The possibilities of linearized inversion of internally scattered seismic data
Aldawood, Ali; Alkhalifah, Tariq Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George
2014-01-01
Least-square migration is an iterative linearized inversion scheme that tends to suppress the migration artifacts and enhance the spatial resolution of the migrated image. However, standard least-square migration, based on imaging single scattering energy, may not be able to enhance events that are mainly illuminated by internal multiples such as vertical and nearly vertical faults. To alleviate this problem, we propose a linearized inversion framework to migrate internally multiply scattered energy. We applied this least-square migration of internal multiples to image a vertical fault. Tests on synthetic data demonstrate the ability of the proposed method to resolve a vertical fault plane that is poorly resolved by least-square imaging using primaries only. We, also, demonstrate the robustness of the proposed scheme in the presence of white Gaussian random observational noise and in the case of imaging the fault plane using inaccurate migration velocities.
The possibilities of linearized inversion of internally scattered seismic data
Aldawood, Ali
2014-08-05
Least-square migration is an iterative linearized inversion scheme that tends to suppress the migration artifacts and enhance the spatial resolution of the migrated image. However, standard least-square migration, based on imaging single scattering energy, may not be able to enhance events that are mainly illuminated by internal multiples such as vertical and nearly vertical faults. To alleviate this problem, we propose a linearized inversion framework to migrate internally multiply scattered energy. We applied this least-square migration of internal multiples to image a vertical fault. Tests on synthetic data demonstrate the ability of the proposed method to resolve a vertical fault plane that is poorly resolved by least-square imaging using primaries only. We, also, demonstrate the robustness of the proposed scheme in the presence of white Gaussian random observational noise and in the case of imaging the fault plane using inaccurate migration velocities.
Alvarez-Estrada, R.F.
1979-01-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly
Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H
2016-05-01
The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.
Inversion assuming weak scattering
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Some results on inverse scattering
Ramm, A.G.
2008-01-01
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with 'incomplete' data, (4) Inverse scattering for inhomogeneous Schroedinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, (7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, (9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties. (author)
Introduction to Schroedinger inverse scattering
Roberts, T.M.
1991-01-01
Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)
Support minimized inversion of acoustic and elastic wave scattering
Safaeinili, A.
1994-01-01
This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion
Inverse scattering problems with multi-frequencies
Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi
2015-01-01
This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)
Inverse problems in linear transport theory
Dressler, K.
1988-01-01
Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)
Lectures on the inverse scattering method
Zakharov, V.E.
1983-06-01
In a series of six lectures an elementary introduction to the theory of inverse scattering is given. The first four lectures contain a detailed theory of solitons in the framework of the KdV equation, together with the inverse scattering theory of the one-dimensional Schroedinger equation. In the fifth lecture the dressing method is described, while the sixth lecture gives a brief review of the equations soluble by the inverse scattering method. (author)
Applications of inverse and algebraic scattering theories
Amos, K. [Qinghua Univ., Beijing, BJ (China). Dept. of Physics
1997-06-01
Inverse scattering theories, algebraic scattering theory and exactly solvable scattering potentials are diverse ways by which scattering potentials can be defined from S-functions specified by fits to fixed energy, quantal scattering data. Applications have been made in nuclear (heavy ion and nucleon-nucleus scattering), atomic and molecular (electron scattering from simple molecules) systems. Three inverse scattering approaches are considered in detail; the semiclassical WKB and fully quantal Lipperheide-Fiedeldey method, than algebraic scattering theory is applied to heavy ion scattering and finally the exactly solvable Ginocchio potentials. Some nuclear results are ambiguous but the atomic and molecular inversion potentials are in good agreement with postulated forms. 21 refs., 12 figs.
Phaseless tomographic inverse scattering in Banach spaces
Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.
2016-01-01
In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Fréchet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a L p Banach space iterative regularization method which acts on the dual space L p* . Indeed, it is well known that regularization in special Banach spaces, such us L p with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown. (paper)
Inverse acoustic problem of N homogeneous scatterers
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Uniqueness in inverse elastic scattering with finitely many incident waves
Elschner, Johannes; Yamamoto, Masahiro
2009-01-01
We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)
Uniqueness and numerical methods in inverse obstacle scattering
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
Multiple scattering processes: inverse and direct
Kagiwada, H.H.; Kalaba, R.; Ueno, S.
1975-01-01
The purpose of the work is to formulate inverse problems in radiative transfer, to introduce the functions b and h as parameters of internal intensity in homogeneous slabs, and to derive initial value problems to replace the more traditional boundary value problems and integral equations of multiple scattering with high computational efficiency. The discussion covers multiple scattering processes in a one-dimensional medium; isotropic scattering in homogeneous slabs illuminated by parallel rays of radiation; the theory of functions b and h in homogeneous slabs illuminated by isotropic sources of radiation either at the top or at the bottom; inverse and direct problems of multiple scattering in slabs including internal sources; multiple scattering in inhomogeneous media, with particular reference to inverse problems for estimation of layers and total thickness of inhomogeneous slabs and to multiple scattering problems with Lambert's law and specular reflectors underlying slabs; and anisotropic scattering with reduction of the number of relevant arguments through axially symmetric fields and expansion in Legendre functions. Gaussian quadrature data for a seven point formula, a FORTRAN program for computing the functions b and h, and tables of these functions supplement the text
Angle-domain inverse scattering migration/inversion in isotropic media
Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan
2018-07-01
The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.
Direct and inverse scattering for viscoelastic media
Ammicht, E.; Corones, J.P.; Krueger, R.J.
1987-01-01
A time domain approach to direct and inverse scattering problems for one-dimensional viscoelastic media is presented. Such media can be characterized as having a constitutive relation between stress and strain which involves the past history of the strain through a memory function, the relaxation modulus. In the approach in this article, the relaxation modulus of a material is shown to be related to the reflection properties of the material. This relation provides a constructive algorithm for direct and inverse scattering problems. A numerical implementation of this algorithm is tested on several problems involving realistic relaxation moduli
Formal solutions of inverse scattering problems. III
Prosser, R.T.
1980-01-01
The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions
Inverse Scattering in a Multipath Environment
A. Cuccaro
2016-09-01
Full Text Available In this contribution an inverse scattering problem is ad- dressed in a multipath environment. In particular, multipath is created by known ”extra” point-like scatterers (passive elements expressely deployed between the scene under in- vestigation and the source/measurement domains. Through a back-projection imaging scheme, the role of the passive elements on the achievable performance is shown and com- pared to the free-space case.
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
Inverse Scattering Method and Soliton Solution Family for String Effective Action
Ya-Jun, Gao
2009-01-01
A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained
Inverse scattering with supersymmetric quantum mechanics
Baye, Daniel; Sparenberg, Jean-Marc
2004-01-01
The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The use of singular potentials allows adding or removing states from the bound spectrum without contradicting the Levinson theorem. Physical applications of phase-equivalent potentials in nuclear reactions and in three-body systems are described. Derivation of a potential from the phase shift at fixed orbital momentum can also be performed with the supersymmetric inversion by using a Bargmann-type approximation of the scattering matrix or phase shift. A unique singular potential without bound states can be obtained from any phase shift. A limited number of bound states depending on the singularity can then be added. This inversion procedure is illustrated with nucleon-nucleon scattering
Support Minimized Inversion of Acoustic and Elastic Wave Scattering
Safaeinili, Ali
Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work
Extended resolvent and inverse scattering with an application to KPI
Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B.
2003-08-01
We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schrödinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given.
Extended resolvent and inverse scattering with an application to KPI
Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Prinari, B.
2003-01-01
We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schroedinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given
On quasiclassical approximation in the inverse scattering method
Geogdzhaev, V.V.
1985-01-01
Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem
A two-stage method for inverse medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based
Scattering-angle based filtering of the waveform inversion gradients
Alkhalifah, Tariq Ali
2014-01-01
Full waveform inversion (FWI) requires a hierarchical approach to maneuver the complex non-linearity associated with the problem of velocity update. In anisotropic media, the non-linearity becomes far more complex with the potential trade-off between the multiparameter description of the model. A gradient filter helps us in accessing the parts of the gradient that are suitable to combat the potential non-linearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which the low scattering angle of the gradient update is initially muted out in the FWI implementation, in what we may refer to as a scattering angle continuation process. The result is a low wavelength update dominated by the transmission part of the update gradient. In this case, even 10 Hz data can produce vertically near-zero wavenumber updates suitable for a background correction of the model. Relaxing the filtering at a later stage in the FWI implementation allows for smaller scattering angles to contribute higher-resolution information to the model. The benefits of the extended domain based filtering of the gradient is not only it's ability in providing low wavenumber gradients guided by the scattering angle, but also in its potential to provide gradients free of unphysical energy that may correspond to unrealistic scattering angles.
Scattering-angle based filtering of the waveform inversion gradients
Alkhalifah, Tariq Ali
2014-11-22
Full waveform inversion (FWI) requires a hierarchical approach to maneuver the complex non-linearity associated with the problem of velocity update. In anisotropic media, the non-linearity becomes far more complex with the potential trade-off between the multiparameter description of the model. A gradient filter helps us in accessing the parts of the gradient that are suitable to combat the potential non-linearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which the low scattering angle of the gradient update is initially muted out in the FWI implementation, in what we may refer to as a scattering angle continuation process. The result is a low wavelength update dominated by the transmission part of the update gradient. In this case, even 10 Hz data can produce vertically near-zero wavenumber updates suitable for a background correction of the model. Relaxing the filtering at a later stage in the FWI implementation allows for smaller scattering angles to contribute higher-resolution information to the model. The benefits of the extended domain based filtering of the gradient is not only it\\'s ability in providing low wavenumber gradients guided by the scattering angle, but also in its potential to provide gradients free of unphysical energy that may correspond to unrealistic scattering angles.
Inverse scattering problem in turbulent magnetic fluctuations
R. A. Treumann
2016-08-01
Full Text Available We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand–Levitan–Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes
Inverse problems and inverse scattering of plane waves
Ghosh Roy, Dilip N
2001-01-01
The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.
Linearized least-square imaging of internally scattered data
Aldawood, Ali; Hoteit, Ibrahim; Turkiyyah, George M.; Zuberi, M. A H; Alkhalifah, Tariq Ali
2014-01-01
Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single-scattering energy such as nearly vertical faults. Standard migration of these multiples provide subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. Hence, we apply a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. Application to synthetic data demonstrated the effectiveness of the proposed inversion in imaging a reflector that is poorly illuminated by single-scattering energy. The least-square inversion of doublescattered data helped delineate that reflector with minimal acquisition fingerprint.
On the quantum inverse scattering problem
Maillet, J.M.; Terras, V.
2000-01-01
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains
Multi-scattering inversion for low model wavenumbers
Alkhalifah, Tariq Ali; Wu, Zedong
2015-01-01
modeled from the source and those corresponding to single and double scattering to update both the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2012-01-01
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Inverse scattering theory foundations of tomography with diffracting wavefields
Devaney, A.J.
1987-01-01
The underlying mathematical models employed in reflection and transmission computed tomography using diffracting wavefields (called diffraction tomography) are reviewed and shown to have a rigorous basis in inverse scattering theory. In transmission diffraction tomography the underlying wave model is shown to be the Rytov approximation to the complex phase of the wavefield transmitted by the object being probed while in reflection diffraction tomography the underlying wave model is shown to be the Born approximation to the backscattered wavefield from the object. In both cases the goal of the reconstruction process is the determination of the objects's complex index of refraction as a function of position r/sup →/ and, possibly, the frequency ω of the probing wavefield. By use of these approximations the reconstruction problem for both transmission and reflection diffraction tomography can be cast into the simple and elegant form of linearized inverse scattering theory. Linearized inverse scattering theory is shown to lead directly to generalized projection-slice theorems for both reflection and transmission diffraction tomography that provide a simple mathematical relationship between the object's complex index of refraction (the unknown) and the data (the complex phase of the transmitted wave or the complex amplitude of the reflected wave). The conventional projection-slice theorem of X-ray CT is shown to result from the generalized projection-slice theorem for transmission diffraction tomography in the limit of vanishing wavelength (in the absence of wave effects). Fourier based and back-projection type reconstruction algorithms are shown to be directly derivable from the generalized projection-slice theorems
Energy-dependent inversion of p+16O scattering data
Cooper, S.G.
1997-01-01
A fast iterative procedure is developed to determine potentials by inversion from elastic cross section, analysing powers and reaction cross-section measurements covering a wide energy range. The procedure incorporates both energy and parity dependence. The method is applied to extensive p+ 16 O scattering data for an energy range from 27.3 to 46.1 MeV, giving a solution which simultaneously reproduces the data at all energies. The wide angle data is well reproduced by including parity dependence and a linear energy dependence is established for the real potential, including the parity-dependent component. The real terms agree qualitatively with potentials derived from the single channel RGM, but the central and spin-orbit imaginary components have distinct features strongly suggestive of further non-local contributions, possibly arising from channel coupling. The large data set is found essential to reduce the potential ambiguities present when fitting scattering data. (orig.)
Obtaining the crystal potential by inversion from electron scattering intensities
Allen, L.T.; Josefsson, T.W.; Leeb, H.
1998-01-01
A method to obtain the crystal potential from the intensities of the diffracted beams in high energy electron diffraction is proposed. It is based on a series of measurements for specific well determined orientations of the incident beam which determine the moduli of all elements of the scattering matrix. Using unitarity and the specific form of the scattering matrix (including symmetries) an overdetermined set of non-linear equations is obtained from these data. Solution of these equations yields the required phase information and allows the determination of a (projected) crystal potential by inversion which is unique up to an arbitrary shift of the origin. The reconstruction of potentials from intensities is illustrated for two realistic examples, a [111] systematic row case in ZnS and a [110] zone axis orientation in GaAs (both noncentrosymmetric crystals)
Invariant imbedding equations for linear scattering problems
Apresyan, L.
1988-01-01
A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation
Efficient scattering angle filtering for Full waveform inversion
Alkhalifah, Tariq Ali
2015-01-01
Controlling the scattering angles between the state and the adjoint variables for the energy admitted into an inversion gradient or an image can help improve these functions for objectives in full waveform inversion (FWI) or seismic imaging. However, the access of the scattering angle information usually requires an axis extension that could be costly, especially in 3D. For the purpose of a scattering angle filter, I develop techniques that utilize the mapping nature (no domain extension) of the filter for constant-velocity background models to interpolate between such filtered gradients using the actual velocity. The concept has well known roots in the application of phase-shift-plus-interpolation utilized commonly in the downward continuation process. If the difference between the minimum and maximum velocity of the background medium is large, we obtain filtered gradients corresponding to more constant velocity backgrounds and use linear interpolation between such velocities. The accuracy of this approximation for the Marmousi model gradient demonstrates the e ectiveness of the approach.
Efficient scattering angle filtering for Full waveform inversion
Alkhalifah, Tariq Ali
2015-08-19
Controlling the scattering angles between the state and the adjoint variables for the energy admitted into an inversion gradient or an image can help improve these functions for objectives in full waveform inversion (FWI) or seismic imaging. However, the access of the scattering angle information usually requires an axis extension that could be costly, especially in 3D. For the purpose of a scattering angle filter, I develop techniques that utilize the mapping nature (no domain extension) of the filter for constant-velocity background models to interpolate between such filtered gradients using the actual velocity. The concept has well known roots in the application of phase-shift-plus-interpolation utilized commonly in the downward continuation process. If the difference between the minimum and maximum velocity of the background medium is large, we obtain filtered gradients corresponding to more constant velocity backgrounds and use linear interpolation between such velocities. The accuracy of this approximation for the Marmousi model gradient demonstrates the e ectiveness of the approach.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Agaltsov, A. D.; Novikov, R. G.
2014-01-01
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given
The algebraic method of the scattering inverse problem solution under untraditional statements
Popushnoj, M N
2001-01-01
The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated
An Entropic Estimator for Linear Inverse Problems
Amos Golan
2012-05-01
Full Text Available In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists, and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.
Point sources and multipoles in inverse scattering theory
Potthast, Roland
2001-01-01
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.With interest in extracting information about an object through scattered waves at an all-ti...
Constraint on Parameters of Inverse Compton Scattering Model for ...
B2319+60, two parameters of inverse Compton scattering model, the initial Lorentz factor and the factor of energy loss of relativistic particles are constrained. Key words. Pulsar—inverse Compton scattering—emission mechanism. 1. Introduction. Among various kinds of models for pulsar radio emission, the inverse ...
Microlocal analysis of a seismic linearized inverse problem
Stolk, C.C.
1999-01-01
The seismic inverse problem is to determine the wavespeed c x in the interior of a medium from measurements at the boundary In this paper we analyze the linearized inverse problem in general acoustic media The problem is to nd a left inverse of the linearized forward map F or equivalently to nd the
Linearized inversion frameworks toward high-resolution seismic imaging
Aldawood, Ali
2016-09-01
internally multiply scattered seismic waves to obtain highly resolved images delineating vertical faults that are otherwise not easily imaged by primaries. Seismic interferometry is conventionally based on the cross-correlation and convolution of seismic traces to transform seismic data from one acquisition geometry to another. The conventional interferometric transformation yields virtual data that suffers from low temporal resolution, wavelet distortion, and correlation/convolution artifacts. I therefore incorporate a least-squares datuming technique to interferometrically transform vertical-seismic-profile surface-related multiples to surface-seismic-profile primaries. This yields redatumed data with high temporal resolution and less artifacts, which are subsequently imaged to obtain highly resolved subsurface images. Tests on synthetic examples demonstrate the efficiency of the proposed techniques, yielding highly resolved migrated sections compared with images obtained by imaging conventionally redatumed data. I further advance the recently developed cost-effective Generalized Interferometric Multiple Imaging procedure, which aims to not only image first but also higher-order multiples as well. I formulate this procedure as a linearized inversion framework and solve it as a least-squares problem. Tests of the least-squares Generalized Interferometric Multiple imaging framework on synthetic datasets and demonstrate that it could provide highly resolved migrated images and delineate vertical fault planes compared with the standard procedure. The results support the assertion that this linearized inversion framework can illuminate subsurface zones that are mainly illuminated by internally scattered energy.
Scattering theory of the linear Boltzmann operator
Hejtmanek, J.
1975-01-01
In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de
Rational reflection coefficient and inverse scattering on the line
Sabatier, P.C.
1983-01-01
Inverse scattering for the Schroedinger equation on the line is studied for reflection and transmission coefficients that satisfy the usual regularity conditions and are rational functions of k. The origin is still a particular point, but the potentials do not need to be cut at this point like in previous studies. Giving up this restriction corresponds to the existence of poles for both reflection coefficients in both upper and lower half k-planes. It is shown that the problem reduces to solving a linear algebraic system. A different algorithm, made of a sequence of Darboux-Backlund transforms, gives also the solution in closed form and enables to study separately modifications of both sides of the potential due to the introduction of poles. Thus it paves the way for approximation studies. Generalizations and particular problems will be studied in forthcoming papers
Multi-scattering inversion for low model wavenumbers
Alkhalifah, Tariq Ali
2015-08-19
A successful full wavenumber inversion (FWI) implementation updates the low wavenumber model components first for proper wavefield propagation description, and slowly adds the high-wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded data given by direct arrivals or the transmission parts of the single and double-scattering wave-fields developed from a predicted scatter field. We develop a combined inversion of data modeled from the source and those corresponding to single and double scattering to update both the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering angle filter is used to divide the gradient of the combined inversion so initially the high wavenumber (low scattering angle) components of the gradient is directed to the perturbation model and the low wavenumber (high scattering angle) components to the velocity model. As our background velocity matures, the scattering angle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model.
Discrete inverse scattering theory and the continuum limit
Berryman, J.G.; Greene, R.R.
1978-01-01
The class of satisfactory difference approximations for the Schroedinger equation in discrete inverse scattering theory is shown smaller than previously supposed. A fast algorithm (analogous to the Levinson algorithm for Toeplitz matrices) is found for solving the discrete inverse problem. (Auth.)
Seismic inverse scattering in the downward continuation approach
Stolk, C.C.; de Hoop, M.V.
Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem
Remarks on the inverse scattering transform associated with toda equations
Ablowitz, Mark J.; Villorroel, J.
The Inverse Scattering Transforms used to solve both the 2+1 Toda equation and a novel reduction, the Toda differential-delay equations are outlined. There are a number of interesting features associated with these systems and the related scattering theory.
Inversion of electron-water elastic scattering data
Lun, A.; Chen, X.J.; Allen, L.J.; Amos, K.
1994-01-01
Fixed energy inverse scattering theory has been used to analyse the differential cross-sections for the elastic scattering of electrons from water molecules. Both semiclassical (WKB) and fully quantal inversion methods have been used with data taken in the energy range 100 to 1000 eV. Constrained to be real, the local inversion potentials are found to be energy dependent; a dependence that can be interpreted as the local equivalence of true nonlocality in the actual interaction. 14 refs., 4 tabs., 8 figs
Regularization method for solving the inverse scattering problem
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
Classical limit of the quantum inverse scattering problem
Bogdanov, I.V.
1986-01-01
This paper studies the passage to the limit of classical mechanics which is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number 1>0 in the lowest order of perturbation theory. It is shown how in the limit h→0 in the quantum inverse problem the integral Able transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation
The linearized inversion of the generalized interferometric multiple imaging
Aldawood, Ali
2016-09-06
The generalized interferometric multiple imaging (GIMI) procedure can be used to image duplex waves and other higher order internal multiples. Imaging duplex waves could help illuminate subsurface zones that are not easily illuminated by primaries such as vertical and nearly vertical fault planes, and salt flanks. To image first-order internal multiple, the GIMI framework consists of three datuming steps, followed by applying the zero-lag cross-correlation imaging condition. However, the standard GIMI procedure yields migrated images that suffer from low spatial resolution, migration artifacts, and cross-talk noise. To alleviate these problems, we propose a least-squares GIMI framework in which we formulate the first two steps as a linearized inversion problem when imaging first-order internal multiples. Tests on synthetic datasets demonstrate the ability to localize subsurface scatterers in their true positions, and delineate a vertical fault plane using the proposed method. We, also, demonstrate the robustness of the proposed framework when imaging the scatterers or the vertical fault plane with erroneous migration velocities.
Chaichian, M.; Kulish, P. P.
1978-04-01
Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi
2013-09-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data. © 2013 IOP Publishing Ltd.
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
LinvPy : a Python package for linear inverse problems
Beaud, Guillaume François Paul
2016-01-01
The goal of this project is to make a Python package including the tau-estimator algorithm to solve linear inverse problems. The package must be distributed, well documented, easy to use and easy to extend for future developers.
Off-shell T-matrices from inverse scattering
Von Geramb, H.V.; Amos, K.A.
1989-01-01
Inverse scattering theory is used to determine local, energy independent, coordinate space nucleon-nucleon potentials. Inversions are made of phase shifts obtained by analyzes of data and from meson exchange theory, in particular the Paris and the Bonn parametrizations. Half off-shell T-matrices are generated to compare the exact meson theoretical results with those of inversion and it is found that phase equivalent interactions have essentially the same off-shell behaviour for any physically significant range of momenta. 8 refs., 8 figs
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi
2012-01-10
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.
Physical optics far field inverse scattering in the time domain
Bleistein, N.
1976-01-01
The physical optics far field inverse scattering (POFFIS) identity relates the phase and range normalized far field back scattering amplitude to the spatial Fourier transform of the characteristic function of the scattering obstacle. The characteristic function is equal to unity in the region occupied by the obstacle and zero elsewhere. The original identity was derived by Bojarski for impulsive point sources. The result is extended to sources of arbitrary time dependence. One obtains an alternative form of Bojarski's POFFIS identity. One also derives a POFFIS identity in the time domain. Numerically synthesized checks on the method are provided
A two-stage method for inverse medium scattering
Ito, Kazufumi
2013-03-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.
Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line
Raffaele Persico
2017-09-01
Full Text Available Linear inverse scattering problems can be solved by regularized inversion of a matrix, whose calculation and inversion may require significant computing resources, in particular, a significant amount of RAM memory. This effort is dependent on the extent of the investigation domain, which drives a large amount of data to be gathered and a large number of unknowns to be looked for, when this domain becomes electrically large. This leads, in turn, to the problem of inversion of excessively large matrices. Here, we consider the problem of a ground-penetrating radar (GPR survey in two-dimensional (2D geometry, with antennas at an electrically short distance from the soil. In particular, we present a strategy to afford inversion of large investigation domains, based on a shifting zoom procedure. The proposed strategy was successfully validated using experimental radar data.
An analytical approach to estimate the number of small scatterers in 2D inverse scattering problems
Fazli, Roohallah; Nakhkash, Mansor
2012-01-01
This paper presents an analytical method to estimate the location and number of actual small targets in 2D inverse scattering problems. This method is motivated from the exact maximum likelihood estimation of signal parameters in white Gaussian noise for the linear data model. In the first stage, the method uses the MUSIC algorithm to acquire all possible target locations and in the next stage, it employs an analytical formula that works as a spatial filter to determine which target locations are associated to the actual ones. The ability of the method is examined for both the Born and multiple scattering cases and for the cases of well-resolved and non-resolved targets. Many numerical simulations using both the coincident and non-coincident arrays demonstrate that the proposed method can detect the number of actual targets even in the case of very noisy data and when the targets are closely located. Using the experimental microwave data sets, we further show that this method is successful in specifying the number of small inclusions. (paper)
On the inverse problem of dissipative scattering theory. 3
Neidhardt, H.
1988-01-01
Considering a scattering theory in the class of contractions on Hilbert spaces one solves the inverse problem in an operaor-theoretical manner. The solution is obtained underthe very general assumptions that the free evolutions are different for different time directions that not only the perturbed or full evolutions but also the free evolutions are given by contractions. It is shown that the class of contractive Hankel operators can be viewed as a set of scattering operators. This implies the possibility that the scattering operator can be compact. Moreover, the result is applied to the so-called Lax-Phillips scattering theory with losses restoring a result of B.S. Pavlov on the completion of this theory in a quite different manner. 15 refs
Inverse scattering and GPR data processing: an Introduction
Persico, Raffaele
2014-05-01
Inverse scattering and GPR data processing: an Introduction Raffaele Persico This abstract is meant to propose a brief overview of the book "Introduction to Ground Penetrating Radar: Inverse scattering and data processing", edited by Wiley Press (ISBN 9781118305003). The reason why I propose this contribution is the fact that, in spite of the large relevant literature, to the best of my knowledge it is not very common to find a text entirely devoted to the physical-mathematical aspects (a part of them, of course) of GPR data processing. Also due to this, probably a sort of gap between the GPR practice and the underlying theory has been created, and indeed we can meet practitioners convinced that the quality of the achieved results is indefinitely improvable by making narrower the spatial step of the data, or that it is desirable to have extremely directive antennas because this would improve the resolution. In order to provide a work hopefully able to address these and other aspects and hopefully able to give a contribution to the correction of these imprecise beliefs, a dealing from the beginning has been proposed, i.e. a sequential, relatively plane, and as much as possible self consistent, dealing starting from the Maxwell's equations and reaching the most commonly exploited migration formulas and linear inversion algorithms, both within a 2D and a 3D framework. This follows the didactic aim to provide to the reader an insight about what can be reasonably achieved and what should be reasonably done in the field and during the processing phase in order to achieve satisfying results. In particular, the reader will be hopefully made aware not only of the mathematical passages, but also of the involved approximations, the needed assumptions and the physical limits of the final algorithms. The results have been also back-upped with numerical exercises and with some experimental tests, all of which conceived on purpose for this text, and some questions with the
New rigorous asymptotic theorems for inverse scattering amplitudes
Lomsadze, Sh.Yu.; Lomsadze, Yu.M.
1984-01-01
The rigorous asymptotic theorems both of integral and local types obtained earlier and establishing logarithmic and in some cases even power correlations aetdeen the real and imaginary parts of scattering amplitudes Fsub(+-) are extended to the inverse amplitudes 1/Fsub(+-). One also succeeds in establishing power correlations of a new type between the real and imaginary parts, both for the amplitudes themselves and for the inverse ones. All the obtained assertions are convenient to be tested in high energy experiments when the amplitudes show asymptotic behaviour
«Paralipomena» on uniqueness in inverse scattering from a finite number of data
R. Persico
2007-06-01
Full Text Available This paper shows new proof of non-uniqueness of the solution for the retrieving of a compact-supported function starting from a finite number of samples of its spectrum. As will be shown, this is relevant for linear inverse scattering problems, that in many cases can be recast as the reconstruction of a compact supported function from a finite set of samples of its spectrum. Since this reconstruction is not unique, from a practical point of view, any linear inverse scattering algorithm that can be recast in terms of a Fourier relationship between unknowns and data necessarily «trusts» on the absence of invisible objects in the particular situation at hand.
Scattering angle base filtering of the inversion gradients
Alkhalifah, Tariq Ali
2014-01-01
Full waveform inversion (FWI) requires a hierarchical approach based on the availability of low frequencies to maneuver the complex nonlinearity associated with the problem of velocity inversion. I develop a model gradient filter to help us access the parts of the gradient more suitable to combat this potential nonlinearity. The filter is based on representing the gradient in the time-lag normalized domain, in which low scattering angles of the gradient update are initially muted. The result are long-wavelength updates controlled by the ray component of the wavefield. In this case, even 10 Hz data can produce near zero wavelength updates suitable for a background correction of the model. Allowing smaller scattering angle to contribute provides higher resolution information to the model.
Relevance vector machine technique for the inverse scattering problem
Wang Fang-Fang; Zhang Ye-Rong
2012-01-01
A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)
Inverse scattering scheme for the Dirac equation at fixed energy
Leeb, H.; Lehninger, H.; Schilder, C.
2001-01-01
Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)
Multi-frequency direct sampling method in inverse scattering problem
Kang, Sangwoo; Lambert, Marc; Park, Won-Kwang
2017-10-01
We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.
Introduction to ground penetrating radar inverse scattering and data processing
Persico, Raffaele
2014-01-01
This book presents a comprehensive treatment of ground penetrating radar using both forward and inverse scattering mathematical techniques. Use of field data instead of laboratory data enables readers to envision real-life underground imaging; a full color insert further clarifies understanding. Along with considering the practical problem of achieving interpretable underground images, this book also features significant coverage of the problem's mathematical background. This twofold approach provides a resource that will appeal both to application oriented geologists and testing specialists,
Quantum method of the inverse scattering problem. Pt. 1
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino
2006-01-01
The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla
2014-07-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Absorption line profiles in a moving atmosphere - A single scattering linear perturbation theory
Hays, P. B.; Abreu, V. J.
1989-01-01
An integral equation is derived which linearly relates Doppler perturbations in the spectrum of atmospheric absorption features to the wind system which creates them. The perturbation theory is developed using a single scattering model, which is validated against a multiple scattering calculation. The nature and basic properties of the kernels in the integral equation are examined. It is concluded that the kernels are well behaved and that wind velocity profiles can be recovered using standard inversion techniques.
Darrh, A.; Downs, C. M.; Poppeliers, C.
2017-12-01
Born Scattering Inversion (BSI) of electromagnetic (EM) data is a geophysical imaging methodology for mapping weak conductivity, permeability, and/or permittivity contrasts in the subsurface. The high computational cost of full waveform inversion is reduced by adopting the First Born Approximation for scattered EM fields. This linearizes the inverse problem in terms of Born scattering amplitudes for a set of effective EM body sources within a 3D imaging volume. Estimation of scatterer amplitudes is subsequently achieved by solving the normal equations. Our present BSI numerical experiments entail Fourier transforming real-valued synthetic EM data to the frequency-domain, and minimizing the L2 residual between complex-valued observed and predicted data. We are testing the ability of BSI to resolve simple scattering models. For our initial experiments, synthetic data are acquired by three-component (3C) electric field receivers distributed on a plane above a single point electric dipole within a homogeneous and isotropic wholespace. To suppress artifacts, candidate Born scatterer locations are confined to a volume beneath the receiver array. Also, we explore two different numerical linear algebra algorithms for solving the normal equations: Damped Least Squares (DLS), and Non-Negative Least Squares (NNLS). Results from NNLS accurately recover the source location only for a large dense 3C receiver array, but fail when the array is decimated, or is restricted to horizontal component data. Using all receiver stations and all components per station, NNLS results are relatively insensitive to a sub-sampled frequency spectrum, suggesting that coarse frequency-domain sampling may be adequate for good target resolution. Results from DLS are insensitive to diminishing array density, but contain spatially oscillatory structure. DLS-generated images are consistently centered at the known point source location, despite an abundance of surrounding structure.
Rayleigh scattering and nonlinear inversion of elastic waves
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Inverse scattering solution of the Chew-Low equation
Nakano, K.
1985-01-01
Techniques for solving the inverse scattering problem are applied to the Chew-Low equation to obtain the nucleon form factor directly from the experimental phase shifts. A new dispersion relation is derived for the P 11 wave because of its sign-changing phase shift. A self-consistent solution for each channel is obtained, but the universality of form factor is not confirmed. Also, an iterative procedure based on Omnes' method is developed in order to solve coupled-channel, singular integral equations. (orig.)
On reciprocal Baecklund transformations of inverse scattering schemes
Rogers, C.; Wong, P.
1984-01-01
The notion of reciprocally related inverse scattering schemes is introduced and is shown to be a key component in the link between the AKNS and WKI schemes. Reciprocal auto-Baecklund transformations are represented both for a generalised Harry-Dym equation and an equation descriptive of nonlinear oscillation of elastic beams. Further, the N-loop soliton solution of the KIW equation is generated in a convenient parametric form via reciprocal Baecklund transformations. Finally, an important reduction to canonical spectral form is shown to be a reciprocal transformation. (Auth.)
One-dimensional scattering problem for inverse square potential
Mineev, V.S.
1990-01-01
Analytical continuation of the solution for the Schroedinger equation of inverse square potential, together with the modified method for variation of constants makes it possible to construct admittable self-adjoint extensions and to completely analyze the respective scattering problem along the entire line. In this case, the current density conservation and the wave function continuity when passing through the singular point x=0 require, that a 8-shaped induced potential should be introduced in the Schroedinger equation. The relevant calculations have shown that the potential x -2 can be either absolutely penetrable or absolutely impenetrable. 16 refs
Inverse electronic scattering by Green's functions and singular values decomposition
Mayer, A.; Vigneron, J.-P.
2000-01-01
An inverse scattering technique is developed to enable a sample reconstruction from the diffraction figures obtained by electronic projection microscopy. In its Green's functions formulation, this technique takes account of all orders of diffraction by performing an iterative reconstruction of the wave function on the observation screen. This scattered wave function is then backpropagated to the sample to determine the potential-energy distribution, which is assumed real valued. The method relies on the use of singular values decomposition techniques, thus providing the best least-squares solutions and enabling a reduction of noise. The technique is applied to the analysis of a two-dimensional nanometric sample that is observed in Fresnel conditions with an electronic energy of 25 eV. The algorithm turns out to provide results with a mean relative error of the order of 5% and to be very stable against random noise
Pulsar high energy emission due to inverse Compton scattering
Lyutikov, Maxim
2013-06-15
We discuss growing evidence that pulsar high energy is emission is generated via Inverse Compton mechanism. We reproduce the broadband spectrum of Crab pulsar, from UV to very high energy gamma-rays - nearly ten decades in energy, within the framework of the cyclotron-self-Compton model. Emission is produced by two counter-streaming beams within the outer gaps, at distances above ∼ 20 NS radii. The outward moving beam produces UV-X-ray photons via Doppler-booster cyclotron emission, and GeV photons by Compton scattering the cyclotron photons produced by the inward going beam. The scattering occurs in the deep Klein-Nishina regime, whereby the IC component provides a direct measurement of particle distribution within the magnetosphere. The required plasma multiplicity is high, ∼10{sup 6} – 10{sup 7}, but is consistent with the average particle flux injected into the pulsar wind nebula.
Direct sampling methods for inverse elastic scattering problems
Ji, Xia; Liu, Xiaodong; Xi, Yingxia
2018-03-01
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
Benzi, M.; Tůma, Miroslav
1998-01-01
Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998
The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data
Yao Mao
2015-01-01
Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.
Lebrun, D.
1997-05-22
The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.
Frequency-domain full-waveform inversion with non-linear descent directions
Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.
2018-05-01
Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a
Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrodinger equation
Klibanov, Michael V.; Romanov, Vladimir G.
2014-01-01
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. Therefore, a long standing problem posed in 1977 by K. Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum Scattering Theory" is solved.
Scattering of linearly polarized Bessel beams by dielectric spheres
Shoorian, Hamed
2017-09-01
The scattering of a Linearly Polarized Bessel Beam (LPBB) by an isotropic and homogenous dielectric sphere is investigated. Using analytical relation between the cylindrical and the spherical vector wave functions, all the closed- form analytical expressions, in terms of spherical wave-functions expansions, are derived for the scattered field. It is shown that in the case of conical angle of incident Bessel beam is equal to zero, the Linearly Polarized Bessel Beam becomes a plane wave and its scattering coefficients become the same as the expansion coefficients of plane wave in Mie theory. The transverse Cartesian and spherical components of the electric field, scattered by a sphere are shown in the z-plane for different cases, moreover the intensity of the incident Bessel beam and the effects of its conical angle on the scattered field and the field inside the sphere are investigated. To quantitatively study the scattering phenomenon and the variations of the fields inside and outside of the sphere, the scattering and absorption efficiencies are obtained for the scattering of the linearly-polarized Bessel beam, and are compared with those of the plane wave scattering.
Linearized versus non-linear inverse methods for seismic localization of underground sources
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...
Using mixed data in the inverse scattering problem
Lassaut, M.; Larsen, S.Y.; Sofianos, S.A.; Wallet, J.C.
2008-01-01
Consider the fixed-l inverse scattering problem. We show that the zeros of the regular solution of the Schroedinger equation, τ n (E), which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the τ n (E) range from zero to infinity. This suggest that the use of the mixed data of phase-shifts (δ(l 0 , k),k ≥ k 0 ) set-theoretic union (δ(l,k 0 ),l ≥ l 0 ), for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way. (author)
Inelastic Proton Scattering on 21Na in Inverse Kinematics
Austin, Roby
2009-10-01
R.A.E. Austin, R. Kanungo, S. Reeve, Saint Mary's University; D.G. Jenkins, C.Aa.Diget, A. Robinson, A.G. Tuff, O. Roberts, University of York, UK; P.J. Woods, T. Davinson, G. J. Lotay, University of Edinburgh; C.-Y. Wu, Lawrence Livermore National Laboratory; H. Al Falou, G.C. Ball, M. Djongolov, A. Garnsworthy, G. Hackman, J.N. Orce, C.J. Pearson, S. Triambak, S.J. Williams, TRIUMF; C. Andreiou, D.S. Cross, N. Galinski, R. Kshetri, Simon Fraser University; C. Sumithrarachchi, M.A. Schumaker, University of Guelph; M.P. Jones, S.V. Rigby, University of Liverpool; D. Cline, A. Hayes, University of Rochester; T.E. Drake, University of Toronto; We describe an experiment and associated technique [1] to measure resonances of interest in astrophysical reactions. At the TRIUMF ISAC-II radioactive beam accelerator facility in Canada, particles inelastically scattered in inverse kinematics are detected with Bambino, a δE-E silicon telescope spanning 15-40 degrees in the lab. We use the TIGRESS to detect gamma rays in coincidence with the charged particles to cleanly select inelastic scattering events. We measured resonances above the alpha threshold in ^22Mg of relevance to the rate of break-out from the hot-CNO cycle via the reaction ^ 18Ne(α,p)^21Na. [1] PJ Woods et al. Rex-ISOLDE proposal 424 Cern (2003).
Detection of inverse Compton scattering in plasma wakefield experiments
Bohlen, Simon
2016-12-15
Inverse Compton scattering (ICS) is the process of scattering of photons and electrons, where the photons gain a part of the electrons energy. In combination with plasma wakefield acceleration (PWA), ICS offers a compact MeV γ-ray source. A numerical study of ICS radiation produced in PWA experiments at FLASHForward was performed, using an ICS simulation code and the results from particle-in-cell modelling. The possibility of determining electron beam properties from measurements of the γ-ray source was explored for a wide range of experimental conditions. It was found that information about the electron divergence, the electron spectrum and longitudinal information can be obtained from measurements of the ICS beams for some cases. For the measurement of the ICS profile at FLASHForward, a CsI(Tl) scintillator array was chosen, similar to scintillators used in other ICS experiments. To find a suitable detector for spectrum measurements, an experimental test of a Compton spectrometer at the RAL was conducted. This test showed that a similar spectrometer could also be used at FLASHForward. However, changes to the spectrometer could be needed in order to use the pair production effect. In addition, further studies using Geant4 could lead to a better reconstruction of the obtained data. The studies presented here show that ICS is a promising method to analyse electron parameters from PWA experiments in further detail.
Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis
Khuri, N. N.
2002-01-01
It is well known that the s-wave Jost function for a potential, λV, is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the 'coupling constant', λ, will all be real and negative, λ n (0) n n =1/2+iγ n . Thus, finding a repulsive V whose coupling constant spectrum coincides with the Riemann zeros will establish the Riemann hypothesis, but this will be a very difficult and unguided search.In this paper we make a significant enlargement of the class of potentials needed for a generalization of the above idea. We also make this new class amenable to construction via inverse scattering methods. We show that all one needs is a one parameter class of potentials, U(s;x), which are analytic in the strip, 0≤Res≤1, Ims>T 0 , and in addition have an asymptotic expansion in powers of [s(s-1)] -1 , i.e. U(s;x)=V 0 (x)+gV 1 (x)+g 2 V 2 (x)+...+O(g N ), with g=[s(s-1)] -1 . The potentials V n (x) are real and summable. Under suitable conditions on the V n 's and the O(g N ) term we show that the condition, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx≠0, where f 0 is the zero energy and g=0 Jost function for U, is sufficient to guarantee that the zeros g n are real and, hence, s n =1/2+iγ n , for γ n ≥T 0 .Starting with a judiciously chosen Jost function, M(s,k), which is constructed such that M(s,0) is Riemann's ξ(s) function, we have used inverse scattering methods to actually construct a U(s;x) with the above properties. By necessity, we had to generalize inverse methods to deal with complex potentials and a nonunitary S-matrix. This we have done at least for the special cases under consideration.For our specific example, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx=0 and, hence, we get no restriction on Img n or Res n . The reasons for the vanishing of the above integral are given, and they give us hints on what one needs to proceed further. The problem
Resonant Inverse Compton Scattering Spectra from Highly Magnetized Neutron Stars
Wadiasingh, Zorawar; Baring, Matthew G.; Gonthier, Peter L.; Harding, Alice K.
2018-02-01
Hard, nonthermal, persistent pulsed X-ray emission extending between 10 and ∼150 keV has been observed in nearly 10 magnetars. For inner-magnetospheric models of such emission, resonant inverse Compton scattering of soft thermal photons by ultrarelativistic charges is the most efficient production mechanism. We present angle-dependent upscattering spectra and pulsed intensity maps for uncooled, relativistic electrons injected in inner regions of magnetar magnetospheres, calculated using collisional integrals over field loops. Our computations employ a new formulation of the QED Compton scattering cross section in strong magnetic fields that is physically correct for treating important spin-dependent effects in the cyclotron resonance, thereby producing correct photon spectra. The spectral cutoff energies are sensitive to the choices of observer viewing geometry, electron Lorentz factor, and scattering kinematics. We find that electrons with energies ≲15 MeV will emit most of their radiation below 250 keV, consistent with inferred turnovers for magnetar hard X-ray tails. More energetic electrons still emit mostly below 1 MeV, except for viewing perspectives sampling field-line tangents. Pulse profiles may be singly or doubly peaked dependent on viewing geometry, emission locale, and observed energy band. Magnetic pair production and photon splitting will attenuate spectra to hard X-ray energies, suppressing signals in the Fermi-LAT band. The resonant Compton spectra are strongly polarized, suggesting that hard X-ray polarimetry instruments such as X-Calibur, or a future Compton telescope, can prove central to constraining model geometry and physics.
The shifting zoom: new possibilities for inverse scattering on electrically large domains
Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien
2017-04-01
Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C
Strong WW scattering at photon linear colliders
Berger, M.S.
1994-06-01
We investigate the possibility of observing strong interactions of longitudinally polarized weak vector bosons in the process γγ → ZZ at a photon linear collider. We make use of polarization of the photon beams and cuts on the decay products of the Z bosons to enhance the signal relative to the background of transversely polarized ZZ pairs. We find that the background overwhelms the signal unless there are strong resonant effects, as for instance from a technicolor analogue of the hadronic f 2 (1270) meson
Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics
1990-03-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).
Zhou Xin
1990-01-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)
Simulation of inverse Compton scattering and its implications on the scattered linewidth
Ranjan, N.; Terzić, B.; Krafft, G. A.; Petrillo, V.; Drebot, I.; Serafini, L.
2018-03-01
Rising interest in inverse Compton sources has increased the need for efficient models that properly quantify the behavior of scattered radiation given a set of interaction parameters. The current state-of-the-art simulations rely on Monte Carlo-based methods, which, while properly expressing scattering behavior in high-probability regions of the produced spectra, may not correctly simulate such behavior in low-probability regions (e.g. tails of spectra). Moreover, sampling may take an inordinate amount of time for the desired accuracy to be achieved. In this paper, we present an analytic derivation of the expression describing the scattered radiation linewidth and propose a model to describe the effects of horizontal and vertical emittance on the properties of the scattered radiation. We also present an improved version of the code initially reported in Krafft et al. [Phys. Rev. Accel. Beams 19, 121302 (2016), 10.1103/PhysRevAccelBeams.19.121302], that can perform the same simulations as those present in cain and give accurate results in low-probability regions by integrating over the emissions of the electrons. Finally, we use these codes to carry out simulations that closely verify the behavior predicted by the analytically derived scaling law.
Point source reconstruction principle of linear inverse problems
Terazono, Yasushi; Matani, Ayumu; Fujimaki, Norio; Murata, Tsutomu
2010-01-01
Exact point source reconstruction for underdetermined linear inverse problems with a block-wise structure was studied. In a block-wise problem, elements of a source vector are partitioned into blocks. Accordingly, a leadfield matrix, which represents the forward observation process, is also partitioned into blocks. A point source is a source having only one nonzero block. An example of such a problem is current distribution estimation in electroencephalography and magnetoencephalography, where a source vector represents a vector field and a point source represents a single current dipole. In this study, the block-wise norm, a block-wise extension of the l p -norm, was defined as the family of cost functions of the inverse method. The main result is that a set of three conditions was found to be necessary and sufficient for block-wise norm minimization to ensure exact point source reconstruction for any leadfield matrix that admit such reconstruction. The block-wise norm that satisfies the conditions is the sum of the cost of all the observations of source blocks, or in other words, the block-wisely extended leadfield-weighted l 1 -norm. Additional results are that minimization of such a norm always provides block-wisely sparse solutions and that its solutions form cones in source space
Krywonos, Andrey; Harvey, James E; Choi, Narak
2011-06-01
Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.
On the solution of the inverse scattering problem on a ray
Egikyan, R.S.; Zhidkov, E.P.
1988-01-01
Quantum inverse scattering problem (ISP) is considered within the framework of two-particle scattering for local interaction case depending only on the scattering between particles. Constructing the solution of secondary integral equation solution of ISP is described in the clear image. Numerical calculations are conducted using a direct method
Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos
2008-01-01
Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events
An inverse-scattering approach to the physics of transition metals ...
A method is developed for the deduction of a transition metal ion potential from a knowledge of the phase-shift. The method used is based the distorted plane – wave scattering approximation for the deduction of non singular potentials from scattering phase shifts in an inverse scattering approach. The resulting electron ...
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Rayleigh scattering and depolarization ratio in linear alkylbenzene
Liu, Qian; Zhou, Xiang; Huang, Wenqian; Zhang, Yuning; Wu, Wenjie; Luo, Wentai; Yu, Miao; Zheng, Yangheng; Zhou, Li; Cao, Jun; Wang, Yifang
2015-01-01
It is planned to use linear alkylbenzene (LAB) as the organic solvent for the Jiangmen Underground Neutrino Observatory (JUNO) liquid scintillator detectors, due to its ultra-transparency. However, the current Rayleigh scattering length calculation for LAB disagrees with the experimental measurement. This paper reports for the first time that the Rayleigh scattering of LAB is anisotropic, with a depolarization ratio of 0.31±0.01(stat.)±0.01(sys.). We use an indirect method for Rayleigh scattering measurement with the Einstein–Smoluchowski–Cabannes formula, and the Rayleigh scattering length of LAB is determined to be 28.2±1.0 m at 430 nm
Inversion of the total cross sections for electron-molecule and electron-atom scattering
Lun, D.R.; Amos, K.; Allen, L.J.
1994-01-01
Inverse scattering theory has been applied to construct the interaction potentials from total cross sections as a function of energy for electrons scattered off of atoms and molecules. The underlying potentials are assumed to be real and energy independent and are evaluated using the Eikonal approximation and with real phase shifts determined from the total cross sections. The inversion potentials have been determined using either a high energy limit approximation or by using a fixed energy inversion method at select energies. These procedures have been used to analyse e - - CH 4 , e - - SiH 4 , e - -Kr and e - -Xe scattering data in particular. 14 refs., 1 tabs., 3 figs
Linearized inversion frameworks toward high-resolution seismic imaging
Aldawood, Ali
2016-01-01
installed along the earth surface or down boreholes. Seismic imaging is a powerful tool to map these reflected and scattered energy back to their subsurface scattering or reflection points. Seismic imaging is conventionally based on the single
Faraday effect on stimulated Raman scattering in the linear region
Liu, Z. J.; Li, B.; Xiang, J.; Cao, L. H.; Zheng, C. Y.; Hao, L.
2018-04-01
The paper presents the effect of Faraday rotation on stimulated Raman scattering (SRS). When light propagates along the magnetic field upon plasma, Faraday rotation occurs. The rotation angle can be expressed as {{d}}θ /{{d}}{s}=2.93× {10}-4B\\tfrac{{n}e/{n}c}{\\sqrt{1-{n}e/{n}c}} {cm}}-1 approximately, where θ is the rotation angle and s is distance, n e is the electron density, n c is the critical density and B is magnetic field in unit of Gauss. Both the incident light and Raman light have Faraday effects. The angle between the polarization directions of incident light and Raman light changes with position. The driven force of electron plasma wave also reduces, and then SRS scattering level is reduced. Faraday rotation effect can increase the laser intensity threshold of Raman scattering, even if the magnetic field strength is small. The circularly polarized light incident case is also compared with that of the linearly polarized light incident. The Raman scattering level of linearly polarized light is much smaller than that of circularly polarized light in the magnetized plasma. The difference between linearly and circularly polarized lights is also discussed.
Inverse scattering and solitons in An-1 affine Toda field theories
Beggs, E.J.; Johnson, P.R.
1997-01-01
We implement the inverse scattering method in the case of the A n affine Toda field theories, by studying the space-time evolution of simple poles in the underlying loop group. We find the known single-soliton solutions, as well as additional solutions with non-linear modes of oscillation around the standard solution, by studying the particularly simple case where the residue at the pole is a rank-one projection. We show that these solutions with extra modes have the same mass and topological charges as the standard solutions, so we do not shed any light on the missing topological charge problem in these models. From the monodromy matrix it is shown that these solutions have the same higher conserved charges as the standard solutions. We also show that the integrated energy-momentum density can be calculated from the central extension of the loop group. (orig.)
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST
Multi-parameter Analysis and Inversion for Anisotropic Media Using the Scattering Integral Method
Djebbi, Ramzi
2017-01-01
the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic
Potentials of the inverse scattering problem in the three-nucleon problem
Pushkash, A.M.; Simenog, I.V.; Shapoval, D.V.
1993-01-01
Possibilities of using the method of the inverse scattering problem for describing simultaneously the two-nucleon and the low-energy three-nucleon data in the S-interaction approximation are examined. 20 refs., 3 figs., 1 tab
Wu, Zedong
2017-07-04
Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current RWI implementations usually neglect the multi-scattered energy, which will cause some artifacts in the image and the update of the background. To improve existing RWI implementations in taking multi-scattered energy into consideration, we split the velocity model into background and perturbation components, integrate them directly in the wave equation, and formulate a new optimization problem for both components. In this case, the perturbed model is no longer a single-scattering model, but includes all scattering. Through introducing a new cheap implementation of scattering angle enrichment, the separation of the background and perturbation components can be implemented efficiently. We optimize both components simultaneously to produce updates to the velocity model that is nonlinear with respect to both the background and the perturbation. The newly introduced perturbation model can absorb the non-smooth update of the background in a more consistent way. We apply the proposed approach on the Marmousi model with data that contain frequencies starting from 5 Hz to show that this method can converge to an accurate velocity starting from a linearly increasing initial velocity. Also, our proposed method works well when applied to a field data set.
Review of the inverse scattering problem at fixed energy in quantum mechanics
Sabatier, P. C.
1972-01-01
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
On analyticity of linear waves scattered by a layered medium
Nicholls, David P.
2017-10-01
The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.
On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder
Nakamura, Gen; Wang, Haibing; Sleeman, Brian D
2012-01-01
We consider an inverse problem for the scattering of an obliquely incident electromagnetic wave by an impedance cylinder. In previous work, we have shown that the direct scattering problem is governed by a pair of Helmholtz equations subject to coupled oblique boundary conditions, where the wave number depends on the frequency and the incident angle with respect to the axis of the cylinder. In this paper, we are concerned with the inverse problem of uniquely identifying the cross-section of an unknown cylinder and the impedance function from the far-field patterns at fixed frequency and a range of incident angles. A uniqueness result for such an inverse scattering problem is established. Our method is based on the analyticity of solution to the direct scattering problem, which is justified by using the Lax–Phillips method together with the perturbation theory of Fredholm operators. (paper)
Non-Linear Rheological Properties and Neutron Scattering Investigation on Dilute Ring-Linear Blends
Pyckhout-Hintzen, W.; Bras, A.R.; Wischnewski, A.
in a filament stretching rheometer, followed by quenching, strong anisotropic scattering patterns were obtained which were described by affinely deformed rings which function as giant, polymeric chemical crosslinks or sliplinks and more or less isotropic topological contributions from the entangling...... with interpenetrating linear chains. At the same time the non-linear rheological and mechanical data fit to a non-affine slip-tube model as for moderately crosslinked networks and to interchain pressure models or a modified non-linear Doi-Edwards description for the observed strain hardening during the extensional...
Heavy ion scattering; a fixed energy inverse problem
Amos, K.
1993-01-01
Heavy ion scattering has been studied quite intensively in the last decade and central in most analyses of data from such experiments be they on fusion, particle transfer or internal state excitations of the colliding pair, is the inter-ion interaction affecting their relative motion. It is customary to use the elastic scattering data to constrain solutions of the (nonrelativistic) Schroedinger equation to ascertain the character of that (central and complex) heavy ion potential. These matters for projectiles ranging from the lightest 'heavy' ion, a proton, to Oxygen nuclei are considered in brief herein. The targets range from 12 C to 208 Pb. The central entity in the analyses to be discussed will be the S-function, and so for completeness, the simple potential scattering theory details are presented that specify the S-function and relate it to measured cross-sections. 20 refs., 18 figs
Inverse scattering with mixed spectrum from δ-potentials
Lin Jiancheng.
1987-03-01
The inverse problem is studied in a system with mixed spectrum, i.e. the continuous part of the spectrum coincides with that of a repulsive δ-potential and the discrete part coincides with that of an attractive δ-potential. (author). 2 refs, 5 figs
Uniqueness of inverse scattering problem in local quantum physics
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2001-06-01
It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)
Precision measurements of linear scattering density using muon tomography
Åström, E.; Bonomi, G.; Calliari, I.; Calvini, P.; Checchia, P.; Donzella, A.; Faraci, E.; Forsberg, F.; Gonella, F.; Hu, X.; Klinger, J.; Sundqvist Ökvist, L.; Pagano, D.; Rigoni, A.; Ramous, E.; Urbani, M.; Vanini, S.; Zenoni, A.; Zumerle, G.
2016-07-01
We demonstrate that muon tomography can be used to precisely measure the properties of various materials. The materials which have been considered have been extracted from an experimental blast furnace, including carbon (coke) and iron oxides, for which measurements of the linear scattering density relative to the mass density have been performed with an absolute precision of 10%. We report the procedures that are used in order to obtain such precision, and a discussion is presented to address the expected performance of the technique when applied to heavier materials. The results we obtain do not depend on the specific type of material considered and therefore they can be extended to any application.
Namjoo, A.; Sarvari, S.M. Hosseini; Behzadmehr, A.; Mansouri, S.H.
2009-01-01
In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.
A simple method for solving the inverse scattering problem
Melnikov, V.N.; Rudyak, B.V.; Zakhariev, V.N.
1977-01-01
A new method is proposed for approximate reconstruction of a potential as a step function from scattering data using the completeness relation of solutions of the Schroedinger equation. The suggested method allows one to take into account exactly the additional centrifugal barrier for partial waves with angular momentum l>0, and also the Coulomb potential. The method admits different generalizations. Numerical calculations for checking the method have been performed
On the evolution equations, solvable through the inverse scattering method
Gerdjikov, V.S.; Khristov, E.Kh.
1979-01-01
The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation
Park, J. J.
2017-12-01
Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Alkhalifah, Tariq Ali; Choi, Yun Seok
2012-01-01
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, B; Scheid, W
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure
Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method
Urazboev, Gayrat
2012-01-01
In this work, there is shown that the solutions of Toda lattice with self-consistent source can be found by the inverse scattering method for the discrete Sturm-Liuville operator. For the considered problem the one-soliton solution is obtained.
A Literature Survey on Inverse Scattering for Electron Density Profile Determination. Volume II.
1981-09-24
THE INVERSE SCATTERING PROBLEM4 FOR THE EQUAT ION Of ACOUSTIC$ AVILA, G.S.S. DEPT. DE MATEMATICA . INST. DE CIENCIAS EXATAS. UNIV. Of BRASILIA...of Colict support Portinari. Joao C. Departamento do Matematica . Pontificia Universidade Catolica do Rio de Janeiro, Rio do Janeiro. Brasil J. Math
Tropospheric nitrogen dioxide inversions based on spectral measurements of scattered sunlight
Vlemmix, T.
2011-01-01
This thesis describes the development of inversion methods for tropospheric nitrogen dioxide (NO2), based on ground based observations of scattered sunlight with themulti-axis differential optical absorption spectroscopy (MAX-DOAS) technique. NO2 is an atmospheric trace gas which, when present near
Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation
Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.
1989-01-01
The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs
Inverse scattering problem for a magnetic field in the Glauber approximation
Bogdanov, I.V.
1985-01-01
New results in the general theory of scattering are obtained. An inverse problem at fixed energy for an axisymmetric magnetic field is formulated and solved within the frames of the quantum-mechanical Glauber approximation. The solution is found in quadratures in the form of an explicit inversion algorithm reproducing a vector potential by the angular dependence of the scattering amplitude. Extreme transitions from the eikonal inversion method to the classical and Born ones are investigated. Integral and differential equations are derived for the eikonal amplitude that ensure the real value of the vector potential and its energy independence. Magnetoelectric analogies the existence of equivalent axisymmetric electric and magnetic fields scattering charged particles in the same manner both in the Glauber and Born approximation are established. The mentioned analogies permit to simulate ion-potential scattering by potential one that is of interest from the practical viewpoint. Three-dimensional (excentral) eikonal inverse problems for the electric and magnetic fields are discussed. The results of the paper can be used in electron optics
Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations
Nakamura, Gen; Vashisth, Manmohan
2017-01-01
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...
Elastic scattering of protons on 8Li nucleus in inverse kinematics
Zhusupov, M.A.; Ibraeva, E.T.; Sanfirova, A.B.; Imambekov, O.
2002-01-01
In the present paper the proton elastic scattering on 8 Li in inverse kinematics is studies. The inverse kinematics means that a beam of radioactive nuclei is scattered on a stable hydrogen target. Proton as a target has an advantage during the interaction since it is stable and mechanism of proton-nucleus scattering is quite simple. 8 Li nucleus is considered in the three-body αtn-model with realistic potential of inter-cluster interactions. The wave function of this nucleus is calculated in the work where it was shown that such model well describes the main spectroscopic characteristics of the nucleus, root-mean square radius, binding energy, location of low laying energy levels, magnetic momentum and also total cross section and 7 Li(n, γ) 8 Li reaction rate at a wide energy region. Within Glauber-Sitenko multiply scattering theory, the differential cross section of elastic p 8 Li-scattering has been calculated. The first and the second multiplicities of scattering on nucleons and clusters of the nucleus were taken into account in Ω multiply scattering operator. There were considered several cases when as the initial parameters both amplitudes of nucleon-nucleon and nucleon-cluster scattering were taken. Sensitivity of the differential cross section both to the different wave functions of the target-nucleus and to the parameters of the elementary amplitudes and sensitivity to the scattering multiplicities at several beam energies has been investigated. Comparison with differential cross sections of elastic p 6 Li- and p 7 Li scattering has been carried out
A modified linear algebraic approach to electron scattering using cubic splines
Kinney, R.A.
1986-01-01
A modified linear algebraic approach to the solution of the Schrodiner equation for low-energy electron scattering is presented. The method uses a piecewise cubic-spline approximation of the wavefunction. Results in the static-potential and the static-exchange approximations for e - +H s-wave scattering are compared with unmodified linear algebraic and variational linear algebraic methods. (author)
Quantitative photoplethysmography: Lambert-Beer law or inverse function incorporating light scatter.
Cejnar, M; Kobler, H; Hunyor, S N
1993-03-01
Finger blood volume is commonly determined from measurement of infra-red (IR) light transmittance using the Lambert-Beer law of light absorption derived for use in non-scattering media, even when such transmission involves light scatter around the phalangeal bone. Simultaneous IR transmittance and finger volume were measured over the full dynamic range of vascular volumes in seven subjects and outcomes compared with data fitted according to the Lambert-Beer exponential function and an inverse function derived for light attenuation by scattering materials. Curves were fitted by the least-squares method and goodness of fit was compared using standard errors of estimate (SEE). The inverse function gave a better data fit in six of the subjects: mean SEE 1.9 (SD 0.7, range 0.7-2.8) and 4.6 (2.2, 2.0-8.0) respectively (p < 0.02, paired t-test). Thus, when relating IR transmittance to blood volume, as occurs in the finger during measurements of arterial compliance, an inverse function derived from a model of light attenuation by scattering media gives more accurate results than the traditional exponential fit.
Otero, F A; Frontini, G L; Elicabe, G E
2011-01-01
An analytic model for the scattering of a spherical particle with spherical inclusions has been proposed under the RG approximation. The model can be used without limitations to describe an X-ray scattering experiment. However, for light scattering several conditions must be fulfilled. Based on this model an inverse methodology is proposed to estimate the radii of host particle and inclusions, the number of inclusions and the Distance Distribution Functions (DDF's) of the distances between inclusions and the distances between inclusions and the origin of coordinates. The methodology is numerically tested in a light scattering example in which the host particle is eliminated by matching the refractive indices of host particle and medium. The results obtained for this cluster particle are very satisfactory.
Continuity and general perturbation of the Drazin inverse for closed linear operators
N. Castro González
2002-01-01
Full Text Available We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
Treating experimental data of inverse kinetic method by unitary linear regression analysis
Zhao Yusen; Chen Xiaoliang
2009-01-01
The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)
Fixed energy inversion of 5 eV e-Xe atom scattering
Lovell, A.; Amos, K.
2000-01-01
Fixed energy inverse scattering theory has been used to define central and spin-orbit Schroedinger potentials for the scattering of 5 eV polarized electrons from Xe atoms. The results are typical for a range of such data; including energies above threshold when the potentials become complex. The phase shifts obtained from an analysis of the measured differential cross section and analyzing power has been used as input data. Both semi-classical (WKB) and fully quantal inversion methods have been used to extract central and spin-orbit interactions. The analysis shows that information additional to the set of input phase shifts extracted from this (and similar) data may be needed to ascertain physical potentials
Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements
Eberspaecher, M.; Amos, K.; Apagyi, B.
1999-12-01
The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
Le Louër, Frédérique
2015-01-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)
Understanding of phase modulation in two-level systems through inverse scattering
Hasenfeld, A.; Hammes, S.L.; Warren, W.S.
1988-01-01
Analytical and numerical calculations describe the effects of shaped radiation pulses on two-level systems in terms of quantum-mechanical scattering. Previous results obtained in the reduced case of amplitude modulation are extended to the general case of simultaneous amplitude and phase modulation. We show that an infinite family of phase- and amplitude-modulated pulses all generate rectangular inversion profiles. Experimental measurements also verify the theoretical analysis
Lax-pair operators for squared eigenfunctions in the inverse scattering transformations
Iino, Kazuhiro; Ichikawa, Yoshihiko.
1982-05-01
Modification of the algorithm of Chen, Lee and Liu enables us to construct alternative Lax-pair operators for the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. These Lax-pair operators stand as the Lax-pair operators for the squared eigenfunction and the sum of squared eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation for these celebrated nonlinear evolution equations. (author)
Development and characterization of a tunable ultrafast X-ray source via inverse-Compton-scattering
Jochmann, Axel
2014-01-01
Ultrashort, nearly monochromatic hard X-ray pulses enrich the understanding of the dynamics and function of matter, e.g., the motion of atomic structures associated with ultrafast phase transitions, structural dynamics and (bio)chemical reactions. Inverse Compton backscattering of intense laser pulses from relativistic electrons not only allows for the generation of bright X-ray pulses which can be used in a pump-probe experiment, but also for the investigation of the electron beam dynamics at the interaction point. The focus of this PhD work lies on the detailed understanding of the kinematics during the interaction of the relativistic electron bunch and the laser pulse in order to quantify the influence of various experiment parameters on the emitted X-ray radiation. The experiment was conducted at the ELBE center for high power radiation sources using the ELBE superconducting linear accelerator and the DRACO Ti:sapphire laser system. The combination of both these state-of-the-art apparatuses guaranteed the control and stability of the interacting beam parameters throughout the measurement. The emitted X-ray spectra were detected with a pixelated detector of 1024 by 256 elements (each 26μm by 26μm) to achieve an unprecedented spatial and energy resolution for a full characterization of the emitted spectrum to reveal parameter influences and correlations of both interacting beams. In this work the influence of the electron beam energy, electron beam emittance, the laser bandwidth and the energy-anglecorrelation on the spectra of the backscattered X-rays is quantified. A rigorous statistical analysis comparing experimental data to ab-initio 3D simulations enabled, e.g., the extraction of the angular distribution of electrons with 1.5% accuracy and, in total, provides predictive capability for the future high brightness hard X-ray source PHOENIX (Photon electron collider for Narrow bandwidth Intense X-rays) and potential all optical gamma-ray sources. The results
Full waveform inversion based on scattering angle enrichment with application to real dataset
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity to the migrated image. We propose a combined FWI and RWI optimization problem through dividing the velocity into the background and perturbed components. We optimize both the background and perturbed components, as independent parameters. The new objective function is quadratic with respect to the perturbed component, which will reduce the nonlinearity of the optimization problem. Solving this optimization provides a true amplitude image and utilizes the diving waves to update the velocity of the shallow parts. To insure a proper wavenumber continuation, we use an efficient scattering angle filter to direct the inversion at the early stages to direct energy corresponding to large (smooth velocity) scattering angles to the background velocity update and the small (high wavenumber) scattering angles to the perturbed velocity update. This efficient implementation of the filter is fast and requires less memory than the conventional approach based on extended images. Thus, the new FWI procedure updates the background velocity mainly along the wavepath for both diving and reflected waves in the initial stages. At the same time, it updates the perturbation with mainly reflections (filtering out the diving waves). To demonstrate the capability of this method, we apply it to a real 2D marine dataset.
Robust inverse scattering full waveform seismic tomography for imaging complex structure
Nurhandoko, Bagus Endar B.; Sukmana, Indriani; Wibowo, Satryo; Deny, Agus; Kurniadi, Rizal; Widowati, Sri; Mubarok, Syahrul; Susilowati; Kaswandhi
2012-01-01
Seismic tomography becomes important tool recently for imaging complex subsurface. It is well known that imaging complex rich fault zone is difficult. In this paper, The application of time domain inverse scattering wave tomography to image the complex fault zone would be shown on this paper, especially an efficient time domain inverse scattering tomography and their run in cluster parallel computer which has been developed. This algorithm is purely based on scattering theory through solving Lippmann Schwienger integral by using Born's approximation. In this paper, it is shown the robustness of this algorithm especially in avoiding the inversion trapped in local minimum to reach global minimum. A large data are solved by windowing and blocking technique of memory as well as computation. Parameter of windowing computation is based on shot gather's aperture. This windowing technique reduces memory as well as computation significantly. This parallel algorithm is done by means cluster system of 120 processors from 20 nodes of AMD Phenom II. Benchmarking of this algorithm is done by means Marmoussi model which can be representative of complex rich fault area. It is shown that the proposed method can image clearly the rich fault and complex zone in Marmoussi model even though the initial model is quite far from the true model. Therefore, this method can be as one of solution to image the very complex mode.
Robust inverse scattering full waveform seismic tomography for imaging complex structure
Nurhandoko, Bagus Endar B.; Sukmana, Indriani; Wibowo, Satryo; Deny, Agus; Kurniadi, Rizal; Widowati, Sri; Mubarok, Syahrul; Susilowati; Kaswandhi [Wave Inversion and Subsurface Fluid Imaging Research (WISFIR) Lab., Complex System Research Division, Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung. and Rock Fluid Imaging Lab., Rock Physics and Cluster C (Indonesia); Rock Fluid Imaging Lab., Rock Physics and Cluster Computing Center, Bandung (Indonesia); Physics Department of Institut Teknologi Bandung (Indonesia); Rock Fluid Imaging Lab., Rock Physics and Cluster Computing Center, Bandung, Indonesia and Institut Teknologi Telkom, Bandung (Indonesia); Rock Fluid Imaging Lab., Rock Physics and Cluster Computing Center, Bandung (Indonesia)
2012-06-20
Seismic tomography becomes important tool recently for imaging complex subsurface. It is well known that imaging complex rich fault zone is difficult. In this paper, The application of time domain inverse scattering wave tomography to image the complex fault zone would be shown on this paper, especially an efficient time domain inverse scattering tomography and their run in cluster parallel computer which has been developed. This algorithm is purely based on scattering theory through solving Lippmann Schwienger integral by using Born's approximation. In this paper, it is shown the robustness of this algorithm especially in avoiding the inversion trapped in local minimum to reach global minimum. A large data are solved by windowing and blocking technique of memory as well as computation. Parameter of windowing computation is based on shot gather's aperture. This windowing technique reduces memory as well as computation significantly. This parallel algorithm is done by means cluster system of 120 processors from 20 nodes of AMD Phenom II. Benchmarking of this algorithm is done by means Marmoussi model which can be representative of complex rich fault area. It is shown that the proposed method can image clearly the rich fault and complex zone in Marmoussi model even though the initial model is quite far from the true model. Therefore, this method can be as one of solution to image the very complex mode.
Inverse random source scattering for the Helmholtz equation in inhomogeneous media
Li, Ming; Chen, Chuchu; Li, Peijun
2018-01-01
This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
Quantal inversion of cross-section for the elastic scattering of 200 MeV protons from 12C
Allen, L.J.; Amos, K.; Dortmans, P.J.
1994-01-01
Fixed energy quantal inverse scattering theory has been used to analyse the differential cross-section from the elastic scattering of 200 MeV protons from 12 C. Ambiguities in obtaining the scattering function from the differential cross-section are discussed and by means of example it is illustrated that not all scattering functions lead to physically reasonable potentials. 8 refs., 2 tabs., 4 figs
Allen, L.J.; Spargo, A.E.C.; Leeb, H.
1998-01-01
The retrieval of a unique crystal potential from the scattering matrix S in high energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S-matrix. An algorithm for the extraction of the crystal potential from the S-matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered
Inverse Raman scattering in silicon: A free-carrier enhanced effect
Solli, D. R.; Koonath, P.; Jalali, B.
2009-01-01
Stimulated Raman scattering has been harnessed to produce the first silicon lasers and amplifiers. The Raman effect can also produce intensity-dependent nonlinear loss through a corollary process, inverse Raman scattering (IRS). This process has never been observed in a semiconductor. We demonstrate IRS in silicon--a process that is substantially modified by optically generated free carriers--achieving attenuation levels >15 dB with a pump intensity of 4 GW/cm 2 . Surprisingly, free-carrier absorption, the detrimental effect that generally suppresses nonlinear effects in silicon, actually facilitates IRS by delaying the onset of contamination from coherent anti-Stokes Raman scattering. Silicon-based IRS could be a valuable tool for chip-scale signal processing.
On The Structure of The Inverse of a Linear Constant Multivariable ...
On The Structure of The Inverse of a Linear Constant Multivariable System. ... It is shown that the use of this representation has certain advantages in the design of multivariable feedback systems. typical examples were considered to indicate the corresponding application. Keywords: Stability Functions, multivariable ...
Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays
Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.
2005-04-01
We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
Multi-parameter Analysis and Inversion for Anisotropic Media Using the Scattering Integral Method
Djebbi, Ramzi
2017-10-24
The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth\\'s subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the
Characterization of a material by probability of linear scattering using effect of target thickness
Nghiep, T.D.; Khai, N.T.; Cong, N.T.; Minh, D.T.N.
2013-01-01
We report on an experimental test with 662 keV gamma photons scattered from a set of samples from 6 C, 13 Al, 26 Fe, 29 Cu, 47 Ag, 82 Pb and stainless steel for determination of probability of linear scattering, which can be used for characterization of a material. The results show that for the given target and scattering angle, the effect of target thickness in gamma photons scattering relates to single and multiple scattering and that the scattered events exponentially increase with an increase in target thickness and saturation at some values of thickness. The experimental results correlate with the typical function of energy transfer model. (author)
Delbary, Fabrice; Piana, Michele; Aramini, Riccardo; Brignone, Massimo; Bozza, Giovanni
2008-01-01
Microwave tomography is a non-invasive approach to the early diagnosis of breast cancer. However the problem of visualizing tumors from diffracted microwaves is a difficult nonlinear ill-posed inverse scattering problem. We propose a qualitative approach to the solution of such a problem, whereby the shape and location of cancerous tissues can be detected by means of a combination of the Reciprocity Gap Functional method and the Linear Sampling method. We validate this approach to synthetic near-fields produced by a finite element method for boundary integral equations, where the breast is mimicked by the axial view of two nested cylinders, the external one representing the skin and the internal one representing the fat tissue.
Delbary, Fabrice; Aramini, Riccardo; Bozza, Giovanni; Brignone, Massimo; Piana, Michele
2008-11-01
Microwave tomography is a non-invasive approach to the early diagnosis of breast cancer. However the problem of visualizing tumors from diffracted microwaves is a difficult nonlinear ill-posed inverse scattering problem. We propose a qualitative approach to the solution of such a problem, whereby the shape and location of cancerous tissues can be detected by means of a combination of the Reciprocity Gap Functional method and the Linear Sampling method. We validate this approach to synthetic near-fields produced by a finite element method for boundary integral equations, where the breast is mimicked by the axial view of two nested cylinders, the external one representing the skin and the internal one representing the fat tissue.
Zhou, Xin
1990-03-01
For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.
Fukuda, J.; Johnson, K. M.
2009-12-01
Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress
Single- and coupled-channel radial inverse scattering with supersymmetric transformations
Baye, Daniel; Sparenberg, Jean-Marc; Pupasov-Maksimov, Andrey M; Samsonov, Boris F
2014-01-01
The present status of the three-dimensional inverse-scattering method with supersymmetric transformations is reviewed for the coupled-channel case. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a complete, efficient and elegant solution to the inverse-scattering problem for the radial Schrödinger equation with short-range interactions. A special emphasis is put on the differences between conservative and non-conservative transformations, i.e. transformations that do or do not conserve the behaviour of solutions of the radial Schrödinger equation at the origin. In particular, we show that for the zero initial potential, a non-conservative transformation is always equivalent to a pair of conservative transformations. These single-channel results are illustrated on the inversion of the neutron–proton triplet eigenphase shifts for the S- and D-waves. We then summarize and extend our previous works on the coupled-channel case, i.e. on systems of coupled radial Schrödinger equations, and stress remaining difficulties and open questions of this problem by putting it in perspective with the single-channel case. We mostly concentrate on two-channel examples to illustrate general principles while keeping mathematics as simple as possible. In particular, we discuss the important difference between the equal-threshold and different-threshold problems. For equal thresholds, conservative transformations can provide non-diagonal Jost and scattering matrices. Iterations of such transformations in the two-channel case are studied and shown to lead to practical algorithms for inversion. A convenient particular technique where the mixing parameter can be fitted without modifying the eigenphases is developed with iterations of pairs of conjugate transformations. This technique is applied to the neutron–proton triplet S–D scattering matrix, for which exactly-solvable matrix potential models are constructed
Inverse kinematics of a dual linear actuator pitch/roll heliostat
Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh
2017-06-01
This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.
A systematic approach to robust preconditioning for gradient-based inverse scattering algorithms
Nordebo, Sven; Fhager, Andreas; Persson, Mikael; Gustafsson, Mats
2008-01-01
This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient or quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust in the sense that the scaling, i.e. the diagonal Fisher information, is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique
Wu, Zedong; Alkhalifah, Tariq Ali
2017-01-01
Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current
Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.
2018-04-01
We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.
Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.
2015-03-01
Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.
A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem
Park, Taehoon; Park, Won-Kwang
2015-01-01
Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation. (paper)
Non-local currents in 2D QFT: an alternative To - the quantum inverse scattering method
Bernard, D.; Leclair, A.; Cornell Univ., Ithaca, NY
1990-01-01
The formalism based on non-local charges that we propose provides an alternative to the quantum inverse scattering method for solving integrable quantum field theories in 2D. The content of the paper is: 1. Introduction: historical background. 2. The NLC approach to 2D QFT: a summary. 3 Exchange algebras and on-shell conservation laws: why non-local charges are useful. 4. The lattice construction: the geometrical origin of non-local conserved currents. 5. The continuum construction: how to deal with non-local conserved currents. 6. Examples: Yangian and quantum group currents. 7 Conclusions: open problems. 22 refs., 4 figs
A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem
Park, Taehoon; Park, Won-Kwang
2015-09-01
Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.
Entekhabi, Mozhgan Nora; Isakov, Victor
2018-05-01
In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.
Chernichenko, Yu.D.
2005-01-01
Within the relativistic quasipotential approach to quantum field theory, the relativistic inverse scattering problem is solved for the case where the total quasipotential describing the interaction of two relativistic spinless particles having different masses is a superposition of a nonlocal separable and a local quasipotential. It is assumed that the local component of the total quasipotential is known and that there exist bound states in this local component. It is shown that the nonlocal separable component of the total interaction can be reconstructed provided that the local component, an increment of the phase shift, and the energies of bound states are known
Arians, S.
1997-01-01
We consider the Hamiltonian H=(p-A(x)) 2 /(2m)+V(x) of a quantum particle in a magnetic field B=rotA and a potential V in space dimensions ν≥2. If V is of short range, then the high-velocity limit of the scattering operator uniquely determines the magnetic field B and the potential V. If, in addition, long-range potentials V l are present, some knowledge of (the far out tail of) V l is needed to define a modified Dollard wave operator and a scattering operator S D . Again its high- velocity limit uniquely determines B and V=V s +V l . Moreover, we give explicit error bounds which are inverse proportional to the velocity. copyright 1997 American Institute of Physics
Smith, James A.
1992-01-01
The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI 1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.
Xin-Jia Meng
2015-01-01
Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.
A multifrequency MUSIC algorithm for locating small inhomogeneities in inverse scattering
Griesmaier, Roland; Schmiedecke, Christian
2017-01-01
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves with sparse multifrequency far field data-sets. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far fields of scattered waves corresponding to incident plane waves with one fixed incident direction but several different frequencies. We assume that the far field is measured at a few observation directions only. Taking advantage of the smallness of the scatterers with respect to wavelength we utilize an asymptotic representation formula for the far field to design and analyze a MUSIC-type reconstruction method for this setup. We establish lower bounds on the number of frequencies and receiver directions that are required to recover the number and the positions of an ensemble of scatterers from the given measurements. Furthermore we briefly sketch a possible application of the reconstruction method to the practically relevant case of multifrequency backscattering data. Numerical examples are presented to document the potentials and limitations of this approach. (paper)
On the internal stability of non-linear dynamic inversion: application to flight control
Alam, M.; Čelikovský, Sergej
2017-01-01
Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf
Zhou, Xiang; Zhang, Zhenyu [Wuhan University, Hubei Nuclear Solid Physics Key Laboratory, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan (China); Liu, Qian; Zheng, Yangheng [University of Chinese Academy of Sciences, School of Physics, Beijing (China); Han, Junbo [Huazhong University of Science and Technology, Wuhan National High Magnetic Field Center, Wuhan (China); Zhang, Xuan; Ding, Yayun; Zhou, Li; Cao, Jun; Wang, Yifang [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2015-11-15
We have set up a light scattering spectrometer to study the depolarization of light scattering in linear alkylbenzene. The scattering spectra show that the depolarized part of light scattering is due to Rayleigh scattering. The additional depolarized Rayleigh scattering can make the effective transparency of linear alkylbenzene much better than expected. Therefore, sufficient scintillation photons can transmit through large liquid scintillator detector, such as that of the JUNO experiment. Our study is crucial to achieving an unprecedented energy resolution of 3 %/√(E(MeV)) required for the JUNO experiment to determine the neutrino mass hierarchy. The spectroscopic method can also be used to examine the depolarization of other organic solvents used in neutrino experiments. (orig.)
Zhou, Xiang, E-mail: xiangzhou@whu.edu.cn [Hubei Nuclear Solid Physics Key Laboratory, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, 430072, Wuhan (China); Liu, Qian, E-mail: liuqian@ucas.ac.cn [School of Physics, University of Chinese Academy of Sciences, 100049, Beijing (China); Han, Junbo [Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074, Wuhan (China); Zhang, Zhenyu [Hubei Nuclear Solid Physics Key Laboratory, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, 430072, Wuhan (China); Zhang, Xuan; Ding, Yayun [Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing (China); Zheng, Yangheng [School of Physics, University of Chinese Academy of Sciences, 100049, Beijing (China); Zhou, Li; Cao, Jun; Wang, Yifang [Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing (China)
2015-11-21
We have set up a light scattering spectrometer to study the depolarization of light scattering in linear alkylbenzene. The scattering spectra show that the depolarized part of light scattering is due to Rayleigh scattering. The additional depolarized Rayleigh scattering can make the effective transparency of linear alkylbenzene much better than expected. Therefore, sufficient scintillation photons can transmit through large liquid scintillator detector, such as that of the JUNO experiment. Our study is crucial to achieving an unprecedented energy resolution of 3 %/√(E(MeV)) required for the JUNO experiment to determine the neutrino mass hierarchy. The spectroscopic method can also be used to examine the depolarization of other organic solvents used in neutrino experiments.
Palmai, T.; Apagyi, B.; Horvath, M.
2008-01-01
Solution of the Cox-Thompson inverse scattering problem at fixed energy 1-3 is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered. (author)
Advanced Thomson scattering system for high-flux linear plasma generator
Meiden, van der H.J.; Lof, A.R.; Berg, van den M.A.; Brons, S.; Donné, A.J.H.; Eck, van H.J.N.; Koelman, Peter; Koppers, W.R.; Kruijt, O.G.; Naumenko, N.N.; Oyevaar, T.; Prins, P.R.; Rapp, J.; Scholten, J.; Schram, D.C.; Smeets, P.H.M.; Star, van der G.; Tugarinov, S.N.; Zeijlmans van Emmichoven, P.A.
2012-01-01
An advanced Thomson scattering system has been built for a linear plasma generator for plasma surface interaction studies. The Thomson scattering system is based on a Nd:YAG laser operating at the second harmonic and a detection branch featuring a high etendue (f /3) transmission grating
Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-11-15
One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.
Compact FEL-driven inverse compton scattering gamma-ray source
Placidi, M. [Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Di Mitri, S., E-mail: simone.dimitri@elettra.eu [Elettra - Sincrotrone Trieste S.C.p.A., 34149 Basovizza, Trieste (Italy); Pellegrini, C. [SLAC National Accelerator Laboratory, Menlo Park, CA 94025 (United States); University of California, Los Angeles, CA 90095 (United States); Penn, G. [Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2017-05-21
Many research and applications areas require photon sources capable of producing gamma-ray beams in the multi-MeV energy range with reasonably high fluxes and compact footprints. Besides industrial, nuclear physics and security applications, a considerable interest comes from the possibility to assess the state of conservation of cultural assets like statues, columns etc., via visualization and analysis techniques using high energy photon beams. Computed Tomography scans, widely adopted in medicine at lower photon energies, presently provide high quality three-dimensional imaging in industry and museums. We explore the feasibility of a compact source of quasi-monochromatic, multi-MeV gamma-rays based on Inverse Compton Scattering (ICS) from a high intensity ultra-violet (UV) beam generated in a free-electron laser by the electron beam itself. This scheme introduces a stronger relationship between the energy of the scattered photons and that of the electron beam, resulting in a device much more compact than a classic ICS for a given scattered energy. The same electron beam is used to produce gamma-rays in the 10–20 MeV range and UV radiation in the 10–15 eV range, in a ~4×22 m{sup 2} footprint system.
The factorization method for inverse acoustic scattering in a layered medium
Bondarenko, Oleksandr; Kirsch, Andreas; Liu, Xiaodong
2013-01-01
In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equation F-tilde g =φ z is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, F-tilde is a self-adjoint operator related to the far field operator and ϕ z is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and sound-hard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples. (paper)
Korolev, G. A.; Dobrovolsky, A. V.; Inglessi, A. G.; Alkhazov, G. D.; Egelhof, P.; Estradé, A.; Dillmann, I.; Farinon, F.; Geissel, H.; Ilieva, S.; Ke, Y.; Khanzadeev, A. V.; Kiselev, O. A.; Kurcewicz, J.; Le, X. C.; Litvinov, Yu. A.; Petrov, G. E.; Prochazka, A.; Scheidenberger, C.; Sergeev, L. O.; Simon, H.; Takechi, M.; Tang, S.; Volkov, V.; Vorobyov, A. A.; Weick, H.; Yatsoura, V. I.
2018-05-01
The absolute differential cross section for small-angle proton elastic scattering on the proton-rich 8B nucleus has been measured in inverse kinematics for the first time. The experiment was performed using a secondary radioactive beam with an energy of 0.7 GeV/u at GSI, Darmstadt. The active target, namely hydrogen-filled time projection ionization chamber IKAR, was used to measure the energy, angle and vertex point of the recoil protons. The scattering angle of the projectiles was simultaneously determined by the tracking detectors. The measured differential cross section is analyzed on the basis of the Glauber multiple scattering theory using phenomenological nuclear-density distributions with two free parameters. The radial density distribution deduced for 8B exhibits a halo structure with the root-mean-square (rms) matter radius Rm = 2.58 (6) fm and the rms halo radius Rh = 4.24 (25) fm. The results on 8B are compared to those on the mirror nucleus 8Li investigated earlier by the same method. A comparison is also made with previous experimental results and theoretical predictions for both nuclei.
An investigation on the solutions for the linear inverse problem in gamma ray tomography
Araujo, Bruna G.M.; Dantas, Carlos C.; Santos, Valdemir A. dos; Finkler, Christine L.L.; Oliveira, Eric F. de; Melo, Silvio B.; Santos, M. Graca dos
2009-01-01
This paper the results obtained in single beam gamma ray tomography are investigated according to direct problem formulation and the applied solution for the linear system of equations. By image reconstruction based algebraic computational algorithms are used. The sparse under and over-determined linear system of equations was analyzed. Build in functions of Matlab software were applied and optimal solutions were investigate. Experimentally a section of the tube is scanned from various positions and at different angles. The solution, to find the vector of coefficients μ, from the vector of measured p values through the W matrix inversion, constitutes an inverse problem. A industrial tomography process requires a numerical solution of the system of equations. The definition of inverse problem according to Hadmard's is considered and as well the requirement of a well posed problem to find stable solutions. The formulation of the basis function and the computational algorithm to structure the weight matrix W were analyzed. For W full rank matrix the obtained solution is unique as expected. Total Least Squares was implemented which theory and computation algorithm gives adequate treatment for the problems due to non-unique solutions of the system of equations. Stability of the solution was investigating by means of a regularization technique and the comparison shows that it improves the results. An optimal solution as a function of the image quality, computation time and minimum residuals were quantified. The corresponding reconstructed images are shown in 3D graphics in order to compare with the solution. (author)
Ishikawa, R. [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan); Asensio Ramos, A.; Manso Sainz, R.; Trujillo Bueno, J. [Instituto de Astrofisica de Canarias, E-38205 La Laguna, Tenerife (Spain); Belluzzi, L. [Istituto Ricerche Solari Locarno (IRSOL), via Patocchi, 6605 Locarno Monti (Switzerland); Štěpán, J. [Astronomical Institute of the Academy of Sciences, Fričova 298, 251 65 Ondřejov (Czech Republic); Goto, M. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292 (Japan); Tsuneta, S., E-mail: ryoko.ishikawa@nao.ac.jp [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210 (Japan)
2014-06-01
Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio β is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyα line at 121.6 nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes I) and the linear polarization profiles (Q/I and U/I) of the hydrogen Lyα line. In this paper, we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical Q/I and U/I profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyα is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments.
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
Dixneuf, Sophie; Rachet, Florent; Chrysos, Michael
2015-01-01
Owing in part to the p orbitals of its filled L shell, neon has repeatedly come on stage for its peculiar properties. In the context of collision-induced Raman spectroscopy, in particular, we have shown, in a brief report published a few years ago [M. Chrysos et al., Phys. Rev. A 80, 054701 (2009)], that the room-temperature anisotropic Raman lineshape of Ne–Ne exhibits, in the far wing of the spectrum, a peculiar structure with an aspect other than a smooth wing (on a logarithmic plot) which contrasts with any of the existing studies, and whose explanation lies in the distinct way in which overlap and exchange interactions interfere with the classical electrostatic ones in making the polarizability anisotropy, α ∥ − α ⊥ . Here, we delve deeper into that study by reporting data for that spectrum up to 450 cm −1 and for even- and odd-order spectral moments up to M 6 , as well as quantum lineshapes, generated from SCF, CCSD, and CCSD(T) models for α ∥ − α ⊥ , which are critically compared with the experiment. On account of the knowledge of the spectrum over the augmented frequency domain, we show how the inverse scattering problem can be tackled both effectively and economically, and we report an analytic function for the anisotropy whose quantum lineshape faithfully reproduces our observations
Brilliant GeV gamma-ray flash from inverse Compton scattering in the QED regime
Gong, Z.; Hu, R. H.; Lu, H. Y.; Yu, J. Q.; Wang, D. H.; Fu, E. G.; Chen, C. E.; He, X. T.; Yan, X. Q.
2018-04-01
An all-optical scheme is proposed for studying laser plasma based incoherent photon emission from inverse Compton scattering in the quantum electrodynamic regime. A theoretical model is presented to explain the coupling effects among radiation reaction trapping, the self-generated magnetic field and the spiral attractor in phase space, which guarantees the transfer of energy and angular momentum from electromagnetic fields to particles. Taking advantage of a prospective ˜ 1023 W cm-2 laser facility, 3D particle-in-cell simulations show a gamma-ray flash with unprecedented multi-petawatt power and brightness of 1.7 × 1023 photons s-1 mm-2 mrad-2/0.1% bandwidth (at 1 GeV). These results bode well for new research directions in particle physics and laboratory astrophysics exploring laser plasma interactions.
Mittag–Leffler's function, Vekua transform and an inverse obstacle scattering problem
Ikehata, Masaru
2010-01-01
This paper studies a prototype of inverse obstacle scattering problems whose governing equation is the Helmholtz equation in two dimensions. An explicit method to extract information about the location and shape of unknown obstacles from the far-field operator with a fixed wave number is given. The method is based on an explicit construction of a modification of Mittag–Leffler's function via the Vekua transform and the study of the asymptotic behaviour; an explicit density in the Herglotz wavefunction that approximates the modification of Mittag–Leffler's function in the bounded domain surrounding unknown obstacles; a system of inequalities derived from Kirsch's factorization formula of the far-field operator. Then an indicator function which can be calculated from the far-field operator acting on the density is introduced. It is shown that the asymptotic behaviour of the indicator function yields information about the visible part of the exterior of the obstacles
Scaling laws in high-energy inverse compton scattering. II. Effect of bulk motions
Nozawa, Satoshi; Kohyama, Yasuharu; Itoh, Naoki
2010-01-01
We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have nonzero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function P 1,K (s) as P 1 (s) which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the x-ray and gamma-ray emission models from various astrophysical objects with nonzero bulk motions such as radio galaxies and astrophysical jets.
Chen, Xudong
2010-01-01
This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging
Desmal, Abdulla
2014-07-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.
Guliyev, Namig J.
2008-01-01
International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.
Exclusive measurements of quasi-free proton scattering reactions in inverse and complete kinematics
V. Panin
2016-02-01
Full Text Available Quasi-free scattering reactions of the type (p,2p were measured for the first time exclusively in complete and inverse kinematics, using a 12C beam at an energy of ∼400 MeV/u as a benchmark. This new technique has been developed to study the single-particle structure of exotic nuclei in experiments with radioactive-ion beams. The outgoing pair of protons and the fragments were measured simultaneously, enabling an unambiguous identification of the reaction channels and a redundant measurement of the kinematic observables. Both valence and deeply-bound nucleon orbits are probed, including those leading to unbound states of the daughter nucleus. Exclusive (p,2p cross sections of 15.8(18 mb, 1.9(2 mb and 1.5(2 mb to the low-lying 0p-hole states overlapping with the ground state (3/2− and with the bound excited states of 11B at 2.125 MeV (1/2− and 5.02 MeV (3/2−, respectively, were determined via γ-ray spectroscopy. Particle-unstable deep-hole states, corresponding to proton removal from the 0s-orbital, were studied via the invariant-mass technique. Cross sections and momentum distributions were extracted and compared to theoretical calculations employing the eikonal formalism. The obtained results are in a good agreement with this theory and with direct-kinematics experiments. The dependence of the proton–proton scattering kinematics on the internal momentum of the struck proton and on its separation energy was investigated for the first time in inverse kinematics employing a large-acceptance measurement.
Indoor detection of passive targets recast as an inverse scattering problem
Gottardi, G.; Moriyama, T.
2017-10-01
The wireless local area networks represent an alternative to custom sensors and dedicated surveillance systems for target indoor detection. The availability of the channel state information has opened the exploitation of the spatial and frequency diversity given by the orthogonal frequency division multiplexing. Such a fine-grained information can be used to solve the detection problem as an inverse scattering problem. The goal of the detection is to reconstruct the properties of the investigation domain, namely to estimate if the domain is empty or occupied by targets, starting from the measurement of the electromagnetic perturbation of the wireless channel. An innovative inversion strategy exploiting both the frequency and the spatial diversity of the channel state information is proposed. The target-dependent features are identified combining the Kruskal-Wallis test and the principal component analysis. The experimental validation points out the detection performance of the proposed method when applied to an existing wireless link of a WiFi architecture deployed in a real indoor scenario. False detection rates lower than 2 [%] have been obtained.
Bernard, Simon; Cloutier, Guy
2017-10-01
Inversion methods in shear wave elastography use simplifying assumptions to recover the mechanical properties of soft tissues. Consequently, these methods suffer from artifacts when applied to media containing strong stiffness contrasts, and do not provide a map of the viscosity. In this work, the shear wave field recorded inside and around an inclusion was used to estimate the viscoelastic properties of the inclusion and surrounding medium, based on an inverse problem approach assuming local homogeneity of both media. An efficient semi-analytical method was developed to model the scattering of an elastic wave by an irregular inclusion, based on a decomposition of the field by Bessel functions and on a decomposition of the boundaries as Fourier series. This model was validated against finite element modeling. Shear waves were experimentally induced by acoustic radiation force in soft tissue phantoms containing stiff and soft inclusions, and the displacement field was imaged at a high frame rate using plane wave imaging. A nonlinear least-squares algorithm compared the model to the experimental data and adjusted the geometrical and mechanical parameters. The estimated shear storage and loss moduli were in good agreement with reference measurements, as well as the estimated inclusion shape. This approach provides an accurate estimation of geometry and viscoelastic properties for a single inclusion in a homogeneous background in the context of radiation force elastography.
Approximate solution to neutron transport equation with linear anisotropic scattering
Coppa, G.; Ravetto, P.; Sumini, M.
1983-01-01
A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)
Analytical description of photon beam phase spaces in inverse Compton scattering sources
C. Curatolo
2017-08-01
Full Text Available We revisit the description of inverse Compton scattering sources and the photon beams generated therein, emphasizing the behavior of their phase space density distributions and how they depend upon those of the two colliding beams of electrons and photons. The main objective is to provide practical formulas for bandwidth, spectral density, brilliance, which are valid in general for any value of the recoil factor, i.e. both in the Thomson regime of negligible electron recoil, and in the deep Compton recoil dominated region, which is of interest for gamma-gamma colliders and Compton sources for the production of multi-GeV photon beams. We adopt a description based on the center of mass reference system of the electron-photon collision, in order to underline the role of the electron recoil and how it controls the relativistic Doppler/boost effect in various regimes. Using the center of mass reference frame greatly simplifies the treatment, allowing us to derive simple formulas expressed in terms of rms momenta of the two colliding beams (emittance, energy spread, etc. and the collimation angle in the laboratory system. Comparisons with Monte Carlo simulations of inverse Compton scattering in various scenarios are presented, showing very good agreement with the analytical formulas: in particular we find that the bandwidth dependence on the electron beam emittance, of paramount importance in Thomson regime, as it limits the amount of focusing imparted to the electron beam, becomes much less sensitive in deep Compton regime, allowing a stronger focusing of the electron beam to enhance luminosity without loss of mono-chromaticity. A similar effect occurs concerning the bandwidth dependence on the frequency spread of the incident photons: in deep recoil regime the bandwidth comes out to be much less dependent on the frequency spread. The set of formulas here derived are very helpful in designing inverse Compton sources in diverse regimes, giving a
van der Hilst, R. D.; de Hoop, M. V.; Shim, S. H.; Shang, X.; Wang, P.; Cao, Q.
2012-04-01
Over the past three decades, tremendous progress has been made with the mapping of mantle heterogeneity and with the understanding of these structures in terms of, for instance, the evolution of Earth's crust, continental lithosphere, and thermo-chemical mantle convection. Converted wave imaging (e.g., receiver functions) and reflection seismology (e.g. SS stacks) have helped constrain interfaces in crust and mantle; surface wave dispersion (from earthquake or ambient noise signals) characterizes wavespeed variations in continental and oceanic lithosphere, and body wave and multi-mode surface wave data have been used to map trajectories of mantle convection and delineate mantle regions of anomalous elastic properties. Collectively, these studies have revealed substantial ocean-continent differences and suggest that convective flow is strongly influenced by but permitted to cross the upper mantle transition zone. Many questions have remained unanswered, however, and further advances in understanding require more accurate depictions of Earth's heterogeneity at a wider range of length scales. To meet this challenge we need new observations—more, better, and different types of data—and methods that help us extract and interpret more information from the rapidly growing volumes of broadband data. The huge data volumes and the desire to extract more signal from them means that we have to go beyond 'business as usual' (that is, simplified theory, manual inspection of seismograms, …). Indeed, it inspires the development of automated full wave methods, both for tomographic delineation of smooth wavespeed variations and the imaging (for instance through inverse scattering) of medium contrasts. Adjoint tomography and reverse time migration, which are closely related wave equation methods, have begun to revolutionize seismic inversion of global and regional waveform data. In this presentation we will illustrate this development - and its promise - drawing from our work
Oh, Ju-Won
2016-07-04
Multiparameter full waveform inversion (FWI) applied to an elastic orthorhombic model description of the subsurface requires in theory a nine-parameter representation of each pixel of the model. Even with optimal acquisition on the Earth surface that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter, and specifically, its scattering radiation patterns. We investigate such radiation patterns for diffraction and for scattering from a horizontal reflector considering a background isotropic model. The radiation patterns show considerable potential for trade-off between the parameters and the potentially limited resolution in their recovery. The radiation patterns of C11, C22, and C33 are well separated so that we expect to recover these parameters with limited trade-offs. However, the resolution of their recovery represented by recovered range of model wavenumbers varies between these parameters. We can only invert for the short wavelength components (reflection) of C33 while we can mainly invert for the long wavelength components (transmission) of the elastic coefficients C11 and C22 if we have large enough offsets. The elastic coefficients C13, C23, and C12 suffer from strong trade-offs with C55, C44, and C66, respectively. The trade-offs between C13 and C55, as well as C23 and C44, can be partially mitigated if we acquire P–SV and SV–SV waves. However, to reduce the trade-offs between C12 and C66, we require credible SH–SH waves. The analytical radiation patterns of the elastic constants are supported by numerical gradients of these parameters.
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Melchert, O; Scheid, W; Apagyi, B
2006-01-01
The Cox-Thompson inverse scattering method at fixed energy has been generalized to treat complex phase shifts derived from experiments. New formulae for relating phase shifts to shifted angular momenta are derived. The method is applied to phase shifts of known potentials in order to test its quality and stability and, further, it is used to invert experimental n-α and n- 12 C phase shifts
Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV.
Taylor, P L; Rodgers, J E; Shobe, J
1999-08-01
Computation of shielding requirements for a linear accelerator must take into account the amount of radiation scattered from the patient to areas outside the primary beam. Currently, the most frequently used data are from NCRP 49 that only includes data for x-ray energies up to 6 MV and angles from 30 degrees to 135 degrees. In this work we have determined by Monte Carlo simulation the scattered fractions of dose for a wide range of energies and angles of clinical significance including 6, 10, 18, and 24 MV and scattering angles from 10 degrees to 150 degrees. Calculations were made for a 400 cm2 circular field size impinging onto a spherical phantom. Scattered fractions of dose were determined at 1 m from the phantom. Angles from 10 degrees to 30 degrees are of concern for higher energies where the scatter is primarily in the forward direction. An error in scatter fraction may result in too little secondary shielding near the junction with the primary barrier. The Monte Carlo code ITS (Version 3.0) developed at Sandia National Laboratory and NIST was used to simulate scatter from the patient to the barrier. Of significance was the variation of calculated scattered dose with depth of measurement within the barrier indicating that accurate values may be difficult to obtain. Mean energies of scatter x-ray spectra are presented.
Resolution limits of migration and linearized waveform inversion images in a lossy medium
Schuster, Gerard T.; Dutta, Gaurav; Li, Jing
2017-01-01
The vertical-and horizontal-resolution limits Delta x(lossy) and Delta z(lossy) of post-stack migration and linearized waveform inversion images are derived for lossy data in the far-field approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy vertical-resolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.
Resolution limits of migration and linearized waveform inversion images in a lossy medium
Schuster, Gerard T.
2017-03-10
The vertical-and horizontal-resolution limits Delta x(lossy) and Delta z(lossy) of post-stack migration and linearized waveform inversion images are derived for lossy data in the far-field approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy vertical-resolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.
Trombetti, T.
1990-01-01
The exact kernel method is presented for linear transport problems with azimuth-dependent angular fluxes. It is based on the evaluation of average scattering densities (ASD's) that fully describe the neutron (or particle) transfer between subsets of the unit sphere of directions by anisotropic scattering. Reciprocity and other ASD functional properties are proved and combined with the symmetry properties of suitable SN quadrature sets. This greatly reduces the number of independent ASD's to be computed and stored. An approach for performing ASD computations with reciprocity checks is presented. ASD expressions of the scattering source for typical 2D geometries are explicitly given. (author)
Bellis, Cédric; Bonnet, Marc; Cakoni, Fioralba
2013-01-01
Originally formulated in the context of topology optimization, the concept of topological derivative has also proved effective as a qualitative inversion tool for a wave-based identification of finite-sized objects. This approach remains, however, largely based on a heuristic interpretation of the topological derivative, whereas most other qualitative approaches to inverse scattering are backed by a mathematical justification. As an effort toward bridging this gap, this study focuses on a topological derivative approach applied to the L 2 -norm of the misfit between far-field measurements. Either an inhomogeneous medium or a finite number of point-like scatterers are considered, using either the Born approximation or a full-scattering model. Topological derivative-based imaging functionals are analyzed using a suitable factorization of the far-field operator, for each of the considered cases, in order to characterize their behavior and assess their ability to reconstruct the unknown scatterer(s). Results include the justification of the usual sign heuristic underpinning the method for (i) the Born approximation and (ii) full-scattering models limited to moderately strong scatterers. Semi-analytical and numerical examples are presented. Within the chosen framework, the topological derivative approach is finally discussed and compared to other well-known qualitative methods. (paper)
Mickols, W.; Maestre, M.F.
1988-01-01
A differential polarization microscope that couples the sensitivity of single-beam measurement of circular dichroism and circular differential scattering with the simultaneous measurement of linear dichroism and linear differential scattering has been developed. The microscope uses a scanning microscope stage and single-point illumination to give the very shallow depth of field found in confocal microscopy. This microscope can operate in the confocal mode as well as in the near confocal condition that can allow one to program the coherence and spatial resolution of the microscope. This microscope has been used to study the change in the structure of chromatin during the development of sperm in Drosophila
Maksudov, F.G.; Gusejnov, G.Sh.
1986-01-01
Inverse scattering problem for the quadratic bundle of the Schroedinger one-dimensional operators in the whole axis is solved. The problem solution is given on the assumption of the discrete spectrum absence. In the discrete spectrum presence the inverse scattering problem solution is known for the Shroedinger differential equation considered
The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws
DonghaiLI; XuezhiJIANG; 等
1997-01-01
The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.
Kuchment, Peter
2015-05-10
© 2015, Springer Basel. In the previous paper (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012), the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities could turn extremely unstable techniques, such as optical tomography or electrical impedance tomography, into stable, good-resolution procedures. It was shown that in all cases of interest, the Fréchet derivative of the forward mapping is a pseudo-differential operator with an explicitly computable principal symbol. If one can set up the imaging procedure in such a way that the symbol is elliptic, this would indicate that the problem was stabilized. In the cases when the symbol is not elliptic, the technique suggests how to change the procedure (e.g., by adding extra measurements) to achieve ellipticity. In this article, we consider the situation arising in acousto-optical tomography (also called ultrasound modulated optical tomography), where the internal data available involves the Green’s function, and thus depends globally on the unknown parameter(s) of the equation and its solution. It is shown that the technique of (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012) can be successfully adopted to this situation as well. A significant part of the article is devoted to results on generic uniqueness for the linearized problem in a variety of situations, including those arising in acousto-electric and quantitative photoacoustic tomography.
Electron re-scattering from aligned linear molecules using the R-matrix method
Harvey, A G; Tennyson, J
2009-01-01
Electron re-scattering in a strong laser field provides an important probe of molecular structure and processes. The laser field drives the ionization of the molecule, followed by acceleration and subsequent recollision of the electron with the parent molecular ion, the scattered electrons carry information about the nuclear geometry and electronic states of the molecular ion. It is advantageous in strong field experiments to work with aligned molecules, which introduces extra physics compared to the standard gas-phase, electron-molecule scattering problem. The formalism for scattering from oriented linear molecules is presented and applied to H 2 and CO 2 . Differential cross sections are presented for (re-)scattering by these systems concentrating on the most common, linear alignment. In H 2 these cross sections show significant angular structure which, particularly for a scattering angle of 90 deg., are predicted to vary significantly between re-collisions stimulated by an even or an odd number of photons. In CO 2 these cross sections are zero indicating the necessity of using non-parallel alignment with this molecule.
Hassager, Ole; Mortensen, Kell; Bach, Anders
2012-01-01
We use small-angle neutron scattering to measure the molecular stretching in polystyrene melts undergoing steady elongational flow at large stretch rates. The radius of gyration of the central segment of a partly deuterated polystyrene molecule is, in the stretching direction, increasing...... exhibited by the linear polystyrene melt....
Inversion of the pahse diagram in polymer blends studied by small-angle neutron scattering
Jinnai, Hiroshi; Hasegawa, Hirokazu; Hashimoto, Takeji; Han, C.C.
1993-01-01
The miscibility of an amorphous mixture of normal (protonated) polybutadiend (HPB) and perdeuterated polybutadiene (DPB) has been extensively studied and was characterized by an upper critical solution temperature (UCST). In this study the miscibility of HPB and DPB as a function of temperature was studied by small-angle neutron scattering (SANS). The vinyl component of the DPB was held constant at 16%, while the vinyl frantion of the HPB was varied from 17-80%. The binary interaction parameter, χ, was obtained. The mixtures of DPB and HPB with 17-39% vinyl show UCST behaviors; i.e., χ increases with decreasing temperature. The mixture of DPB and HPB with 52% vinyl was found to have almost no temperature dependence. However, the mixture of DPB and HPB with 65-80% show a lower critical solution temperature (LCST) behavior; i.e., χ increases with increasing temperature. This inversion of the phase diagram from UCST to LCST has never been observed. (author)
Some aspects of the inverse problem of scattering at fixed energy
Coudray, C.
1979-01-01
The first two chapters deal with the Newton-Sabatier method. Numerical tests are performed for real and complex potentials. They allow the study of the respective influences of energy, and of the internal parameters of the potential: its shape, depth and range. Within certain limits, good agreements are obtained. In particular, it is shown that they always require energies larger than a 'critical' energy, the dependence of which in function of the internal parameters of the potential being analyzed. Then the third chapter is devoted to transparent and quasi-transparent potentials in Born approximation. A class of such potentials is exhibited and studied. All of them oscillate, and their decrease at infinity may be chosen according to any arbitrary power of the variable. One of them is the Born approximation of the transparent potential of the Newton-Sabatier method. The last chapter concerns finite range complex potentials belonging to a well-defined class. For such potentials, a set of coherent inverse scattering date is given. The corresponding fundamental equation is written and shown to possess an unique solution [fr
Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng
2018-03-01
Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.
Moura, C.A. de.
1976-09-01
We propose an algorithm for computing the potential V(x) associated to the one-dimensional Schroedinger operator E identical to - d 2 /dx 2 + V(x) -infinite < x< infinite from knowledge of the S.matrix, more exactly, of one of the reelection coefficients. The convergence of the algorithm is guaranteed by the stability results obtained for both the direct and inverse problems
Wyatt, Philip
2009-03-01
The electromagnetic inverse scattering problem suggests that if a homogeneous and non-absorbing object be illuminated with a monochromatic light source and if the far field scattered light intensity is known at sufficient scattering angles, then, in principle, one could derive the dielectric structure of the scattering object. In general, this is an ill-posed problem and methods must be developed to regularize the search for unique solutions. An iterative procedure often begins with a model of the scattering object, solves the forward scattering problem using this model, and then compares these calculated results with the measured values. Key to any such solution is instrumentation capable of providing adequate data. To this end, the development of the first laser based absolute light scattering photometers is described together with their continuing evolution and some of the remarkable discoveries made with them. For particles much smaller than the wavelength of the incident light (e.g. macromolecules), the inverse scattering problems are easily solved. Among the many solutions derived with this instrumentation are the in situ structure of bacterial cells, new drug delivery mechanisms, the development of new vaccines and other biologicals, characterization of wines, the possibility of custom chemotherapy, development of new polymeric materials, identification of protein crystallization conditions, and a variety discoveries concerning protein interactions. A new form of the problem is described to address bioterrorist threats. Over the many years of development and refinement, one element stands out as essential for the successes that followed: the R and D teams were always directed and executed by physics trained theorists and experimentalists. 14 Ph. D. physicists each made his/her unique contribution to the development of these evolving instruments and the interpretation of their results.
Braicovich, L., E-mail: lucio.braicovich@polimi.it; Minola, M.; Dellea, G.; Ghiringhelli, G. [CNR-SPIN and Dipartimento di Fisica, Politecnico di Milano, piazza Leonardo Da Vinci 32, Milano I-20133 (Italy); Le Tacon, M. [Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart (Germany); Moretti Sala, M.; Morawe, C.; Peffen, J.-Ch.; Yakhou, F.; Brookes, N. B. [European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble F-38043 (France); Supruangnet, R. [Synchrotron Light Research Institute, Nakhon Ratchasima (Thailand)
2014-11-15
Resonant Inelastic X-ray Scattering (RIXS) in the soft x-ray range is an element-specific energy-loss spectroscopy used to probe the electronic and magnetic excitations in strongly correlated solids. In the recent years, RIXS has been progressing very quickly in terms of energy resolution and understanding of the experimental results, but the interpretation of spectra could further improve, sometimes decisively, from a full knowledge of the polarization of incident and scattered photons. Here we present the first implementation, in a high resolution soft-RIXS spectrometer used to analyze the scattered radiation, of a device allowing the measurement of the degree of linear polarization. The system, based on a graded W/B{sub 4}C multilayer mirror installed in proximity of the CCD detector, has been installed on the AXES spectrometer at the ESRF (European Synchrotron Radiation Facility); it has been fully characterized and it has been used for a demonstration experiment at the Cu L{sub 3} edge on a high-T{sub c} superconducting cuprate. The loss in efficiency suffered by the spectrometer equipped with this test facility was a factor 17.5. We propose also a more advanced version, suitable for a routine use on the next generation of RIXS spectrometers and with an overall efficiency up to 10%.
An optical potential from inversion of the 350 MeV 16 O - 16 O scattering data
Allen, L.J.; Berge, L.; Steward, C.; Lipperheide, R.; Froebrich, P.
1992-01-01
A quantal inversion of the 16 O- 16 O scattering data at 350 MeV yields an optical potential which gives an excellent fit (χ 2 /F = 1.65) to the measured cross-section. The real part of this potential is shallower than any potential used by others for distances between 2 and 6 fm. The imaginary potential is also relatively weak. This potential does not favour a rainbow interpretation of the structure in data observed at large scattering angles. 12 refs., 1 tab., 4 figs
Full waveform inversion based on scattering angle enrichment with application to real dataset
Wu, Zedong; Alkhalifah, Tariq Ali
2015-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity
Planktonic food webs revisited: Reanalysis of results from the linear inverse approach
Hlaili, Asma Sakka; Niquil, Nathalie; Legendre, Louis
2014-01-01
Identification of the trophic pathway that dominates a given planktonic assemblage is generally based on the distribution of biomasses among food-web compartments, or better, the flows of materials or energy among compartments. These flows are obtained by field observations and a posteriori analyses, including the linear inverse approach. In the present study, we re-analysed carbon flows obtained by inverse analysis at 32 stations in the global ocean and one large lake. Our results do not support two "classical" views of plankton ecology, i.e. that the herbivorous food web is dominated by mesozooplankton grazing on large phytoplankton, and the microbial food web is based on microzooplankton significantly consuming bacteria; our results suggest instead that phytoplankton are generally grazed by microzooplankton, of which they are the main food source. Furthermore, we identified the "phyto-microbial food web", where microzooplankton largely feed on phytoplankton, in addition to the already known "poly-microbial food web", where microzooplankton consume more or less equally various types of food. These unexpected results led to a (re)definition of the conceptual models corresponding to the four trophic pathways we found to exist in plankton, i.e. the herbivorous, multivorous, and two types of microbial food web. We illustrated the conceptual trophic pathways using carbon flows that were actually observed at representative stations. The latter can be calibrated to correspond to any field situation. Our study also provides researchers and managers with operational criteria for identifying the dominant trophic pathway in a planktonic assemblage, these criteria being based on the values of two carbon ratios that could be calculated from flow values that are relatively easy to estimate in the field.
Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping
2015-10-01
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Electron-electron scattering in linear transport in two-dimensional systems
Hu, Ben Yu-Kuang; Flensberg, Karsten
1996-01-01
We describe a method for numerically incorporating electron-electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature T and density n, a symmetric matrix needs to be evaluated only...... once, and henceforth it can be used to describe electron-electron scattering in any Boltzmann equation linear-response calculation for that particular T and n. Using this method, we calculate the distribution function and mobility for electrons in a quantum well, including full finite...
Inverse and Ill-posed Problems Theory and Applications
Kabanikhin, S I
2011-01-01
The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.
Barford, Thomas; Birse, Michael C
2005-01-01
A distorted-wave version of the renormalization group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wavefunction satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalization of the three-body interactions, with the renormalization-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces
S. Bagchi
2015-12-01
Full Text Available The Isoscalar Giant Monopole Resonance (ISGMR and the Isoscalar Giant Dipole Resonance (ISGDR compression modes have been studied in the doubly-magic unstable nucleus 56Ni. They were measured by inelastic α-particle scattering in inverse kinematics at 50 MeV/u with the MAYA active target at the GANIL facility. The centroid of the ISGMR has been obtained at Ex=19.1±0.5 MeV. Evidence for the low-lying part of the ISGDR has been found at Ex=17.4±0.7 MeV. The strength distribution for the dipole mode shows similarity with the prediction from the Hartree–Fock (HF based random-phase approximation (RPA [1]. These measurements confirm inelastic α-particle scattering as a suitable probe for exciting the ISGMR and the ISGDR modes in radioactive isotopes in inverse kinematics.
Rijssel, Jos van; Kuipers, Bonny W.M.; Erné, Ben H.
2014-01-01
A numerical inversion method known from the analysis of light scattering by colloidal dispersions is now applied to magnetization curves of ferrofluids. The distribution of magnetic particle sizes or dipole moments is determined without assuming that the distribution is unimodal or of a particular shape. The inversion method enforces positive number densities via a non-negative least squares procedure. It is tested successfully on experimental and simulated data for ferrofluid samples with known multimodal size distributions. The created computer program MINORIM is made available on the web. - Highlights: • A method from light scattering is applied to analyze ferrofluid magnetization curves. • A magnetic size distribution is obtained without prior assumption of its shape. • The method is tested successfully on ferrofluids with a known size distribution. • The practical limits of the method are explored with simulated data including noise. • This method is implemented in the program MINORIM, freely available online
Li Qi; Duan Qiuyuan; Zhang Jianbing
2012-01-01
The mixed discrete modified Korteweg-de Vries (mKdV) hierarchy and the Lax pair are derived. The hierarchy related to the Ablowitz-Ladik spectral problem is reduced to the isospectral discrete mKdV hierarchy and to the non-isospectral discrete mKdV hierarchy. N-soliton solutions of the hierarchies are obtained through inverse scattering transform.
Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem
Park, Won-Kwang
2017-07-01
MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.
Application of the method of continued fractions for electron scattering by linear molecules
Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF
1995-01-01
The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)
Cluster explosion investigated by linearly chirped spectral scattering of an expanding plasma sphere
Liu Jiansheng; Wang Cheng; Liu Bingchen; Shuai Bin; Wang Wentao; Cai Yi; Li Hongyu; Ni Guoquan; Li Ruxin; Xu Zhizhan
2006-01-01
Femtosecond explosive processes of argon clusters irradiated by linearly chirped ultraintense laser pulses have been investigated by 90 deg. side spectral scattering. The spectral redshift and blueshift, which correlate with the cluster explosion processes have been measured for negatively and positively chirped driving laser pulses, respectively. The evolution of the heated-cluster polarizability indicates that the core of the cluster is shielded from the laser field in the beginning of the explosion and enhanced scattering occurs after the fast explosion initiates. Evidence of resonant heating is found from the coincidence of enhanced scattering with enhanced absorption measured using the transmitted spectra. Anomalously large-size clusters with very low gas density have been observed in this way and can be used as clean and important cluster targets
On a finite moment perturbation of linear functionals and the inverse Szegö transformation
Edinson Fuentes
2016-05-01
Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.
Surface waves tomography and non-linear inversion in the southeast Carpathians
Raykova, R.B.; Panza, G.F.
2005-11-01
A set of shear-wave velocity models of the lithosphere-asthenosphere system in the southeast Carpathians is determined by the non-linear inversion of surface wave group velocity data, obtained from a tomographic analysis. The local dispersion curves are assembled for the period range 7 s - 150 s, combining regional group velocity measurements and published global Rayleigh wave dispersion data. The lithosphere-asthenosphere velocity structure is reliably reconstructed to depths of about 250 km. The thickness of the lithosphere in the region varies from about 120 km to 250 km and the depth of the asthenosphere between 150 km and 250 km. Mantle seismicity concentrates where the high velocity lid is detected just below the Moho. The obtained results are in agreement with recent seismic refraction, receiver function, and travel time P-wave tomography investigations in the region. The similarity among the results obtained from different kinds of structural investigations (including the present work) highlights some new features of the lithosphere-asthenosphere system in southeast Carpathians, as the relatively thin crust under Transylvania basin and Vrancea zone. (author)
Linear algebraic analyses of structures with one predominant type of anomalous scatterer
Karle, J.
1989-01-01
Further studies have been made of the information content of the exact linear equations for analyzing anomalous dispersion data in one-wavelength experiments. The case of interest concerns structures containing atoms that essentially do not scatter anomalously and one type of anomalously scattering atoms. For this case, there are three alternative ways of writing the equations. The alternative sets of equations and the transformations for transforming one set into the other are given explicitly. Comparison calculations were made with different sets of equations. Isomorphous replacement information is readily introduced into the calculations and the advantage of doing so is clearly illustrated by the results. Another aspect of the potential of the exact linear algebraic theory is its application to multiple-wavelength experiments. Successful applications of the latter have been made by several collaborative groups of investigators. (orig.)
Linear estimates of structure functions from deep inelastic lepton-nucleon scattering data. Part 1
Anikeev, V.B.; Zhigunov, V.P.
1991-01-01
This paper concerns the linear estimation of structure functions from muon(electron)-nucleon scattering. The expressions obtained for the structure functions estimate provide correct analysis of the random error and the bias The bias arises because of the finite number of experimental data and the finite resolution of experiment. The approach suggested may become useful for data handling from experiments at HERA. 9 refs
Stimulated Raman scattering and ion dynamics: the role of Langmuir wave non-linearities
Bonnaud, G.; Pesme, D.
1988-02-01
The non-linear evolution of stimulated Raman scattering by coupling of the SRS-driven Langmuir waves to ion acoustic waves is studied numerically, in a homogeneous density laser-irradiated plasma. The coupled wave amplitude behaviour is represented either by envelope equations or by complete wave-like equations. The various physical phenomena which are involved are described. This preliminary work has been presented at the 17th Anomalous Absorption Conference, held in last May, in Lake Tahoe City (USA) [fr
V. Lancellotti
2014-01-01
Full Text Available Linear embedding via Green’s operators (LEGO is a domain decomposition method particularly well suited for the solution of scattering and radiation problems comprised of many objects. The latter are enclosed in simple-shaped subdomains (electromagnetic bricks which are in turn described by means of scattering operators. In this paper we outline the extension of the LEGO approach to the case of penetrable objects with dyadic permittivity or permeability. Since a volume integral equation is only required to solve the scattering problem inside a brick and the scattering operators are inherently surface operators, the LEGO procedure per se can afford a reduction of the number of unknowns in the numerical solution with the Method of Moments and subsectional basis functions. Further substantial reduction is achieved with the eigencurrents expansion method (EEM which employs the eigenvectors of the scattering operator as local entire-domain basis functions over a brick’s surface. Through a few selected numerical examples we discuss the validation and the efficiency of the LEGO-EEM technique applied to clusters of anisotropic bodies.
Caiyan Qin
2017-12-01
Full Text Available Due to its simple mechanical structure and high motion stability, the H-shaped platform has been increasingly widely used in precision measuring, numerical control machining and semiconductor packaging equipment, etc. The H-shaped platform is normally driven by multiple (three permanent magnet synchronous linear motors. The main challenges for H-shaped platform-control include synchronous control between the two linear motors in the Y direction as well as total positioning error of the platform mover, a combination of position deviation in X and Y directions. To deal with the above challenges, this paper proposes a control strategy based on the inverse system method through state feedback and dynamic decoupling of the thrust force. First, mechanical dynamics equations have been deduced through the analysis of system coupling based on the platform structure. Second, the mathematical model of the linear motors and the relevant coordinate transformation between dq-axis currents and ABC-phase currents are analyzed. Third, after the main concept of inverse system method being explained, the inverse system model of the platform control system has been designed after defining relevant system variables. Inverse system model compensates the original nonlinear coupled system into pseudo-linear decoupled linear system, for which typical linear control methods, like PID, can be adopted to control the system. The simulation model of the control system is built in MATLAB/Simulink and the simulation result shows that the designed control system has both small synchronous deviation and small total trajectory tracking error. Furthermore, the control program has been run on NI controller for both fixed-loop-time and free-loop-time modes, and the test result shows that the average loop computation time needed is rather small, which makes it suitable for real industrial applications. Overall, it proves that the proposed new control strategy can be used in
The inside–outside duality for inverse scattering problems with near field data
Lechleiter, Armin; Peters, Stefan
2015-01-01
We derive an inside–outside duality for near field scattering data generated by time-harmonic scattering of acoustic point sources from a sound-soft scatterer. This duality in particular rigorously characterizes interior Dirichlet eigenvalues of the scattering object by near field operators for an interval of wave numbers. As a crucial new concept to prove this duality we exploit the numerical ranges of certain modifications of these near field operators. We also show that our theoretical results can be numerically used to approximate interior Dirichlet eigenvalues from multi-frequency near field measurements. (paper)
Linear GPR inversion for lossy soil and a planar air-soil interface
Meincke, Peter
2001-01-01
A three-dimensional inversion scheme for fixed-offset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air-soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function...
Spurr, Robert; Stamnes, Knut; Eide, Hans; Li Wei; Zhang Kexin; Stamnes, Jakob
2007-01-01
In this paper and the sequel, we investigate the application of classic inverse methods based on iterative least-squares cost-function minimization to the simultaneous retrieval of aerosol and ocean properties from visible and near infrared spectral radiance measurements such as those from the SeaWiFS and MODIS instruments. Radiance measurements at the satellite are simulated directly using an accurate coupled atmosphere-ocean-discrete-ordinate radiative transfer (CAO-DISORT) code as the main component of the forward model. For this kind of cost-function inverse problem, we require the forward model to generate weighting functions (radiance partial derivatives) with respect to the aerosol and marine properties to be retrieved, and to other model parameters which are sources of error in the retrievals. In this paper, we report on the linearization of the CAO-DISORT model. This linearization provides a complete analytic differentiation of the coupled-media radiative transfer theory, and it allows the model to generate analytic weighting functions for any atmospheric or marine parameter. For high solar zenith angles, we give an implementation of the pseudo-spherical (P-S) approach to solar beam attenuation in the atmosphere in the linearized model. We summarize a number of performance enhancements such as the use of an exact single-scattering calculation to improve accuracy. We derive inherent optical property inputs for the linearized CAO-DISORT code for a simple 2-parameter bio-optical model for the marine environment coupled to a 2-parameter bimodal atmospheric aerosol medium
Magnetic corrections to π -π scattering lengths in the linear sigma model
Loewe, M.; Monje, L.; Zamora, R.
2018-03-01
In this article, we consider the magnetic corrections to π -π scattering lengths in the frame of the linear sigma model. For this, we consider all the one-loop corrections in the s , t , and u channels, associated to the insertion of a Schwinger propagator for charged pions, working in the region of small values of the magnetic field. Our calculation relies on an appropriate expansion for the propagator. It turns out that the leading scattering length, l =0 in the S channel, increases for an increasing value of the magnetic field, in the isospin I =2 case, whereas the opposite effect is found for the I =0 case. The isospin symmetry is valid because the insertion of the magnetic field occurs through the absolute value of the electric charges. The channel I =1 does not receive any corrections. These results, for the channels I =0 and I =2 , are opposite with respect to the thermal corrections found previously in the literature.
Retrieval of collision kernels from the change of droplet size distributions with linear inversion
Onishi, Ryo; Takahashi, Keiko [Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama Kanagawa 236-0001 (Japan); Matsuda, Keigo; Kurose, Ryoichi; Komori, Satoru [Department of Mechanical Engineering and Science, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: onishi.ryo@jamstec.go.jp, E-mail: matsuda.keigo@t03.mbox.media.kyoto-u.ac.jp, E-mail: takahasi@jamstec.go.jp, E-mail: kurose@mech.kyoto-u.ac.jp, E-mail: komori@mech.kyoto-u.ac.jp
2008-12-15
We have developed a new simple inversion scheme for retrieving collision kernels from the change of droplet size distribution due to collision growth. Three-dimensional direct numerical simulations (DNS) of steady isotropic turbulence with colliding droplets are carried out in order to investigate the validity of the developed inversion scheme. In the DNS, air turbulence is calculated using a quasi-spectral method; droplet motions are tracked in a Lagrangian manner. The initial droplet size distribution is set to be equivalent to that obtained in a wind tunnel experiment. Collision kernels retrieved by the developed inversion scheme are compared to those obtained by the DNS. The comparison shows that the collision kernels can be retrieved within 15% error. This verifies the feasibility of retrieving collision kernels using the present inversion scheme.
Coen, S.
1981-01-01
The theory given by Moses and deRidder is modified so that the derivative of the solution of the Gelfand-Levitan integral equation is not required. Based on this modification, a numerical procedure is developed which approximately constructs the dielectric profile of the layered half-space from the impulse response. Moreover, an inverse scattering theory is developed for a Goupillaud-type dielectric medium, and a fast numerical procedure based on the Berryman and Greene algorithm is presented. The performance of the numerical algorithms is examined by applying them to pecise and imprecise artificial impulse response data. 11 refs
Mihalcea, D.; Murokh, A.; Piot, P.; Ruan, J.
2017-07-01
A high-brilliance (~10^{22} photon s^{-1} mm^{-2} mrad^{-2} /0.1%) gamma-ray source experiment is currently being planned at Fermilab (E_{γ}≃1.1 MeV). The source implements a high-repetition-rate inverse Compton scattering by colliding electron bunches formed in a ~300-MeV superconducting linac with a high-intensity laser pulse. This paper describes the design rationale along with some of technical challenges associated to producing high-repetition-rate collision. The expected performances of the gamma-ray source are also presented.
Moeller scattering polarimetry for high energy e sup + e sup - linear colliders
Alexander, G
2002-01-01
The general features of the Moeller scattering and its use as an electron polarimeter are described and studied in view of the planned future high energy e sup + e sup - linear colliders. In particular the study concentrates on the TESLA collider which is planned to operate with longitudinal polarised beams at a centre of mass energy of the order of 0.5 TeV with a luminosity of 3.4x10 sup 3 sup 4 cm sup - sup 2 s sup - sup 1.
Daudé, Thierry
2017-01-01
In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)-that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of ...
Sparse frequencies data inversion and the role of multi-scattered energy
Alkhalifah, Tariq Ali
2017-01-01
time to inject more energy of those frequencies at a reduced cost. Such additional energy is necessary to the recording of more multi-scattered events. The objective of this new paradigm is a high resolution model of the Earth.
Oh, Juwon; Alkhalifah, Tariq Ali
2016-01-01
that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures.
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures
Scattered fractions of dose from 18 and 25 MV X-ray radiotherapy linear accelerators
Shobe, J.; Rodgers, J.E.; Taylor, P.L.; Jackson, J.; Popescu, G.
1996-01-01
Over the years, measurements have been made at a few energies to estimate the scattered fraction of dose from the patient in medical radiotherapy operations. This information has been a useful aid in the determination of shielding requirements for these facilities. With these measurements, known characteriztics of photons, and various other known parameters, Monte Carlo codes are being used to calculate the scattered fractions and hence the shielding requirements for the photons of other energies commonly used in radiotherapeutic applications. The National Institute of Standards and Technology (NIST) acquired a Sagittaire medical linear accelerator (linac) which was previously located at the Yale-New Haven Hospital. This linac provides an X-ray beam of 25 MV photons and electron beams with energies up to 32 MeV. The housing on the gantry was permanently removed from the accelerator during installation. A Varian Clinac 1800 linear accelerator was used to produce the 18 MV photons at the Frederick Memorial Hospital Regional Cancer Therapy Center in Frederick, MD. This paper represents a study of the photon dose scattered from a patient in typical radiation treatment situations as it relates to the dose delivered at the isocenter in water. The results of these measurements will be compared to Monte Carlo calculations. Photon spectral measurements were not made at this time. Neutron spectral measurements were made on this Sagittaire machine in its previous location and that work was not repeated here, although a brief study of the neutron component of the 18 and 25 MV linacs was performed utilizing thermoluminescent dosimetry (TLD) to determine the isotropy of the neutron dose. (author)
Design of a 4.8-m ring for inverse Compton scattering x-ray source
H. S. Xu
2014-07-01
Full Text Available In this paper we present the design of a 50 MeV compact electron storage ring with 4.8-meter circumference for the Tsinghua Thomson scattering x-ray source. The ring consists of four dipole magnets with properly adjusted bending radii and edge angles for both horizontal and vertical focusing, and a pair of quadrupole magnets used to adjust the horizontal damping partition number. We find that the dynamic aperture of compact storage rings depends essentially on the intrinsic nonlinearity of the dipole magnets with small bending radius. Hamiltonian dynamics is found to agree well with results from numerical particle tracking. We develop a self-consistent method to estimate the equilibrium beam parameters in the presence of the intrabeam scattering, synchrotron radiation damping, quantum excitation, and residual gas scattering. We also optimize the rf parameters for achieving a maximum x-ray flux.
Schumacher, F.; Friederich, W.; Lamara, S.
2016-02-01
We present a new conceptual approach to scattering-integral-based seismic full waveform inversion (FWI) that allows a flexible, extendable, modular and both computationally and storage-efficient numerical implementation. To achieve maximum modularity and extendability, interactions between the three fundamental steps carried out sequentially in each iteration of the inversion procedure, namely, solving the forward problem, computing waveform sensitivity kernels and deriving a model update, are kept at an absolute minimum and are implemented by dedicated interfaces. To realize storage efficiency and maximum flexibility, the spatial discretization of the inverted earth model is allowed to be completely independent of the spatial discretization employed by the forward solver. For computational efficiency reasons, the inversion is done in the frequency domain. The benefits of our approach are as follows: (1) Each of the three stages of an iteration is realized by a stand-alone software program. In this way, we avoid the monolithic, unflexible and hard-to-modify codes that have often been written for solving inverse problems. (2) The solution of the forward problem, required for kernel computation, can be obtained by any wave propagation modelling code giving users maximum flexibility in choosing the forward modelling method. Both time-domain and frequency-domain approaches can be used. (3) Forward solvers typically demand spatial discretizations that are significantly denser than actually desired for the inverted model. Exploiting this fact by pre-integrating the kernels allows a dramatic reduction of disk space and makes kernel storage feasible. No assumptions are made on the spatial discretization scheme employed by the forward solver. (4) In addition, working in the frequency domain effectively reduces the amount of data, the number of kernels to be computed and the number of equations to be solved. (5) Updating the model by solving a large equation system can be
Terrano, Daniel; Tsuper, Ilona; Maraschky, Adam; Holland, Nolan; Streletzky, Kiril
Temperature sensitive nanoparticles were generated from a construct (H20F) of three chains of elastin-like polypeptides (ELP) linked to a negatively charged foldon domain. This ELP system was mixed at different ratios with linear chains of ELP (H40L) which lacks the foldon domain. The mixed system is soluble at room temperature and at a transition temperature (Tt) will form swollen micelles with the hydrophobic linear chains hidden inside. This system was studied using depolarized dynamic light scattering (DDLS) and static light scattering (SLS) to determine the size, shape, and internal structure of the mixed micelles. The mixed micelle in equal parts of H20F and H40L show a constant apparent hydrodynamic radius of 40-45 nm at the concentration window from 25:25 to 60:60 uM (1:1 ratio). At a fixed 50 uM concentration of the H20F, varying H40L concentration from 5 to 80 uM resulted in a linear growth in the hydrodynamic radius from about 11 to about 62 nm, along with a 1000-fold increase in VH signal. A possible simple model explaining the growth of the swollen micelles is considered. Lastly, the VH signal can indicate elongation in the geometry of the particle or could possibly be a result from anisotropic properties from the core of the micelle. SLS was used to study the molecular weight, and the radius of gyration of the micelle to help identify the structure and morphology of mixed micelles and the tangible cause of the VH signal.
Fokas, A. S.; Pogrebkov, A. K.
2003-03-01
We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.
An inverse method for non linear ablative thermics with experimentation of automatic differentiation
Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr
2008-11-01
Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.
The effect of dendrimer charge inversion in complexes with linear polyelectrolytes
Lyulin, S.V.; Lyulin, A.V.; Darinskii, A.A.; Emri, I.
2005-01-01
The structure of complexes formed by charged dendrimers and oppositely charged linear chains with a charge of at least the same as that of dendrimers was studied by computer simulation using the Brownian dynamics method. The freely jointed, free-draining model of the dendrimer and the linear chain
Friedrich, R.; Drewelow, W.
1978-01-01
An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.
Sakurai, K; Shima, H [OYO Corp., Tokyo (Japan)
1996-10-01
This paper proposes a modeling method of one-dimensional complex resistivity using linear filter technique which has been extended to the complex resistivity. In addition, a numerical test of inversion was conducted using the monitoring results, to discuss the measured frequency band. Linear filter technique is a method by which theoretical potential can be calculated for stratified structures, and it is widely used for the one-dimensional analysis of dc electrical exploration. The modeling can be carried out only using values of complex resistivity without using values of potential. In this study, a bipolar method was employed as a configuration of electrodes. The numerical test of one-dimensional complex resistivity inversion was conducted using the formulated modeling. A three-layered structure model was used as a numerical model. A multi-layer structure with a thickness of 5 m was analyzed on the basis of apparent complex resistivity calculated from the model. From the results of numerical test, it was found that both the chargeability and the time constant agreed well with those of the original model. A trade-off was observed between the chargeability and the time constant at the stage of convergence. 3 refs., 9 figs., 1 tab.
Sparse frequencies data inversion and the role of multi-scattered energy
Alkhalifah, Tariq Ali
2017-05-26
In trying to extract a broad spectrum of model wavenumbers from the data, necessary to build a plausible model of the Earth, we are, in theory, bounded at the high end by the diffraction resolution limit, which is proportional to the highest usable frequency in the data. At the low end, and courtesy of our multi-dimensional acquisition, the principles behind diffraction tomography theoretically extend our range to zero-wavenumbers, mainly provided by transmissions like diving waves. Within certain regions of the subsurface (i.e. deep), we face the prospective of having a model wavenumber gap in representing the velocity. Here, I demonstrate that inverting for multi scattered energy, we can recover additional wavenumbers not provided by single scattering gradients, that may feed the high and low ends of the model wavenumber spectrum, as well as help us fill in the infamous intermediate wavenumber gap. Thus, I outline a scenario in which we acquire dedicated sparse frequency data, allowing for more time to inject more energy of those frequencies at a reduced cost. Such additional energy is necessary to the recording of more multi-scattered events. The objective of this new paradigm is a high resolution model of the Earth.
Validation of head scatter factor for an Elekta synergy platform linear accelerator
Johannes, N.B.
2013-07-01
A semi-empirical method has been proposed and developed to model and compute head or collimator scatter factors for 6 and 15 MV photon beams from Elekta Synergy platform linear accelerator at the radiation oncology centre of 'Sweden-Ghana Medical Centre Limited', East Legon Hills in Accra. The proposed model was based on two dimensional Gaussian distribution, whose output was compared to measured head scatter factor data for the linear accelerator obtained during commissioning of the teletherapy machine. The two dimensions Gaussian distribution model used physical specifications and configuration of the head unit (collimator system) of the linear accelerator, which were obtained from the user manual provided by the manufacturer of the linear accelerator. The algorithm for the model was implemented using Matlab software in the Microsoft windows environment. The model was done for both square and rectangular fields, and the output compared with corresponding measured data. The comparisons for the square fields were used to establish an error term in the Gaussian distribution function. The error term was determined by plotting the difference between the output factors from MatLab and the corresponding measured data as function of one side of a square field (equivalent square field). The correlation equation of the curve obtained was chosen as the error term, which was incorporated into the Gaussian distribution function. This was repeated for two photon beam energies (6 and 15 MV). The refined Gaussian distributions were then used to determine head scatter factors for square and rectangular fields. For the rectangular fields, Sterling's proposed formula was used to find equivalent square used to obtain the equivalent square fields found in the error terms of the proposed formula was sed to find equivalent square used to obtain the equivalent square fields found in the error terms of the proposed and developed model. The output of the 2D Gaussian distribution without
Linearity of bulk-controlled inverter ring VCO in weak and strong inversion
Wismar, Ulrik Sørensen; Wisland, D.; Andreani, Pietro
2007-01-01
In this paper linearity of frequency modulation in voltage controlled inverter ring oscillators for non feedback sigma delta converter applications is studied. The linearity is studied through theoretical models of the oscillator operating at supply voltages above and below the threshold voltage......, process variations and temperature variations have also been simulated to indicate the advantages of having the soft rail bias transistor in the VCO....
Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging
Fowler, Michael James [Clarkson Univ., Potsdam, NY (United States)
2014-04-25
In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy
Masakazu Washio; Kazuyuki Sakaue; Yoshimasa Hama; Yoshio Kamiya; Tomoko Gowa; Akihiko Masuda; Aki Murata; Ryo Moriyama; Shigeru Kashiwagi; Junji Urakawa
2007-01-01
High quality beam generation project based on High-Tech Research Center Project, which has been approved by Ministry of Education, Culture, Sports, Science and Technology in 1999, has been conducted by advance research institute for science and engineering, Waseda University. In the project, laser photo-cathode RF-gun has been selected for the high quality electron beam source. RF cavities with low dark current, which were made by diamond turning technique, have been successfully manufactured. The low emittance electron beam was realized by choosing the modified laser injection technique. The obtained normalized emmitance was about 3 m.mrad at 100 pC of electron charge. The soft x-ray beam generation with the energy of 370 eV, which is in the energy region of so-called water window, by inverse Compton scattering has been performed by the collision between IR laser and the low emmitance electron beams. (Author)
Pozdnyakov, Yu.A.; Terenetskij, K.O.
1981-01-01
The approximate method for solution of the inverse scattering problem (ISP) at fixed energy for complex spherically symmetric potentials decreasing faster 1/r is considered. The method is based on using a generalized WKB approximation. For the designed potential V(r) a sufficiently ''close'' reference potential V(r) has been chosen. For both potentials S-matrix elements (ME) have been calculated and inversion procedure has been carried out. S-ME have been calculated for integral-valued and intermediate angular moment values. S-ME are presented in a graphical form for being restored reference, and restored potentials for proton scattering with Esub(p)=49.48 MeV energy on 12 C nuclei. The restoration is the better the ''closer'' the sought-for potential to the reference one. This allows to specify the potential by means of iterations: the restored potential can be used as a reference one, etc. The operation of a restored potential smoothing before the following iteration is introduced. Drawbacks and advantages of the ISP solution method under consideration are pointed out. The method application is strongly limited by the requirement that the energy should be higher than a certain ''critical'' one. The method is applicable in a wider region of particle energies (in the low-energies direction) than the ordinary WKB method. The method is more simple in realization conformably to complex potentials. The investigations carried out of the proposed ISP solution method at fixed energy for complex spherically-symmetric potentials allow to conclude that the method can be successFully applied to specify the central part of interaction of nucleons, α-particles and heavy ions of average and high energies with atomic nuclei [ru
van der Laan, John D.; Wright, Jeremy B.; Scrymgeour, David A.; Kemme, Shanalyn A.; Dereniak, Eustace L.
2016-05-01
We present experimental and simulation results for a laboratory-based forward-scattering environment, where 1 μm diameter polystyrene spheres are suspended in water to model the optical scattering properties of fog. Circular polarization maintains its degree of polarization better than linear polarization as the optical thickness of the scattering environment increases. Both simulation and experiment quantify circular polarization's superior persistence, compared to that of linear polarization, and show that it is much less affected by variations in the field of view and collection area of the optical system. Our experimental environment's lateral extent was physically finite, causing a significant difference between measured and simulated degree of polarization values for incident linearly polarized light, but not for circularly polarized light. Through simulation we demonstrate that circular polarization is less susceptible to the finite environmental extent as well as the collection optic's limiting configuration.
Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.
2010-01-01
The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.
Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang
2015-06-01
This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.
Sharma, Pavan K.; Gera, B.; Ghosh, A.K.; Kushwaha, H.S.
2010-01-01
Scalar dispersion in the atmosphere is an important area wherein different approaches are followed in development of good analytical model. The analyses based on Computational Fluid Dynamics (CFD) codes offer an opportunity of model development based on first principles of physics and hence such models have an edge over the existing models. Both forward and backward calculation methods are being developed for atmospheric dispersion around NPPs at BARC Forward modeling methods, which describe the atmospheric transport from sources to receptors, use forward-running transport and dispersion models or computational fluid dynamics models which are run many times, and the resulting dispersion field is compared to observations from multiple sensors. Backward or inverse modeling methods use only one model run in the reverse direction from the receptors to estimate the upwind sources. Inverse modeling methods include adjoint and tangent linear models, Kalman filters, and variational data assimilation, and neural network. The present paper is aimed at developing a new approach where the identified specific signatures at receptor points form the basis for source estimation or inversions. This approach is expected to reduce the large transient data sets to reduced and meaningful data sets. In fact this reduces the inherently transient data set into a time independent mean data set. Forward computation were carried out with CFD code for various case to generate a large set of data to train the ANN. Specific signature analysis was carried out to find the parameters of interest for ANN training like peak concentration, time to reach peak concentration and time to fall, the ANN was trained with data and source strength and location were predicted from ANN. Inverse problem was performed using ANN approach in long range atmospheric dispersion. An illustration of application of CFD code for atmospheric dispersion studies for a hypothetical case is also included in the paper. (author)
Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses
Martinez-Luaces, Victor
2009-01-01
In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…
Geodynamic inversion to constrain the non-linear rheology of the lithosphere
Baumann, T. S.; Kaus, Boris J. P.
2015-08-01
One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology
Williams, Benjamin S. (Inventor); Hu, Qing (Inventor)
2009-01-01
The present invention provides quantum cascade lasers and amplifier that operate in a frequency range of about 1 Terahertz to about 10 Terahertz. In one aspect, a quantum cascade laser of the invention includes a semiconductor heterostructure that provides a plurality of lasing modules connected in series. Each lasing module includes a plurality of quantum well structure that collectively generate at least an upper lasing state, a lower lasing state, and a relaxation state such that the upper and the lower lasing states are separated by an energy corresponding to an optical frequency in a range of about 1 to about 10 Terahertz. The lower lasing state is selectively depopulated via resonant LO-phonon scattering of electrons into the relaxation state.
Inverse estimation of multiple muscle activations based on linear logistic regression.
Sekiya, Masashi; Tsuji, Toshiaki
2017-07-01
This study deals with a technology to estimate the muscle activity from the movement data using a statistical model. A linear regression (LR) model and artificial neural networks (ANN) have been known as statistical models for such use. Although ANN has a high estimation capability, it is often in the clinical application that the lack of data amount leads to performance deterioration. On the other hand, the LR model has a limitation in generalization performance. We therefore propose a muscle activity estimation method to improve the generalization performance through the use of linear logistic regression model. The proposed method was compared with the LR model and ANN in the verification experiment with 7 participants. As a result, the proposed method showed better generalization performance than the conventional methods in various tasks.
Eilon, Zachary; Fischer, Karen M.; Dalton, Colleen A.
2018-04-01
We present a methodology for 1-D imaging of upper mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parameterisation based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed VS and VP velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S-p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.
Li Qi; Zhang Dajun; Chen Dengyuan
2010-01-01
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. (general)
Arahman, Nasrul; Maimun, Teuku; Mukramah, Syawaliah
2017-01-01
The composition of polymer solution and the methods of membrane preparation determine the solidification process of membrane. The formation of membrane structure prepared via non-solvent induced phase separation (NIPS) method is mostly determined by phase separation process between polymer, solvent, and non-solvent. This paper discusses the phase separation process of polymer solution containing Polyethersulfone (PES), N-methylpirrolidone (NMP), and surfactant Tetronic 1307 (Tet). Cloud point experiment is conducted to determine the amount of non-solvent needed on induced phase separation. Amount of water required as a non-solvent decreases by the addition of surfactant Tet. Kinetics of phase separation for such system is studied by the light scattering measurement. With the addition of Tet., the delayed phase separation is observed and the structure growth rate decreases. Moreover, the morphology of fabricated membrane from those polymer systems is analyzed by scanning electron microscopy (SEM). The images of both systems show the formation of finger-like macrovoids through the cross-section.
Fitting the two-compartment model in DCE-MRI by linear inversion.
Flouri, Dimitra; Lesnic, Daniel; Sourbron, Steven P
2016-09-01
Model fitting of dynamic contrast-enhanced-magnetic resonance imaging-MRI data with nonlinear least squares (NLLS) methods is slow and may be biased by the choice of initial values. The aim of this study was to develop and evaluate a linear least squares (LLS) method to fit the two-compartment exchange and -filtration models. A second-order linear differential equation for the measured concentrations was derived where model parameters act as coefficients. Simulations of normal and pathological data were performed to determine calculation time, accuracy and precision under different noise levels and temporal resolutions. Performance of the LLS was evaluated by comparison against the NLLS. The LLS method is about 200 times faster, which reduces the calculation times for a 256 × 256 MR slice from 9 min to 3 s. For ideal data with low noise and high temporal resolution the LLS and NLLS were equally accurate and precise. The LLS was more accurate and precise than the NLLS at low temporal resolution, but less accurate at high noise levels. The data show that the LLS leads to a significant reduction in calculation times, and more reliable results at low noise levels. At higher noise levels the LLS becomes exceedingly inaccurate compared to the NLLS, but this may be improved using a suitable weighting strategy. Magn Reson Med 76:998-1006, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
Ruggeri, Fabrizio
2016-05-12
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
Murray L. Ireland
2015-06-01
Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.
Nucleon-nucleon scattering in the functional quantum theory of the non-linear spinor field
Philipp, W.
1975-01-01
The nucleon-nucleon and nucleon-antinucleon scattering cross sections are calculated in the frame of the functional quantum field theory by means of two different approximation methods: averaging by integration of indefinite integrals and pulse averaging. The results for nucleon-nucleon scattering are compared with experimental data, with calculations using a modified functional scalar product and with results in first order perturbation theory (V-A-coupling). As for elastic nucleon-antinucleon scattering, the S matrix is investigated for crossing symmetry. Scattering of 'nucleons' of different mass results in different cross sections even in the lowest-order approximation. (BJ) [de
Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-05-15
One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.
2012-01-01
In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.
Khachaturov, R. V.
2014-06-01
A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.
Liu, Yishan; Han, Ping [School of Biological Sciences, The University of Hong Kong, Pokfulam Road, Hong Kong (China); Li, Xiao-yan; Shih, Kaimin [Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong (China); Gu, Ji-Dong, E-mail: jdgu@hkucc.hku.hk [School of Biological Sciences, The University of Hong Kong, Pokfulam Road, Hong Kong (China); The Swire Institute of Marine Science, The University of Hong Kong, Shek O, Cape d' Aguilar, Hong Kong (China)
2011-09-15
Highlights: {yields} We isolated a Xanthobacter flavus strain PA1 utilizing the racemic 2-PBA and the single enantiomers as the sole source of carbon and energy. {yields} Both (R) and (S) forms of enantiomers can be degraded in a sequential manner in which the (S) disappeared before the (R) form. {yields} The biochemical degradation pathway involves an initial oxidation of the alkyl side chain before aromatic ring cleavage. - Abstract: Microbial degradation of the chiral 2-phenylbutyric acid (2-PBA), a metabolite of surfactant linear alkylbenzene sulfonates (LAS), was investigated using both racemic and enantiomer-pure compounds together with quantitative stereoselective analyses. A pure culture of bacteria, identified as Xanthobacter flavus strain PA1 isolated from the mangrove sediment of Hong Kong Mai Po Nature Reserve, was able to utilize the racemic 2-PBA as well as the single enantiomers as the sole source of carbon and energy. In the presence of the racemic compounds, X. flavus PA1 degraded both (R) and (S) forms of enantiomers to completion in a sequential manner in which the (S) enantiomer disappeared much faster than the (R) enantiomer. When the single pure enantiomer was supplied as the sole substrate, a unidirectional chiral inversion involving (S) enantiomer to (R) enantiomer was evident. No major difference was observed in the degradation intermediates with either of the individual enantiomers when used as the growth substrate. Two major degradation intermediates were detected and identified as 3-hydroxy-2-phenylbutanoic acid and 4-methyl-3-phenyloxetan-2-one, using a combination of liquid chromatography-mass spectrometry (LC-MS), and {sup 1}H and {sup 13}C nuclear magnetic resonance (NMR) spectroscopy. The biochemical degradation pathway follows an initial oxidation of the alkyl side chain before aromatic ring cleavage. This study reveals new evidence for enantiomeric inversion catalyzed by pure culture of environmental bacteria and emphasizes the
Bulut, S.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.
2007-01-01
H N and singular eigenfunction methods are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Different expansions of the exit distribution are used: the expansion in powers of μ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+μ). The results are compared to each other. In the second part of our work, the transport equation and the infinite medium Green function are used. The numerical results of the extrapolation length obtained for the different expansions is discussed. (orig.)
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
Khattab, K.M.; Larsen, E.W.
1992-01-01
The diffusion synthetic acceleration (DSA) algorithm effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analysis that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented. (author). 10 refs., 7 figs., 5 tabs
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
Khattab, K.M.; Larsen, E.W.
1991-01-01
This paper reports on the diffusion synthetic acceleration (DSA) algorithm that effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analyses that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented
Chaleil, A.; Le Flanchec, V.; Binet, A.; Nègre, J.P.; Devaux, J.F.; Jacob, V.; Millerioux, M.; Bayle, A.; Balleyguier, P. [CEA DAM DIF, F-91297 Arpajon (France); Prazeres, R. [CLIO/LCP, Bâtiment 201, Université Paris-Sud, F-91450 Orsay (France)
2016-12-21
An inverse Compton scattering source is under development at the ELSA linac of CEA, Bruyères-le-Châtel. Ultra-short X-ray pulses are produced by inverse Compton scattering of 30 ps-laser pulses by relativistic electron bunches. The source will be able to operate in single shot mode as well as in recurrent mode with 72.2 MHz pulse trains. Within this framework, an optical multipass system that multiplies the number of emitted X-ray photons in both regimes has been designed in 2014, then implemented and tested on ELSA facility in the course of 2015. The device is described from both geometrical and timing viewpoints. It is based on the idea of folding the laser optical path to pile-up laser pulses at the interaction point, thus increasing the interaction probability. The X-ray output gain measurements obtained using this system are presented and compared with calculated expectations.
Broome, J.
1965-11-01
The programme SCATTER is a KDF9 programme in the Egtran dialect of Fortran to generate normalized angular distributions for elastically scattered neutrons from data input as the coefficients of a Legendre polynomial series, or from differential cross-section data. Also, differential cross-section data may be analysed to produce Legendre polynomial coefficients. Output on cards punched in the format of the U.K. A. E. A. Nuclear Data Library is optional. (author)
Florian Schumacher
2016-01-01
Full Text Available Due to increasing computational resources, the development of new numerically demanding methods and software for imaging Earth’s interior remains of high interest in Earth sciences. Here, we give a description from a user’s and programmer’s perspective of the highly modular, flexible and extendable software package ASKI–Analysis of Sensitivity and Kernel Inversion–recently developed for iterative scattering-integral-based seismic full waveform inversion. In ASKI, the three fundamental steps of solving the seismic forward problem, computing waveform sensitivity kernels and deriving a model update are solved by independent software programs that interact via file output/input only. Furthermore, the spatial discretizations of the model space used for solving the seismic forward problem and for deriving model updates, respectively, are kept completely independent. For this reason, ASKI does not contain a specific forward solver but instead provides a general interface to established community wave propagation codes. Moreover, the third fundamental step of deriving a model update can be repeated at relatively low costs applying different kinds of model regularization or re-selecting/weighting the inverted dataset without need to re-solve the forward problem or re-compute the kernels. Additionally, ASKI offers the user sensitivity and resolution analysis tools based on the full sensitivity matrix and allows to compose customized workflows in a consistent computational environment. ASKI is written in modern Fortran and Python, it is well documented and freely available under terms of the GNU General Public License (http://www.rub.de/aski.
High resolution Thomson scattering system for steady-state linear plasma sources
Lee, K. Y.; Lee, K. I.; Kim, J. H.; Lho, T.
2018-01-01
The high resolution Thomson scattering system with 63 points along a 25 mm line measures the radial electron temperature (Te) and its density (ne) in an argon plasma. By using a DC arc source with lanthanum hexaboride (LaB6) electrode, plasmas with electron temperature of over 5 eV and densities of 1.5 × 1019 m-3 have been measured. The system uses a frequency doubled (532 nm) Nd:YAG laser with 0.25 J/pulse at 20 Hz. The scattered light is collected and sent to a triple-grating spectrometer via optical-fibers, where images are recorded by an intensified charge coupled device (ICCD) camera. Although excellent in stray-light reduction, a disadvantage comes with its relatively low optical transmission and in sampling a tiny scattering volume. Thus requires accumulating multitude of images. In order to improve photon statistics, pixel binning in the ICCD camera as well as enlarging the intermediate slit-width inside the triple-grating spectrometer has been exploited. In addition, the ICCD camera capture images at 40 Hz while the laser is at 20 Hz. This operation mode allows us to alternate between background and scattering shot images. By image subtraction, influences from the plasma background are effectively taken out. Maximum likelihood estimation that uses a parameter sweep finds best fitting parameters Te and ne with the incoherent scattering spectrum.
Marleau, G.; Debos, E.
1998-01-01
One of the main problems encountered in cell calculations is that of spatial homogenization where one associates to an heterogeneous cell an homogeneous set of cross sections. The homogenization process is in fact trivial when a totally reflected cell without leakage is fully homogenized since it involved only a flux-volume weighting of the isotropic cross sections. When anisotropic leakages models are considered, in addition to homogenizing isotropic cross sections, the anisotropic scattering cross section must also be considered. The simple option, which consists of using the same homogenization procedure for both the isotropic and anisotropic components of the scattering cross section, leads to inconsistencies between the homogeneous and homogenized transport equation. Here we will present a method for homogenizing the anisotropic scattering cross sections that will resolve these inconsistencies. (author)
Khattab, K.M.
1998-01-01
The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotopic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) methods is proposed. This method converges (Clock time) faster than the MDSA method. It is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented. (author). 9 refs., 2 tabs., 5 figs
Khattab, K.M.
1997-01-01
The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotropic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) method is proposed that converges (clock time) faster than the MDSA method. This method is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented
Thach, Trung Thanh; Shin, Donghyuk; Han, Seungsu; Lee, Sangho
2016-04-01
The conformational flexibility of linkage-specific polyubiquitin chains enables ubiquitylated proteins and their receptors to be involved in a variety of cellular processes. Linear or Met1-linked polyubiquitin chains, associated with nondegradational cellular signalling pathways, have been known to adopt multiple conformations from compact to extended conformations. However, the extent of such conformational flexibility remains open. Here, the crystal structure of linear Ub2 was determined in a more compact conformation than that of the previously known structure (PDB entry 3axc). The two structures differ significantly from each other, as shown by an r.m.s.d. between C(α) atoms of 3.1 Å. The compactness of the linear Ub2 structure in comparison with PDB entry 3axc is supported by smaller values of the radius of gyration (Rg; 18 versus 18.9 Å) and the maximum interatomic distance (Dmax; 55.5 versus 57.8 Å). Extra intramolecular hydrogen bonds formed among polar residues between the distal and proximal ubiquitin moieties seem to contribute to stabilization of the compact conformation of linear Ub2. An ensemble of three semi-extended and extended conformations of linear Ub2 was also observed by small-angle X-ray scattering (SAXS) analysis in solution. In addition, the conformational heterogeneity in linear polyubiquitin chains is clearly manifested by SAXS analyses of linear Ub3 and Ub4: at least three distinct solution conformations are observed in each chain, with the linear Ub3 conformations being compact. The results expand the extent of conformational space of linear polyubiquitin chains and suggest that changes in the conformational ensemble may be pivotal in mediating multiple signalling pathways.
Chai, Xintao; Tang, Genyang; Peng, Ronghua; Liu, Shaoyong
2018-03-01
Full-waveform inversion (FWI) reconstructs the subsurface properties from acquired seismic data via minimization of the misfit between observed and simulated data. However, FWI suffers from considerable computational costs resulting from the numerical solution of the wave equation for each source at each iteration. To reduce the computational burden, constructing supershots by combining several sources (aka source encoding) allows mitigation of the number of simulations at each iteration, but it gives rise to crosstalk artifacts because of interference between the individual sources of the supershot. A modified Gauss-Newton FWI (MGNFWI) approach showed that as long as the difference between the initial and true models permits a sparse representation, the ℓ _1-norm constrained model updates suppress subsampling-related artifacts. However, the spectral-projected gradient ℓ _1 (SPGℓ _1) algorithm employed by MGNFWI is rather complicated that makes its implementation difficult. To facilitate realistic applications, we adapt a linearized Bregman (LB) method to sparsity-promoting FWI (SPFWI) because of the efficiency and simplicity of LB in the framework of ℓ _1-norm constrained optimization problem and compressive sensing. Numerical experiments performed with the BP Salt model, the Marmousi model and the BG Compass model verify the following points. The FWI result with LB solving ℓ _1-norm sparsity-promoting problem for the model update outperforms that generated by solving ℓ _2-norm problem in terms of crosstalk elimination and high-fidelity results. The simpler LB method performs comparably and even superiorly to the complicated SPGℓ _1 method in terms of computational efficiency and model quality, making the LB method a viable alternative for realistic implementations of SPFWI.
Impact of optical phonon scattering on inversion channel mobility in 4H-SiC trenched MOSFETs
Kutsuki, Katsuhiro; Kawaji, Sachiko; Watanabe, Yukihiko; Onishi, Toru; Fujiwara, Hirokazu; Yamamoto, Kensaku; Yamamoto, Toshimasa
2017-04-01
Temperature characteristics of the channel mobility were investigated for 4H-SiC trenched MOSFETs in the range from 30 to 200 °C. The conventional model of channel mobility limited by carrier scattering is based on Si-MOSFETs and shows a greatly different channel mobility from the experimental value, especially at high temperatures. On the other hand, our improved mobility model taking into account optical phonon scattering yielded results in excellent agreement with experimental results. Moreover, the major factors limiting the channel mobility were found to be Coulomb scattering in a low effective field (<0.7 MV/cm) and optical phonon scattering in a high effective field.
High resolution electron scattering facility at the Darmstadt Linear Accelerator (DALINAC). Pt. 4
Foh, J.; Frey, R.; Schneider, R.; Schuell, D.; Schwierczinski, A.; Theissen, H.; Titze, O.
1977-11-01
The computer system installed for the electron scattering facility and its usage is described. For on-line control a dedicated system of two tightly coupled computers (PDP 11/20, H116) is used wheras a PDP 11/45 is provided for all other data processing work resulting from the experiments. Special interfaces, graphic terminals, system software and a complete set of application programs have been developed. (orig.) [de
Synthetic acceleration methods for linear transport problems with highly anisotropic scattering
Khattab, K.M.
1989-01-01
One of the iterative methods which is used to solve the discretized transport equation is called the Source Iteration Method (SI). The SI method converges very slowly for problems with optically thick regions and scattering ratios (σ s /σ t ) near unity. The Diffusion-Synthetic Acceleration method (DSA) is one of the methods which has been devised to improve the convergence rate of the SI method. The DSA method is a good tool to accelerate the SI method, if the particle which is being dealt with is a neutron. This is because the scattering process for neutrons is not severely anisotropic. However, if the particle is a charged particle (electron), DSA becomes ineffective as an acceleration device because here the scattering process is severely anisotropic. To improve the DSA algorithm for electron transport, the author approaches the problem in two different ways in this thesis. He develops the first approach by accelerating more angular moments (φ 0 , φ 1 , φ 2 , φ 3 ,...) than is done in DSA; he calls this approach the Modified P N Synthetic Acceleration (MPSA) method. In the second approach he modifies the definition of the transport sweep, using the physics of the scattering; he calls this approach the Modified Diffusion Synthetic Acceleration (MDSA) method. In general, he has developed, analyzed, and implemented the MPSA and MDSA methods in this thesis and has shown that for a high order quadrature set and mesh widths about 1.0 cm, they are each about 34 times faster (clock time) than the DSA method. Also, he has found that the MDSA spectral radius decreases as the mesh size increases. This makes the MDSA method a better choice for large spatial meshes
Gagliardi, S; Dagger, A; Semlyen, A J
2002-01-01
In this study we report small-angle neutron-scattering measurements of cyclic and linear polydimethylsiloxane (PDMS) in the melt. It has been suggested that due to the presence of topological constraints, rings in the melt may be more compact than Gaussian chains. We show that the cyclic chains are partially collapsed and do not follow Gaussian statistics: the weight-average radius of gyration R sub g sub , sub w is found to be proportional to M sub w sup 0 sup . sup 5 sup 3 and M sub w sup 0 sup . sup 4 sup 0 in the case of linear and cyclic PDMS, respectively. The results are in agreement with recent computer simulations, which predict R sub g to be proportional to N sup 2 sup / sup 5 , where N is the degree of polymerisation. (orig.)
K. Horikawa
2014-10-01
Full Text Available In 1957, Agodi predicted that the neutron angular distribution in (γ, n reactions with a 100% linearly polarized γ-ray beam for dipole excitation should be anisotropic and universally described by the simple function of a+b⋅cos(2ϕ at the polar angle θ=90°, where ϕ is the azimuthal angle. However, this prediction has not been experimentally confirmed in over half a century. We have verified experimentally this angular distribution in the (γ, n reaction for 197Au, 127I, and natural Cu targets using linearly polarized laser Compton scattering γ-rays. The result suggests that the (γ→, n reaction is a novel tool to study nuclear physics in the giant dipole resonance region.
Murata, M; Uchida, T; Yang, Y; Lezhava, A; Kinashi, H
2011-04-01
We have comprehensively analyzed the linear chromosomes of Streptomyces griseus mutants constructed and kept in our laboratory. During this study, macrorestriction analysis of AseI and DraI fragments of mutant 402-2 suggested a large chromosomal inversion. The junctions of chromosomal inversion were cloned and sequenced and compared with the corresponding target sequences in the parent strain 2247. Consequently, a transposon-involved mechanism was revealed. Namely, a transposon originally located at the left target site was replicatively transposed to the right target site in an inverted direction, which generated a second copy and at the same time caused a 2.5-Mb chromosomal inversion. The involved transposon named TnSGR was grouped into a new subfamily of the resolvase-encoding Tn3 family transposons based on its gene organization. At the end, terminal diversity of S. griseus chromosomes is discussed by comparing the sequences of strains 2247 and IFO13350.
Faggiani Dias, D.; Subramanian, A. C.; Zanna, L.; Miller, A. J.
2017-12-01
Sea surface temperature (SST) in the Pacific sector is well known to vary on time scales from seasonal to decadal, and the ability to predict these SST fluctuations has many societal and economical benefits. Therefore, we use a suite of statistical linear inverse models (LIMs) to understand the remote and local SST variability that influences SST predictions over the North Pacific region and further improve our understanding on how the long-observed SST record can help better guide multi-model ensemble forecasts. Observed monthly SST anomalies in the Pacific sector (between 15oS and 60oN) are used to construct different regional LIMs for seasonal to decadal prediction. The forecast skills of the LIMs are compared to that from two operational forecast systems in the North American Multi-Model Ensemble (NMME) revealing that the LIM has better skill in the Northeastern Pacific than NMME models. The LIM is also found to have comparable forecast skill for SST in the Tropical Pacific with NMME models. This skill, however, is highly dependent on the initialization month, with forecasts initialized during the summer having better skill than those initialized during the winter. The forecast skill with LIM is also influenced by the verification period utilized to make the predictions, likely due to the changing character of El Niño in the 20th century. The North Pacific seems to be a source of predictability for the Tropics on seasonal to interannual time scales, while the Tropics act to worsen the skill for the forecast in the North Pacific. The data were also bandpassed into seasonal, interannual and decadal time scales to identify the relationships between time scales using the structure of the propagator matrix. For the decadal component, this coupling occurs the other way around: Tropics seem to be a source of predictability for the Extratropics, but the Extratropics don't improve the predictability for the Tropics. These results indicate the importance of temporal
Ranaivo Nomenjanahary, F.; Rakoto, H.; Ratsimbazafy, J.B.
1994-08-01
This paper is concerned with resistivity sounding measurements performed from single site (vertical sounding) or from several sites (profiles) within a bounded area. The objective is to present an accurate information about the study area and to estimate the likelihood of the produced quantitative models. The achievement of this objective obviously requires quite relevant data and processing methods. It also requires interpretation methods which should take into account the probable effect of an heterogeneous structure. In front of such difficulties, the interpretation of resistivity sounding data inevitably involves the use of inversion methods. We suggest starting the interpretation in simple situation (1-D approximation), and using the rough but correct model obtained as an a-priori model for any more refined interpretation. Related to this point of view, special attention should be paid for the inverse problem applied to the resistivity sounding data. This inverse problem is nonlinear, while linearity inherent in the functional response used to describe the physical experiment. Two different approaches are used to build an approximate but higher dimensional inversion of geoelectrical data: the linear approach and the bayesian statistical approach. Some illustrations of their application in resistivity sounding data acquired at Tritrivakely volcanic lake (single site) and at Mahitsy area (several sites) will be given. (author). 28 refs, 7 figs
Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, A.
2016-01-01
Roč. 9, č. 11 (2016), s. 4297-4311 ISSN 1991-959X R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Linear inverse problem * Bayesian regularization * Source-term determination * Variational Bayes method Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.458, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/tichy-0466029.pdf
Luescher, M.; Pohlmeyer, K.
1977-09-01
Finite energy solutions of the field equations of the non-linear sigma-model are shown to decay asymptotically into massless lumps. By means of a linear eigenvalue problem connected with the field equations we then find an infinite set of dynamical conserved charges. They, however, do not provide sufficient information to decode the complicated scattering of lumps. (orig.) [de
Nielsen, Tim; Brendel, Bernhard; Ziegler, Ronny; Beek, Michiel van; Uhlemann, Falk; Bontus, Claas; Koehler, Thomas
2009-01-01
Diffuse optical tomography (DOT) is a potential new imaging modality to detect or monitor breast lesions. Recently, Philips developed a new DOT system capable of transmission and fluorescence imaging, where the investigated breast is hanging freely into the measurement cup containing scattering fluid. We present a fast and robust image reconstruction algorithm that is used for the transmission measurements. The algorithm is based on the Rytov approximation. We show that this algorithm can be used over a wide range of tissue optical properties if the reconstruction is adapted to each patient. We use estimates of the breast shape and average tissue optical properties to initialize the reconstruction, which improves the image quality significantly. We demonstrate the capability of the measurement system and reconstruction to image breast lesions by clinical examples
Stimulated Raman scattering and ion dynamics: the role of Langmuir wave non-linearities
Bonnaud, G.; Pesme, D.
1987-01-01
The saturation of the Stimulated Raman Scattering (SRS) is studied by means of wave-coupling numerical simulations. A new code (CHEOPS) has been designed in order to model these couplings, in real 1-D space, with aperiodic boundary conditions. Each wave can be represented either by a complete amplitude or by an envelope amplitude only. The choice of the wave set to be coupled allows to investigate separately some mechanisms relevant in long time SRS evolution. The various mechanisms which may inhibit SRS growth are reviewed and the SRS saturation scenarios are exhibited in an homogeneous density plasma slab. The ion dependent mechanisms appear to be the most efficient ones to saturate SRS. Their importance is strongly bound to the electron temperature and to the ion fluctuation level at time when SRS has already grown many e-foldings
Sanchez, Richard.
1975-11-01
The Integral Transform Method for the neutron transport equation has been developed in last years by Asaoka and others. The method uses Fourier transform techniques in solving isotropic one-dimensional transport problems in homogeneous media. The method has been extended to linearly anisotropic transport in one-dimensional homogeneous media. Series expansions were also obtained using Hembd techniques for the new anisotropic matrix elements in cylindrical geometry. Carlvik spatial-spherical harmonics method was generalized to solve the same problem. By applying a relation between the isotropic and anisotropic one-dimensional kernels, it was demonstrated that anisotropic matrix elements can be calculated by a linear combination of a few isotropic matrix elements. This means in practice that the anisotropic problem of order N with the N+2 isotropic matrix for the plane and spherical geometries, and N+1 isotropic matrix for cylindrical geometries can be solved. A method of solving linearly anisotropic one-dimensional transport problems in homogeneous media was defined by applying Mika and Stankiewicz observations: isotropic matrix elements were computed by Hembd series and anisotropic matrix elements then calculated from recursive relations. The method has been applied to albedo and critical problems in cylindrical geometries. Finally, a number of results were computed with 12-digit accuracy for use as benchmarks [fr
Viallet, E.; Heinfling, G.
2005-01-01
Due to increased potentialities of computers, it is nowadays possible to perform dynamic non-linear computation of structures to evaluate their ultimate behavior under seismic loads using refined finite element models. Nevertheless, one key parameter for such complex computations is the input load (i.e. input time histories) which may lead to important discrepancies in the results and therefore difficulties to deal with for engineering purpose (variability, number of time histories to use...). In this situation, the number of accelerograms to be used and the way to deal with the results is to be carefully assessed. The objective of this study is to give some elements concerning (i) the number of accelerograms to be used for transient non-linear computations and (ii) the way to account for scattering of results. For this purpose, some simplified non-linear models are used. These models represent characteristic types of non-linearities such as : - Reinforce concrete (RC) structure model (with plastic non-linearity), - PWR core model (with impact non-linearity). For each type of non-linearity, different sets of accelerograms are used (artificial and natural ones). Each set is composed of a relatively high number of accelerograms in order to get proper trends. The results are expressed in term of average and standard deviation values of the characteristic parameters for each non-linearity (i.e. ductility drift for RC structure model and impact force for PWR core model). The results show that, a relatively large number of time histories may be necessary to get proper predictions of the average value of the characteristic non-linear parameter under consideration. In that situation, it should be difficult to deal with such a result for complex studies on reel structures. Nevertheless, it may be necessarily to perform transient non-linear seismic computations for design analyses but with a reduced number of calculations. For this purpose, the previous results are analyzed
Inverse radiative transfer problems in two-dimensional heterogeneous media
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
Vadim N. Pelevin
2001-12-01
Full Text Available A method for estimating the water backscattering coefficient was put forward on the basis of experimental data of diffuse attenuation coefficient for downwelling irradiance and irradiance reflectance. Calculations were carried out for open sea waters of different types and the spectral dependencies were found ("anomalous" spectra and explained. On this basis, a new model of light backscattering on particles in the sea is proposed. This model may be useful for modelling remote sensing reflectance spectra in order to solve the inverse problems of estimating the concentration of natural admixtures in shelf waters.
Exact potential and scattering amplitudes from the tachyon non-linear β -function
Coletti, E.; Forini, V.; Nardelli, G.; Orselli, M.; Grignani, G.
2004-01-01
We compute, on the disk, the non-linear tachyon β-function, β T , of the open bosonic string theory. β T is determined both in an expansion to the third power of the field and to all orders in derivatives and in an expansion to any power of the tachyon field in the leading order in derivatives. We construct the Witten-Shatashvili (WS) space-time effective action S and prove that it has a very simple universal form in terms of the renormalized tachyon field and β T . The expression for S is well suited to studying both processes that are far off-shell, such as tachyon condensation, and close to the mass-shell, such as perturbative on-shell amplitudes. We evaluate S in a small derivative expansion, providing the exact tachyon potential. The normalization of S is fixed by requiring that the field redefinition that maps S into the tachyon effective action derived from the cubic string field theory is regular on-shell. The normalization factor is in precise agreement with the one required for verifying all the conjectures on tachyon condensation. The coordinates in the space of couplings in which the tachyon β-function is non linear are the most appropriate to study RG fixed points that can be interpreted as solitons of S, i.e. D-branes. (author)
Pontedeiro, E.M.B.D.; Maiorino, J.R.
1982-01-01
The linear equation transport, monoenergetic, with anysotropic scattering, in multiregions, by F sub(N) method, is resolved. The mathematical analysis used for this method consists in to use parcially the expansion method in singular autofunctions, or Case's method, aiming to derive a set of integral equations coupled to the angular distribution in the boundaries and interfaces, and then to approximate these distributions by polynomics of N order, aiming to derive, with the use of these boundary and continuity conditions in the interfaces, a set of algebric equations for the coef. of polynomical approximation. With the goal to obtain numerical results, a computer code (FNAM-1) with options for the number of regions, boundary conditions, F sub(N) approx order, were developed. Numerical results were then obtained for various sample problems and compared with the results published in the literature with the objective to demonstrate the precision and applicability of the F sub(N) method. (E.G.) [pt
Barnett, Alex H.; Nelson, Bradley J.; Mahoney, J. Matthew
2015-09-01
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ + E +x2) u (x1 ,x2) = 0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.
Bhabha vs. Moeller scattering as a contact-interaction analyzer at a polarized linear collider
Pankov, A A
2002-01-01
We discuss electron-electron contact-interaction searches in the processes e sup + e sup -->e sup + e sup - and e sup - e sup -->e sup - e sup - at planned Linear Colliders run in the e sup + e sup - and e sup - e sup - modes with both beams longitudinally polarized. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections, and allows to simultaneously take into account the general set of electron contact interaction couplings as independent, non-zero, parameters thus avoiding the simplifying choice of a model. We evaluate the corresponding model-independent constraints on the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity, as far as the chirality of the constants is concerned, of the two processes in giving the best constraints. We also make a comparison with the potential of e sup + e sup --> mu supmu sup - at the same energy and initial beams polarization.
Bhabha vs. Moeller scattering as a contact-interaction analyzer at a polarized linear collider
Pankov, A.; Paver, N.
2002-10-01
We discuss electron-electron contact-interaction searches in the processes e + e - →e + e - and e - e - →e - e - at planned Linear Colliders run in the e + e - and e - e - modes with both beams longitudinally polarized. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections, and allows to simultaneously take into account the general set of electron contact interaction couplings as independent, non-zero, parameters thus avoiding the simplifying choice of a model. We evaluate the corresponding model-independent constraints on the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity, as far as the chirality of the constants is concerned, of the two processes in giving the best constraints. We also make a comparison with the potential of e + e - →μ μ- at the same energy and initial beams polarization. (author)
Wapenaar, Kees; Thorbecke, Jan; van der Neut, Joost
2016-04-01
Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.
Larin, S.V.; Lyulin, S.V.; Lyulin, A.V.; Darinskii, A.A.
2009-01-01
Complexes of fully ionized third-generation dendrimers with oppositely charged linear polyelectrolyte chains are studied by the Brownian dynamics method. A freely jointed model of a dendrimer and a linear chain is used. Electrostatic interactions are considered within the Debye-Hückel approximation
Tonellot, Th.L.
2000-03-24
In this thesis, we propose a method which takes into account a priori information (geological, diagraphic and stratigraphic knowledge) in linearized pre-stack seismic data inversion. The approach is based on a formalism in which the a priori information is incorporated in an a priori model of elastic parameters - density, P and S impedances - and a model covariance operator which describes the uncertainties in the model. The first part of the thesis is dedicated to the study of this covariance operator and to the norm associated to its inverse. We have generalized the exponential covariance operator in order to describe the uncertainties in the a priori model elastic parameters and their correlations at each location. We give the analytical expression of the covariance operator inverse in 1-D, 2-D, and 3-D, and we discretized the associated norm with a finite element method. The second part is dedicated to synthetic and real examples. In a preliminary step, we have developed a pre-stack data well calibration method which allows the estimation of the source signal. The impact of different a priori information is then demonstrated on synthetic and real data. (author)
Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem
2008-01-01
In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.
Richardson, J.M.; Fertig, K.W. Jr.
1983-01-01
In order to inspect flaws which lie too close to the surface a Fourier elastodynamic formalism is proposed which enables one to decompose the elastodynamic system into separately charterizable parts by means of planes perpendicular to the z-axis. The process can be represented by a generalized transfer function relating the near-field scattered waves to the waves incident on a slab of material containing the flaw. The Fourier elastodynamics are applied to the characterization of the total scattering process involving a flaw at various distances from a plastic-water interface. An abbreviated discussion of Fourier elastodynamics is presented, and the results specialized to the case of spherical voids and inclusions bear an interface. Finally, the computational results for several ranges of temporal frequency and for a sequence of values of the distance from the flaw center to the interface are discussed
Chudnovsky, D V
1978-09-01
For systems of nonlinear equations having the form [L(n) - ( partial differential/ partial differentialt), L(m) - ( partial differential/ partial differentialy)] = 0 the class of meromorphic solutions obtained from the linear equations [Formula: see text] is presented.
Hikosaka Kenji
2012-11-01
Full Text Available Abstract Background Mitochondrial (mt genomes vary considerably in size, structure and gene content. The mt genomes of the phylum Apicomplexa, which includes important human pathogens such as the malaria parasite Plasmodium, also show marked diversity of structure. Plasmodium has a concatenated linear mt genome of the smallest size (6-kb; Babesia and Theileria have a linear monomeric mt genome (6.5-kb to 8.2-kb with terminal inverted repeats; Eimeria, which is distantly related to Plasmodium and Babesia/Theileria, possesses a mt genome (6.2-kb with a concatemeric form similar to that of Plasmodium; Cryptosporidium, the earliest branching lineage within the phylum Apicomplexa, has no mt genome. We are interested in the evolutionary origin of linear mt genomes of Babesia/Theileria, and have investigated mt genome structures in members of archaeopiroplasmid, a lineage branched off earlier from Babesia/Theileria. Results The complete mt genomes of archaeopiroplasmid parasites, Babesia microti and Babesia rodhaini, were sequenced. The mt genomes of B. microti (11.1-kb and B. rodhaini (6.9-kb possess two pairs of unique inverted repeats, IR-A and IR-B. Flip-flop inversions between two IR-As and between two IR-Bs appear to generate four distinct genome structures that are present at an equi-molar ratio. An individual parasite contained multiple mt genome structures, with 20 copies and 2 – 3 copies per haploid nuclear genome in B. microti and B. rodhaini, respectively. Conclusion We found a novel linear monomeric mt genome structure of B. microti and B. rhodhaini equipped with dual flip-flop inversion system, by which four distinct genome structures are readily generated. To our knowledge, this study is the first to report the presence of two pairs of distinct IR sequences within a monomeric linear mt genome. The present finding provides insight into further understanding of evolution of mt genome structure.
Inverse problems of geophysics
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Liu Guanghui [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Guo Kangxian, E-mail: axguo@sohu.com [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Wang Chao [Institute of Public Administration, Guangzhou University, Guangzhou 510006 (China)
2012-06-15
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
Liu Guanghui; Guo Kangxian; Wang Chao
2012-01-01
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
Washio, M.; Sakaue, K.; Hama, Y.; Kamiya, Y.; Moriyama, R.; Hezume, K.; Saito, T.; Kuroda, R.; Kashiwagi, S.; Ushida, K.; Hayano, H.; Urakawa, J.
2006-01-01
High quality beam generation project based on High-Tech Research Center Project, which has been approved by Ministry of Education, Culture, Sports, Science and Technology in 1999, has been conducted by advance research institute for science and engineering, Waseda University. In the project, laser photo-cathode RF-gun has been selected for the high quality electron beam source. RF cavities with low dark current, which were made by diamond turning technique, have been successfully manufactured. The low emittance electron beam was realized by choosing the modified laser injection technique. The obtained normalized emittance was about 3 mm·mrad at 100 pC of electron charge. The soft X-ray beam generation with the energy of 370 eV, which is in the energy region of so-called 'water window', by inverse Compton scattering has been performed by the collision between IR laser and the low emittance electron beams. (authors)
Gobrecht, Alexia; Bendoula, Ryad; Roger, Jean-Michel; Bellon-Maurel, Véronique
2015-01-01
Visible and Near Infrared (Vis-NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer-Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis-NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer-Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84-0.97 for powdered samples. Copyright © 2014 Elsevier B.V. All rights reserved.
Fagundes, Daniel Almeida
2010-01-01
The theoretical description of high-energy elastic hadron scattering constitutes an open problem in both, the underlying quantum field theory of strong interactions (QCD) and the phenomenological context. In this work the inverse problem in elastic hadron scattering is discussed in the impact parameter and eikonal frameworks, specifically a study on the empirical extraction of the profile, the inelastic overlap and the eikonal functions, from the experimental data and some principles and high-energy theorems (model independent). The analysis is limited to elastic proton-proton scattering in the center of momentum energy interval 19.4 - 62.5 GeV. In particular, a novel representation for the Martin's Real Part Formula is introduced but without the scaling property and suitable for empirical analysis. By means of this representation, and two other parametrizations previously introduced (constrained and unconstrained), several properties of the inelastic overlap function and the imaginary part of the eikonal (opacity) in the momentum transfer space are determined, in special: (1) evidence of a peripheral effect (tail) in the inelastic overlap function in the parameter impact space above 2 fm; (2) development of analytical parametrizations for this function leading to three gaussian components with centers at 0.0, ∼0.7 and ∼1.3 fm; (3) evidence of a finite zero (change of sign) in the opacity function in the momentum transfer space; (4) development of empirical parametrization for this function consistent with form factors as a product of two monopoles with constrained masses (not a dipole type) and a term with zero; (5) detailed discussion on the determination of the opacity function in the momentum transfer space through the semi-analytical approach. The applicability of these empirical results in the development of eikonal models (mainly those inspired in QCD) is also discussed. (author)
A. Gogoi
2011-09-01
Full Text Available Scattering properties of bentonite clay particles were investigated at 543.5 nm incident laser wavelength by using a designed and fabricated light scattering setup. The scattering samples were held in front of a laser beam by using a transparent cylindrical thermosetting epoxy matrix.
Krakauer, D.A.
1992-04-01
Electron-neutrino electron elastic scattering and two-body electron- neutrino carbon scattering reactions were observed using a 15 ton fine-grained detector and neutrinos from μ + decay at rest. The data was obtained during an exposure to neutrinos produced in LAMPF proton beam-stop. Based on identification of 262±46 ν e e - events the total cross-section for ν e e - → ν e e - was measured to be σ(ν e E - ) = (3.09±0.54(stat)±0.39(syst)) x 10 -43 cm 2 . The interference between the weak charged and neutral currents was measured for the first time. The interference was found to be destructive, with a magnitude 0.97±0.22 times the value predicted by the WSG theory. The total cross-section was also used to measure sin 2 θ W = 0.24±0.06(stat)±0.04(syst). The data restricts the maximum allowed value of the neutrino magnetic moment to be less than 1.3 x 10 -9 Bohr magnetrons for ν e and 8.8 x 10 -10 for ν mu . In a separate analysis, 182±22 12 C(ν e ,e - ) 12 N(gs) events with subsequent 12 N(β + ) 12 C were observed, corresponding to a total cross-section, σ(ν e 12 C → e - 12 N(gs)) = (1.03 ± 0.12(stat) ± 0.10(sys)) x10 -41 cm 2 . This was the first observation of ν e -induced transitions between specific nuclear states. The results is good agreement with theoretical predictions
Kishimoto, S; Mitsui, T; Haruki, R; Yoda, Y; Taniguchi, T; Shimazaki, S; Ikeno, M; Saito, M; Tanaka, M
2014-11-01
We developed a silicon avalanche photodiode (Si-APD) linear-array detector for use in nuclear resonant scattering experiments using synchrotron X-rays. The Si-APD linear array consists of 64 pixels (pixel size: 100 × 200 μm(2)) with a pixel pitch of 150 μm and depletion depth of 10 μm. An ultrafast frontend circuit allows the X-ray detector to obtain a high output rate of >10(7) cps per pixel. High-performance integrated circuits achieve multichannel scaling over 1024 continuous time bins with a 1 ns resolution for each pixel without dead time. The multichannel scaling method enabled us to record a time spectrum of the 14.4 keV nuclear radiation at each pixel with a time resolution of 1.4 ns (FWHM). This method was successfully applied to nuclear forward scattering and nuclear small-angle scattering on (57)Fe.
Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)
Quasi-free scattering off {sup 12}C in inverse kinematics at the R3B/LAND-setup
Panin, Valerii; Aumann, Thomas [Institut fuer Kernphysik, TU Darmstadt (Germany); Taylor, Jonathan [Department of Physics, University of Liverpool (United Kingdom); Collaboration: R3B-Collaboration
2011-07-01
An important part of the physics program at the future R3B (Reactions with Relativistic Radioactive Beams) experiment at FAIR will be based on the study of proton-induced reactions in a kinematical complete measurement. These are in particular the quasi-free scattering processes of the type (p,2p), (p,pn), (p,p{alpha}) etc, which will be used to investigate the single-particle and cluster structure of neutron-proton asymmetric nuclei and the role of nucleon-nucleon correlations in nuclei. A prototype setup for the detection of high-energy protons in (p,2p) reactions in coincidence with forward emitted light particles and heavy fragments has been built based on an array of Si micro-strip detectors for tracking and thick NaI scintillators for energy measurements. A {sup 12}C beam has been chosen for the bench-mark experiment since its structure is well known, and results from proton- as well as electron-induced knockout reactions are available. First results on two-proton angular correlations and momentum distributions of the knocked-out protons inside {sup 12}C are discussed as well as the excitation energy spectrum of the residual {sup 11}B nuclei.
Ronchin, Erika; Masterlark, Timothy; Dawson, John; Saunders, Steve; Martì Molist, Joan
2017-06-01
We test an innovative inversion scheme using Green's functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green's function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green's functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the
P.D.Gujrati
2002-01-01
Full Text Available Theoretical evidence is presented in this review that architectural aspects can play an important role, not only in the bulk but also in confined geometries by using our recursive lattice theory, which is equally applicable to fixed architectures (regularly branched polymers, stars, dendrimers, brushes, linear chains, etc. and variable architectures, i.e. randomly branched structures. Linear chains possess an inversion symmetry (IS of a magnetic system (see text, whose presence or absence determines the bulk phase diagram. Fixed architectures possess the IS and yield a standard bulk phase diagram in which there exists a theta point at which two critical lines C and C' meet and the second virial coefficient A2 vanishes. The critical line C appears only for infinitely large polymers, and an order parameter is identified for this criticality. The critical line C' exists for polymers of all sizes and represents phase separation criticality. Variable architectures, which do not possess the IS, give rise to a topologically different phase diagram with no theta point in general. In confined regions next to surfaces, it is not the IS but branching and monodispersity, which becomes important in the surface regions. We show that branching plays no important role for polydisperse systems, but become important for monodisperse systems. Stars and linear chains behave differently near a surface.
Ankudze, Bright; Philip, Anish [Department of Chemistry, University of Eastern Finland, P.O. Box 111, F1-80101, Joensuu (Finland); Pakkanen, Tuula T., E-mail: Tuula.Pakkanen@uef.fi [Department of Chemistry, University of Eastern Finland, P.O. Box 111, F1-80101, Joensuu (Finland); Matikainen, Antti; Vahimaa, Pasi [Institute of Photonics, University of Eastern Finland, P.O. Box 111, F1-80101, Joensuu (Finland)
2016-11-30
Highlights: • SERS substrates prepared by infiltration of nanoparticles into SiO{sub 2} inverse opal. • The SERS substrate gives an enhancement factor of 10{sup 7} for 4-aminothiophenol. • The sensitivity of the substrate is mainly attributed to gold nanoparticle clusters. - Abstract: SiO{sub 2} inverse opal (IO) films with embedded gold nanoparticles (AuNPs) for surface-enhanced Raman scattering (SERS) application are reported. SiO{sub 2} IO films were loaded with AuNPs by a simple infiltration in a single cycle to form Au-SiO{sub 2} IOs. The optical property and the morphology of the Au-SiO{sub 2} IO substrates were characterized; it was observed that they retained the Bragg diffraction of SiO{sub 2} IO and the localized surface plasmon resonance (LSPR) of AuNPs. The SERS property of the Au-SiO{sub 2} IO substrates were studied with methylene blue (MB) and 4-aminothiophenol (4-ATP). The SERS enhancement factors were 10{sup 7} and 10{sup 6} for 4-ATP and MB, respectively. A low detection limit of 10{sup −10} M for 4-ATP was also obtained with the Au-SiO{sub 2} IO substrate. A relative standard deviation of 18.5% for the Raman signals intensity at 1077 cm{sup −1} for 4-ATP shows that the Au-SiO{sub 2} IO substrates have good signal reproducibility. The results of this study indicate that the Au-SiO{sub 2} IO substrates can be used in sensing and SERS applications.
Saloranta, Tuomo M; Andersen, Tom; Naes, Kristoffer
2006-01-01
Rate constant bioaccumulation models are applied to simulate the flow of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in the coastal marine food web of Frierfjorden, a contaminated fjord in southern Norway. We apply two different ways to parameterize the rate constants in the model, global sensitivity analysis of the models using Extended Fourier Amplitude Sensitivity Test (Extended FAST) method, as well as results from general linear system theory, in order to obtain a more thorough insight to the system's behavior and to the flow pathways of the PCDD/Fs. We calibrate our models against observed body concentrations of PCDD/Fs in the food web of Frierfjorden. Differences between the predictions from the two models (using the same forcing and parameter values) are of the same magnitude as their individual deviations from observations, and the models can be said to perform about equally well in our case. Sensitivity analysis indicates that the success or failure of the models in predicting the PCDD/F concentrations in the food web organisms highly depends on the adequate estimation of the truly dissolved concentrations in water and sediment pore water. We discuss the pros and cons of such models in understanding and estimating the present and future concentrations and bioaccumulation of persistent organic pollutants in aquatic food webs.
Jain, Amit; Kuhls-Gilcrist, Andrew T; Gupta, Sandesh K; Bednarek, Daniel R; Rudin, Stephen
2010-03-01
The MTF, NNPS, and DQE are standard linear system metrics used to characterize intrinsic detector performance. To evaluate total system performance for actual clinical conditions, generalized linear system metrics (GMTF, GNNPS and GDQE) that include the effect of the focal spot distribution, scattered radiation, and geometric unsharpness are more meaningful and appropriate. In this study, a two-dimensional (2D) generalized linear system analysis was carried out for a standard flat panel detector (FPD) (194-micron pixel pitch and 600-micron thick CsI) and a newly-developed, high-resolution, micro-angiographic fluoroscope (MAF) (35-micron pixel pitch and 300-micron thick CsI). Realistic clinical parameters and x-ray spectra were used. The 2D detector MTFs were calculated using the new Noise Response method and slanted edge method and 2D focal spot distribution measurements were done using a pin-hole assembly. The scatter fraction, generated for a uniform head equivalent phantom, was measured and the scatter MTF was simulated with a theoretical model. Different magnifications and scatter fractions were used to estimate the 2D GMTF, GNNPS and GDQE for both detectors. Results show spatial non-isotropy for the 2D generalized metrics which provide a quantitative description of the performance of the complete imaging system for both detectors. This generalized analysis demonstrated that the MAF and FPD have similar capabilities at lower spatial frequencies, but that the MAF has superior performance over the FPD at higher frequencies even when considering focal spot blurring and scatter. This 2D generalized performance analysis is a valuable tool to evaluate total system capabilities and to enable optimized design for specific imaging tasks.
Hong, Youngjoon; Nicholls, David P.
2017-09-01
The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.
Inverse planning and optimization: a comparison of solutions
Ringor, Michael [School of Health Sciences, Purdue University, West Lafayette, IN (United States); Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States)
1998-09-01
The basic problem in radiation therapy treatment planning is to determine an appropriate set of treatment parameters that would induce an effective dose distribution inside a patient. One can approach this task as an inverse problem, or as an optimization problem. In this presentation, we compare both approaches. The inverse problem is presented as a dose reconstruction problem similar to tomography reconstruction. We formulate the optimization problem as linear and quadratic programs. Explicit comparisons are made between the solutions obtained by inversion and those obtained by optimization for the case in which scatter and attenuation are ignored (the NS-NA approximation)
Lang, Wen-Jing; Li, Zhi-Qing
2014-07-01
Both the semi-classical and quantum transport properties of F-doped SnO2 thick films (˜1 μm) were investigated experimentally. We found that the resistivity caused by the thermal phonons obeys Bloch-Grüneisen law from ˜90 to 300 K, while only the diffusive thermopower, which varies linearly with temperature from 300 down to 10 K, can be observed. The phonon-drag thermopower is completely suppressed due to the long electron-phonon relaxation time in the compound. These observations, together with the fact that the carrier concentration has negligible temperature dependence, indicate that the conduction electrons in F-doped SnO2 films possess free-electron-like characteristics. At low temperatures, the electron-electron scattering dominates over the electron-phonon scattering and governs the inelastic scattering process. The theoretical predications of scattering rates of large- and small-energy-transfer electron-electron scattering processes, which are negligibly weak in three-dimensional disordered conventional conductors, are quantitatively tested in this lower carrier concentration and free-electron-like highly degenerate semiconductor.
Lang, Wen-Jing; Li, Zhi-Qing
2014-01-01
Both the semi-classical and quantum transport properties of F-doped SnO 2 thick films (∼1 μm) were investigated experimentally. We found that the resistivity caused by the thermal phonons obeys Bloch-Grüneisen law from ∼90 to 300 K, while only the diffusive thermopower, which varies linearly with temperature from 300 down to 10 K, can be observed. The phonon-drag thermopower is completely suppressed due to the long electron-phonon relaxation time in the compound. These observations, together with the fact that the carrier concentration has negligible temperature dependence, indicate that the conduction electrons in F-doped SnO 2 films possess free-electron-like characteristics. At low temperatures, the electron-electron scattering dominates over the electron-phonon scattering and governs the inelastic scattering process. The theoretical predications of scattering rates of large- and small-energy-transfer electron-electron scattering processes, which are negligibly weak in three-dimensional disordered conventional conductors, are quantitatively tested in this lower carrier concentration and free-electron-like highly degenerate semiconductor.
Inverse Compton gamma-rays from pulsars
Morini, M.
1983-01-01
A model is proposed for pulsar optical and gamma-ray emission where relativistic electrons beams: (i) scatter the blackbody photons from the polar cap surface giving inverse Compton gamma-rays and (ii) produce synchrotron optical photons in the light cylinder region which are then inverse Compton scattered giving other gamma-rays. The model is applied to the Vela pulsar, explaining the first gamma-ray pulse by inverse Compton scattering of synchrotron photons near the light cylinder and the second gamma-ray pulse partly by inverse Compton scattering of synchrotron photons and partly by inverse Compton scattering of the thermal blackbody photons near the star surface. (author)
O. Tichý
2016-11-01
Full Text Available Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values as a product of the source-receptor sensitivity (SRS matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.
Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas
2016-11-01
Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.
Sitenko, A.
1991-01-01
This book emerged out of graduate lectures given by the author at the University of Kiev and is intended as a graduate text. The fundamentals of non-relativistic quantum scattering theory are covered, including some topics, such as the phase-function formalism, separable potentials, and inverse scattering, which are not always coverded in textbooks on scattering theory. Criticisms of the text are minor, but the reviewer feels an inadequate index is provided and the citing of references in the Russian language is a hindrance in a graduate text
Ciret, Charles; Gorza, Simon-Pierre
2016-06-15
The scattering of a linear wave on an optical event horizon, induced by a cross-polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with copolarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent of the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations using two coupled full vectorial nonlinear Schrödinger equations fully support the experimental results.
Quantum osp-invariant non-linear Schroedinger equation
Kulish, P.P.
1985-04-01
The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)
Joseph, Rose M.; Hagness, Susan C.; Taflove, Allen
1991-01-01
The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.
Generalized inverses theory and computations
Wang, Guorong; Qiao, Sanzheng
2018-01-01
This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
Iguchi, Toshio; Meneghini, Robert
1993-01-01
Air-borne radar measurements of thunderstorms were made as part of the CaPE (Convection and Precipitation/Electrification) experiment in Florida in July 1991. The radar has two channels, X-band (10 GHz) and Ka-band (34.5 GHz), and is capable of measuring cross-polarized returns as well as co-polarized returns. In stratiform rain, the cross-polarized components can be observed only at the bright band region and from the surface reflection. The linear depolarization ratios (LDR's) measured at X-band and Ka-band at the bright band are nearly equal. In convective rain, however, the LDR in Ka-band often exceeds the X-band LDR by several dB, and sometimes by more than 10 dB, reaching LDR values of up to -5 dB over heavy convective rain. For randomly oriented hydrometeors, such high LDR values cannot be explained by single scattering from non-spherical scattering particles alone. Because the LDR by single backscatter depends weakly on the wavelength, the difference between the Ka-band and X-band LDR's suggests that multiple scattering effects prevail in the Ka-band LDR. In order to test this inference, the magnitude of the cross-polarized component created by double scattering was calculated using the parameters of the airborne radar, which for both frequencies has beamwidths of 5.1 degrees and pulse widths of 0.5 microsecond. Uniform rain beyond the range of 3 km is assumed.
On the connection between the inverse transform method and the exact quantum eigenstates
Honerkamp, J.; Weber, P.; Wiesler, A.
1979-01-01
The 'inverse scattering transformation', which has been used to solve certain nonlinear field theories classically, is discussed in the context of the quantized version of these theories. In particular the non-linear Schroedinger equation and the massive Thirring model are considered. It is found that certain Jost functions of the associated scattering problem lead already, in quantizing the theory, to creation operators for the exact eigenstates of the corresponding Hamiltonians. (Auth.)
X-ray scatter removal by deconvolution
Seibert, J.A.; Boone, J.M.
1988-01-01
The distribution of scattered x rays detected in a two-dimensional projection radiograph at diagnostic x-ray energies is measured as a function of field size and object thickness at a fixed x-ray potential and air gap. An image intensifier-TV based imaging system is used for image acquisition, manipulation, and analysis. A scatter point spread function (PSF) with an assumed linear, spatially invariant response is modeled as a modified Gaussian distribution, and is characterized by two parameters describing the width of the distribution and the fraction of scattered events detected. The PSF parameters are determined from analysis of images obtained with radio-opaque lead disks centrally placed on the source side of a homogeneous phantom. Analytical methods are used to convert the PSF into the frequency domain. Numerical inversion provides an inverse filter that operates on frequency transformed, scatter degraded images. Resultant inverse transformed images demonstrate the nonarbitrary removal of scatter, increased radiographic contrast, and improved quantitative accuracy. The use of the deconvolution method appears to be clinically applicable to a variety of digital projection images
Parameterization analysis and inversion for orthorhombic media
Masmoudi, Nabil
2018-05-01
Accounting for azimuthal anisotropy is necessary for the processing and inversion of wide-azimuth and wide-aperture seismic data because wave speeds naturally depend on the wave propagation direction. Orthorhombic anisotropy is considered the most effective anisotropic model that approximates the azimuthal anisotropy we observe in seismic data. In the framework of full wave form inversion (FWI), the large number of parameters describing orthorhombic media exerts a considerable trade-off and increases the non-linearity of the inversion problem. Choosing a suitable parameterization for the model, and identifying which parameters in that parameterization could be well resolved, are essential to a successful inversion. In this thesis, I derive the radiation patterns for different acoustic orthorhombic parameterization. Analyzing the angular dependence of the scattering of the parameters of different parameterizations starting with the conventionally used notation, I assess the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. In order to build practical inversion strategies, I suggest new parameters (called deviation parameters) for a new parameterization style in orthorhombic media. The novel parameters denoted ∈d, ƞd and δd are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature of the deviation parameters consists of keeping the scattering of the vertical transversely isotropic (VTI) parameters stationary with azimuth. Using these scattering features, we can condition FWI to invert for the parameters which the data are sensitive to, at different stages, scales, and locations in the model. With this parameterization, the data are mainly sensitive to the scattering of 3 parameters (out of six that describe an acoustic orthorhombic medium): the horizontal velocity in the x1 direction, ∈1 which provides scattering mainly near
Hulett, L.D. Jr.; Lewis, T.A.; Alsmiller, R.G. Jr.; Peelle, R.; Pendyale, S.; Dale, J.M.; Rosseel, T.M.
1986-01-01
A tungsten moderator will be placed behind the target of the Oak Ridge Electron Linear Accelerator (ORELA) to convert gamma radiation to slow positrons. These will be extracted and led through evacuated solenoids to an experiment room. A Penning trap will be used to extend the slow positron pulses to achieve duty factors of 10% or greater. The facility will be used for atomic and molecular physics studies, positron microscopy, and materials research. Operations will be inexpensive and will not interfere with the normal function of ORELA, the measurement of neutron cross sections by flight-time spectrometry
Gupta, Mayanak K.; Singh, Baltej; Mittal, Ranjan; Zbiri, Mohamed; Cairns, Andrew B.; Goodwin, Andrew L.; Schober, Helmut; Chaplot, Samrath L.
2017-12-01
We present temperature-dependent inelastic-neutron-scattering measurements, accompanied by ab initio calculations of the phonon spectra and elastic properties as a function of pressure to quantitatively explain an unusual combination of negative thermal expansion and negative linear compressibility behavior of ZnAu2(CN) 4 . The mechanism of the negative thermal expansion is identified in terms of specific anharmonic phonon modes that involve bending of the -Zn-NC-Au-CN-Zn- linkage. The soft phonon at the L point at the Brillouin zone boundary quantitatively relates to the high-pressure phase transition at about 2 GPa. The ambient pressure structure is also found to be close to an elastic instability that leads to a weakly first-order transition.
Hashimoto, Takeji; Suehiro, Shoji; Shibayama, Mitsuhiro; Saijo, Kenji; Kawai, Hiromichi
1981-01-01
An apparatus for high speed measurements of small-angle X-ray scattering (SAXS) is described. This apparatus utilizes a 12 kW rotating anode X-ray generator, a linear position sensitive proportional counter (multicathode delay line PSPC), and a two-parameter multichannel pulse height analyzer (MCA) with 12 kwords (16 bits/word) memory area available for SAXA intensity data as a function of position (scattering angles) and time slice. The two-parameter MCA is constructed within a microcomputer system, by utilizing its R/W memory for data storage, and the memory incrementing and real-time CRT display is implemented by using two direct memory access (DMA) controllers. The cycle time of the access is about 10 μs. The measuring time for SAXS profiles with this apparatus can be shortened approximately by three orders of magnitude in comparison with the measuring time with SAXS apparatuses utilizing a conventional step-scanning goniometer and a conventional X-ray tube, thus permitting time-resolved analyses of SAXS profiles. Some applications of the apparatus to dynamic SAXS measurements are presented for polymeric systems, the preliminary results of which seem to indicate the possibility of obtaining a new class of data on dynamics in structural transformation, deformation, formation and annihilation in the scale of a few tens to several hundred Angstroms. (author)
Safronov, A.N.
2007-01-01
Full text: The pion-nucleon dynamics is one of the most fundamental problems in nuclear and particle physics. It is now widely believed that QCD is fundamental theory of strong interactions. On this basis all hadron-hadron interactions are completely determined by the underlying quark-gluon dynamics. However, due to the formidable mathematical problems raised by the non-perturbative character of QCD at low and intermediate energies, we are still far from a quantitative understanding hadron-hadron interactions from this point of view. Recently the relativistic approaches to constructing effective interaction operators between strongly interacting composite particles has been proposed on the basis of analytic S-matrix theory and methods for solving the inverse quantum scattering problem. The kernel of Marchenko equation in theory of inverse scattering problem can be expressed in terms of the discontinuity of the partial wave amplitude on dynamic cut in the complex s=k 2 plane, k being the relative momentum of colliding particles. The discontinuities of partial-wave amplitudes are determined by model-independent quantities (renormalized vertex constants and amplitudes of sub-processes involving on-mass-shell particles off physical region) and can be calculated by methods of relativistic quantum field theory within various dynamical approaches. In particular, effective field theory can be used to calculate the discontinuities across dynamical cuts closest to physical region. In present work a new manifestly Poincare-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. With the help of N/D-equations it was earlier shown that solution of a scattering problem in case of nonzero angular momentum does not exist for arbitrary discontinuity of partial-wave amplitude. The method is elaborated allowing to determine contributions of
Agamalian, M.M.; Alamo, R.G.; Londono, J.D.; Mandelkern, L.; Wignall, G.D.
1999-01-01
SANS experiments on blends of linear, high density (HD) and long chain branched, low density (LD) polyethylenes indicate that these systems form a one-phase mixture in the melt. However, the maximum spatial resolution of pinhole cameras is approximately equal to 10 3 and it has therefore been suggested that data might also be interpreted as arising from a bi-phasic melt with large a particle size ( 1 m), because most of the scattering from the different phases would not be resolved. We have addressed this hypothesis by means of USANS experiments, which confirm that HDPEILDPE blends are homogenous in the melt on length scales up to 20 m. We have also studied blends of HDPE and short-chain branched linear low density polyethylenes (LLDPEs), which phase separate when the branch content is sufficiently high. LLDPEs prepared with Ziegler-Natta catalysts exhibit a wide distribution of compositions, and may therefore be thought of as a blend of different species. When the composition distribution is broad enough, a fraction of highly branched chains may phase separate on m-length scales, and USANS has also been used to quantify this phenomenon
Libotte, Rafael Barbosa; Alves Filho, Hermes; Oliva, Amaury Muñoz
2017-01-01
The physical phenomenon of transport of neutral particles in a host environment is of interest in various scientific applications, e.g., nuclear reactors, shielding calculations, radiological protection, nuclear medicine, agronomy, materials science, oil prospecting, etc. In all these areas there is a need for an accurate description of the transport of the particles in the host medium. In this class of applications are the neutron shielding problems, also referred to as 'fixed-source' problems, where the interaction of the particles with the medium does not produce new neutrons, i.e., non-multiplicative medium. In this context, the development of tools that model these problems is relevant and of a beneficial return to society. In this work, we propose the development of deterministic mathematical and computational modeling of neutron transport using the linearized equation of Boltzmann applied to neutron shielding problems. Here we present also the development of a spectro-nodal method (coarse mesh) considering the scattering phenomenon as being linearly anisotropic. We show the results using a computational application, developed in Java language, version 1.8.0 9 1
Van Aert, S.; Chen, J.H.; Van Dyck, D.
2010-01-01
A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has
Migration of scattered teleseismic body waves
Bostock, M. G.; Rondenay, S.
1999-06-01
The retrieval of near-receiver mantle structure from scattered waves associated with teleseismic P and S and recorded on three-component, linear seismic arrays is considered in the context of inverse scattering theory. A Ray + Born formulation is proposed which admits linearization of the forward problem and economy in the computation of the elastic wave Green's function. The high-frequency approximation further simplifies the problem by enabling (1) the use of an earth-flattened, 1-D reference model, (2) a reduction in computations to 2-D through the assumption of 2.5-D experimental geometry, and (3) band-diagonalization of the Hessian matrix in the inverse formulation. The final expressions are in a form reminiscent of the classical diffraction stack of seismic migration. Implementation of this procedure demands an accurate estimate of the scattered wave contribution to the impulse response, and thus requires the removal of both the reference wavefield and the source time signature from the raw record sections. An approximate separation of direct and scattered waves is achieved through application of the inverse free-surface transfer operator to individual station records and a Karhunen-Loeve transform to the resulting record sections. This procedure takes the full displacement field to a wave vector space wherein the first principal component of the incident wave-type section is identified with the direct wave and is used as an estimate of the source time function. The scattered displacement field is reconstituted from the remaining principal components using the forward free-surface transfer operator, and may be reduced to a scattering impulse response upon deconvolution of the source estimate. An example employing pseudo-spectral synthetic seismograms demonstrates an application of the methodology.
Isomorphs in the phase diagram of a model liquid without inverse power law repulsion
Veldhorst, Arnold Adriaan; Bøhling, Lasse; Dyre, J. C.
2012-01-01
scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence...... the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does...... not depend critically on the mathematical form of the repulsion being an inverse power law....
A high-energy, high-flux source of gamma-rays from all-optical non-linear Thomson scattering
Corvan, D.J., E-mail: dcorvan01@qub.ac.uk; Zepf, M.; Sarri, G.
2016-09-01
γ-Ray sources are among the most fundamental experimental tools currently available to modern physics. As well as the obvious benefits to fundamental research, an ultra-bright source of γ-rays could form the foundation of scanning of shipping containers for special nuclear materials and provide the bases for new types of cancer therapy. However, for these applications to prove viable, γ-ray sources must become compact and relatively cheap to manufacture. In recent years, advances in laser technology have formed the cornerstone of optical sources of high energy electrons which already have been used to generate synchrotron radiation on a compact scale. Exploiting the scattering induced by a second laser, one can further enhance the energy and number of photons produced provided the problems of synchronisation and compact γ-ray detection are solved. Here, we report on the work that has been done in developing an all-optical and hence, compact non-linear Thomson scattering source, including the new methods of synchronisation and compact γ-ray detection. We present evidence of the generation of multi-MeV (maximum 16–18 MeV) and ultra-high brilliance (exceeding 10{sup 20} photons s{sup −1}mm{sup −2}mrad{sup −2} 0.1% BW at 15 MeV) γ-ray beams. These characteristics are appealing for the paramount practical applications mentioned above. - Highlights: • How synchrotron radiation can be produced in an all optical setting using laser-plasmas. • Generating high-energy, high-flux gamma ray beams. • Presenting results from a recent NLTS experimental campaign. • Reveal insight into the experimental techniques employed.
Ilieva, Stoyanka
2008-01-01
In the current experiment, the differential cross sections for proton elastic scattering on the isotopes 7,9,10,11,12,14 Be and 8 B were measured. As results from the experiment, the absolute differential cross sections dσ/dt as a function of the four momentum transfer t were obtained. In this work the differential cross sections for elastic p- 12 Be, p- 14 Be and p- 8 B scattering at low t (t≤0.05(GeV/c) 2 ) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The determined rms matter radius is 3.11±0.04±0.13 fm. In the case of the 12 Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of 2.82±0.03±0.12 fm was determined. An interesting result is that the free 12 Be nucleus behaves differently from the core of 14 Be and is much more extended than it. Preliminary experimental results for the isotope 8 B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is 2.60±0.02±0.26 fm. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented. (orig.)
Burkhard, N.R.
1979-01-01
The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables
The seismic reflection inverse problem
Symes, W W
2009-01-01
The seismic reflection method seeks to extract maps of the Earth's sedimentary crust from transient near-surface recording of echoes, stimulated by explosions or other controlled sound sources positioned near the surface. Reasonably accurate models of seismic energy propagation take the form of hyperbolic systems of partial differential equations, in which the coefficients represent the spatial distribution of various mechanical characteristics of rock (density, stiffness, etc). Thus the fundamental problem of reflection seismology is an inverse problem in partial differential equations: to find the coefficients (or at least some of their properties) of a linear hyperbolic system, given the values of a family of solutions in some part of their domains. The exploration geophysics community has developed various methods for estimating the Earth's structure from seismic data and is also well aware of the inverse point of view. This article reviews mathematical developments in this subject over the last 25 years, to show how the mathematics has both illuminated innovations of practitioners and led to new directions in practice. Two themes naturally emerge: the importance of single scattering dominance and compensation for spectral incompleteness by spatial redundancy. (topical review)
Scherer, Artur; Valiron, Benoît; Mau, Siun-Chuon; Alexander, Scott; van den Berg, Eric; Chapuran, Thomas E.
2017-03-01
We provide a detailed estimate for the logical resource requirements of the quantum linear-system algorithm (Harrow et al. in Phys Rev Lett 103:150502, 2009) including the recently described elaborations and application to computing the electromagnetic scattering cross section of a metallic target (Clader et al. in Phys Rev Lett 110:250504, 2013). Our resource estimates are based on the standard quantum-circuit model of quantum computation; they comprise circuit width (related to parallelism), circuit depth (total number of steps), the number of qubits and ancilla qubits employed, and the overall number of elementary quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set { X, Y, Z, H, S, T, { CNOT } }. In order to perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper quantum programming language and compiler. Our estimates pertain to the explicit example problem size N=332{,}020{,}680 beyond which, according to a crude big-O complexity comparison, the quantum linear-system algorithm is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy ɛ =0.01 requires an approximate circuit width 340 and circuit depth of order 10^{25} if oracle costs are excluded, and a circuit width and circuit depth of order 10^8 and 10^{29}, respectively, if the resource requirements of oracles are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly (using a fine-grained approach rather than relying on coarse big-O asymptotic approximations) how these impressively large numbers arise with an actual circuit implementation of a quantum algorithm. While our estimates may prove to be conservative as more efficient
Rutkevich, Sergei B; Diehl, H W
2015-06-01
The O(n) ϕ(4) model on a strip bounded by a pair of planar free surfaces at separation L can be solved exactly in the large-n limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the L=∞ semi-infinite case in the scaling regime for all values of the temperature scaling field t=(T-T(c))/T(c) above and below the bulk critical temperature T(c). These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of x=t(L/ξ(+))(1/ν) are determined for x→-∞. In addition, the asymptotic x→-∞ forms of the universal finite-size scaling functions Θ(x) and ϑ(x) of the residual free energy and the Casimir force are computed exactly to order 1/x, including their x(-1)ln|x| anomalies.
Namatame, Hirofumi; Taniguchi, Masaki
1994-01-01
Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)
Li, Mengkui; Zhang, Shuangxi; Bodin, Thomas; Lin, Xu; Wu, Tengfei
2018-06-01
Inversion of receiver functions is commonly used to recover the S-wave velocity structure beneath seismic stations. Traditional approaches are based on deconvolved waveforms, where the horizontal component of P-wave seismograms is deconvolved by the vertical component. Deconvolution of noisy seismograms is a numerically unstable process that needs to be stabilized by regularization parameters. This biases noise statistics, making it difficult to estimate uncertainties in observed receiver functions for Bayesian inference. This study proposes a method to directly invert observed radial waveforms and to better account for data noise in a Bayesian formulation. We illustrate its feasibility with two synthetic tests having different types of noises added to seismograms. Then, a real site application is performed to obtain the 1-D S-wave velocity structure beneath a seismic station located in the Tengchong volcanic area, Southwestern China. Surface wave dispersion measurements spanning periods from 8 to 65 s are jointly inverted with P waveforms. The results show a complex S-wave velocity structure, as two low velocity zones are observed in the crust and uppermost mantle, suggesting the existence of magma chambers, or zones of partial melt. The upper magma chambers may be the heart source that cause the thermal activity on the surface.
Zhan, Weijia; S. Rodrigues, Fabiano
2018-01-01
Previous studies have suggested that weakening downward plasma drifts can produce favorable conditions for the ionospheric Generalized Rayleigh-Taylor (GRT) instability and explain the occurrence of postmidnight equatorial spread F (ESF). We evaluated this hypothesis using numerical simulations aided by measurements and attempted to explain ESF events observed in the American sector during June solstice, low solar flux conditions. We analyzed plasma drifts and ESF measurements made by the incoherent scatter radar of the Jicamarca Radio Observatory (11.95° S, 76.87° W, ˜1° dip). We found adequate measurements during a prototypical, quiet time event on 4-5 June 2008 when the downward drifts weakened and a fully developed ESF appeared. The measured drifts were used as input for the SAMI2 model. SAMI2 reproduced an "apparent" uplift of the ionosphere based on h'F measurements that was consistent with expectations and observations. SAMI2 also provided parameters for estimation of the flux tube linear growth rates of GRT instability associated with the weakening drift event. We found that the weakening drifts did produce unstable conditions with positive growth rates. The growth rates, however, were slower than those obtained for typical, premidnight ESF events and those obtained for similar drift conditions in other longitude sectors. We show, however, that departures in the wind pattern, from climatological model predictions, can produce favorable conditions for instability development. Following the hypothesis of Huba and Krall (2013) and using SAMI2 simulations, we show that equatorward winds, when combined with weakening drifts, could have contributed to the unstable conditions responsible for the postmidnight ESF events.
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....
Inverse Monte Carlo: a unified reconstruction algorithm for SPECT
Floyd, C.E.; Coleman, R.E.; Jaszczak, R.J.
1985-01-01
Inverse Monte Carlo (IMOC) is presented as a unified reconstruction algorithm for Emission Computed Tomography (ECT) providing simultaneous compensation for scatter, attenuation, and the variation of collimator resolution with depth. The technique of inverse Monte Carlo is used to find an inverse solution to the photon transport equation (an integral equation for photon flux from a specified source) for a parameterized source and specific boundary conditions. The system of linear equations so formed is solved to yield the source activity distribution for a set of acquired projections. For the studies presented here, the equations are solved using the EM (Maximum Likelihood) algorithm although other solution algorithms, such as Least Squares, could be employed. While the present results specifically consider the reconstruction of camera-based Single Photon Emission Computed Tomographic (SPECT) images, the technique is equally valid for Positron Emission Tomography (PET) if a Monte Carlo model of such a system is used. As a preliminary evaluation, experimentally acquired SPECT phantom studies for imaging Tc-99m (140 keV) are presented which demonstrate the quantitative compensation for scatter and attenuation for a two dimensional (single slice) reconstruction. The algorithm may be expanded in a straight forward manner to full three dimensional reconstruction including compensation for out of plane scatter
Ingram, WT
2012-01-01
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen
Javier Hernádez Benítez
2012-12-01
Full Text Available In reactor design phase bubble column type (CBT is required to have the distribution of solids within the reactor. This distribution satisfies an ordinary differential equation (ODE of order two, with boundary conditions that was developed by D. R. Cova [2], followed by D. N. Smith and J. A. Ruether [8]. Some elements of this equation are given by correlations that depend on certain parameters that are unknown but may be obtained from experimental data. The methodology used to determine these parameters is the sub- piecewise linear underestimation developed by O. L. Mangasarian, J. B. Rosen, M. E. Thompson. // RESUMEN: En el diseño de reactores trifásicos tipo columna de burbujeo (CBT, se requiere tener la distribución de solidos dentro del reactor. Esta distribución satisface una ecuación diferencial ordinaria (EDO de orden dos, con condiciones de frontera que fue desarrollada por D. R. Cova [2], y posteriormente por D. N. Smith y J. A. Ruether [8]. Algunos elementos de esta ecuación están dados por correlaciones que dependen de ciertos parámetros que son desconocidos, pero se pueden obtener a partir de datos experimentales. La metodología utilizada para determinar dichos parámetros es la sub-estimación lineal a trozos desarrollada por O. L. Mangasarian, J. B. Rosen y M. E. Thompson.
Waveform inversion for acoustic VTI media in frequency domain
Wu, Zedong; Alkhalifah, Tariq Ali
2016-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong; Alkhalifah, Tariq Ali
2015-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
Ronchin, Erika; Masterlark, Timothy; Dawson, John; Saunders, Steve; Martí Molist, Joan
2015-04-01
In this study, we present a method to fully integrate a family of finite element models (FEMs) into the regularized linear inversion of InSAR data collected at Rabaul caldera (PNG) between February 2007 and December 2010. During this period the caldera experienced a long-term steady subsidence that characterized surface movement both inside the caldera and outside, on its western side. The inversion is based on an array of FEM sources in the sense that the Green's function matrix is a library of forward numerical displacement solutions generated by the sources of an array common to all FEMs. Each entry of the library is the LOS surface displacement generated by injecting a unity mass of fluid, of known density and bulk modulus, into a different source cavity of the array for each FEM. By using FEMs, we are taking advantage of their capability of including topography and heterogeneous distribution of elastic material properties. All FEMs of the family share the same mesh in which only one source is activated at the time by removing the corresponding elements and applying the unity fluid flux. The domain therefore only needs to be discretized once. This precludes remeshing for each activated source, thus reducing computational requirements, often a downside of FEM-based inversions. Without imposing an a-priori source, the method allows us to identify, from a least-squares standpoint, a complex distribution of fluid flux (or change in pressure) with a 3D free geometry within the source array, as dictated by the data. The results of applying the proposed inversion to Rabaul InSAR data show a shallow magmatic system under the caldera made of two interconnected lobes located at the two opposite sides of the caldera. These lobes could be consistent with feeding reservoirs of the ongoing Tavuvur volcano eruption of andesitic products, on the eastern side, and of the past Vulcan volcano eruptions of more evolved materials, on the western side. The interconnection and
Multiscattering inversion for low-model wavenumbers
Alkhalifah, Tariq Ali; Wu, Zedong
2016-01-01
A successful full-waveform inversion implementation updates the low-wavenumber model components first for a proper description of the wavefield propagation and slowly adds the high wavenumber potentially scattering parts of the model. The low
Inverse scale space decomposition
Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane
2018-01-01
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...
Inversion of the star transform
Zhao, Fan; Schotland, John C; Markel, Vadim A
2014-01-01
We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of conventional x-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically. (paper)
Multiscattering inversion for low-model wavenumbers
Alkhalifah, Tariq Ali
2016-09-21
A successful full-waveform inversion implementation updates the low-wavenumber model components first for a proper description of the wavefield propagation and slowly adds the high wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded wavefield emanating directly from the source or the transmission parts from the single- or double-scattered wavefield computed from a predicted scatter field acting as secondary sources.We use a combined inversion of data modeled from the source and those corresponding to single and double scattering to update the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering-angle filter is used to divide the gradient of the combined inversion, so initially the high-wavenumber (low-scattering-angle) components of the gradient are directed to the perturbation model and the low-wavenumber (highscattering- angle) components are directed to the velocity model. As our background velocity matures, the scatteringangle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model. Synthetic examples including the Marmousi model are used to demonstrate the additional illumination and improved velocity inversion obtained when including multiscattered energy. © 2016 Society of Exploration Geophysicists.
Merabet, H; Hanni, J; Bailey, M; Godunov, A L; McGuire, J H; Fursa, D V; Bray, I; Bartschat, K; Tseng, H C; Lin, C D
2003-01-01
Experimental scattering-angle-integrated (total) cross-sections sigma-bar, (scattering) angle-integrated magnetic sublevel cross-sections sigma-bar sub M sub sub L , and degree of linear polarization data have been measured in the extreme ultraviolet (EUV) wavelength region following decay of HeI (1snp) sup 1 P sup 0 (n=2-5) states induced by electron and proton impact on a neutral helium target. These measurements are compared with a first Born approach as well as more sophisticated theoretical calculations. Specifically, theoretical values for electron impact include convergent close-coupling (CCC) and R-matrix with pseudo states (RMPS) methods in addition to first Born (Born 1) approximation while proton induced excitation cross-sections are compared with atomic-orbital close-coupling (AOCC) and first Born predictions.
Inverse scattering problem for quantum graph vertices
Cheon, T.; Exner, Pavel; Turek, O.
2011-01-01
Roč. 83, č. 6 (2011), 062715/1-062715/4 ISSN 1050-2947 R&D Projects: GA MŠk LC06002; GA ČR GAP203/11/0701 Institutional research plan: CEZ:AV0Z10480505 Keywords : WIRES Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.878, year: 2011
Introduction to neutron scattering
Fischer, W E [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1996-11-01
We give here an introduction to the theoretical principles of neutron scattering. The relationship between scattering- and correlation-functions is particularly emphasized. Within the framework of linear response theory (justified by the weakness of the basic interaction) the relation between fluctuation and dissipation is discussed. This general framework explains the particular power of neutron scattering as an experimental method. (author) 4 figs., 4 refs.
Adaptive regularization of noisy linear inverse problems
Hansen, Lars Kai; Madsen, Kristoffer Hougaard; Lehn-Schiøler, Tue
2006-01-01
In the Bayesian modeling framework there is a close relation between regularization and the prior distribution over parameters. For prior distributions in the exponential family, we show that the optimal hyper-parameter, i.e., the optimal strength of regularization, satisfies a simple relation: T......: The expectation of the regularization function, i.e., takes the same value in the posterior and prior distribution. We present three examples: two simulations, and application in fMRI neuroimaging....
An accurate solver for forward and inverse transport
Monard, Francois; Bal, Guillaume
2010-01-01
This paper presents a robust and accurate way to solve steady-state linear transport (radiative transfer) equations numerically. Our main objective is to address the inverse transport problem, in which the optical parameters of a domain of interest are reconstructed from measurements performed at the domain's boundary. This inverse problem has important applications in medical and geophysical imaging, and more generally in any field involving high frequency waves or particles propagating in scattering environments. Stable solutions of the inverse transport problem require that the singularities of the measurement operator, which maps the optical parameters to the available measurements, be captured with sufficient accuracy. This in turn requires that the free propagation of particles be calculated with care, which is a difficult problem on a Cartesian grid. A standard discrete ordinates method is used for the direction of propagation of the particles. Our methodology to address spatial discretization is based on rotating the computational domain so that each direction of propagation is always aligned with one of the grid axes. Rotations are performed in the Fourier domain to achieve spectral accuracy. The numerical dispersion of the propagating particles is therefore minimal. As a result, the ballistic and single scattering components of the transport solution are calculated robustly and accurately. Physical blurring effects, such as small angular diffusion, are also incorporated into the numerical tool. Forward and inverse calculations performed in a two-dimensional setting exemplify the capabilities of the method. Although the methodology might not be the fastest way to solve transport equations, its physical accuracy provides us with a numerical tool to assess what can and cannot be reconstructed in inverse transport theory.
Subhash, P V; Madhavan, S; Chaturvedi, S
2008-01-01
Two-dimensional (2D) magneto-hydrodynamic (MHD) liner-on-plasma computations have been performed to study the growth of instabilities in a magnetized target fusion system involving the cylindrical compression of an inverse Z-pinch target plasma by a metallic liner. The growth of modes in the plasma can be divided into two phases. During the first phase, the plasma continues to be Kadomtsev stable. The dominant mode in the liner instability is imposed upon the plasma in the form of a growing perturbation. This mode further transfers part of its energy to its harmonics. During the second phase, however, non-uniform implosion of the liner leads to axial variations in plasma quantities near the liner-plasma interface, such that certain regions of the plasma locally violate the Kadomtsev criteria. Further growth ofthe plasma modes is then due to plasma instability. The above numerical study has been complemented with a linear stability analysis for the plasma, the boundary conditions for this analysis being obtained from the liner-on-plasma simulation. The stability of axisymmetric modes in the first phase is found to satisfy the Kadomtsev condition Q 0 1 modes, using equilibrium profiles from the 2D MHD study, shows that their growth rates can exceed those for m=0 by as much as an order of magnitude
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
Classical theory of atom-surface scattering: The rainbow effect
Miret-Artés, Salvador; Pollak, Eli
2012-07-01
The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.
Joel Sereno
2010-01-01
Full Text Available Inverse kinematics is the process of converting a Cartesian point in space into a set of joint angles to more efficiently move the end effector of a robot to a desired orientation. This project investigates the inverse kinematics of a robotic hand with fingers under various scenarios. Assuming the parameters of a provided robot, a general equation for the end effector point was calculated and used to plot the region of space that it can reach. Further, the benefits obtained from the addition of a prismatic joint versus an extra variable angle joint were considered. The results confirmed that having more movable parts, such as prismatic points and changing angles, increases the effective reach of a robotic hand.
Hesford, Andrew J.; Waag, Robert C.
2010-10-01
The fast multipole method (FMM) is applied to the solution of large-scale, three-dimensional acoustic scattering problems involving inhomogeneous objects defined on a regular grid. The grid arrangement is especially well suited to applications in which the scattering geometry is not known a priori and is reconstructed on a regular grid using iterative inverse scattering algorithms or other imaging techniques. The regular structure of unknown scattering elements facilitates a dramatic reduction in the amount of storage and computation required for the FMM, both of which scale linearly with the number of scattering elements. In particular, the use of fast Fourier transforms to compute Green's function convolutions required for neighboring interactions lowers the often-significant cost of finest-level FMM computations and helps mitigate the dependence of FMM cost on finest-level box size. Numerical results demonstrate the efficiency of the composite method as the number of scattering elements in each finest-level box is increased.
Desesquelles, P.
1997-01-01
Computer Monte Carlo simulations occupy an increasingly important place between theory and experiment. This paper introduces a global protocol for the comparison of model simulations with experimental results. The correlated distributions of the model parameters are determined using an original recursive inversion procedure. Multivariate analysis techniques are used in order to optimally synthesize the experimental information with a minimum number of variables. This protocol is relevant in all fields if physics dealing with event generators and multi-parametric experiments. (authors)
Algebraic properties of generalized inverses
Cvetković‐Ilić, Dragana S
2017-01-01
This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, Ph...
Bayesian seismic AVO inversion
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
Waveform inversion for acoustic VTI media in frequency domain
Wu, Zedong
2016-09-06
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current RWI methods are mostly based on isotropic media assumption. We extend the idea of the combining inversion for the background model and perturbations to address transversely isotropic with a vertical axis of symmetry (VTI) media taking into consideration of the optimal parameter sensitivity information. As a result, we apply Born modeling corresponding to perturbations in only for the variable e to derive the relative reflected waveform inversion formulation. To reduce the number of parameters, we assume the background part of η = ε and work with a single variable to describe the anisotropic part of the wave propagation. Thus, the optimization variables are the horizontal velocity v, η = ε and the e perturbation. Application to the anisotropic version of Marmousi model with a single frequency of 2.5 Hz shows that this method can converge to the accurate result starting from a linearly increasing isotropic initial velocity. Application to a real dataset demonstrates the versatility of the approach.
Full waveform inversion for time-distance helioseismology
Hanasoge, Shravan M.; Tromp, Jeroen
2014-01-01
Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L 2 norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.
2.5D Inversion Algorithm of Frequency-Domain Airborne Electromagnetics with Topography
Jianjun Xi
2016-01-01
Full Text Available We presented a 2.5D inversion algorithm with topography for frequency-domain airborne electromagnetic data. The forward modeling is based on edge finite element method and uses the irregular hexahedron to adapt the topography. The electric and magnetic fields are split into primary (background and secondary (scattered field to eliminate the source singularity. For the multisources of frequency-domain airborne electromagnetic method, we use the large-scale sparse matrix parallel shared memory direct solver PARDISO to solve the linear system of equations efficiently. The inversion algorithm is based on Gauss-Newton method, which has the efficient convergence rate. The Jacobian matrix is calculated by “adjoint forward modelling” efficiently. The synthetic inversion examples indicated that our proposed method is correct and effective. Furthermore, ignoring the topography effect can lead to incorrect results and interpretations.
Inverse problem in nuclear physics
Zakhariev, B.N.
1976-01-01
The method of reconstruction of interaction from the scattering data is formulated in the frame of the R-matrix theory in which the potential is determined by position of resonance Esub(lambda) and their reduced widths γ 2 lambda. In finite difference approximation for the Schroedinger equation this new approach allows to make the logics of the inverse problem IP more clear. A possibility of applications of IP formalism to various nuclear systems is discussed. (author)
Probabilistic inversion in priority setting of emerging zoonoses.
Kurowicka, D.; Bucura, C.; Cooke, R.; Havelaar, A.H.
2010-01-01
This article presents methodology of applying probabilistic inversion in combination with expert judgment in priority setting problem. Experts rank scenarios according to severity. A linear multi-criteria analysis model underlying the expert preferences is posited. Using probabilistic inversion, a
Statistical perspectives on inverse problems
Andersen, Kim Emil
of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...
Gupta, Sandesh K; Jain, Amit; Bednarek, Daniel R; Rudin, Stephen
2011-01-01
In this study, we evaluated the imaging characteristics of the high-resolution, high-sensitivity micro-angiographic fluoroscope (MAF) with 35-micron pixel-pitch when used with different commercially-available 300 micron thick phosphors: the high resolution (HR) and high light (HL) from Hamamatsu. The purpose of this evaluation was to see if the HL phosphor with its higher screen efficiency could be replaced with the HR phosphor to achieve improved resolution without an increase in noise resulting from the HR's decreased light-photon yield. We designated the detectors MAF-HR and MAF-HL and compared them with a standard flat panel detector (FPD) (194 micron pixel pitch and 600 micron thick CsI(Tl)). For this comparison, we used the generalized linear-system metrics of GMTF, GNNPS and GDQE which are more realistic measures of total system performance since they include the effect of scattered radiation, focal spot distribution, and geometric un-sharpness. Magnifications (1.05-1.15) and scatter fractions (0.28 and 0.33) characteristic of a standard head phantom were used. The MAF-HR performed significantly better than the MAF-HL at high spatial frequencies. The ratio of GMTF and GDQE of the MAF-HR compared to the MAF-HL at 3(6) cycles/mm was 1.45(2.42) and 1.23(2.89), respectively. Despite significant degradation by inclusion of scatter and object magnification, both MAF-HR and MAF-HL provide superior performance over the FPD at higher spatial frequencies with similar performance up to the FPD's Nyquist frequency of 2.5 cycles/mm. Both substantially higher resolution and improved GDQE can be achieved with the MAF using the HR phosphor instead of the HL phosphor.
Liu, K M; Juang, C H; Hsu, S Y [Department of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan (China); Umansky, V, E-mail: syhsu@mail.nctu.edu.t [Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot 76100 (Israel)
2010-10-06
We have studied the linear conductance and source-drain bias spectroscopies of clean and disordered quantum wires (QWs) against thermal cycling and lateral shifting, which change the impurity configuration. Conductance quantization and the zero bias anomaly (ZBA) are robust in clean QWs. In contrast, disordered QWs show complexities in the ways of conductance resonance, peak splitting and trace crossing in source-drain bias spectroscopies. The experimental results and theoretical predictions are in congruence. Moreover, the resonant state arising from the impurities results in either a single peak or double-splitting peaks in the spectroscopies from the detailed impurity configurations. The resonant splitting peaks are found to influence the ZBA, indicating that a clean QW is crucial for investigating the intrinsic characteristics of the ZBA of QWs.
Liu, K M; Juang, C H; Hsu, S Y; Umansky, V
2010-01-01
We have studied the linear conductance and source-drain bias spectroscopies of clean and disordered quantum wires (QWs) against thermal cycling and lateral shifting, which change the impurity configuration. Conductance quantization and the zero bias anomaly (ZBA) are robust in clean QWs. In contrast, disordered QWs show complexities in the ways of conductance resonance, peak splitting and trace crossing in source-drain bias spectroscopies. The experimental results and theoretical predictions are in congruence. Moreover, the resonant state arising from the impurities results in either a single peak or double-splitting peaks in the spectroscopies from the detailed impurity configurations. The resonant splitting peaks are found to influence the ZBA, indicating that a clean QW is crucial for investigating the intrinsic characteristics of the ZBA of QWs.
Sanchez, Richard.
1975-04-01
For the one-dimensional geometries, the transport equation with linearly anisotropic scattering can be reduced to a single integral equation; this is a singular-kernel FREDHOLM equation of the second kind. When applying a conventional projective method that of GALERKIN, to the solution of this equation the well-known collision probability algorithm is obtained. Piecewise polynomial expansions are used to represent the flux. In the ANILINE code, the flux is supposed to be linear in plane geometry and parabolic in both cylindrical and spherical geometries. An integral relationship was found between the one-dimensional isotropic and anisotropic kernels; this allows to reduce the new matrix elements (issuing from the anisotropic kernel) to classic collision probabilities of the isotropic scattering equation. For cylindrical and spherical geometries used an approximate representation of the current was used to avoid an additional numerical integration. Reflective boundary conditions were considered; in plane geometry the reflection is supposed specular, for the other geometries the isotropic reflection hypothesis has been adopted. Further, the ANILINE code enables to deal with an incoming isotropic current. Numerous checks were performed in monokinetic theory. Critical radii and albedos were calculated for homogeneous slabs, cylinders and spheres. For heterogeneous media, the thermal utilization factor obtained by this method was compared with the theoretical result based upon a formula by BENOIST. Finally, ANILINE was incorporated into the multigroup APOLLO code, which enabled to analyse the MINERVA experimental reactor in transport theory with 99 groups. The ANILINE method is particularly suited to the treatment of strongly anisotropic media with considerable flux gradients. It is also well adapted to the calculation of reflectors, and in general, to the exact analysis of anisotropic effects in large-sized media [fr
Inverse Faraday Effect Revisited
Mendonça, J. T.; Ali, S.; Davies, J. R.
2010-11-01
The inverse Faraday effect is usually associated with circularly polarized laser beams. However, it was recently shown that it can also occur for linearly polarized radiation [1]. The quasi-static axial magnetic field by a laser beam propagating in plasma can be calculated by considering both the spin and the orbital angular momenta of the laser pulse. A net spin is present when the radiation is circularly polarized and a net orbital angular momentum is present if there is any deviation from perfect rotational symmetry. This orbital angular momentum has recently been discussed in the plasma context [2], and can give an additional contribution to the axial magnetic field, thus enhancing or reducing the inverse Faraday effect. As a result, this effect that is usually attributed to circular polarization can also be excited by linearly polarized radiation, if the incident laser propagates in a Laguerre-Gauss mode carrying a finite amount of orbital angular momentum.[4pt] [1] S. ALi, J.R. Davies and J.T. Mendonca, Phys. Rev. Lett., 105, 035001 (2010).[0pt] [2] J. T. Mendonca, B. Thidé, and H. Then, Phys. Rev. Lett. 102, 185005 (2009).
Finite-dimensional linear algebra
Gockenbach, Mark S
2010-01-01
Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq
Muralidhar K
2007-01-01
Full Text Available Measurements designed to find the collimator backscatter into the beam monitor chamber from Micro Multileaf collimator of 6 MV photon beams of the Siemens Primus linear accelerator were made with the help of dose rate feedback control. The photons and electrons backscattered from the upper and lower secondary collimator jaws give rise to a significant increase in the ion charge measured by monitor chamber. This increase varies between the different accelerators. The output measurements were carried out in air at the isocenter. The effect of collimator backscatter was investigated by measuring the pulse width, number of beam pulses per monitor unit, monitor unit rate and dose for different mMLC openings. These measurements were made with and without dose rate feedback control, i.e., with constant electron beam current in the accelerator. Monitor unit rate (MU/min was almost constant for all field sizes. The maximum variation between the open and the closed feedback control circuits was 2.5%. There was no difference in pulse width and negligible difference in pulse frequency. Maximum value of backscattered radiation from the micro Multileaf collimator into the beam monitor chamber was found to be 0.5%.
Full waveform inversion using envelope-based global correlation norm
Oh, Juwon
2018-01-28
Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.
Shcherbakov, Alexandre S; Arellanes, Adan Omar
2017-12-01
During subsequent development of the recently proposed multi-frequency parallel spectrometer for precise spectrum analysis of wideband radio-wave signals, we study potentials of new acousto-optical cells exploiting selected crystalline materials at the limits of their capabilities. Characterizing these wide-aperture cells is non-trivial due to new features inherent in the chosen regime of an advanced non-collinear one-phonon anomalous light scattering by elastic waves with significantly elevated acoustic losses. These features can be observed simpler in uniaxial, tetragonal, and trigonal crystals possessing linear acoustic attenuation. We demonstrate that formerly studied additional degree of freedom, revealed initially for multi-phonon regimes of acousto-optical interaction, can be identified within the one-phonon geometry as well and exploited for designing new cells. We clarify the role of varying the central acoustic frequency and acoustic attenuation using the identified degree of freedom. Therewith, we are strongly restricted by a linear regime of acousto-optical interaction to avoid the origin of multi-phonon processes within carrying out a multi-frequency parallel spectrum analysis of radio-wave signals. Proof-of-principle experiments confirm the developed approaches and illustrate their applicability to innovative technique for an advanced spectrum analysis of wideband radio-wave signals with the improved resolution in an extended frequency range.
Inverse Raman effect: applications and detection techniques
Hughes, L.J. Jr.
1980-08-01
The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented
Inverse Raman effect: applications and detection techniques
Hughes, L.J. Jr.
1980-08-01
The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented.
Inverse m-matrices and ultrametric matrices
Dellacherie, Claude; San Martin, Jaime
2014-01-01
The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.
Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I
2017-01-01
This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.
Optimization for nonlinear inverse problem
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
The possibilities of least-squares migration of internally scattered seismic energy
Aldawood, Ali
2015-05-26
Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.
The possibilities of least-squares migration of internally scattered seismic energy
Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad; Turkiyyah, George; Alkhalifah, Tariq Ali
2015-01-01
Approximate images of the earth’s subsurface structures are usually obtained by migrating surface seismic data. Least-squares migration, under the single-scattering assumption, is used as an iterative linearized inversion scheme to suppress migration artifacts, deconvolve the source signature, mitigate the acquisition fingerprint, and enhance the spatial resolution of migrated images. The problem with least-squares migration of primaries, however, is that it may not be able to enhance events that are mainly illuminated by internal multiples, such as vertical and nearly vertical faults or salt flanks. To alleviate this problem, we adopted a linearized inversion framework to migrate internally scattered energy. We apply the least-squares migration of first-order internal multiples to image subsurface vertical fault planes. Tests on synthetic data demonstrated the ability of the proposed method to resolve vertical fault planes, which are poorly illuminated by the least-squares migration of primaries only. The proposed scheme is robust in the presence of white Gaussian observational noise and in the case of imaging the fault planes using inaccurate migration velocities. Our results suggested that the proposed least-squares imaging, under the double-scattering assumption, still retrieved the vertical fault planes when imaging the scattered data despite a slight defocusing of these events due to the presence of noise or velocity errors.
Evolution of the transfer function characterization of surface scatter phenomena
Harvey, James E.; Pfisterer, Richard N.
2016-09-01
Based upon the empirical observation that BRDF measurements of smooth optical surfaces exhibited shift-invariant behavior when plotted versus o , the original Harvey-Shack (OHS) surface scatter theory was developed as a scalar linear systems formulation in which scattered light behavior was characterized by a surface transfer function (STF) reminiscent of the optical transfer function (OTF) of modern image formation theory (1976). This shift-invariant behavior combined with the inverse power law behavior when plotting log BRDF versus log o was quickly incorporated into several optical analysis software packages. Although there was no explicit smooth-surface approximation in the OHS theory, there was a limitation on both the incident and scattering angles. In 1988 the modified Harvey-Shack (MHS) theory removed the limitation on the angle of incidence; however, a moderate-angle scattering limitation remained. Clearly for large incident angles the BRDF was no longer shift-invariant as a different STF was now required for each incident angle. In 2011 the generalized Harvey-Shack (GHS) surface scatter theory, characterized by a two-parameter family of STFs, evolved into a practical modeling tool to calculate BRDFs from optical surface metrology data for situations that violate the smooth surface approximation inherent in the Rayleigh-Rice theory and/or the moderate-angle limitation of the Beckmann-Kirchhoff theory. And finally, the STF can be multiplied by the classical OTF to provide a complete linear systems formulation of image quality as degraded by diffraction, geometrical aberrations and surface scatter effects from residual optical fabrication errors.
FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems
Vourc'h, Eric; Rodet, Thomas
2015-11-01
, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.
FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)
2014-10-01
workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet
Mafra Neto, F.
1992-01-01
The dose of gamma radiation from a linear source of cesium 137 is obtained, presenting two difficulties: oblique filtration of radiation when cross the platinum wall, in different directions, and dose connection due to the scattering by the material mean of propagation. (C.G.C.)
Gravitational scattering of electromagnetic radiation
Brooker, J. T.; Janis, A. I.
1980-01-01
The scattering of electromagnetic radiation by linearized gravitational fields is studied to second order in a perturbation expansion. The incoming electromagnetic radiation can be of arbitrary multipole structure, and the gravitational fields are also taken to be advanced fields of arbitrary multipole structure. All electromagnetic multipole radiation is found to be scattered by gravitational monopole and time-varying dipole fields. No case has been found, however, in which any electromagnetic multipole radiation is scattered by gravitational fields of quadrupole or higher-order multipole structure. This lack of scattering is established for infinite classes of special cases, and is conjectured to hold in general. The results of the scattering analysis are applied to the case of electromagnetic radiation scattered by a moving mass. It is shown how the mass and velocity may be determined by a knowledge of the incident and scattered radiation.
A hybrid Scatter/Transform cloaking model
Gad Licht
2015-01-01
Full Text Available A new Scatter/Transform cloak is developed that combines the light bending of refraction characteristic of a Transform cloak with the scatter cancellation characteristic of a Scatter cloak. The hybrid cloak incorporates both Transform’s variable index of refraction with modified linear intrusions to maximize the Scatter cloak effect. Scatter/Transform improved the scattering cross-section of cloaking in a 2-dimensional space to 51.7% compared to only 39.6% or 45.1% respectively with either Scatter or Transform alone. Metamaterials developed with characteristics based on the new ST hybrid cloak will exhibit superior cloaking capabilities.
Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao
2018-01-01
Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the
Ilieva, Stoyanka
2008-07-01
In the current experiment, the differential cross sections for proton elastic scattering on the isotopes {sup 7,9,10,11,12,14}Be and {sup 8}B were measured. As results from the experiment, the absolute differential cross sections d{sigma}/dt as a function of the four momentum transfer t were obtained. In this work the differential cross sections for elastic p-{sup 12}Be, p-{sup 14}Be and p-{sup 8}B scattering at low t (t{<=}0.05(GeV/c){sup 2}) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The determined rms matter radius is 3.11{+-}0.04{+-}0.13 fm. In the case of the {sup 12}Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of 2.82{+-}0.03{+-}0.12 fm was determined. An interesting result is that the free {sup 12}Be nucleus behaves differently from the core of {sup 14}Be and is much more extended than it. Preliminary experimental results for the isotope {sup 8}B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is 2.60{+-}0.02{+-}0.26 fm. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented. (orig.)
Time-independent inverse compton spectrum for photons from a ...
The general theoretical aspects of inverse Compton scattering was investigated and an equation for the timeindependent inverse Compton spectrum for photons from a plasma cloud of finite extent was derived. This was done by convolving the Kompaneets equation used for describing the evolution of the photon spectrum ...
Level set methods for inverse scattering—some recent developments
Dorn, Oliver; Lesselier, Dominique
2009-01-01
We give an update on recent techniques which use a level set representation of shapes for solving inverse scattering problems, completing in that matter the exposition made in (Dorn and Lesselier 2006 Inverse Problems 22 R67) and (Dorn and Lesselier 2007 Deformable Models (New York: Springer) pp 61–90), and bringing it closer to the current state of the art
Liu, Xiaodong
2017-08-01
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.
Alzahrani, Hani Ataiq
2014-09-01
ABSTRACT Testing the Feasibility of Using PERM to Apply Scattering-Angle Filtering in the Image-Domain for FWI Applications Hani Ataiq Alzahrani Full Waveform Inversion (FWI) is a non-linear optimization problem aimed to estimating subsurface parameters by minimizing the mis t between modeled and recorded seismic data using gradient descent methods, which are the only practical choice because of the size of the problem. Due to the high non-linearity of the problem, gradient methods will converge to a local minimum if the starting model is not close to the true one. The accuracy of the long-wavelength components of the initial model controls the level of non-linearity of the inversion. In order for FWI to converge to the global minimum, we have to obtain the long wavelength components of the model before inverting for the short wavelengths. Ultra-low temporal frequencies are sensitive to the smooth (long wavelength) part of the model, and can be utilized by waveform inversion to resolve that part. Un- fortunately, frequencies in this range are normally missing in eld data due to data- acquisition limitations. The lack of low frequencies can be compensated for by uti- lizing wide-aperture data, as they include arrivals that are especially sensitive to the long wavelength components of the model. The higher the scattering angle of a 5 recorded event, the higher the model wavelength it can resolve. Based on this prop- erty, a scattering-angle ltering algorithm is proposed to start the inversion process with events corresponding to the highest scattering angle available in the data, and then include lower scattering angles progressively. The large scattering angles will resolve the smooth part of the model and reduce the non-linearity of the problem, then the lower ones will enhance the resolution of the model. Recorded data is rst migrated using Pre-stack Exploding Re ector Migration (PERM), then the resulting pre-stack image is transformed into angle gathers to which
inverse correction of fourier transforms for one-dimensional strongly ...
Hsin Ying-Fei
2016-05-01
May 1, 2016 ... As it is widely used in periodic lattice design theory and is particularly useful in aperiodic lattice design [12,13], the accuracy of the FT algorithm under strong scattering conditions is the focus of this paper. We propose an inverse correction approach for the inaccurate FT algorithm in strongly scattering ...
Vector boson scattering at CLIC
Kilian, Wolfgang; Fleper, Christian [Department Physik, Universitaet Siegen, 57068 Siegen (Germany); Reuter, Juergen [DESY Theory Group, 22603 Hamburg (Germany); Sekulla, Marco [Institut fuer Theoretische Physik, Karlsruher Institut fuer Technologie, 76131 Karlsruhe (Germany)
2016-07-01
Linear colliders operating in a range of multiple TeV are able to investigate the details of vector boson scattering and electroweak symmetry breaking. We calculate cross sections with the Monte Carlo generator WHIZARD for vector boson scattering processes at the future linear e{sup +} e{sup -} collider CLIC. By finding suitable cuts, the vector boson scattering signal processes are isolated from the background. Finally, we are able to determine exclusion sensitivities on the non-Standard Model parameters of the relevant dimension eight operators.
Effects of the electron's anomaly in relativistic laser-assisted Mott scattering
Ngoko Djiokap, J.M.; Tetchou Nganso, H.M.; Kwato Njock, M.G.
2006-02-01
We investigate the influence of the electron's anomalous magnetic moment on the process of relativistic Mott scattering in a powerful electromagnetic plane wave for which the ponderomotive energy is of the order of the magnitude of the electron's rest mass. For this purpose, we use the Coulomb-Dirac-Volkov and the Dirac-Volkov functions with the electron's anomaly to describe the initial and final states respectively. First-order Born differential cross sections of induced and inverse bremsstrahlung are obtained for linearly polarized laser light. Numerical calculations are carried out for various parameters values (i.e. scattering angle, the nucleus charge, photon energy, electrical field) and are compared with results obtained by Li et al. It is found that for parameters used in the present work, incorporating the anomaly of the electron in the initial and final states yields cross sections which are strongly modified whatever the scattering geometry, as compared to the outcome of the previous treatment. (author)
Non-linear wave equations:Mathematical techniques
1978-01-01
An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es
Full-model wavenumber inversion: An emphasis on the appropriate wavenumber continuation
Alkhalifah, Tariq Ali
2016-04-06
A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7 Hz muted out further validated the versatility of the scattering angle filtering.
Full-model wavenumber inversion: An emphasis on the appropriate wavenumber continuation
Alkhalifah, Tariq Ali
2016-01-01
A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7 Hz muted out further validated the versatility of the scattering angle filtering.
An inverse method for radiation transport
Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)
2004-01-01
Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.
A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion
CUI, C.; Hou, W.
2017-12-01
Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.
Electron scattering off hydrogen and deuterium at 500 and 600
Atwood, W.B.
1975-06-01
The inelastic scattering of electrons for both protons and neutrons has been measured at scattering angles of fifty and sixty degrees and for incident energies between 6.5 GeV and 19.5 GeV. Elastic scattering from protons was also observed. The measurements were made at the Stanford Linear Accelerator Center using the 1.6-GeV spectrometer located in End Station A. The experimental techniques used in making the measurements are detailed. The resulting cross sections are large, indicative of a charged point-like substructure within the nucleon and match the extrapolation from previous measurements to the kinematic region to within forty percent. The measurements are found to be compatible with some existing theoretical expectations. The W 1 structure function is not found to ''scale'' in previously suggested scaling variables. The introduction of propagator scale breaking is investigated and shown to be compatible with the measurements. An alternative scaling variable is proposed in which W 1 is found to scale. The elastic scattering measurements are consistent with an inverse fourth power dependence on four-momenta transfer. The measured neutron-proton ratio is in agreement with previous measurements. (55 figures, 27 tables) (auth)
Recurrent Neural Network for Computing Outer Inverse.
Živković, Ivan S; Stanimirović, Predrag S; Wei, Yimin
2016-05-01
Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural networks is based on the matrix-valued differential equation, a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion, the Moore-Penrose inversion, as well as the Drazin inversion, under the condition of zero initial state. The application of the first approach is conditioned by the properties of the spectrum of a certain matrix; the second approach eliminates this drawback, though at the cost of increasing the number of matrix operations. The cases corresponding to the most common generalized inverses are defined. The conditions that ensure stability of the proposed neural network are presented. Illustrative examples present the results of numerical simulations.
Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Polivanov, M.C.
1993-01-01
The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. The authors demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schroedinger equation as an example, it is shown that all types of solutions of the linear problem, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated. 7 refs
Hategan, Cornel; Comisel, Horia; Ionescu, Remus A.
2004-01-01
The quasiresonant scattering consists from a single channel resonance coupled by direct interaction transitions to some competing reaction channels. A description of quasiresonant Scattering, in terms of generalized reduced K-, R- and S- Matrix, is developed in this work. The quasiresonance's decay width is, due to channels coupling, smaller than the width of the ancestral single channel resonance (resonance's direct compression). (author)
Donne, A. J. H.
1994-01-01
Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is
Advanced linear algebra for engineers with Matlab
Dianat, Sohail A
2009-01-01
Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu
Scattered X-ray beam nondestructive testing
Harding, G.; Kosanetzky, J.
1988-01-01
X-ray scatter interactions generally dominate the linear attenuation coefficient at the photon energies typical of medical and industrial radiography. Specific advantages of X-ray scatter imaging, including a flexible choice of measurement geometry, direct 3D-imaging capability (tomography) and improved information for material characterization, are illustrated with results from Compton and coherent scatter devices. Applications of a Compton backscatter scanner (ComScan) in the aerospace industry and coherent scatter imaging in security screening are briefly considered [pt
Podgornova, O.; Leaney, S.; Liang, L.
2018-03-01
Extracting medium properties from seismic data faces some limitations due to the finite frequency content of the data and restricted spatial positions of the sources and receivers. Some distributions of the medium properties make low impact on the data (including none). If these properties are used as the inversion parameters, then the inverse problem becomes over-parametrized, leading to ambiguous results. We present an analysis of multiparameter resolution for the linearized inverse problem in the framework of elastic full-waveform inversion. We show that the spatial and multiparameter sensitivities are intertwined and non-sensitive properties are spatial distributions of some non-trivial combinations of the conventional elastic parameters. The analysis accounts for the Hessian information and frequency content of the data; it is semi-analytical (in some scenarios analytical), easy to interpret, and enhances results of the widely used radiation pattern analysis. Single-type scattering is shown to have limited sensitivity, even for full-aperture data. Finite-frequency data lose multiparameter sensitivity at smooth and fine spatial scales. Also, we establish ways to quantify a spatial-multiparameter coupling and demonstrate that the theoretical predictions agree well with the numerical results.
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Amos, K.; Allen, L.J.; Steward, C.; Hodgson, P.E.; Sofianos, S.A.
1995-01-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs
Amos, K.; Allen, L.J.; Steward, C. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Hodgson, P.E. [Oxford Univ. (United Kingdom). Dept. of Physics; Sofianos, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics
1995-10-01
Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs.
Hatch, Andrew G; Smith, Ralph C; De, Tathagata; Salapaka, Murti V
2005-01-01
.... In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear...
Induced Compton scattering effects in radiation transport approximations
Gibson, D.R. Jr.
1982-01-01
In this thesis the method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions
Induced Compton-scattering effects in radiation-transport approximations
Gibson, D.R. Jr.
1982-02-01
The method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions
Stirling, W.G.; Perry, S.C.
1996-01-01
We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO 3 is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs
Time-dependent angularly averaged inverse transport
Bal, Guillaume; Jollivet, Alexandre
2009-01-01
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. Such measurement settings find applications in medical and geophysical imaging. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain
Acute puerperal uterine inversion
Hussain, M.; Liaquat, N.; Noorani, K.; Bhutta, S.Z; Jabeen, T.
2004-01-01
Objective: To determine the frequency, causes, clinical presentations, management and maternal mortality associated with acute puerperal inversion of the uterus. Materials and Methods: All the patients who developed acute puerperal inversion of the uterus either in or outside the JPMC were included in the study. Patients of chronic uterine inversion were not included in the present study. Abdominal and vaginal examination was done to confirm and classify inversion into first, second or third degrees. Results: 57036 deliveries and 36 acute uterine inversions occurred during the study period, so the frequency of uterine inversion was 1 in 1584 deliveries. Mismanagement of third stage of labour was responsible for uterine inversion in 75% of patients. Majority of the patients presented with shock, either hypovolemic (69%) or neurogenic (13%) in origin. Manual replacement of the uterus under general anaesthesia with 2% halothane was successfully done in 35 patients (97.5%). Abdominal hysterectomy was done in only one patient. There were three maternal deaths due to inversion. Conclusion: Proper education and training regarding placental delivery, diagnosis and management of uterine inversion must be imparted to the maternity care providers especially to traditional birth attendants and family physicians to prevent this potentially life-threatening condition. (author)
General inverse problems for regular variation
Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan
2014-01-01
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...
Kimura, W.D.
1993-01-01
The final report describes work performed to investigate inverse Cherenkov acceleration (ICA) as a promising method for laser particle acceleration. In particular, an improved configuration of ICA is being tested in a experiment presently underway on the Accelerator Test Facility (ATF). In the experiment, the high peak power (∼ 10 GW) linearly polarized ATF CO 2 laser beam is converted to a radially polarized beam. This is beam is focused with an axicon at the Cherenkov angle onto the ATF 50-MeV e-beam inside a hydrogen gas cell, where the gas acts as the phase matching medium of the interaction. An energy gain of ∼12 MeV is predicted assuming a delivered laser peak power of 5 GW. The experiment is divided into two phases. The Phase I experiments, which were completed in the spring of 1992, were conducted before the ATF e-beam was available and involved several successful tests of the optical systems. Phase II experiments are with the e-beam and laser beam, and are still in progress. The ATF demonstrated delivery of the e-beam to the experiment in Dec. 1992. A preliminary ''debugging'' run with the e-beam and laser beam occurred in May 1993. This revealed the need for some experimental modifications, which have been implemented. The second run is tentatively scheduled for October or November 1993. In parallel to the experimental efforts has been ongoing theoretical work to support the experiment and investigate improvement and/or offshoots. One exciting offshoot has been theoretical work showing that free-space laser acceleration of electrons is possible using a radially-polarized, axicon-focused laser beam, but without any phase-matching gas. The Monte Carlo code used to model the ICA process has been upgraded and expanded to handle different types of laser beam input profiles
Bayesian inversion of refraction seismic traveltime data
Ryberg, T.; Haberland, Ch
2018-03-01
We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test
Inverse compton emission of gamma rays near the pulsar surface
Morini, M.
1981-01-01
The physical conditions near pulsar surface that might give rise to gamma ray emission from Crab and Vela pulsars are not yet well understood. Here I suggest that, in the context of the vacuum discharge mechanism proposed by Ruderman and Sutherland (1975), gamma rays are produced by inverse Compton scattering of secondary electrons with the thermal radiation of the star surface as well as for curvature and synchotron radiation. It is found that inverse Compton scattering is relevant if the neutron star surface temperature is greater than 10 6 K or of the polar cap temperature is of the order of 5 x 10 6 K. Inverse Compton scattering in anisotropic photon fields and Klein-Nishina regime is here carefully considered. (orig.)
Inverse logarithmic potential problem
Cherednichenko, V G
1996-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Inverse Kinematics using Quaternions
Henriksen, Knud; Erleben, Kenny; Engell-Nørregård, Morten
In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection....
Khaniani, Hassan
boundary condition of the wave equation is set up along reflection surfaces. Hence, the surface integral Kirchhoff approximation is used as a mathematical framework instead of the volume integral of the Born approximation. In addition, I study the feasibility of iterative coupling of ray theory with the Kirchhoff approximation for inversion. For the amplitude considerations, the direct relationship between the scattering potential of the Born approximation with the reflectivity function of the asymptotic Kirchhoff approximation for elastic waves is used. Therefore, I use the linearized Zoeppritz approximation of Aki and Richards (1980) for computation of the forward modeling and migration operators as well as gradient function from Amplitude vs Offset (AVO) inversion. The multiparameter elastic inversion approach is applicable to all types of reflected wavefields such as P-to-P, P-to-S, S-to-S and S-to-P. Traveltime estimation of forward modeling and migration/inversion operators are based on the DSR equation. All operators involved in inversion, including the background model for DSR and AVO are updated at each iteration. The migration/inversion procedure maps the mode converted waves to the traveltime of incident waves which fixes the registration problem of events that travel from source to scatter point. The inversion of the reflected P-to-P and P-to-S synthetic and field data are provided for the numerical examples. This approach is applicable for complex structures however, to estimate the traveltime of scatterpoints, ray tracing can be added to the algorithm. For such a medium, the scatterpoint traveltime approximations from the PSTM, is compared to the PSDM approach using numerical analysis of ray- and FDTD-based modeling. In part of this thesis, I further improve the conventional velocity analysis of Common Scatter Point (CSP) gathers by including the tilt effects. I show that travel time response of scatter points beneath a dipping interface experiences an
Botto, D.J.; Pratt, R.H.
1979-05-01
The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A -2 based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required
Botto, D.J.; Pratt, R.H.
1979-05-01
The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A/sup -2/ based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required.
Bursting behaviours in cascaded stimulated Brillouin scattering
Liu Zhan-Jun; He Xian-Tu; Zheng Chun-Yang; Wang Yu-Gang
2012-01-01
Stimulated Brillouin scattering is studied by numerically solving the Vlasov—Maxwell system. A cascade of stimulated Brillouin scattering can occur when a linearly polarized laser pulse propagates in a plasma. It is found that a stimulated Brillouin scattering cascade can reduce the scattering and increase the transmission of light, as well as introduce a bursting behaviour in the evolution of the laser-plasma interaction. The bursting time in the reflectivity is found to be less than half the ion acoustic period. The ion temperature can affect the stimulated Brillouin scattering cascade, which can repeat several times at low ion temperatures and can be completely eliminated at high ion temperatures. For stimulated Brillouin scattering saturation, higher-harmonic generation and wave—wave interaction of the excited ion acoustic waves can restrict the amplitude of the latter. In addition, stimulated Brillouin scattering cascade can restrict the amplitude of the scattered light. (physics of gases, plasmas, and electric discharges)
Inverse transport theory of photoacoustics
Bal, Guillaume; Jollivet, Alexandre; Jugnon, Vincent
2010-01-01
We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high-frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient g(x) in a Henyey–Greenstein phase function model. Finally, we derive stability estimates for the reconstructions
Wavefield separation by energy norm Born scattering
Sun, Bingbing
2017-08-17
In Reflection Based Waveform Inversion, the gradient is computed by cross-correlating the direct and Born scattered wavefield with their adjoints applied to the data residuals. In this case, the transmitted part of the Born scattered wavefield produces high wavenumber artifacts, which would harm the convergence of the inversion process. We propose an efficient Energy Norm Born Scattering (ENBS) to attenuate the transmission components of the Born modeling, and allow it to produce only reflections. ENBS is derived from the adjoint of the Energy Norm (inverse scattering) imaging condition and in order to get deeper insights of how this method works, we show analytically that given an image, in which reflectivity is represented by a Dirac delta function, ENBS attenuates transmission energy perfectly. We use numerical examples to demonstrate that ENBS works in both the time and the frequency domain. We also show that in reflection waveform inversion (RWI) the wave path constructed by ENBS would be cleaner and free of high wavenumber artifacts associated with conventional Born scattering.
Wavefield separation by energy norm Born scattering
Sun, Bingbing; Alkhalifah, Tariq Ali
2017-01-01
In Reflection Based Waveform Inversion, the gradient is computed by cross-correlating the direct and Born scattered wavefield with their adjoints applied to the data residuals. In this case, the transmitted part of the Born scattered wavefield produces high wavenumber artifacts, which would harm the convergence of the inversion process. We propose an efficient Energy Norm Born Scattering (ENBS) to attenuate the transmission components of the Born modeling, and allow it to produce only reflections. ENBS is derived from the adjoint of the Energy Norm (inverse scattering) imaging condition and in order to get deeper insights of how this method works, we show analytically that given an image, in which reflectivity is represented by a Dirac delta function, ENBS attenuates transmission energy perfectly. We use numerical examples to demonstrate that ENBS works in both the time and the frequency domain. We also show that in reflection waveform inversion (RWI) the wave path constructed by ENBS would be cleaner and free of high wavenumber artifacts associated with conventional Born scattering.
Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.
1992-11-01
The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.
Approximation of the inverse G-frame operator
... projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Scattering theory and orthogonal polynomials
Geronimo, J.S.
1977-01-01
The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms
Minimal-Inversion Feedforward-And-Feedback Control System
Seraji, Homayoun
1990-01-01
Recent developments in theory of control systems support concept of minimal-inversion feedforward-and feedback control system consisting of three independently designable control subsystems. Applicable to the control of linear, time-invariant plant.