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A Nonlinear Inversion Method for 3DElectromagnetic Imaging Using Adjoint Fields
 Inverse Problems
, 1999
"... Electromagnetic Imaging is modeled as an inverse problem for the 3D system of Maxwell's equations of which the isotropic conductivity distribution in the domain of interest has to be reconstructed. The main application we have in mind is the monitoring of conducting contaminant plumes out of surf ..."
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Cited by 13 (1 self)
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Electromagnetic Imaging is modeled as an inverse problem for the 3D system of Maxwell's equations of which the isotropic conductivity distribution in the domain of interest has to be reconstructed. The main application we have in mind is the monitoring of conducting contaminant plumes out of surface and borehole electromagnetic imaging data. The essential feature of the method developed here is the use of adjoint elds for the reconstruction task, combined with a splitting of the data into smaller groups which dene subproblems of the inversion problem. The method works iteratively, and can be considered as a nonlinear generalization of the Algebraic Reconstruction Technique (ART) in xray tomography. Starting out from some initial guess for the conductivity distribution, an update for this guess is computed by solving one forward and one adjoint problem of the 3D Maxwell system at a time. Numerical experiments are performed for a layered background medium in which one or t...
NETWORK APPROXIMATION FOR EFFECTIVE VISCOSITY OF CONCENTRATED SUSPENSIONS WITH COMPLEX GEOMETRY ∗
"... Abstract. We study suspensions of rigid particles (inclusions) in a viscous incompressible fluid. The particles are close to touching one another, so that the suspension is near the packing limit, and the flow at small Reynolds number is modeled by the Stokes equations. The objective is to determine ..."
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Cited by 4 (2 self)
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Abstract. We study suspensions of rigid particles (inclusions) in a viscous incompressible fluid. The particles are close to touching one another, so that the suspension is near the packing limit, and the flow at small Reynolds number is modeled by the Stokes equations. The objective is to determine the dependence of the effective viscosity 〈μ 〉 on the geometric properties of the particle array. We study spatially irregular arrays, for which the volume fraction alone is not sufficient to estimate the effective viscosity. We use the notion of the interparticle distance parameter δ, based on the Voronoi tessellation, and we obtain a discrete network approximation of 〈μ〉, asδ → 0. The asymptotic formulas for 〈μ〉, derived in dimensions two and three, take into account translational and rotational motions of the particles. The leading term in the asymptotics is rigorously justified in two dimensions by constructing matching upper and lower variational bounds on 〈μ〉. While the upper bound is obtained by patching together local approximate solutions, the construction of the lower bound cannot be obtained by a similar local analysis because the boundary conditions at fluidsolid interfaces must be resolved for all particles simultaneously. We observe that satisfying these boundary conditions, as well as the incompressibility condition, amounts to solving a certain algebraic system. The matrix of this system is determined by the total number of particles and their coordination numbers (number of neighbors of each particle). We show that the solvability of this system is determined by the properties of the network graph (which is uniquely defined by the array of particles) as well as by the conditions imposed at the external boundary.
Low Frequency Electromagnetic Fields in High Contrast Media
"... . Using variational principles we construct discrete network approximations for the Dirichlet to Neumann or Neumann to Dirichlet maps of high contrast, low frequency electromagnetic media. 1 Introduction Imaging of the electrical conductivity and permittivity of a heterogeneous body by means of low ..."
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Cited by 2 (1 self)
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. Using variational principles we construct discrete network approximations for the Dirichlet to Neumann or Neumann to Dirichlet maps of high contrast, low frequency electromagnetic media. 1 Introduction Imaging of the electrical conductivity and permittivity of a heterogeneous body by means of lowfrequency electrical or electromagnetic field measurements is an inverse problem, often called "impedance tomography", "electromagnetic induction tomography", "magnetotellurics" and so on. Applications arise in many areas, for example in medicine with diagnostic imaging, in nondestructive testing, in oil recovery, in subsurface flow monitoring, in underground contaminant detection, etc. In this paper we will focus attention on imaging heterogeneous media with large variations in the magnitude of their electrical properties. This is relevant in many geophysical applications where the conductivity can vary over several orders of magnitude. For example, a dry rock matrix is insulating compared...
High Performance Algorithms for Multiple Streaming Time Series
, 2006
"... “To my parents and my wife, for all they did for me” Dedicated to all that helped me v Acknowledgements This dissertation would never have materialized without the contribution of many individuals to whom I have the pleasure of expressing my appreciation and gratitude. First of all, I gratefully ack ..."
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Cited by 1 (0 self)
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“To my parents and my wife, for all they did for me” Dedicated to all that helped me v Acknowledgements This dissertation would never have materialized without the contribution of many individuals to whom I have the pleasure of expressing my appreciation and gratitude. First of all, I gratefully acknowledge the persistent support and encouragement from my advisor, Professor Dennis Shasha. He provided constant academic guidance and inspired many of the ideas presented here. Dennis is a superb teacher and a great friend. Secondly, I wish to express my deep gratitude to Professor Richard Cole. He has been offering his generous help since the beginning of my Ph.D. study, which is not limited to academic research. In particular, his help was indispensable for me to go through my first semester at NYU, four extremely tough months.
Error of the network approximation for densely packed
, 2001
"... composites with irregular geometry ..."
ASYMPTOTIC APPROXIMATION OF THE DIRICHLET TO NEUMANN MAP OF HIGH CONTRAST CONDUCTIVE MEDIA
, 2013
"... Abstract. We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to ze ..."
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Abstract. We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to zero.