Author
Adrian I. Nachman
Other affiliations: University of Rochester, Clarkson University, Sunnybrook Health Sciences Centre ...read more
Bio: Adrian I. Nachman is an academic researcher from University of Toronto. The author has contributed to research in topics: Inverse scattering problem & Boundary value problem. The author has an hindex of 30, co-authored 67 publications receiving 3846 citations. Previous affiliations of Adrian I. Nachman include University of Rochester & Clarkson University.
Papers published on a yearly basis
Papers
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TL;DR: In this article, it was shown that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary.
Abstract: We show that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction pro
973 citations
TL;DR: In this paper, the authors define la forme quadratique Qγ sur H 1/2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u (x)| 2 dx ou u∈H 1 (Ω), est la solution unique a Lγu=0 dans Ω, u| ∂ Ω =f.
Abstract: Soit Ω un domaine borne dans R n , n≥3 avec une frontiere C 1,1 . On considere l'operateur Lγ(u)=⊇•(γ⊇u) ou γ(x) est une fonction a valeur reelle dans C 1,1 (Ω) avec une borne superieure positive. On definit la forme quadratique Qγ sur H 1/2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u(x)| 2 dx ou u∈H 1 (Ω) est la solution unique a Lγu=0 dans Ω, u| ∂Ω =f. On etudie la reconstruction de γ a partir de Qγ
716 citations
TL;DR: In this paper, it was shown that the potential of the Schrodinger operator is uniquely determined by the spectrum and boundary values of the normal derivatives of the eigenfunctions of the operator −Δ+q with Dirichlet boundary conditions.
Abstract: We show that the potentialq is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrodinger operator −Δ+q with Dirichlet boundary conditions on a bounded domain Ω in ℝ n . This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.
222 citations
TL;DR: Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method, however, numerical results also indicate that it is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties.
Abstract: Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x)/spl les/c/sub 0/) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.
170 citations
TL;DR: For a general class of nonlinear Schrodinger equations, this article showed that the function a(x, u) can be recovered from knowledge of the corresponding Dirichlet-to-Neumann map on the boundary dQ.
Abstract: For a general class of nonlinear Schrodinger equations -Au+a(x, u) = 0 in a bounded planar domain £2 we show that the function a(x, u) can be recovered from knowledge of the corresponding Dirichlet-to-Neumann map on the boundary dQ .
138 citations
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TL;DR: This work describes here the first practical realization of a cloak of invisibility, constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies.
Abstract: A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.
6,830 citations
Book•
01 Jan 1992
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Abstract: Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index
5,126 citations
TL;DR: A general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics is developed, which can be applied to escape detection by other electromagnetic waves or sound.
Abstract: An invisibility device should guide light around an object as if nothing were there, regardless of where the light comes from. Ideal invisibility devices are impossible, owing to the wave nature of light. This study develops a general recipe for the design of media that create perfect invisibility within the accuracy of geometrical optics. The imperfections of invisibility can be made arbitrarily small to hide objects that are much larger than the wavelength. With the use of modern metamaterials, practical demonstrations of such devices may be possible. The method developed here can also be applied to escape detection by other electromagnetic waves or sound.
3,850 citations
TL;DR: A survey of the work in electrical impedance tomography can be found in this article, where the authors survey some of the most important works in the field. Butt.t.
Abstract: t. This paper surveys some of the work our group has done in electrical impedance tomography.
1,726 citations
TL;DR: By comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces and the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
Abstract: A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
1,629 citations