the anisotropic conductivity of a body described by a compact, orientable, Riemannian manifold M with boundary @M, when measurements of electric voltages and currents are taken on all of @M. Specifically we consider a one parameter family of conductivity tensors, extending results obtained in [3] where the simpler Euclidean case is considered. Our problem is equivalent to the geometric one of determining a Riemannian metric in monotone one parameter family of metrics from its Dirichlet to Neumann map on @M