Target Identification Using Dictionary Matching of Generalized Polarization Tensors

The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified.Comment: Keywords: generalized polarization tensors, target identification, shape representation, stability analysis. Submitted to Foundations of Computational Mathematic

Shape recognition and classification in electro-sensing

This paper aims at advancing the field of electro-sensing. It exhibits the physical mechanism underlying shape perception for weakly electric fish. These fish orient themselves at night in complete darkness by employing their active electrolocation system. They generate a stable, high-frequency, weak electric field and perceive the transdermal potential modulations caused by a nearby target with different admittivity than the surrounding water. In this paper, we explain how weakly electric fish might identify and classify a target, knowing by advance that the latter belongs to a certain collection of shapes. Our model of the weakly electric fish relies on differential imaging, i.e., by forming an image from the perturbations of the field due to targets, and physics-based classification. The electric fish would first locate the target using a specific location search algorithm. Then it could extract, from the perturbations of the electric field, generalized (or high-order) polarization tensors of the target. Computing, from the extracted features, invariants under rigid motions and scaling yields shape descriptors. The weakly electric fish might classify a target by comparing its invariants with those of a set of learned shapes. On the other hand, when measurements are taken at multiple frequencies, the fish might exploit the shifts and use the spectral content of the generalized polarization tensors to dramatically improve the stability with respect to measurement noise of the classification procedure in electro-sensing. Surprisingly, it turns out that the first-order polarization tensor at multiple frequencies could be enough for the purpose of classification. A procedure to eliminate the background field in the case where the permittivity of the surrounding medium can be neglected, and hence improve further the stability of the classification process, is also discussed.Comment: 10 pages, 15 figure

Generalized polarization tensors for shape description

With each domain and material parameter, an infinite number of tensors, called the Generalized Polarization Tensors (GPTs), is associated. The GPTs contain significant information on the shape of the domain. In the recent paper [9], a recursive optimal control scheme to recover fine shape details of a given domain using GPTs is proposed. In this paper, we show that the GPTs can be used for shape description. We also show that high-frequency oscillations of the boundary of a domain are only contained in its high-order GPTs. Indeed, we provide a stability and resolution analysis for the reconstruction of small shape changes from the GPTs. By developing a level set version of the recursive optimization scheme, we make the change of topology possible and show that the GPTs can capture the topology of the domain. We provide numerical evidence that GPTs can capture topology and high-frequency shape oscillations. Both the analytical and numerical results of this paper clearly show that the concept of GPTs is a very promising new tool for shape description

Stress-defect transport interactions in ionic solids

Mixed ionic electronic conductors (MIEC) have gained importance recently due to their roles in energy conversion devices such as solid oxide fuel cells (SOFC). Recent experimental data have shown that an increased vacancy concentration in a MIEC changes its elastic modulus and causes volumetric expansion. Since the MIEC in a device is constrained mechanically, the volumetric changes can induce substantial mechanical stresses. Such stresses not only lead to premature failure but can also alter the electrochemical performance of the device. In order to fully understand the interactions between stresses and defect transport a coupled theory is needed. This thesis develops a framework to study stress-defect transport interactions. The framework is based on a proper construction of the stress dependent electrochemical potential by introducing two material properties, namely the coefficient of chemical expansion (CCE) and the open system elastic constants (OSEC). The CCE characterizes the strains due to non-stoichiometry while the OSEC represents the stoichiometry dependent elastic stiffness. In this work these parameters are determined using atomistic simulations. The system of equations that govern the coupled electrochemical and mechanical fields is solved using a combination of numerical and analytical techniques. The developed solutions are analyzed to provide insights into the nature and the extent of the interactions. It is found that the non-stoichiometry-induced stress is in the same order of magnitude or even higher than that induced by thermal mismatch in a typical SOFC. In the vicinity of material flaws (cracks, voids, etc.), such stresses are further intensified which may cause fracture of the MIEC. In addition, non-stoichiometry-induced stresses can significantly alter the distribution of point defects, thus affecting the electrochemical performance of the ionic device. Furthermore, the non-stoichiometry induced stresses increases the thickness of the surface charge layer. The thermodynamic framework and the computational algorithms developed in this work provides effective methodologies and tools to analyze stress-defect transport interactions in ionic solids for designing and reliability analysis of ionic devices such as fuel cells, oxygen pumps, chemical sensors, etc.Ph.D.Committee Chair: Qu, Jianmin; Committee Member: Kohl,Paul A.; Committee Member: Liu, Meilin; Committee Member: McDowell, David L.; Committee Member: Zhu, Tin