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Cheney, M.; Rose, J.H.; DeFacio, B.

Ames Lab., IA (USA)

Ames Lab., IA (USA)

AbstractAbstract

[en] We consider the problem of obtaining information about an inaccessible region of space from scattering experiments. Inverse scattering theory for the time-independent Schroedinger equation [Δ + h

^{2}- V(x)]psi(k,x) = 0 is summarized. It is most easily understood by considering the associated hyperbolic equation [Δ - ∂/sub tt/ - V(x)]u(t,x) = 0. Particular attention is paid to those aspects of the theory that hold for the wave equation [Δ - n^{2}(x)δ/sub tt/lu(t,x) = 0. 12 refs., 2 figsPrimary Subject

Source

1986; 9 p; Inverse problems conference; Oberwolfach (Germany, F.R.); 1 May 1986; CONF-8605202--1; Available from NTIS, PC A02/MF A01; 1 as DE87000968; Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted.

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Cheney, M.

Indiana State Univ., Terre Haute (USA)

Indiana State Univ., Terre Haute (USA)

AbstractAbstract

[en] Before the two-dimensional inverse problem can be formulated, the direct problem must be studied, namely, the asymptotic form for the solution psi of the Schroedinger equation must be found. This is done by first using a Grossman-Wu factorization to transform the Schroedinger equation into an integral equation on an L

^{2}space; then an investigation of the kernal of the integral operator shows that psi has the form (plane wave) + (outgoing spherical wave) + (L^{2}function), where the amplitude of the outgoing spherical wave is the scattering amplitude. Thus the above formulation of the inverse problem makes sense. Indeed, an estimate on the kernel of the integral operator shows that the potential is uniquely determined by the high energy limit of the scattering amplitude as it is in three dimensions. Next it is shown that aside from the bound state energies, zero is the only energy for which the integral operator is not invertible. With this information it is possible to show that the number of bound states is determined via a two-dimensional generalization of the Levinson theorem by the change in phase of a quantity associated with the scattering amplitude. The fact that the scattering operator maps incoming waves to outgoing waves is then combined with analyticity information to form a Riemann-Hilbert problem (also called a Wiener-Hopf factorization problem). Fourier transformation of the Hilbert problem gives rise to the Marchenko equation, from whose solution the potential V(x) is extracted. Although the two-dimensional results are similar to the three-dimensional ones, the technical details differ significantly because of differences in the behavior of the kernel of the above-mentioned integral operator; most of the thesis is in fact concerned with these detailsPrimary Subject

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1982; 130 p; University Microfilms Order No. 83-01,098; Thesis (Ph. D.).

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Rose, J.H.; Cheney, M.; DeFacio, B.

Ames Lab., IA (USA); Duke Univ., Durham, NC (USA); Missouri Univ., Columbia (USA). Dept. of Physics

Ames Lab., IA (USA); Duke Univ., Durham, NC (USA); Missouri Univ., Columbia (USA). Dept. of Physics

AbstractAbstract

[en] The use of inverse scattering methods in electromagnetic remote sensing, seismic exploration and ultrasonic imaging is rapidly expanding. For these cases which involve classical wave equations with variable velocity, no exact inversion methods exist for general three-dimensional (3d) scatterers. However, exact inversion methods (for example, those based on the Born series and the Newton-Marchenko equation) do exist for the 3d Schroedinger equation. In this paper, these inversion methods for Schroedinger's equation will be rewritten in a form which brings out certain analogies with classical wave equations. It is hoped these analogies will eventually contribute to a common exact inversion method for both types of equations. 13 references

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1984; 7 p; Progress in quantitative NDE; San Diego, CA (USA); 8-13 Jul 1984; CONF-840738--14; Available from NTIS, PC A02/MF A01 as DE85005914

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AbstractAbstract

[en] The Utility PhotoVoltaic Group (UPVG) is a nonprofit association of over 100 energy service providers (electric utilities and energy service companies) cooperating to develop photovoltaic power as a thriving commercial energy option for the benefit of its members and their customers. The U. S. Department of Energy (DOE) and UPVG are sponsoring an initiative named TEAM-UP that has co-funded 37 business ventures since 1995 that are resulting in more than 2,500 PV installations, totaling more than 7.5 megawatts of power in 30 states. The TEAM-UP

^{1}ventures are significantly leveraging the federal funds. Under TEAM-UP, venture teams are investing four dollars for every dollar invested by the U. S. taxpayer. The UPVG programs are increasing the experience of electric utilities and their customers with photovoltaics and are stimulating growth in the demand for solar power. This paper describes these efforts and outlines the current status of the TEAM-UP program. copyright 1999 American Institute of PhysicsPrimary Subject

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15. National Center for Photovoltaics program review conference; Denver, CO (United States); 9-11 Sep 1998; CONF-980935--

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Wang, D.; Shin, J.J.; Cheney, M.; Sposito, G.; Spiro, T.

Rutgers University, New Brunswick, NJ (United States). Funding organisation: US Department of Energy (United States)

Rutgers University, New Brunswick, NJ (United States). Funding organisation: US Department of Energy (United States)

AbstractAbstract

[en] The herbicide atrazine is widely distributed in the environment, and its reactivity with soil minerals is an important issue. We have studied atrazine degradation on the surface of synthetic(delta)-MnO(sub 2)(birnessite) using UV resonance raman spectroscopy and gas chromatography. The products are mainly mono and didealkyl atrazine. Atrazine disappearance is rapid(tau)1/2(approx) 5 h at 30C and independent of whether O(sub 2) is present or not

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16 Sep 1999; 6 p; FG02-97ER14755; Available from Environmental Science and Technology (Sept. 1999) v.33(18): 3160-3165

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Miscellaneous

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AbstractAbstract

[en] Recent work on the two-dimensional inverse scattering problem for the Schroedinger equation has resulted in a generalized Marchenko integral equation. The main result of this paper is that the integral operator appearing in this Marchenko equation is of Hilbert--Schmidt type. A result of Newton's shows that its spectrum therefore consists of point eigenvalues whose moduli are at most 1

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Journal Article

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J. Math. Phys. (N.Y.); ISSN 0022-2488; ; v. 26(4); p. 743-752

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AbstractAbstract

[en] This paper considers the three-dimensional inverse scattering problem for the wave equation with variable velocity. A possible solution is presented in terms of equations whose self-consistent solution determines the velocity from scattering data. These self-consistent equations are (1) the wave equation in integral form, (2) a linear integral equation which relates the wave field and scattering data, and (3) a novel formula for the velocity in terms of the wave field

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[en] We obtain a high-frequency asymptotic expansion of Newton's Marchenko equation for three-dimensional inverse scattering. We find that the inhomogeneous term contains the same high-frequency information as does the Born approximation. We show that recovery of the potential via Newton's Marchenko equation plus the ''miracle'' depends on low-frequency information

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J. Math. Phys. (N.Y.); ISSN 0022-2488; ; v. 26(3); p. 436-439

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[en] A recent exact multidimensional inverse-scattering method, developed for Schroumldinger's equation, establishes a linear integral equation which determines the wave field at all space-time points from the scattering data. We present a new derivation of this integral equation which depends only on very general features of the scattering process such as causality, linearity, and the far-field decay of the wave field. Consequently, this integral equation is shown to hold for a wide class of wave equations (including, for example, the acoustic wave equation)

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[en] An infinite number of ways are developed for representing a function in terms of the (generalized) eigenfunctions of a three-dimensional scattering problem and simple known auxiliary functions. The freedom represented by this variety of expansions arises from the causal nature of the wave equations considered. The new expansions are shown to generalize both the Fourier and Radon transforms. An application of the new expansions to the inverse scattering problem is given. It is shown (under some restrictions) that the scattering amplitude and potential are related via one of the generalized transforms

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