Fernando Guevara Vasquez

Active exterior cloaking for the 2D Laplace and Helmholtz equations.

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D 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 close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.

Electrical impedance tomography with resistor networks

We introduce a novel inversion algorithm for electrical impedance tomography in two dimensions, based on a model reduction approach. The reduced models are resistor networks that arise in five point stencil discretizations of the elliptic partial differential equation satisfied by the electric potential, on adaptive grids that are computed as part of the problem. We prove the unique solvability of the model reduction problem for a broad class of measurements of the Dirichlet-to-Neumann map. The size of the networks is limited by the precision of the measurements. The resulting grids are naturally refined near the boundary, where we measure and expect better resolution of the images. To determine the unknown conductivity, we use the resistor networks to define a nonlinear mapping of the data that behaves as an approximate inverse of the forward map. Then we formulate an efficient Newton-type iteration for finding the conductivity, using this map. We also show how to incorporate a priori information about the conductivity in the inversion scheme.

Edge Illumination and Imaging of Extended Reflectors

We use the singular value decomposition of the array response matrix, frequency by frequency, to image selectively the edges of extended reflectors in a homogeneous medium. We show with numerical simulations in an ultrasound regime, and analytically in the Fraunhofer diffraction regime, that information about the edges is contained in the singular vectors for singular values that are intermediate between the large ones and zero. These transition singular vectors beamform selectively from the array onto the edges of the reflector cross-section facing the array, so that these edges are enhanced in imaging with travel-time migration. Moreover, the illumination with the transition singular vectors is done from the sources at the edges of the array. The theoretical analysis in the Fraunhofer regime shows that the singular values transition to zero at the index

Transformation Elastodynamics and Active Exterior Acoustic Cloaking

N^\star(\om) = |{\cal A}||{\cal B}|/(\lambda L)^2

Leakage pathway estimation using iTOUGH2 in a multiphase flow system for geologic CO 2 storage

. Here

Complete Characterization and Synthesis of the Response Function of Elastodynamic Networks

|{\cal A}|

Imaging with Power Controlled Source Pairs

and

A discrete Liouville identity for numerical reconstruction of Schrödinger potentials

|{\cal B}|

Study of noise effects in electrical impedance tomography with resistor networks

are the areas of the array and the reflector cross-section, respectively,

Imaging Polarizable Dipoles

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