Characterizing the shape and material properties of hidden targets from magnetic induction data

The aim of this paper is to show that, for the eddy current model, the leading order term for the perturbation in the magnetic field, due to the presence of a small conducting magnetic inclusion, can be expressed in terms of a symmetric rank 2 polarization tensor. This tensor contains information about the shape and material properties of the object and is independent of position. We apply a recently derived asymptotic formula for the perturbed magnetic field, due to the presence of a conducting inclusion, which is expressed in terms of a new class of rank 4 polarization tensors (Ammari, H., Chen, J., Chen, Z., Garnier, J. & Volkov, D. (2014) Target detection and characterization from electromagnetic induction data. J. Math. Pures Appl., 101, 54–75.) and show that their result can be written in an alternative form involving a symmetric rank 2 tensor involving 6 instead of 81 complex components in an orthonormal coordinate frame. For objects with rotational and mirror symmetries we show that the number of coefficients is still smaller. We include numerical examples to demonstrate that the new polarization tensors can be accurately computed by solving a vector-valued transmission problem by hp-finite elements and include examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical predictions

On the spectrum of a waveguide with periodic cracks

The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small

Mathematical analysis of plasmonic nanoparticles: the scalar case

Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (ii) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle. Optimal bounds on the enhancement factors are also derived; (iii) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation

Promotion effect in Pt–ZnO catalysts for selective hydrogenation of crotonaldehyde to crotyl alcohol: A structural investigation

Pt–ZnO catalysts prepared from different precursors, H2PtCl6 and Pt(NH3)4(NO3)2, and reduced at increased temperatures are used to achieve high selectivity towards crotyl alcohol in hydrogenation of crotonaldehyde. The ex-chloride catalyst shows a higher activity and selectivity than the ex-nitrate one. Transmission electron microscopy, electron diffraction, high-resolution imaging, energy dispersive X-ray spectroscopy and element mapping are used to characterize the catalysts in order to correlate the microstructure to the catalytic behavior. PtZn alloy formation is confirmed for both ex-chloride and exnitrate catalysts reduced at 673 K. The metal particles in ex-nitrate catalyst are smaller in size than those in ex-chloride. Inmost aggregates of the ex-chloride catalyst, chlorine is distributed homogeneously with low concentration (<1%). The higher chlorine concentration in some region leads to local morphology and microstructure changes. Influences of the observed structural features such as alloy formation, particle size difference, formation of ill-defined material, and chlorine distribution are discussed

Imaging criteria for assessing tumour response: RECIST, mRECIST, Cheson

AbstractMost methods define a limited number of “target” lesions to be measured and other “non-target” lesions to be evaluated qualitatively. RECIST criteria are the most widely used although other criteria have been proposed that are derived from them based on size alone, or size and attenuation. Modified RECIST (mRECIST) criteria only concern hepatocellular carcinoma and only take into account the viable portion (enhanced after injection during the arterial phase). Cheson criteria are more complex as target lesions are defined differently depending on the organ (lymph nodes, liver or spleen, other organs), and involve both CT and PET scans, as well as the clinical examination and bone marrow biopsy

Hacia el manejo sostenible de los bosques de araar (Tetraclinis articulata (Vahl.) Mast.) en Túnez: modelos para las principales variables de árbol

The thuya (Tetraclinis articulata (Vahl.) Mast.) forests are one of the most important ecosystems in semiarid environments in north-western Africa, providing important economic profit and social services to local populations. However, lack of tools aiding sustainable management of these forests is detected. In the present work models for the main tree attributes as total height, crown diameter, height to crown base and stem form are developed for the species, using data from a net of plots installed in JbelLattrech region, in the NE Tunisia. Presented models allow characterizing the actual state and timber production of forests by using variables measured in typical forest inventories and conform a preliminary step for the future development of dynamic growth models.Los bosques de araar (Tetraclinis articulata (Vahl.) Mast.) constituyen uno de los ecosistemas más importantes de los ambientes semiáridos del noroeste de África, siendo además fuente de importantes beneficios económicos y servicios sociales a las poblaciones rurales. Pese a este interés, hasta el momento no se han desarrollado herramientas que faciliten la gesitón sostenible de estas masas forestales. En el presente trabajo se presentan modelos para los principales atributos de árbol individual: altura total, diámetro de copa, altura hasta la base de la copa y ecuación de perfil, desarrollados para la especie a partir de datos obtenidos en una red de parcelas permanentes instalada en la región de JbelLattrech, en el NE de Túnez. Los modelos presentados permiten caracterizar el estado y producción maderera actual de los bosques de thuya a partir de las variables medidas habitualmente en los inventarios forestales para la gestión, y constituyen además un paso preliminar para el desarrollo futuro de modelos dinámicos de crecimiento para la especie

Modeling active electrolocation in weakly electric fish

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure

Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions