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	Graduate Program in Mathematics
		Inverse boundary value problems are a class of problems in which the unknown coefficients of a partial differential equation represent internal parameters of a medium, and the known information consists of boundary measurements of the solutions.
		A related inverse boundary value problem is diffuse tomography, which refers to low-energy imaging in which the paths of the radiant energy are not necessarily straight and are unknown.
		The scattered field is measured, and from this data one attempts to determine the properties of the scatterer.
	www.math.washington.edu /Grads/Connections/invprob.html (1282 words)

	Design of Microwave Filters by Inverse Scattering
		The inverse scattering problem involves reconstruction of the properties of a scatterer, such as shape or density, from knowledge of its scattering data.
		Inverse scattering has previously been used in such diverse areas as the design of corrugated waveguide filters [1], and the design of selective excitation pulses for nuclear magnetic resonance (NMR) imaging [2].
		The inverse scattering problem for this system has been solved by Jaulent [6] but the solution is found to be underdetermined.
	www.atnf.csiro.au /people/proberts/papers/filt/filt.html (2891 words)

	Inverse scattering problem - Wikipedia, the free encyclopedia
		In physics, in the area of scattering theory, the inverse scattering problem is the problem of determining the characteristics of an object (its shape, internal constitution, etc.) from measurement data of radiation or particles scattered from the object.
		Examples of equations that have been solved by inverse scattering are the Schroedinger equation, the KdV equation and the KP equation.
		It is the inverse problem to the direct scattering problem, which is determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer.
	en.wikipedia.org /wiki/Inverse_scattering (184 words)

	Professor McCormick's Publications on Inverse Problems
		This develops special inverse equations that might be more appropriate for extremely anisotropic scattering and relies on a decomposition of the phase function into one portion for the nearly- forward scattering plus another for the moderately-anisotropic scattering in the remaining directions.
		Procedures for determining the single-scattering albedo of an isotropically scattering semi-infinite medium for unpolarized radiation and for polarized radiation in an atmosphere that scatters according to the Rayleigh-Cabannes law are numerically tested.
		The former inverse problem is proven to have a unique solution, while for the latter we construct counterexamples that prove that the problem is underdetermined for the general case of anisotropic sources and prove that it has a unique solution for isotropic sources and scattering.
	faculty.washington.edu /mccor/inverse.html (2585 words)

	Amazon.co.uk: Scattering: Scattering and Inverse Scattering in Pure and Applied Science: Books: Roy Pike,Pierre C. ... (Site not responding. Last check: 2007-11-03)
		Scattering is the collision of two objects that results in a change of trajectory and energy.
		In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains.
		This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium.
	www.amazon.co.uk /Scattering-Inverse-Pure-Applied-Science/dp/0126137609 (522 words)

	Formal Compensation of Sensor-Related Interaction for Iterative Inverse Scattering
		The microwave imaging problem is an inverse scattering problem in which, from the measurement of the scattered field from a test object, the dielectric contrast distribution with respect to the external medium is reconstructed.
		It uses the modulated scattering technique: an array of passive sensors from which each dipole is successively modulated (through a diode) is mecanicly displaced around the test area in front of a receiving antenna with a very large aperture (ensuring a quasi uniform measurement).
		The scattered field computed with the formal compensation method on the sensors is presented on Figure 16, in comparison with the scattered field simulated with the Genoa University model and the measured scattered field.
	www.ccem.uiuc.edu /reschew4.html (2173 words)

	Photoelectrons, Compton and Inverse Compton Scattering
		To show this, Compton scattered x-ray radiation off a graphite block and measured the wavelength of the x-rays before and after they were scattered as a function of the scattering angle.
		Inverse Compton scattering, illustrated in the figure below, takes place when the electron is moving, and has sufficient kinetic energy compared to the photon.
		A good reference for Compton scattering and inverse Compton scattering in the astrophysical regime is in "Radiative Processes in Astrophysics" by George B.
	venables.asu.edu /quant/proj/compton.html (779 words)

	Scattering and Inverse Scattering
		Optimization and variational analyis, inverse scattering and optics.
		Research in scattering theory is mainly focused on developing and analyzing algorithms for computing approximations to scattered acoustic and electromagnetic fields.
		Scattering theory and inverse scattering presentations are often featured in the Applied Mathematics seminar series.
	www.math.udel.edu /research/si/SI.html (241 words)

	Inverse Scattering Study
		Acoustical inverse scattering techniques allow obtaining quantitative information about the distribution of acoustical properties such as speed of sound and attenuation inside an object.
		Such information is obtained by measuring the scattered field using several transmission-reception configurations, and using the wave equation to relate these measurements with the wavenumber function inside the object.
		We believe that this project is perfectly suited to take advantage of the current state of the art inverse scattering methods, and at the same time expand the applicability of these types of techniques.
	www.brl.uiuc.edu /Projects/inverse_scattering_study.php (443 words)

	Application of the Inverse Scattering Transform to Classical Problems of Differential Geometry and General Relativity, ...
		V.E. Zakharov, Application of the inverse scattering transform to classical problems of differential geometry and general relativity, Contemporary Mathematics 301 (2002) [PDF (191 kB)].
		A.A. Belavin, V.E. Zakharov, Yang-Mills equations as inverse scattering problem: in Proceedings of the conference on Mathematical problems in theoretical physics (Rome, 1977); Lecture Notes in Physics 80 (Springer, Berlin-New York, 1978), pp.
		V.E. Zakharov, Inverse scattering method in the theory of waves in nonlinear media: in Theory of Elastisity in Media with Microstructure, ed.
	math.arizona.edu /~zakharov/papers/inverse_scattering.html (1007 words)

	Experimental Inverse Scattering
		In the beginning of the 1990s, a nonlinear inverse scattering imaging algorithm, namely the distorted Born iterative method (DBIM), which accounts for both diffraction and multiple scattering effects was developed and implemented for both CW and transient excitations.
		What was shown was the ability of a nonlinear inverse scattering method to resolve features that are much less than half a wavelength, the criterion dictated by the Rayleigh criterion.
		Hence, in an inverse scattering experiment, even though an object is interrogated with a propagating wave, and that only scattered waves corresponding to propagating waves can be measured, the scattered waves contain high resolution information about the scatterer because of the evanescent=propagating waves conversion in a multiple scattered field.
	www.ccem.uiuc.edu /reschew9.html (461 words)

	Research on Inverse Problems
		The general nature of an inverse problem is to deduce a cause from an effect.
		An important example is the inverse problem of geophysics, in which we seek to investigate the structure of the interior of the earth.
		Inverse problems in differential equations have this general character.
	www.public.iastate.edu /~psacks/inverse_problems.html (663 words)

	UCLA PBPL - Inverse Compton Scattering (Site not responding. Last check: 2007-11-03)
		Depending on the reference frame, it can appear as if the electrons have been energized by the photons upon collision (Thomson scattering) or, in the reference frame (laboratory frame) where the electrons are moving relativisticaly, the energy is instead transferred from electrons to photons, therefore the opposite of Compton scattering (Inverse Compton scattering) [5].
		The scattered ("wiggled") electrons emit radiation as they interact with the laser beam, but because the electrons are moving near the speed of light, the radiation emitted normal to the longitudinal (wiggler) axis is Lorentz contracted in the laboratory frame, forming a cone of radiation in the direction of travel.
		In this method, it is possible to use the physical imperfections of the interior of a waveguide to slow down faster electrons in the bunch and in effect compress it[3].
	pbpl.physics.ucla.edu /Education/Courses/Physics_199/Inverse_Compton (4983 words)

	Graduiertenkolleg 1023: Identifikation in mathematischen Modellen - Inverse Scattering
		This lecture series is designed to be a brief introduction to the field of inverse scattering theory, focusing on a simple model problem connected with the scattering of time-harmonic electromagnetic waves by an imperfectly conducting infinite cylinder.
		We begin with a brief discussion of Bessel functions and Herglotz wave functions, the uniqueness of a solution to the direct scattering problem and the existence of a solution to the direct scattering problem by the method of integral equations.
		We then consider the inverse problem of determining the shape of the scatterer and the surface impedance on the boundary of the scatterer from a knowledge of the asympotic behavior of the scattered wave.
	www.num.math.uni-goettingen.de /gk/index.php?Lehre:Kompaktkurse:Inverse_Scattering (288 words)

	Inverse Obstacle Scattering
		One of the basic inverse problems in scattering theory for time-harmonic acoustic waves is to determine the shape of an obstacle D with boundary B from a knowledge of the incident wave u
		This configuration of measuring the scattered wave at a single point from a sequence of sources from different directions is common in medical imaging.
		Abstract: A quasi-Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting infinitely long cylindrical obstacle from a knowledge of the far field pattern for the scattering of time-harmonic plane waves.
	www.math.tamu.edu /~william.rundell/obstaclescat.html (932 words)

	Numerical Inverse Scattering
		The numerical inverse scattering project is funded by a grant from ONR.
		Our main emphasis of research is to construct fast algorithms for the forward and inverse acoustic and electromagnetic scattering problems in two and three dimensions, for applications such as medical imaging, non-destructive testing, and the detection or classification of underwater objects.
		The primary objective of this research program is to (i) develop a direct, high-order method for the forward scattering problem cast as the Helmholtz equation (ii) use the fast algorithm for the forward problem to solve the inverse problem iteratively with an inversion method introduced in [11].
	www.math.nyu.edu /faculty/yuchen/onr/intro.htm (457 words)

	06w5092 Inverse Problems and Applications
		The inverse problem is to determine some coefficient(s) of the equation given some information about the solutions.
		The complex geometrical optics solutions mentioned preciously sections were used to solve in dimension three or higher the inverse scattering problem at a fixed energy by Novikov.
		An important new area of research in inverse scattering is the case of random media.
	www.pims.math.ca /birs/birspages.php?task=displayevent&event_id=06w5092 (1011 words)

	Solitons, Nonlinear Evolution Equations and Inverse Scattering - Cambridge University Press
		Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ð method.
		Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
		Inverse scattering for the Korteweg-de Vries equation; 3.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521387302 (223 words)

	Andrew E. Yagle:Inverse Scattering
		A.E. Yagle, ``Multiresolution Algorithms for One-Dimensional Inverse Scattering Problems using the Wavelet Transform,'' SIAM Conference on Linear Algebra in Signals, Systems, and Control, Seattle, August 16-19, 1993.
		A.E. Yagle and J. Frolik, ``On the Feasibility of Impulse Reflection Response Data for the Two-Dimensional Inverse Scattering Problem,'' to appear in IEEE Trans.
		J. Frolik and A.E. Yagle, ``Forward and Inverse Scattering for Discrete Layered Lossy and Absorbing Media,'' to appear in IEEE Trans.
	www.eecs.umich.edu /~aey/invscatt.html (1233 words)

	Amazon.com: Qualitative Methods in Inverse Scattering Theory: An Introduction (Interaction of Mechanics and ... (Site not responding. Last check: 2007-11-03)
		Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years.
		One class of such methods comes under the general description of qualitative methods in inverse scattering theory.
		It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.
	amazon.com /Qualitative-Methods-Inverse-Scattering-Theory/dp/3540288449 (640 words)

	CASA - Inverse Scattering Problem (Site not responding. Last check: 2007-11-03)
		A practically important class of inverse problems is Inverse Scattering Problem, where information about unknown object (e.g.
		a body, an inhomogeneity in a material, a potential) is to be recovered from measurements of waves or fields scattered by this object.
		We also describe a method of determining the shape of a scattering object from measurements of the 'far-field pattern' of a scattered acoustic wave.
	www.win.tue.nl /casa/meetings/_old/seminar/inverse/abstract030402.html (108 words)

	Introduction to inverse nuclear scattering (Site not responding. Last check: 2007-11-03)
		One problem remains; because nuclei are very small, our analysis of the scattering must be based on the rules of quantum mechanics which are very different from the normal way we visualize scattering.
		From this model we deduce that the nuclei are unlikely to overlap completely (the probability is small in the centre of the picture, the point 0,0).
		Without passing through the target nuclei the scattered nuclei appear to be focussed to a position just behind the target, before moving away to the detector.
	physics.open.ac.uk /~sgcooper/invs_intro.html (892 words)

	Inverse Scattering
		Inverse Scattering, using Wave Field Splitting and Invariant Imbedding
		Welcome to the home page for research on inverse scattering, using wave field splitting and invariant imbedding.
		This is one outcome of a workshop held in Mölle, Sweden, June 29 - July 1, 1995 (the Inverse Scattering Gathering?).
	www.scl.ameslab.gov /Projects/old/Inverse (328 words)

	Inverse Problems in Engineering Seminar (Site not responding. Last check: 2007-11-03)
		The Fourteenth Inverse Problems in Engineering Seminar is being organized at Iowa State University.
		This event is the continuation of the informal seminars which were initiated at Michigan State University in 1988.
		Papers are solicited from all areas involving inverse methods and their applications.
	www.inverseproblems.org (155 words)

	IngentaConnect Minimum-phase-based inverse scattering algorithm applied to Insti... (Site not responding. Last check: 2007-11-03)
		Laboratory controlled data were recently provided by the Institut Fresnel to assist with the development and validation of inverse scattering algorithms.
		A nonlinear signal processing method is applied to invert the scattered field data from strongly scattering objects.
		In 2D or higher dimensional problems, we describe the conditions for minimum phase and show how a reference wave can be numerically combined with measured complex scattering data in order to enforce this condition.
	www.ingentaconnect.com /content/iop/ip/2005/00000021/00000006/art00s11 (206 words)

	Scattering and Inverse Scattering (Site not responding. Last check: 2007-11-03)
		The workshop will focus on recent developments in scattering and inverse scattering theory.
		The purpose of the workshop will be to bring together people working on different aspects of these fields, to appraise the current status of development and to encourage interaction between mathematicians and scientists and engineers working directly with the applications of scattering and inverse scattering.
		Despite close mathematical connections between the fields of scattering and inverse scattering, there has not always been a strong interaction between these fields.
	www.pims.math.ca /birs/workshops/2003/03w5037 (155 words)

	Spectel --> Inverse Scattering Module
		To correct for the physics influence, measurement algorithms can be developed which are based directly on scan data or simulated images.
		One approach is called the Inverse Scattering Method and determines measurements by searching a database of simulations for the best fit.
		Spectel has undertaken a refinement of this approach termed Adaptive Monte Carlo Inverse Scattering (AMCIS).
	www.spectelresearch.com /inversescat.html (106 words)

	inverse Compton effect concept from the Astronomy knowledge base (Site not responding. Last check: 2007-11-03)
		inverse Compton effect concept from the Astronomy knowledge base
		physical phenomena > event > atomic process > collision > scattering > inverse Compton effect
		Next scattering: Mie scattering Up: scattering Previous scattering: conservative scattering
	www.site.uottawa.ca:4321 /astronomy/inverseComptoneffect.html (60 words)

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