880 research outputs found

    Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

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    This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain

    Thermoacoustic tomography with an arbitrary elliptic operator

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    Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stability estimates are obatined for an arbitrary variable principal part of that operator. Convergence of the Quasi-Reversibility Method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.Comment: 16 page

    A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

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    We consider a transmission wave equation in two embedded domains in R2R^2, where the speed is a1>0a1 > 0 in the inner domain and a2>0a2 > 0 in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and a1>a2a1 > a2 . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement

    Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States

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    We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure

    Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

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    We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

    On the reconstruction of planar lattice-convex sets from the covariogram

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    A finite subset KK of Zd\mathbb{Z}^d is said to be lattice-convex if KK is the intersection of Zd\mathbb{Z}^d with a convex set. The covariogram gKg_K of KZdK\subseteq \mathbb{Z}^d is the function associating to each u \in \integer^d the cardinality of K(K+u)K\cap (K+u). Daurat, G\'erard, and Nivat and independently Gardner, Gronchi, and Zong raised the problem on the reconstruction of lattice-convex sets KK from gKg_K. We provide a partial positive answer to this problem by showing that for d=2d=2 and under mild extra assumptions, gKg_K determines KK up to translations and reflections. As a complement to the theorem on reconstruction we also extend the known counterexamples (i.e., planar lattice-convex sets which are not reconstructible, up to translations and reflections) to an infinite family of counterexamples.Comment: accepted in Discrete and Computational Geometr

    N/P ratio in the PEI2-GNP-DNA complex affects transgene delivery in the human cornea in vitro

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    Recently, we discovered that polyethylenimine-conjugated gold nanoparticles (PEI2- GNP) could be used as gene therapy vector for the cornea. It was hypothesized that DNA concentration, incubation timing and PEI monomer amount in transfection solution affect gene transfer efficiency and toxicity. The aims of this study were to test whether molar ratio of PEI2 nitrogen (N) and phosphate (P) of DNA in PEI2-GNP transfection solution regulates transgene delivery in human corneal fibroblasts in vitro, and examine PEI2-GNP toxicity, uptake and clearance for the cornea in vivo."National Eye Institute, NIH, Bethesda for RO1EY017294 (RRM), Diversity (RRM) and Veteran Health Affairs Merit (RRM) grants and Unrestricted grant from Research to Prevent Blindness, New York

    Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

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    We study Newton type methods for inverse problems described by nonlinear operator equations F(u)=gF(u)=g in Banach spaces where the Newton equations F(un;un+1un)=gF(un)F'(u_n;u_{n+1}-u_n) = g-F(u_n) are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

    Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

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    The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

    Complete determination of the reflection coefficient in neutron specular reflection by absorptive non-magnetic media

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    An experimental method is proposed which allows the complete determination of the complex reflection coefficient for absorptive media for positive and negative values of the momenta. It makes use of magnetic reference layers and is a modification of a recently proposed technique for phase determination based on polarization measurements. The complex reflection coefficient resulting from a simulated application of the method is used for a reconstruction of the scattering density profiles of absorptive non-magnetic media by inversion.Comment: 14 pages, 4 figures, reformulation of abstract, ref.12 added, typographical correction
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