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Sample records for multiple scattering problems

  1. Multiple scattering problems in heavy ion elastic recoil detection analysis

    Johnston, P.N.; El Bouanani, M.; Stannard, W.B.; Bubb, I.F.; Cohen, D.D.; Dytlewski, N.; Siegele, R.

    1998-01-01

    A number of groups use Heavy Ion Elastic Recoil Detection Analysis (HIERDA) to study materials science problems. Nevertheless, there is no standard methodology for the analysis of HIERDA spectra. To overcome this deficiency we have been establishing codes for 2-dimensional data analysis. A major problem involves the effects of multiple and plural scattering which are very significant, even for quite thin (∼100 nm) layers of the very heavy elements. To examine the effects of multiple scattering we have made comparisons between the small-angle model of Sigmund et al. and TRIM calculations. (authors)

  2. A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

    2013-02-01

    obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

  3. On the solution of a few problems of multiple scattering by Monte Carlo method

    Bluet, J.C.

    1966-02-01

    Three problems of multiple scattering arising from neutron cross sections experiments, are reported here. The common hypothesis are: - Elastic scattering is the only possible process - Angular distributions are isotropic - Losses of particle energy are negligible in successive collisions. In the three cases practical results, corresponding to actual experiments are given. Moreover the results are shown in more general way, using dimensionless variable such as the ratio of geometrical dimensions to neutron mean free path. The FORTRAN codes are given together with to the corresponding flow charts, and lexicons of symbols. First problem: Measurement of sodium capture cross-section. A sodium sample of given geometry is submitted to a neutron flux. Induced activity is then measured by means of a sodium iodide cristal. The distribution of active nuclei in the sample, and the counter efficiency are calculated by Monte-Carlo method taking multiple scattering into account. Second problem: absolute measurement of a neutron flux using a glass scintillator. The scintillator is a use of lithium 6 loaded glass, submitted to neutron flux perpendicular to its plane faces. If the glass thickness is not negligible compared with scattering mean free path λ, the mean path e' of neutrons in the glass is different from the thickness. Monte-Carlo calculation are made to compute this path and a relative correction to efficiency equal to (e' - e)/e. Third problem: study of a neutron collimator. A neutron detector is placed at the bottom of a cylinder surrounded with water. A neutron source is placed on the cylinder axis, in front of the water shield. The number of neutron tracks going directly and indirectly through the water from the source to the detector are counted. (author) [fr

  4. Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm

    Malhotra, M. [Stanford Univ., CA (United States)

    1996-12-31

    Finite-element discretizations of time-harmonic acoustic wave problems in exterior domains result in large sparse systems of linear equations with complex symmetric coefficient matrices. In many situations, these matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. For instance, multiple right-hand sides arise in radiation problems due to multiple load cases, and also in scattering problems when multiple angles of incidence of an incoming plane wave need to be considered. In this talk, we discuss the iterative solution of multiple linear systems arising in radiation and scattering problems in structural acoustics by means of a complex symmetric variant of the BL-QMR method. First, we summarize the governing partial differential equations for time-harmonic structural acoustics, the finite-element discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BL-QMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BL-QMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BL-QMR method for multiple radiation and scattering problems in structural acoustics, to identify appropriate preconditioners for these problems, and to demonstrate the importance of deflation in block Krylov-subspace methods. Our numerical results show that the multiple systems arising in structural acoustics can be solved very efficiently with the preconditioned BL-QMR method. In fact, for multiple systems with up to 40 and more different right-hand sides we get consistent and significant speed-ups over solving the systems individually.

  5. The albedo problem in the case of multiple synthetic scattering taking place in a plane-symmetric slab

    Shafiq, A.; Meyer, H.E. de; Grosjean, C.C.

    1985-01-01

    An approximate model based on an improved diffusion-type theory is established for treating multiple synthetic scattering in a homogeneous slab of finite thickness. As in the case of the exact treatment given in the preceding paper (Part I), it appears possible to transform the considered transport problem into an equivalent fictitious one involving multiple isotropic scattering, therefore permitting the application of an established corrected diffusion theory for treating isotropic scattering taking place in a convex homogeneous medium bounded by a vacuum in the presence of various types of sources. The approximate values of the reflection and transmission coefficients are compared with the rigorous values listed in Part I. In this way, the high accuracy of the approximation is clearly demonstrated. (author)

  6. Quantum Optical Multiple Scattering

    Ott, Johan Raunkjær

    . In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled...... states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum...... interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light...

  7. Scattering and multiple scattering in disordered materials

    Weaver, R.L.; Butler, W.H.

    1992-01-01

    The papers in this section were presented at a joint session of symposium V on Applications of Multiple Scattering Theory and of Symposium P on Disordered Systems. They show that the ideas of scattering theory can help us to understand a very broad class of phenomena

  8. 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

  9. Determination of multiple scattering effects

    Langevin, M.

    1981-01-01

    The integration of Sigmund and Winterbon numerical values is extended to the reduced thickness tau=2000. The diagram obtained allows a simple determination of the multiple scattering effect for different targets and projectiles [fr

  10. On the solution of a few problems of multiple scattering by Monte Carlo method; Sur la solution de quelques problemes de diffusions multiples par la methode de Monte-Carlo

    Bluet, J C [Commissariat a l' Energie Atomique, Cadarache (France)

    1966-02-01

    Three problems of multiple scattering arising from neutron cross sections experiments, are reported here. The common hypothesis are: - Elastic scattering is the only possible process - Angular distributions are isotropic - Losses of particle energy are negligible in successive collisions. In the three cases practical results, corresponding to actual experiments are given. Moreover the results are shown in more general way, using dimensionless variable such as the ratio of geometrical dimensions to neutron mean free path. The FORTRAN codes are given together with to the corresponding flow charts, and lexicons of symbols. First problem: Measurement of sodium capture cross-section. A sodium sample of given geometry is submitted to a neutron flux. Induced activity is then measured by means of a sodium iodide cristal. The distribution of active nuclei in the sample, and the counter efficiency are calculated by Monte-Carlo method taking multiple scattering into account. Second problem: absolute measurement of a neutron flux using a glass scintillator. The scintillator is a use of lithium 6 loaded glass, submitted to neutron flux perpendicular to its plane faces. If the glass thickness is not negligible compared with scattering mean free path {lambda}, the mean path e' of neutrons in the glass is different from the thickness. Monte-Carlo calculation are made to compute this path and a relative correction to efficiency equal to (e' - e)/e. Third problem: study of a neutron collimator. A neutron detector is placed at the bottom of a cylinder surrounded with water. A neutron source is placed on the cylinder axis, in front of the water shield. The number of neutron tracks going directly and indirectly through the water from the source to the detector are counted. (author) [French] On traite dans ce rapport de trois problemes avec les hypotheses communes suivantes: 1.- Le seul processus de collision possible est la diffusion electrique. 2.- La distribution angulaire est

  11. Effect of multiple scattering on lidar measurements

    Cohen, A.

    1977-01-01

    The lidar equation in its standard form involves the assumption that the scattered irradiance reaching the lidar receiver has been only singly scattered. However, in the cases of scattering from clouds and thick aerosol layers, it is shown that multiple scattering cannot be neglected. An experimental method for the detection of multiple scattering by depolarization measurement techniques is discussed. One method of theoretical calculations of double-scattering is presented and discussed

  12. Spatial photon correlations in multiple scattering media

    Smolka, Stephan; Muskens, O.; Lagendijk, A.

    2010-01-01

    We present the first angle-resolved measurements of spatial photon correlations that are induced by multiple scattering of light. The correlation relates multiple scattered photons at different spatial positions and depends on incident photon fluctuations.......We present the first angle-resolved measurements of spatial photon correlations that are induced by multiple scattering of light. The correlation relates multiple scattered photons at different spatial positions and depends on incident photon fluctuations....

  13. Wigner representation in scattering problems

    Remler, E.A.

    1975-01-01

    The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems is laid. The foundation for a systematic application of statistical approximations to such problems. The form of the integral equation for scattering as well as its mulitple scattering expansion in this representation are derived. Since this formalism remains unchanged upon taking the classical limit, these results also constitute a general treatment of classical multiparticle collision theory. Quantum corrections to classical propogators are discussed briefly. The basic approximation used in the Monte Carlo method is derived in a fashion that allows for future refinement and includes bound state production. The close connection that must exist between inclusive production of a bound state and of its constituents is brought out in an especially graphic way by this formalism. In particular one can see how comparisons between such cross sections yield direct physical insight into relevant production mechanisms. A simple illustration of scattering by a bound two-body system is treated. Simple expressions for single- and double-scattering contributions to total and differential cross sections, as well as for all necessary shadow corrections thereto, are obtained and compared to previous results of Glauber and Goldberger

  14. Gamma holography from multiple scattering

    Coussement, R.

    2007-01-01

    Since the introduction of heterodyne methods for synchrotron radiation (Cousesement et al. in Phys. Rev. B 54:16003, 1996; Callens et al. in Phys. Rev. 67:104423, 2003) one observes interferences between two scattering amplitudes; the scattering amplitude of resonant nuclei in a reference sample and the scattering amplitude of nuclei in the sample under investigation. Theses interferences can easily been observed as resonances in velocity spectra when one uses a time integrated method. They can also been observed as quantum beats, when one would use the time differential method. For both methods it is important that one uses a reference sample and therefore both methods disserved the name 'heterodyne methods.' As theses interferences are a product of two scattering amplitudes, the amplitude of a wave scattered form the investigated sample can be known with its phase. But it is assumed that the reference wave is known in advance by a proper choice of the reference sample. At first sight it is very likely that multiple scattering would add more complexity but in this paper it is claimed that on the contrary it provide a bonus, especially for single crystals. It provokes only a line broadening and a line shift of the resonances in the velocity spectra (or a change in the damping and frequency of the quantum beats when the time spectra are registered). Moreover these changes in the line shapes can easily be measured and they provide all the information needed to reconstruct a 3-D picture of the atomic arrangement of resonant nuclei and moreover they distinguish between different hyperfine sites. The method may be more practical for measurements on synchrotron radiation but it does also apply to velocity spectra obtained from resonant scattering with strong sources. The use of radioactive sources suffer from the disadvantage of poorer statistics or much longer accumulation times but they enjoy the advantage to be table-top and at-home experiments. As strong sources are

  15. Numerical modelling of multiple scattering between two elastical particles

    Bjørnø, Irina; Jensen, Leif Bjørnø

    1998-01-01

    in suspension have been studied extensively since Foldy's formulation of his theory for isotropic scattering by randomly distributed scatterers. However, a number of important problems related to multiple scattering are still far from finding their solutions. A particular, but still unsolved, problem......Multiple acoustical signal interactions with sediment particles in the vicinity of the seabed may significantly change the course of sediment concentration profiles determined by inversion from acoustical backscattering measurements. The scattering properties of high concentrations of sediments...... is the question of proximity thresholds for influence of multiple scattering in terms of particle properties like volume fraction, average distance between particles or other related parameters. A few available experimental data indicate a significance of multiple scattering in suspensions where the concentration...

  16. Thermal-neutron multiple scattering: critical double scattering

    Holm, W.A.

    1976-01-01

    A quantum mechanical formulation for multiple scattering of thermal-neutrons from macroscopic targets is presented and applied to single and double scattering. Critical nuclear scattering from liquids and critical magnetic scattering from ferromagnets are treated in detail in the quasielastic approximation for target systems slightly above their critical points. Numerical estimates are made of the double scattering contribution to the critical magnetic cross section using relevant parameters from actual experiments performed on various ferromagnets. The effect is to alter the usual Lorentzian line shape dependence on neutron wave vector transfer. Comparison with corresponding deviations in line shape resulting from the use of Fisher's modified form of the Ornstein-Zernike spin correlations within the framework of single scattering theory leads to values for the critical exponent eta of the modified correlations which reproduce the effect of double scattering. In addition, it is shown that by restricting the range of applicability of the multiple scattering theory from the outset to critical scattering, Glauber's high energy approximation can be used to provide a much simpler and more powerful description of multiple scattering effects. When sufficiently close to the critical point, it provides a closed form expression for the differential cross section which includes all orders of scattering and has the same form as the single scattering cross section with a modified exponent for the wave vector transfer

  17. Multiple scattering theory for space filling potentials

    Butler, W.H.; Brown, R.G.; Nesbet, R.K.

    1990-01-01

    Multiple scattering theory (MST) provides an efficient technique for solving the wave equation for the special case of muffin-tin potentials. Here MST is extended to treat space filling non-muffin tin potentials and its validity, accuracy and efficiency are tested by application of the two dimensional empty lattice test. For this test it is found that the traditional formulation of MST does not coverage as the number of partial waves is increased. A simple modification of MST, however, allows this problem to be solved exactly and efficiently. 15 refs., 3 tabs

  18. New method for solving multidimensional scattering problem

    Melezhik, V.S.

    1991-01-01

    A new method is developed for solving the quantum mechanical problem of scattering of a particle with internal structure. The multichannel scattering problem is formulated as a system of nonlinear functional equations for the wave function and reaction matrix. The method is successfully tested for the scattering from a nonspherical potential well and a long-range nonspherical scatterer. The method is also applicable to solving the multidimensional Schroedinger equation with a discrete spectrum. As an example the known problem of a hydrogen atom in a homogeneous magnetic field is analyzed

  19. Significance of multiple scattering in imaging through turbid media

    Zardecki, A.; Gerstl, S.A.W.

    1986-01-01

    The degradation of image quality in a turbid medium is analyzed within the framework of the small-angle approximation, the diffusion approximation, and a rigorous two-dimensional radiative transfer equation. These three approaches allow us to emphasize different aspects of the imaging problem when multiple scattering effects are important. For a medium with a forward-peaked phase function, the separation of multiple scattering into a series of scatterings of various order provides a fruitful technique. The use of the diffusion approximation and transport theory extends the determination of the modulation transfer function to a turbid medium with an arbitrary degree of anisotropy

  20. 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...

  1. 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

  2. Markov chain solution of photon multiple scattering through turbid slabs.

    Lin, Ying; Northrop, William F; Li, Xuesong

    2016-11-14

    This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.

  3. ISOGEOMETRIC SHAPE OPTIMIZATION FOR ELECTROMAGNETIC SCATTERING PROBLEMS

    Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens

    2012-01-01

    We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach...

  4. Multiple scattering of ions in polyatomic materials

    Eastham, D.A.

    1980-01-01

    The equations which determine small angle multiple scattering in the thin polyatomic layers are evaluated numerically for certain cases. A simple approximate method for calculating the scattering in terms of an average target charge which is a function of the target thickness is given and compared with the exact numerical value. The results agree to better than 5% over a wide range of target composition and thickness. (orig.)

  5. Correlation expansion: a powerful alternative multiple scattering calculation method

    Zhao Haifeng; Wu Ziyu; Sebilleau, Didier

    2008-01-01

    We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion

  6. 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

  7. Light propagation in finite-sized photonic crystals: multiple scattering using an electric field integral equation

    Kristensen, Philip Trøst; Lodahl, Peter; Mørk, Jesper

    2010-01-01

    We present an accurate, stable, and efficient solution to the Lippmann–Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with scatterers of arbitrary shape or non-homogenous background mat...

  8. Theory of Multiple Coulomb Scattering from Extended Nuclei

    Cooper, L. N.; Rainwater, J.

    1954-08-01

    Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high energy charged particles traverse a thick scatterer. The results are compared with the theories of Moliere and Olbert.

  9. Lateral displacement in small angle multiple scattering

    Bichsel, H.; Hanson, K.M.; Schillaci, K.M. (Los Alamos National Lab., NM (USA))

    1982-07-01

    Values have been calculated for the average lateral displacement in small angle multiple scattering of protons with energies of several hundred MeV. The calculations incorporate the Moliere distribution which does not make the gaussian approximations of the distribution in projected angle and lateral deflections. Compared to other published data, such approximations can lead to errors in the lateral displacement of up to 10% in water.

  10. Separable expansion for realistic multichannel scattering problems

    Canton, L.; Cattapan, G.; Pisent, G.

    1987-01-01

    A new approach to the multichannel scattering problem with realistic local or nonlocal interactions is developed. By employing the negative-energy solutions of uncoupled Sturmian eigenvalue problems referring to simple auxiliary potentials, the coupling interactions appearing to the original multichannel problem are approximated by finite-rank potentials. By resorting to integral-equation tecniques the coupled-channel equations are then reduced to linear algebraic equations which can be straightforwardly solved. Compact algebraic expressions for the relevant scattering matrix elements are thus obtained. The convergence of the method is tasted in the single-channel case with realistic optical potentials. Excellent agreement is obtained with a few terms in the separable expansion for both real and absorptive interactions

  11. Scattering theory some old and new problems

    Yafaev, Dmitri R

    2000-01-01

    Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

  12. 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)

  13. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    Li, Muxingzi

    2017-01-01

    of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous

  14. New approaches to old scattering problems

    Goldberg, Joshua David

    This thesis is broken into two parts corresponding to the research done before and after the death of Roger Dashen. The first part addresses the problem of high frequency scattering from flat objects. A new formalism, developed by Dashen and Wurmser, is applied to the two dimensional problem of scattering from a soft infinite strip. It is seen that the cross section can be related to a quantity, termed the divergence coefficient, which describes the behavior of the field near the edges. A simple expression for the divergence coefficient and the scattering cross section is derived which, in contrast to traditional results, is uniformly valid in the high frequency limit. The basic procedure is to first express the divergence coefficient in a series form involving Mathieu functions, approximating the terms in this series by their uniform WKB representation, and using the Poisson sum formula to convert the WKB-based series to a more rapidly converging series of integrals which can be evaluated asymptotically. The result is a new expression for the scattering cross section which is compared with previously obtained results. The second part addresses a specific problem in the field of wave propagation in random media: computing the average field for the case of a plane wave incident on a region with a weakly fluctuating sound speed. A review of the existing mathematical methods for treating this problem in both the small and large-scale fluctuation cases is given. In the small-scale regime, previously unrecognized problems with the closure theory are discussed and numerical results are given which illustrate the role played by backscattering in this type of propagation. In the large-scale regime, a new mathematical approach, analogous to the renormalization technique, is described and used to derive a new expression for the mean field valid in this limit. This result is compared with the traditional expressions for this quantity.

  15. Numerical solution of the multichannel scattering problem

    Korobov, V.I.

    1992-01-01

    A numerical algorithm for solving the multichannel elastic and inelastic scattering problem is proposed. The starting point is the system of radial Schroedinger equations with linear boundary conditions imposed at some point R=R m placed somewhere in asymptotic region. It is discussed how the obtained linear equation can be splitted into a zero-order operator and its pertturbative part. It is shown that Lentini - Pereyra variable order finite-difference method appears to be very suitable for solving that kind of problems. The derived procedure is applied to dμ+t→tμ+d inelastic scattering in the framework of the adiabatic multichannel approach. 19 refs.; 1 fig.; 1 tab

  16. Quantum optics in multiple scattering random media

    Lodahl, Peter; Lagendijk, Ad

    2005-01-01

    Quantum Optics in Multiple Scattering Random Media Peter Lodahl Research Center COM, Technical University of Denmark, Dk-2800 Lyngby, Denmark. Coherent transport of light in a disordered random medium has attracted enormous attention both from a fundamental and application point of view. Coherent......-tions that should be readily attainable experimentally is devised. Figure 1. Inverse total transmission of shot noise (left) and technical noise (right) as a function of the thickness of the ran-dom medium. The experimental data are well explained by theory (curves). [1] J. Tworzydlo and C.W.J. Beenakker, Phys. Rev...

  17. Coulomb interaction in multiple scattering theory

    Ray, L.; Hoffmann, G.W.; Thaler, R.M.

    1980-01-01

    The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic T matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus T matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear T matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb T matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV p+ 208 Pb elastic scattering and compared with experimental data

  18. 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.

  19. Static and dynamic properties of multiple light scattering

    Štěpánek, Petr

    1993-11-01

    We have examined the onset and evolution of multiple scattering of light on a series of latex dispersions as a function of increasing volume concentration φ of particles. We have shown that using vertically polarized incident light, the static scattered intensity becomes progressively depolarized, with increasing φ. The polarization of scattered light is completely random in the limit of strong multiple scattering. The spectra of decay times of dynamic light scattering display a region of oligo scattering at intermediate φ where both the single and multiple scattering components can be dynamically identified. For φ≳0.03 the limit of diffusive transport of light is attained. The obtained results confirm that our earlier measurements of dynamic light scattering on systems exhibiting critical opalescence are not influenced by multiple light scattering.

  20. Multiple-scattering corrections to the Beer-Lambert law

    Zardecki, A.

    1983-01-01

    The effect of multiple scattering on the validity of the Beer-Lambert law is discussed for a wide range of particle-size parameters and optical depths. To predict the amount of received radiant power, appropriate correction terms are introduced. For particles larger than or comparable to the wavelength of radiation, the small-angle approximation is adequate; whereas for small densely packed particles, the diffusion theory is advantageously employed. These two approaches are used in the context of the problem of laser-beam propagation in a dense aerosol medium. In addition, preliminary results obtained by using a two-dimensional finite-element discrete-ordinates transport code are described. Multiple-scattering effects for laser propagation in fog, cloud, rain, and aerosol cloud are modeled

  1. Multiple Scattering Approach to Continuum State with Generally Shaped Potential

    Hatada, Keisuke; Hayakawa, Kuniko; Tenore, Antonio; Benfatto, Maurizio; Natoli, Calogero

    2007-01-01

    We present a new scheme for solving the scattering problem for an arbitrarily shaped potential cell that avoids the well known convergence problems in the angular momentum expansion of the cell shape function. Tests of the method against analytically soluble separable model potentials, with and without shape truncation, have been performed with success. By a judicious choice of the shape of the cells partitioning the whole molecular space and use of empty cells when necessary, we set up a multiple scattering scheme that leads to a straightforward generalization of the same equations in the muffin-tin approximation. For example lmax in the angular momentum expansion can still be chosen according to the rule lmax ∼ kR, where R is the radius of the bounding sphere of the cell and all the matrices appearing in the theory are square matrices

  2. Multiple scattering effects in 7Li

    Cox, A.J.; Warner, P.C.

    1985-01-01

    The differential cross-sections for the production of 0.478 MeV γ-rays following the inelastic scattering of 14 MeV neutrons in large samples of LiF, which will be used in fusion reactor blankets, have been measured. The neutrons were produced using the 3 H(d,n) 4 α reaction, with the deuterons being accelerated by a 150 kV SAMES type accelerator. In order to reduce the background level the γ-ray signal was gated, using a time of flight technique based on the α-particle associated with neutron production. Measurements of the γ-ray production differential cross-sections were made for various thicknesses of LiF. The results were compared to the predictions of the Monte Carlo Computer Code, MORSE, with an agreement of +-11% being achieved. In addition a phenomenological expression was found which is capable of predicting the variation in cross-sections with thickness due to multiple scattering effects to within +-12%. (author)

  3. Ultrasound scatter in heterogeneous 3D microstructures: Parameters affecting multiple scattering

    Engle, B. J.; Roberts, R. A.; Grandin, R. J.

    2018-04-01

    This paper reports on a computational study of ultrasound propagation in heterogeneous metal microstructures. Random spatial fluctuations in elastic properties over a range of length scales relative to ultrasound wavelength can give rise to scatter-induced attenuation, backscatter noise, and phase front aberration. It is of interest to quantify the dependence of these phenomena on the microstructure parameters, for the purpose of quantifying deleterious consequences on flaw detectability, and for the purpose of material characterization. Valuable tools for estimation of microstructure parameters (e.g. grain size) through analysis of ultrasound backscatter have been developed based on approximate weak-scattering models. While useful, it is understood that these tools display inherent inaccuracy when multiple scattering phenomena significantly contribute to the measurement. It is the goal of this work to supplement weak scattering model predictions with corrections derived through application of an exact computational scattering model to explicitly prescribed microstructures. The scattering problem is formulated as a volume integral equation (VIE) displaying a convolutional Green-function-derived kernel. The VIE is solved iteratively employing FFT-based con-volution. Realizations of random microstructures are specified on the micron scale using statistical property descriptions (e.g. grain size and orientation distributions), which are then spatially filtered to provide rigorously equivalent scattering media on a length scale relevant to ultrasound propagation. Scattering responses from ensembles of media representations are averaged to obtain mean and variance of quantities such as attenuation and backscatter noise levels, as a function of microstructure descriptors. The computational approach will be summarized, and examples of application will be presented.

  4. Multiple scattering approach to the vibrational excitation of molecules by slow electrons

    Drukarev, G.

    1976-01-01

    Another approach to the problem of vibrational excitation of homonuclear two-atomic molecules by slow electrons possibly accompanied by rotational transitions is presented based on the picture of multiple scattering of an electron inside the molecule. The scattering of two fixed centers in the zero range potential model is considered. The results indicate that the multiple scattering determines the order of magnitude of the vibrational excitation cross sections in the energy region under consideration even if the zero range potential model is used. Also the connection between the multiple scattering approach and quasi-stationary molecular ion picture is established. 9 refs

  5. Complex multiplication and lifting problems

    Chai, Ching-Li; Oort, Frans

    2013-01-01

    Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent the...

  6. 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

  7. 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

  8. Multiple small-angle neutron scattering studies of anisotropic materials

    Allen, A J; Long, G G; Ilavsky, J

    2002-01-01

    Building on previous work that considered spherical scatterers and randomly oriented spheroidal scatterers, we describe a multiple small-angle neutron scattering (MSANS) analysis for nonrandomly oriented spheroids. We illustrate this with studies of the multi-component void morphologies found in plasma-spray thermal barrier coatings. (orig.)

  9. 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

  10. Convergence of the multiple scattering expansion in XAFS and XANES

    Rehr, J.J.

    1992-01-01

    The convergence of the multiple-scattering expansion of XAFS and XANES by explicit path-bypath calculations. The approach is based on the fast scattering matrix formalism of Rehr and Albers, together with an automated path finder and filters that exclude negligible paths. High-order scattering terms are found to be essential, especially at low energies. Several factors including the magnitude of curved wave scattering amplitudes, inelastic losses and multiple-scattering Debye-Waller factors control convergence of the expansion. The convergence is illustrated explicitly for the case of diatomic molecules

  11. Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation

    Li, Muxingzi

    2017-04-24

    Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.

  12. Single and multiple electromagnetic scattering by dielectric obstacles from a resonance perspective

    Riley, D.J.

    1987-03-01

    A new application of the singularity expansion method (SEM) is explored. This application combines the classical theory of wave propagation through a multiple-scattering environment and the SEM. Because the SEM is generally considered to be a theory for describing surface currents on conducting scatters, extensions are made which permit, under certain conditions, a singularity expansion representation for the electromagnetic field scattered by a dielectric scatterer. Application of this expansion is then made to the multiple-scattering case using both single and multiple interactions. A resonance scattering tensor form is used for the SEM description which leds to an associated tensor form for the solution to the multiple-scattering problem with each SEM pole effect appearing explicitly. The coherent field is determined for both spatial and SEM parameter random variations. A numerical example for the case of an ensemble of dielectric spheres which possess frequency-dependent loss is also made. Accurate resonance expansions for the single-scattering problem are derived, and resonance trajectories based on the Debye relaxation model for the refractive index are introduced. Application of these resonance expansions is then made to the multiple-scattering results for a slab containing a distribution of spheres with varying radii. Conditions are discussed which describe when the hybrid theory is appropriate. 53 refs., 21 figs., 9 tabs

  13. 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.

  14. 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

  15. Solution of a simple inelastic scattering problem

    Knudson, S.K.

    1975-01-01

    Simple examples of elastic scattering, typically from square wells, serve as important pedagogical tools in discussion of the concepts and processes involved in elastic scattering events. An analytic solution of a model inelastic scattering system is presented here to serve in this role for inelastic events. The model and its solution are simple enough to be of pedagogical utility, but also retain enough of the important physical features to include most of the special characteristics of inelastic systems. The specific model chosen is the collision of an atom with a harmonic oscillator, interacting via a repulsive square well potential. Pedagogically important features of inelastic scattering, including its multistate character, convergence behavior, and dependence on an ''inelastic potential'' are emphasized as the solution is determined. Results are presented for various energies and strengths of inelastic scattering, which show that the model is capable of providing an elementary representation of vibrationally inelastic scattering

  16. Looking for Multiple Scattering Effects in Backscattered Ultrasonic Grain Noise from Jet-Engine Nickel Alloys

    Margetan, F.J.; Haldipur, Pranaam; Yu Linxiao; Thompson, R.B.

    2005-01-01

    For pulse/echo inspections of metals, models which predict backscattered noise characteristics often make a 'single-scattering' assumption, i.e., multiple-scattering events in which sound is scattered from one grain to another before returning to the transducer are ignored. Models based on the single-scattering assumption have proven to be very useful in simulating inspections of engine-alloy billets and forgings. However, this assumption may not be accurate if grain scattering is too 'strong' (e.g., if the mean grain diameter and/or the inspection frequency is too large). In this work, backscattered grain noise measurements and analyses were undertaken to search for evidence of significant multiple scattering in pulse/echo inspections of jet-engine Nickel alloys. At or above about 7 MHz frequency and 50 micron grain diameter, problems were seen with single-scattering noise models that are likely due to the neglect of multiple scattering by the models. The modeling errors were less severe for focused-probe measurements in the focal zone than for planar probe inspections. Single-scattering noise models are likely adequate for simulating current billet inspections which are carried out using 5-MHz focused transducers. However, multiple scattering effects should be taken into account in some fashion when simulating higher-frequency inspections of Nickel-alloy billets having large mean grain diameters (> 40 microns)

  17. Compton-scatter tissue densitometry: calculation of single and multiple scatter photon fluences

    Battista, J.J.; Bronskill, M.J.

    1978-01-01

    The accurate measurement of in vivo electron densities by the Compton-scatter method is limited by attenuations and multiple scattering in the patient. Using analytic and Monte Carlo calculation methods, the Clarke tissue density scanner has been modelled for incident monoenergetic photon energies from 300 to 2000 keV and for mean scattering angles of 30 to 130 degrees. For a single detector focussed to a central position in a uniform water phantom (25 x 25 x 25 cm 3 ) it has been demonstrated that: (1) Multiple scatter contamination is an inherent limitation of the Compton-scatter method of densitometry which can be minimised, but not eliminated, by improving the energy resolution of the scattered radiation detector. (2) The choice of the incident photon energy is a compromise between the permissible radiation dose to the patient and the tolerable level of multiple scatter contamination. For a mean scattering angle of 40 degrees, the intrinsic multiple-single scatter ratio decreases from 64 to 35%, and the radiation dose (per measurement) increases from 1.0 to 4.1 rad, as the incident photon energy increases from 300 to 2000 keV. These doses apply to a sampled volume of approximately 0.3 cm 3 and an electron density precision of 0.5%. (3) The forward scatter densitometer configuration is optimum, minimising both the dose and the multiple scatter contamination. For an incident photon energy of 1250 keV, the intrinsic multiple-single scatter ratio reduces from 122 to 27%, and the dose reduces from 14.3 to 1.2 rad, as the mean scattering angle decreases from 130 to 30 degrees. These calculations have been confirmed by experimental measurements. (author)

  18. Depth distribution of multiple order X-ray scatter

    Yao Weiguang; Leszczynski, Konrad

    2008-01-01

    Scatter can significantly affect quality of projectional X-ray radiographs and tomographic reconstructions. With this in mind, we examined some of the physical properties of multiple orders of scatter of X-ray photons traversing through a layer of scattering media such as water. Using Monte Carlo techniques, we investigated depth distributions of interactions between incident X-ray photons and water before the resulting scattered photons reach the detector plane. Effects of factors such as radiation field size, air gap, thickness of the layer of scattering medium and X-ray energy, on the scatter were included in the scope of this study. The following scatter characteristics were observed: (1) for a layer of scattering material corresponding to the typical subject thickness in medical imaging, frequency distribution of locations of the last scattering interaction increases approximately exponentially with depth, and the higher the order of scatter or the energy of the incident photon, the narrower is the distribution; (2) for the second order scatter, the distribution of locations of the first interaction is more uniform than that of the last interaction and is dependent on the energy of the primary photons. Theoretical proofs for some of these properties are given. These properties are important to better understanding of effects of scatter on the radiographic and tomographic imaging process and to developing effective methods for scatter correction

  19. On exact solutions of scattering problems

    Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

    1982-01-01

    Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

  20. Regularization of the Coulomb scattering problem

    Baryshevskii, V.G.; Feranchuk, I.D.; Kats, P.B.

    2004-01-01

    The exact solution of the Schroedinger equation for the Coulomb potential is used within the scope of both stationary and time-dependent scattering theories in order to find the parameters which determine the regularization of the Rutherford cross section when the scattering angle tends to zero but the distance r from the center remains finite. The angular distribution of the particles scattered in the Coulomb field is studied on rather a large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is inapplicable in the case when small scattering angles are considered. The unitary property of the scattering matrix is analyzed and the 'optical' theorem for this case is discussed. The total and transport cross sections for scattering the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the effects under consideration can be important for the observed characteristics of the transport processes in semiconductors which are determined by the electron and hole scattering by the field of charged impurity centers

  1. Acoustic scattering by multiple elliptical cylinders using collocation multipole method

    Lee, Wei-Ming

    2012-01-01

    This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

  2. Diffractive scattering on nuclei in multiple scattering theory with inelastic screening

    Zoller, V.R.

    1988-01-01

    The cross sections for the diffractive scattering of hadrons on nuclei are calculated in the two-channel approximation of multiple scattering theory. In contrast to the standard Glauber approach, it is not assumed that the nucleon scattering profile is a Gaussian or that the Regge radius of the hadron is small compared to the nuclear radius. The AGK Reggeon diagrammatic technique is used to calculate the topological cross sections and the cross sections for coherent and incoherent diffractive dissociation and quasielastic scattering. The features of hadron-nucleus scattering at superhigh energies are discussed

  3. Study of multiple scattering effects in heavy ion RBS

    Fang, Z; O` Connor, D J [Newcastle Univ., NSW (Australia). Dept. of Physics

    1997-12-31

    Multiple scattering effect is normally neglected in conventional Rutherford Backscattering (RBS) analysis. The backscattered particle yield normally agrees well with the theory based on the single scattering model. However, when heavy incident ions are used such as in heavy ion Rutherford backscattering (HIRBS), or the incident ion energy is reduced, multiple scattering effect starts to play a role in the analysis. In this paper, the experimental data of 6MeV C ions backscattered from a Au target are presented. In measured time of flight spectrum a small step in front of the Au high energy edge is observed. The high energy edge of the step is about 3.4 ns ahead of the Au signal which corresponds to an energy {approx} 300 keV higher than the 135 degree single scattering energy. This value coincides with the double scattering energy of C ion undergoes two consecutive 67.5 degree scattering. Efforts made to investigate the origin of the high energy step observed lead to an Monte Carlo simulation aimed to reproduce the experimental spectrum on computer. As a large angle scattering event is a rare event, two consecutive large angle scattering is extremely hard to reproduce in a random simulation process. Thus, the simulation has not found a particle scattering into 130-140 deg with an energy higher than the single scattering energy. Obviously faster algorithms and a better physical model are necessary for a successful simulation. 16 refs., 3 figs.

  4. Study of multiple scattering effects in heavy ion RBS

    Fang, Z.; O`Connor, D.J. [Newcastle Univ., NSW (Australia). Dept. of Physics

    1996-12-31

    Multiple scattering effect is normally neglected in conventional Rutherford Backscattering (RBS) analysis. The backscattered particle yield normally agrees well with the theory based on the single scattering model. However, when heavy incident ions are used such as in heavy ion Rutherford backscattering (HIRBS), or the incident ion energy is reduced, multiple scattering effect starts to play a role in the analysis. In this paper, the experimental data of 6MeV C ions backscattered from a Au target are presented. In measured time of flight spectrum a small step in front of the Au high energy edge is observed. The high energy edge of the step is about 3.4 ns ahead of the Au signal which corresponds to an energy {approx} 300 keV higher than the 135 degree single scattering energy. This value coincides with the double scattering energy of C ion undergoes two consecutive 67.5 degree scattering. Efforts made to investigate the origin of the high energy step observed lead to an Monte Carlo simulation aimed to reproduce the experimental spectrum on computer. As a large angle scattering event is a rare event, two consecutive large angle scattering is extremely hard to reproduce in a random simulation process. Thus, the simulation has not found a particle scattering into 130-140 deg with an energy higher than the single scattering energy. Obviously faster algorithms and a better physical model are necessary for a successful simulation. 16 refs., 3 figs.

  5. Reproducibility of artificial multiple scattering media

    Marakis, Evangelos; van Harten, Wouter; Uppu, Ravitej; Pinkse, Pepijn Willemszoon Harry

    2016-01-01

    State of the art authentication systems depend on physical unclonable functions (PUF) [1], physical keys that are assumed unclonable due to technological constraints. Random scattering media, dielectric materials with rapid and random refractive index variations, are considered as ideal optical PUFs

  6. Certain theories of multiple scattering in random media of discrete scatterers

    Olsen, R.L.; Kharadly, M.M.Z.; Corr, D.G.

    1976-01-01

    New information is presented on the accuracy of the heuristic approximations in two important theories of multiple scattering in random media of discrete scatterers: Twersky's ''free-space'' and ''two-space scatterer'' formalisms. Two complementary approaches, based primarily on a one-dimensional model and the one-dimensional forms of the theories, are used. For scatterer distributions of low average density, the ''heuristic'' asymptotic forms for the coherent field and the incoherent intensity are compared with asymptotic forms derived from a systematic analysis of the multiple scattering processes. For distributions of higher density, both in the average number of scatterers per wavelength and in the degree of packing of finite-size scatterers, the analysis is carried out ''experimentally'' by means of a Monte Carlo computer simulation. Approximate series expressions based on the systematic approach are numerically evaluated along with the heuristic expressions. The comparison (for both forward- and back-scattered field moments) is made for the worst-case conditions of strong multiple scattering for which the theories have not previously been evaluated. Several significant conclusions are drawn which have certain practical implications: in application of the theories to describe some of the scattering phenomena which occur in the troposphere, and in the further evaluation of the theories using experiments on physical models

  7. Assessment of Multiple Scattering Errors of Laser Diffraction Instruments

    Strakey, Peter

    2003-01-01

    The accuracy of two commercial laser diffraction instruments was compared under conditions of multiple scattering designed to simulate the high droplet number densities encountered in liquid propellant rocket combustors...

  8. Multiple scattering approach to X-ray absorption spectroscopy

    Benfatto, M.; Wu Ziyu

    2003-01-01

    In this paper authors present the state of the art of the theoretical background needed for analyzing X-ray absorption spectra in the whole energy range. The multiple-scattering (MS) theory is presented in detail with some applications on real systems. Authors also describe recent progress in performing geometrical fitting of the XANES (X-ray absorption near-edge structure) energy region and beyond using a full multiple-scattering approach

  9. Ultrafast collinear scattering and carrier multiplication in graphene.

    Brida, D; Tomadin, A; Manzoni, C; Kim, Y J; Lombardo, A; Milana, S; Nair, R R; Novoselov, K S; Ferrari, A C; Cerullo, G; Polini, M

    2013-01-01

    Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic and nanophotonic materials. The interaction of light with charge carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools emitting phonons. Although the slower relaxation mechanisms have been extensively investigated, the initial stages still pose a challenge. Experimentally, they defy the resolution of most pump-probe setups, due to the extremely fast sub-100 fs carrier dynamics. Theoretically, massless Dirac fermions represent a novel many-body problem, fundamentally different from Schrödinger fermions. Here we combine pump-probe spectroscopy with a microscopic theory to investigate electron-electron interactions during the early stages of relaxation. We identify the mechanisms controlling the ultrafast dynamics, in particular the role of collinear scattering. This gives rise to Auger processes, including charge multiplication, which is key in photovoltage generation and photodetectors.

  10. Radiation of ultrarelativistic charge taking into account for multiple scattering

    Yang, C.

    1977-01-01

    A brief theoretical review of characteristics of X-rays and more hard radiation formed by an ultrarelativistic charged particle passing through a plate or a stack of plates with regard for multiple scattering and the plate material absorptivity is made. Formulas for frequency- angular and frequency distributions of total radiation in the cases of a plate and of a stack of plates with large spacings as well as a stack of sufficiently thick plates are given. A calculation method for the radiation distributions in a general case of an arbitrary stack is pointed out. The frequency distribution of the total radiation consisting of bremsstrahlung and boundary effects is analyzed in detail. A problem of experimental separation of the boundary effect from the total radiation is discussed

  11. Iterative numerical solution of scattering problems

    Tomio, L; Adhikari, S K

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10{sup 10} after some-8-10 iterations. (author). 31 refs, 2 tabs.

  12. Iterative numerical solution of scattering problems

    Tomio, L.; Adhikari, S.K.

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some-8-10 iterations. (author). 31 refs, 2 tabs

  13. Analysis of multiple scattering effects in optical Doppler tomography

    Yura, H.T.; Thrane, L.; Andersen, Peter E.

    2005-01-01

    Optical Doppler tomography (ODT) combines Doppler velocimetry and optical coherence tomography (OCT) to obtain high-resolution cross-sectional imaging of particle flow velocity in scattering media such as the human retina and skin. Here, we present the results of a theoretical analysis of ODT where...... multiple scattering effects are included. The purpose of this analysis is to determine how multiple scattering affects the estimation of the depth-resolved localized flow velocity. Depth-resolved velocity estimates are obtained directly from the corresponding mean or standard deviation of the observed...

  14. SWIMS: a small-angle multiple scattering computer code

    Sayer, R.O.

    1976-07-01

    SWIMS (Sigmund and WInterbon Multiple Scattering) is a computer code for calculation of the angular dispersion of ion beams that undergo small-angle, incoherent multiple scattering by gaseous or solid media. The code uses the tabulated angular distributions of Sigmund and Winterbon for a Thomas-Fermi screened Coulomb potential. The fraction of the incident beam scattered into a cone defined by the polar angle α is computed as a function of α for reduced thicknesses over the range 0.01 less than or equal to tau less than or equal to 10.0. 1 figure, 2 tables

  15. Method for measuring multiple scattering corrections between liquid scintillators

    Verbeke, J.M., E-mail: verbeke2@llnl.gov; Glenn, A.M., E-mail: glenn22@llnl.gov; Keefer, G.J., E-mail: keefer1@llnl.gov; Wurtz, R.E., E-mail: wurtz1@llnl.gov

    2016-07-21

    A time-of-flight method is proposed to experimentally quantify the fractions of neutrons scattering between scintillators. An array of scintillators is characterized in terms of crosstalk with this method by measuring a californium source, for different neutron energy thresholds. The spectral information recorded by the scintillators can be used to estimate the fractions of neutrons multiple scattering. With the help of a correction to Feynman's point model theory to account for multiple scattering, these fractions can in turn improve the mass reconstruction of fissile materials under investigation.

  16. Electron Raman scattering in asymmetrical multiple quantum wells

    Betancourt-Riera, R; Rosas, R; Marin-Enriquez, I; Riera, R; Marin, J L

    2005-01-01

    Optical properties of asymmetrical multiple quantum wells for the construction of quantum cascade lasers are calculated, and expressions for the electronic states of asymmetrical multiple quantum wells are presented. The gain and differential cross-section for an electron Raman scattering process are obtained. Also, the emission spectra for several scattering configurations are discussed, and the corresponding selection rules for the processes involved are studied; an interpretation of the singularities found in the spectra is given. The electron Raman scattering studied here can be used to provide direct information about the efficiency of the lasers

  17. Multiple scattering effects in depth resolution of elastic recoil detection

    Wielunski, L.S.; Harding, G.L.

    1998-01-01

    Elastic Recoil Detection (ERD) is used to profile hydrogen and other low mass elements in thin films at surface and interfaces in a similar way that Rutherford Backscattering Spectroscopy (RBS) is used to detect and profile heavy elements. It is often assumed that the depth resolutions of these two techniques are similar. However, in contrast to typical RBS, the depth resolution of ERD is limited substantially by multiple scattering. In experimental data analysis and/or spectra simulations of a typical RBS measurement multiple scattering effects are often ignored. Computer programs used in IBA, such as RUMP, HYPRA or RBX do not include multiple scattering effects at all. In this paper, using practical thin metal structures with films containing intentionally introduced hydrogen, we demonstrate experimental ERD depth resolution and sensitivity limitations. The effects of sample material and scattering angle are also discussed. (authors)

  18. Multiple scattering effects in depth resolution of elastic recoil detection

    Wielunski, L.S.; Harding, G.L. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), Lindfield, NSW (Australia). Telecommunications and Industrial Physics; Szilagyi, E. [KFKI Research Institute for Particle and Nuclear Physics, Budapest, (Hungary)

    1998-06-01

    Elastic Recoil Detection (ERD) is used to profile hydrogen and other low mass elements in thin films at surface and interfaces in a similar way that Rutherford Backscattering Spectroscopy (RBS) is used to detect and profile heavy elements. It is often assumed that the depth resolutions of these two techniques are similar. However, in contrast to typical RBS, the depth resolution of ERD is limited substantially by multiple scattering. In experimental data analysis and/or spectra simulations of a typical RBS measurement multiple scattering effects are often ignored. Computer programs used in IBA, such as RUMP, HYPRA or RBX do not include multiple scattering effects at all. In this paper, using practical thin metal structures with films containing intentionally introduced hydrogen, we demonstrate experimental ERD depth resolution and sensitivity limitations. The effects of sample material and scattering angle are also discussed. (authors). 19 refs., 4 figs.

  19. The problem of multiple carcinomas

    Kegel, W.; Schmieder, A.

    1982-01-01

    This retrospective study reports on the occurrence of multiple carcinomas among the patients of our Department of Radiotherapy. Examination of 1290 patients during 1978 to 1980 showed in 76 cases (5.8%) simultaneously or successively secondary or tertiary tumours. These multiple tumours were most frequent in the mammary gland, in the female genital organs and in the respiratory system. Women had an incidence which was double of that displayed by men. Diagnosis and therapy of malignant tumours must always consider the possibility of multiplicity of carcinomas, either simultaneously or succesively, appearing spontaneously or as a result of iatrogenic influences. This applies in particular to the multicentric and bilateral occurrence of the early types of cancer of the female breast. (orig.) [de

  20. Concise formulation of the three-dimensional multiple-scattering theory.

    Oyhenart, Laurent; Vignéras, Valérie

    2012-08-01

    The scattering of an electromagnetic wave by a set of dielectric and metallic spheres is a well-known physical problem. We show a mathematical simplification of the multiple-scattering theory. In this paper, we will establish the multiple-scattering equation in two different ways. Through the study of the equation form, we can choose the simplest spherical wave expansion for calculations. Then, we propose concise expressions of the Mie scattering coefficients and translation coefficients for both polarizations. With these simplified expressions, large spheres are studied without loss of accuracy. Far-field expressions, cross-sections, and the scattering matrix are also simplified. Thus, we obtain formulas that can be easily understood from a physical point of view.

  1. The Multiple-markets Problem

    Frankel, Christian

    2015-01-01

    Only few studies in the field of new new economic sociology deal with a simultaneity of multiple markets in the analysis. One central explanation of this situation is limitations inherent in the new new economic sociology. In this review essay I address such limitations as a way to develop research...

  2. Scattering integral equations and four nucleon problem

    Narodetskii, I.M.

    1980-01-01

    Existing results from the application of integral equation technique to the four-nucleon bound states and scattering are reviewed. The first numerical calculations of the four-body integral equations have been done ten years ago. Yet, it is still widely believed that these equations are too complicated to solve numerically. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. The presentation is based on the quasiparticle approach. This permits a simple interpretation of the equations in terms of quasiparticle scattering. The mathematical basis for the quasiparticle approach is the Hilbert-Schmidt method of the Fredholm integral equation theory. The first part of this review contains a detailed discussion of the Hilbert-Schmidt expansion as applied to the 2-particle amplitudes and to the kernel of the four-body equations. The second part contains the discussion of the four-body quasiparticle equations and of the resed forullts obtain bound states and scattering

  3. Multiple scattering theory for superconducting heterostructures

    Ujfalussy, Balazs [Wigner Research Centre for Physics, Budapest (Hungary)

    2016-07-01

    We generalize the screened Korringa-Kohn-Rostoker method for solving the corresponding Kohn-Sham-Bogoliubov-de Gennes equations for surfaces and interfaces. As an application of the theory, we study the quasiparticle spectrum of Au overlayers on a Nb(100) host. We find that within the superconducting gap region, the quasiparticle spectrum consists of Andreev bound states with a dispersion which is closely connected to the underlying electronic structure of the overlayer. We also find that the spectrum has a strongly k-dependent induced gap. The properties of the gap are discussed in relation to the thickness of the overlayer, and it is shown that certain states do not participate in the Andreev scattering process. From the thickness dependence of the gap size we calculate the superconducting critical temperature of Au/Nb(100) heterostructures what we compare with with experiments. Moreover, predictions are made for similar heterostructures of other compounds.

  4. Multiple scattering theory of radiative transfer in inhomogeneous atmospheres.

    Kanal, M.

    1973-01-01

    In this paper we treat the multiple scattering theory of radiative transfer in plane-parallel inhomogeneous atmospheres. The treatment presented here may be adopted to model atmospheres characterized by an optical depth dependent coherent scattering phase function. For the purpose of illustration we consider the semi-infinite medium in which the absorption property of the atmosphere is characterized by an exponential function. The methodology employed here is the extension of the case treated previously by the author for homogeneous atmospheres.

  5. Simulation of multiple scattering background in heavy ion backscattering spectrometry

    Li, M.M.; O'Connor, D.J.

    1999-01-01

    With the development of heavy ion backscattering spectrometry (HIBS) for the detection of trace quantities of heavy-atom impurities on Si surfaces, it is necessary to quantify the multiple scattering contribution to the spectral background. In the present work, the Monte Carlo computer simulation program TRIM has been used to study the backscattering spectrum and the multiple scattering background features for heavy ions C, Ne, Si, Ar and Kr impinging on four types of targets: (1) a single ultra-thin (free standing) Au film of 10 A thickness, (2) a 10 A Au film on a 50 A Si surface, (3) a 10 A Au film on an Si substrate (10 000 A), and (4) a thick target (10 000 A) of pure Si. The ratio of the signal from the Au thin layer to the background due to multiple scattering has been derived by fitting the simulation results. From the simulation results, it is found that the Au film contributes to the background which the Si plays a role in developing due to the ion's multiple scattering in the substrate. Such a background is generated neither by only the Au thin layer nor by the pure Si substrate independently. The corresponding mechanism of multiple scattering in the target can be explained as one large-angle scattering in the Au layer and subsequently several small angle scatterings in the substrate. This study allows an appropriate choice of incident beam species and energy range when the HIBS is utilized to analyse low level impurities in Si wafers

  6. 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)

  7. Analytical multiple scattering correction to the Mie theory: Application to the analysis of the lidar signal

    Flesia, C.; Schwendimann, P.

    1992-01-01

    The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.

  8. Ground Vibration Isolation of Multiple Scattering by Using Rows of Tubular Piles as Barriers

    Miao-miao Sun

    2014-01-01

    Full Text Available A new formal solution for the multiple scattering of plane harmonic waves by a group of arbitrary configuration tubular piles in an elastic total space is derived. Each order of scattering satisfies prescribed boundary conditions at the interface of tubular piles, which is delivered as the sum of incident and scattering waves. The first order performs the scattering wave by each scattered pile and the subsequent orders resulted from the excitation of each pile of first order of scattering from the remaining tubular piles. Advanced scattering orders can be regarded as the same manners. Several series of scattering coefficients are figured out with the aids of addition theorem so that the exact steady-state solution for the scattered displacement and stress is obtained. Particularly, when internal diameter of tubular piles tends to be infinitely small, it degenerates to a solid pile problem. By imposing the normalized displacement amplitudes and transmissibility indices, the influences of specific parameters such as scattering orders, internal and external diameter ratio of piles, pile material rigidity, position and distances between tubular pile and pile rows, and pile numbers are discussed. Certain recommended conclusions have been drawn as the guidelines of practical engineering design for discontinuous barrier of tubular piles.

  9. Monte Carlo simulations of multiple scattering effects in ERD measurements

    Doyle, Barney Lee; Arstila, Kai.; Nordlumd, K.; Knapp, James Arthur

    2003-01-01

    Multiple scattering effects in ERD measurements are studied by comparing two Monte Carlo simulation codes, representing different approaches to obtain acceptable statistics, to experimental spectra measured from a HfO 2 sample with a time-of-flight-ERD setup. The results show that both codes can reproduce the absolute detection yields and the energy distributions in an adequate way. The effect of the choice of the interatomic potential in multiple scattering effects is also studied. Finally the capabilities of the MC simulations in the design of new measurement setups are demonstrated by simulating the recoil energy spectra from a WC x N y sample with a low energy heavy ion beam.

  10. Effects of multiple scattering and target structure on photon emission

    Blankenbecler, R.

    1996-05-01

    The Landau-Pomeranchuk-Migdal effect is the suppression of Bethe-Heitler radiation caused by multiple scattering in the target medium. The quantum treatment given by S.D. Drell and the author for homogeneous targets of finite thickness will be reviewed. It will then be extended to structured targets. In brief, it is shown that radiators composed of separated plates or of a medium with a spatially varying radiation length can exhibit unexpected structure, even coherence maxima and minima, in their photon spectra. Finally, a functional integral method for performing the averaging implicit in multiple scattering will be briefly discussed and the leading corrections to previous results evaluated

  11. Collective hypersonic excitations in strongly multiple scattering colloids.

    Still, T; Gantzounis, G; Kiefer, D; Hellmann, G; Sainidou, R; Fytas, G; Stefanou, N

    2011-04-29

    Unprecedented low-dispersion high-frequency acoustic excitations are observed in dense suspensions of elastically hard colloids. The experimental phononic band structure for SiO(2) particles with different sizes and volume fractions is well represented by rigorous full-elastodynamic multiple-scattering calculations. The slow phonons, which do not relate to particle resonances, are localized in the surrounding liquid medium and stem from coherent multiple scattering that becomes strong in the close-packing regime. Such rich phonon-matter interactions in nanostructures, being still unexplored, can open new opportunities in phononics.

  12. Multiple scattering theory of X-ray absorption. A review

    Fonda, L.

    1991-11-01

    We review the basic elements of the theory of X-ray absorption using the tools provided by the theory of multiple scattering. A momentum space approach of clear physical insight is used where the final formulas expressing EXAFS and XANES, i.e. the structures appearing in the absorption coefficient above the edge of a deep core level threshold, are given in terms of eigenstates of the photoelectron momentum. A simple graphic representation is given for the multiple scattering function. (author). 38 refs, 4 figs, 1 tab

  13. Elastic scattering of protons at the nucleus 6He in the Glauber multiple scattering theory

    Prmantayeva, B.A.; Temerbayev, A.A.; Tleulessova, I.K.; Ibrayeva, E.T.

    2011-01-01

    Calculation is submitted for the differential cross sections of elastic p 6 He-scattering at energies of 70 and 700 MeV/nucleon within the framework of the Glauber theory of multiple diffraction scattering. We used the three-particle wave functions: α-n-n with realistic intercluster potentials. The sensitivity of elastic scattering to the proton-nuclear interaction and the structure of nuclei had been investigated. It is shown that the contribution of small components of the wave function as well as the multiplicity of the scattering operator Ω should be considered to describe a cross-section in broad angular range . A comparison with available experimental data was made. (author)

  14. An empirical correction for moderate multiple scattering in super-heterodyne light scattering.

    Botin, Denis; Mapa, Ludmila Marotta; Schweinfurth, Holger; Sieber, Bastian; Wittenberg, Christopher; Palberg, Thomas

    2017-05-28

    Frequency domain super-heterodyne laser light scattering is utilized in a low angle integral measurement configuration to determine flow and diffusion in charged sphere suspensions showing moderate to strong multiple scattering. We introduce an empirical correction to subtract the multiple scattering background and isolate the singly scattered light. We demonstrate the excellent feasibility of this simple approach for turbid suspensions of transmittance T ≥ 0.4. We study the particle concentration dependence of the electro-kinetic mobility in low salt aqueous suspension over an extended concentration regime and observe a maximum at intermediate concentrations. We further use our scheme for measurements of the self-diffusion coefficients in the fluid samples in the absence or presence of shear, as well as in polycrystalline samples during crystallization and coarsening. We discuss the scope and limits of our approach as well as possible future applications.

  15. Multiple scattering and attenuation corrections in Deep Inelastic Neutron Scattering experiments

    Dawidowski, J; Blostein, J J; Granada, J R

    2006-01-01

    Multiple scattering and attenuation corrections in Deep Inelastic Neutron Scattering experiments are analyzed. The theoretical basis of the method is stated, and a Monte Carlo procedure to perform the calculation is presented. The results are compared with experimental data. The importance of the accuracy in the description of the experimental parameters is tested, and the implications of the present results on the data analysis procedures is examined

  16. Imaging moving objects from multiply scattered waves and multiple sensors

    Miranda, Analee; Cheney, Margaret

    2013-01-01

    In this paper, we develop a linearized imaging theory that combines the spatial, temporal and spectral components of multiply scattered waves as they scatter from moving objects. In particular, we consider the case of multiple fixed sensors transmitting and receiving information from multiply scattered waves. We use a priori information about the multipath background. We use a simple model for multiple scattering, namely scattering from a fixed, perfectly reflecting (mirror) plane. We base our image reconstruction and velocity estimation technique on a modification of a filtered backprojection method that produces a phase-space image. We plot examples of point-spread functions for different geometries and waveforms, and from these plots, we estimate the resolution in space and velocity. Through this analysis, we are able to identify how the imaging system depends on parameters such as bandwidth and number of sensors. We ultimately show that enhanced phase-space resolution for a distribution of moving and stationary targets in a multipath environment may be achieved using multiple sensors. (paper)

  17. High-energy expansion for nuclear multiple scattering

    Wallace, S.J.

    1975-01-01

    The Watson multiple scattering series is expanded to develop the Glauber approximation plus systematic corrections arising from three (1) deviations from eikonal propagation between scatterings, (2) Fermi motion of struck nucleons, and (3) the kinematic transformation which relates the many-body scattering operators of the Watson series to the physical two-body scattering amplitude. Operators which express effects ignored at the outset to obtain the Glauber approximation are subsequently reintroduced via perturbation expansions. Hence a particular set of approximations is developed which renders the sum of the Watson series to the Glauber form in the center of mass system, and an expansion is carried out to find leading order corrections to that summation. Although their physical origins are quite distinct, the eikonal, Fermi motion, and kinematic corrections produce strikingly similar contributions to the scattering amplitude. It is shown that there is substantial cancellation between their effects and hence the Glauber approximation is more accurate than the individual approximations used in its derivation. It is shown that the leading corrections produce effects of order (2kR/subc/) -1 relative to the double scattering term in the uncorrected Glauber amplitude, hk being momentum and R/subc/ the nuclear char []e radius. The leading order corrections are found to be small enough to validate quatitative analyses of experimental data for many intermediate to high energy cases and for scattering angles not limited to the very forward region. In a Gaussian model, the leading corrections to the Glauber amplitude are given as convenient analytic expressions

  18. Multiple scattering in the nuclear rearrangement reactions at medium energy

    Tekou, A.

    1980-09-01

    It is shown that the multiple scattering mechanism is very important in the transfer of the large momenta involved in the nuclear rearrangement reactions at medium energy. In contrast to the usual belief, the reaction cross-section is not very sensitive to the high momenta components of the nuclear wave function. The multiple scattering mechanism is especially important in 4 He(p,d) 3 He reaction around 800 MeV. Here the collisions involving two nucleons of the target nucleus are dominant. The triple collisions contribution is also important. The four collision contribution is negligible in the forward direction and sizeable at large angles. Thus, using the K.M.T. approach in DWBA calculations, the second order term of the optical potential must be included. So, is it not well established that the second term of the K.M.T. optical potential is important for the proton elastic scattering on light nuclei. (author)

  19. Problems in the links between scattering data and interaction potentials

    Amos, K.

    1995-01-01

    The scattering function is of paramount importance in any approaches by which quantitative information on the interaction between colliding quantal systems of nuclear, atomic or molecular type, may be sought from measured, elastic scattering data. Therein there are two possible spectral parameters, the energy and the angular momentum. Most experimental results suggest use of fixed energy and variable angular momentum schemes. Such fixed energy data and their analyses are the subject of this report, with particular emphasis placed upon the problems of the link between data and the scattering function. 18 figs

  20. 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.

  1. Problems in the links between scattering data and interaction potentials

    Amos, K.

    1995-10-01

    The scattering function is of paramount importance in any approaches by which quantitative information on the interaction between colliding quantal systems of nuclear, atomic or molecular type, may be sought from measured, elastic scattering data. Therein there are two possible spectral parameters, the energy and the angular momentum. Most experimental results suggest use of fixed energy and variable angular momentum schemes. Such fixed energy data and their analyses are the subject of this report, with particular emphasis placed upon the problems of the link between data and the scattering function. 18 figs.

  2. Multiple scattering in synchrotron studies of disordered materials

    Poulsen, H.F.; Neuefeind, J.

    1995-01-01

    A formalism for the multiple scattering and self-absorption in synchrotron studies of disordered materials is presented. The formalism goes beyond conventionally used approximations and treat the cross sections, the beam characteristics, the state of polarization, and the electronic correction terms in full. Using hard X-rays it is shown how the simulated distributions can be directly compared to experimental data. ((orig.))

  3. a Proposed Benchmark Problem for Scatter Calculations in Radiographic Modelling

    Jaenisch, G.-R.; Bellon, C.; Schumm, A.; Tabary, J.; Duvauchelle, Ph.

    2009-03-01

    Code Validation is a permanent concern in computer modelling, and has been addressed repeatedly in eddy current and ultrasonic modeling. A good benchmark problem is sufficiently simple to be taken into account by various codes without strong requirements on geometry representation capabilities, focuses on few or even a single aspect of the problem at hand to facilitate interpretation and to avoid that compound errors compensate themselves, yields a quantitative result and is experimentally accessible. In this paper we attempt to address code validation for one aspect of radiographic modeling, the scattered radiation prediction. Many NDT applications can not neglect scattered radiation, and the scatter calculation thus is important to faithfully simulate the inspection situation. Our benchmark problem covers the wall thickness range of 10 to 50 mm for single wall inspections, with energies ranging from 100 to 500 keV in the first stage, and up to 1 MeV with wall thicknesses up to 70 mm in the extended stage. A simple plate geometry is sufficient for this purpose, and the scatter data is compared on a photon level, without a film model, which allows for comparisons with reference codes like MCNP. We compare results of three Monte Carlo codes (McRay, Sindbad and Moderato) as well as an analytical first order scattering code (VXI), and confront them to results obtained with MCNP. The comparison with an analytical scatter model provides insights into the application domain where this kind of approach can successfully replace Monte-Carlo calculations.

  4. Multiple-scattering in radar systems: A review

    Battaglia, Alessandro; Tanelli, Simone; Kobayashi, Satoru; Zrnic, Dusan; Hogan, Robin J.; Simmer, Clemens

    2010-01-01

    Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces. Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude). This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is

  5. Continuum multiple-scattering approach to electron-molecule scattering and molecular photoionization

    Dehmer, J.L.; Dill, D.

    1979-01-01

    The multiple-scattering approach to the electronic continuum of molecules is described. The continuum multiple-scattering model (CMSM) was developed as a survey tool and, as such was required to satisfy two requirements. First, it had to have a very broad scope, which means (i) molecules of arbitrary geometry and complexity containing any atom in the periodic system, (ii) continuum electron energies from 0-1000 eV, and (iii) capability to treat a large range of processes involving both photoionization and electron scattering. Second, the structure of the theory was required to lend itself to transparent, physical interpretation of major spectral features such as shape resonances. A comprehensive theoretical framework for the continuum multiple scattering method is presented, as well as its applications to electron-molecule scattering and molecular photoionization. Highlights of recent applications in these two areas are reviewed. The major impact of the resulting studies over the last few years has been to establish the importance of shape resonances in electron collisions and photoionization of practically all (non-hydride) molecules

  6. Renormalized multiple-scattering theory of photoelectron diffraction

    Biagini, M.

    1993-01-01

    The current multiple-scattering cluster techniques for the calculation of x-ray photoelectron and Auger-electron diffraction patterns consume much computer time in the intermediate-energy range (200--1000 eV); in fact, because of the large value of the electron mean free path and of the large forward-scattering amplitude at such energies, the electron samples a relatively large portion of the crystal, so that the number of paths to be considered becomes dramatically high. An alternative method is developed in the present paper: instead of calculating the individual contribution from each single path, the scattering matrix of each plane parallel to the surface is calculated with a renormalization process that calculates every scattering event in the plane up to infinite order. Similarly the scattering between two planes is calculated up to infinite order, and the double-plane scattering matrix is introduced. The process may then be applied to the calculation of a larger set of atomic layers. The advantage of the method is that a relatively small number of internuclear vectors have been used to obtain convergence in the calculation

  7. Comparison of four software packages applied to a scattering problem

    Albertsen, Niels Christian; Chesneaux, Jean-Marie; Christiansen, Søren

    1999-01-01

    We investigate characteristic features of four different software packages by applying them to the numerical solution of a non-trivial physical problem in computer simulation, viz., scattering of waves from a sinusoidal boundary. The numerical method used is based on boundary collocation. This le......We investigate characteristic features of four different software packages by applying them to the numerical solution of a non-trivial physical problem in computer simulation, viz., scattering of waves from a sinusoidal boundary. The numerical method used is based on boundary collocation...

  8. Canonical quantization of gravity and a problem of scattering

    Rubakov, V.A.

    1980-01-01

    Linearized theory of gravity is quantized both in a naive way and as a proper limit of the Dirac-Wheeler-De Witt approach to the quantization of the full theory. The equivalence between the two approaches is established. The problem of scattering in the canonically quantized theory of gravitation is investigated. The concept of the background metric naturally appears in the canonical formalism for this case. The equivalence between canonical and path-integral approaches is established for the problem of scattering. Some kinetical properties of functionals in Wheeler superspace are studied in an appendix. (author)

  9. Charged particle multiplicities in deep inelastic scattering at HERA

    Aid, S.; Anderson, M.; Andreev, V.

    1996-08-01

    Using the H1 detector at HERA, charged particle multiplicity distributions in deep inelastic e + p scattering have been measured over a large kinematical region. The evolution with W and Q 2 of the multiplicity distribution and of the multiplicity moments in pseudorapidity domains of varying size is studied in the current fragmentation region of the hadronic centre-of-mass frame. The results are compared with data from fixed target lepton-nucleon interactions, e + e - annihilations and hadron-hadron collisions as well as with expectations from QCD based parton models. Fits to the negative binomial and lognormal distributions are presented. (orig.)

  10. SWIMS, Sigmund and Winterbon Multiple Scattering of Ion Beams

    Eyeberger, L.

    1999-01-01

    1 - Description of program or function - SWIMS calculates the angular dispersion of ion beams that undergo small-angle, incoherent multiple scattering by gaseous or solid media. 2 - Method of solution - SWIMS uses the tabulated angular distributions of Sigmund and Winterbon for a Thomas-Fermi screened Coulomb potential. The fraction of the incident beam scattered into a cone defined by the polar angle is computed as a function of that angle for a reduced thickness over the rang of 0.01 to 10

  11. A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

    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.

  12. 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

  13. The hydrogen anomaly problem in neutron Compton scattering

    Karlsson, Erik B.

    2018-03-01

    Neutron Compton scattering (also called ‘deep inelastic scattering of neutrons’, DINS) is a method used to study momentum distributions of light atoms in solids and liquids. It has been employed extensively since the start-up of intense pulsed neutron sources about 25 years ago. The information lies primarily in the width and shape of the Compton profile and not in the absolute intensity of the Compton peaks. It was therefore not immediately recognized that the relative intensities of Compton peaks arising from scattering on different isotopes did not always agree with values expected from standard neutron cross-section tables. The discrepancies were particularly large for scattering on protons, a phenomenon that became known as ‘the hydrogen anomaly problem’. The present paper is a review of the discovery, experimental tests to prove or disprove the existence of the hydrogen anomaly and discussions concerning its origin. It covers a twenty-year-long history of experimentation, theoretical treatments and discussions. The problem is of fundamental interest, since it involves quantum phenomena on the subfemtosecond time scale, which are not visible in conventional thermal neutron scattering but are important in Compton scattering where neutrons have two orders of magnitude times higher energy. Different H-containing systems show different cross-section deficiencies and when the scattering processes are followed on the femtosecond time scale the cross-section losses disappear on different characteristic time scales for each H-environment. The last section of this review reproduces results from published papers based on quantum interference in scattering on identical particles (proton or deuteron pairs or clusters), which have given a quantitative theoretical explanation both regarding the H-cross-section reduction and its time dependence. Some new explanations are added and the concluding chapter summarizes the conditions for observing the specific quantum

  14. Coastal Zone Color Scanner atmospheric correction algorithm - Multiple scattering effects

    Gordon, Howard R.; Castano, Diego J.

    1987-01-01

    Errors due to multiple scattering which are expected to be encountered in application of the current Coastal Zone Color Scanner (CZCS) atmospheric correction algorithm are analyzed. The analysis is based on radiative transfer computations in model atmospheres, in which the aerosols and molecules are distributed vertically in an exponential manner, with most of the aerosol scattering located below the molecular scattering. A unique feature of the analysis is that it is carried out in scan coordinates rather than typical earth-sun coordinates, making it possible to determine the errors along typical CZCS scan lines. Information provided by the analysis makes it possible to judge the efficacy of the current algorithm with the current sensor and to estimate the impact of the algorithm-induced errors on a variety of applications.

  15. High count problems in elemental analysis using pulsed neutron inelastic scattering

    Vartsky, D; Wielopolski, L; Ellis, K J; Cohn, S H [Brookhaven National Lab., Upton, NY (USA). Medical Dept.

    1983-03-01

    Elemental analysis by neutron inelastic scattering using a miniature intense pulsed neutron source ('Zetatron') was evaluated. The particular problems associated with detector pulse-pile-up during the neutron burst and the limited ability of the analyzer to process on average more than one detector pulse per neutron burst were examined. The severity of these problems is described and a solution using a multiple ADC system is proposed.

  16. Comparison of matrix methods for elastic wave scattering problems

    Tsao, S.J.; Varadan, V.K.; Varadan, V.V.

    1983-01-01

    This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error

  17. Approximate solutions of some problems of scattering of surface ...

    A Choudhary

    Abstract. A class of mixed boundary value problems (bvps), occurring in the study of scattering of surface water waves by thin vertical rigid barriers placed in water of finite depth, is examined for their approximate solutions. Two different placings of vertical barriers are analyzed, namely, (i) a partially immersed barrier and.

  18. 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)

  19. Canonical transformations method in the potential scattering problem

    Pavlenko, Yu.G.

    1984-01-01

    Canonical formalism of the first order is used in the present paper to solve the problem of scattering and other problems of quantum mechanics. The theory of canonical transformations (CT) being the basis of hamiltonian approach permits to develop several methods of integration being beyond the scope of the standard theory of perturbations. In this case it is essential for numerical counting that the theory permits to obtain algorithm for plotting highest approximations

  20. Interstitial integrals in the multiple-scattering model

    Swanson, J.R.; Dill, D.

    1982-01-01

    We present an efficient method for the evaluation of integrals involving multiple-scattering wave functions over the interstitial region. Transformation of the multicenter interstitial wave functions to a single center representation followed by a geometric projection reduces the integrals to products of analytic angular integrals and numerical radial integrals. The projection function, which has the value 1 in the interstitial region and 0 elsewhere, has a closed-form partial-wave expansion. The method is tested by comparing its results with exact normalization and dipole integrals; the differences are 2% at worst and typically less than 1%. By providing an efficient means of calculating Coulomb integrals, the method allows treatment of electron correlations using a multiple scattering basis set

  1. Quantum correlations induced by multiple scattering of quadrature squeezed light

    Lodahl, Peter

    2006-01-01

    Propagating quadrature squeezed light through a multiple scattering random medium is found to induce pronounced spatial quantum correlations that have no classical analogue. The correlations are revealed in the number of photons transported through the sample that can be measured from the intensity...... fluctuations of the total transmission or reflection. In contrast, no pronounced spatial quantum correlations appear in the quadrature amplitudes where excess noise above the shot noise level is found....

  2. Multiple-scattering theory. New developments and applications

    Ernst, Arthur

    2007-12-04

    Multiple-scattering theory (MST) is a very efficient technique for calculating the electronic properties of an assembly of atoms. It provides explicitly the Green function, which can be used in many applications such as magnetism, transport and spectroscopy. This work gives an overview on recent developments of multiple-scattering theory. One of the important innovations is the multiple scattering implementation of the self-interaction correction approach, which enables realistic electronic structure calculations of systems with localized electrons. Combined with the coherent potential approximation (CPA), this method can be applied for studying the electronic structure of alloys and as well as pseudo-alloys representing charge and spin disorder. This formalism is extended to finite temperatures which allows to investigate phase transitions and thermal fluctuations in correlated materials. Another novel development is the implementation of the self-consistent non-local CPA approach, which takes into account charge correlations around the CPA average and chemical short range order. This formalism is generalized to the relativistic treatment of magnetically ordered systems. Furthermore, several improvements are implemented to optimize the computational performance and to increase the accuracy of the KKR Green function method. The versatility of the approach is illustrated in numerous applications. (orig.)

  3. Multiple-scattering theory. New developments and applications

    Ernst, Arthur

    2007-01-01

    Multiple-scattering theory (MST) is a very efficient technique for calculating the electronic properties of an assembly of atoms. It provides explicitly the Green function, which can be used in many applications such as magnetism, transport and spectroscopy. This work gives an overview on recent developments of multiple-scattering theory. One of the important innovations is the multiple scattering implementation of the self-interaction correction approach, which enables realistic electronic structure calculations of systems with localized electrons. Combined with the coherent potential approximation (CPA), this method can be applied for studying the electronic structure of alloys and as well as pseudo-alloys representing charge and spin disorder. This formalism is extended to finite temperatures which allows to investigate phase transitions and thermal fluctuations in correlated materials. Another novel development is the implementation of the self-consistent non-local CPA approach, which takes into account charge correlations around the CPA average and chemical short range order. This formalism is generalized to the relativistic treatment of magnetically ordered systems. Furthermore, several improvements are implemented to optimize the computational performance and to increase the accuracy of the KKR Green function method. The versatility of the approach is illustrated in numerous applications. (orig.)

  4. 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

  5. Resolvent-Techniques for Multiple Exercise Problems

    Christensen, Sören; Lempa, Jukka

    2015-01-01

    We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples

  6. Resolvent-Techniques for Multiple Exercise Problems

    Christensen, Sören, E-mail: christensen@math.uni-kiel.de [Christian–Albrechts-University in Kiel, Mathematical Institute (Germany); Lempa, Jukka, E-mail: jukka.lempa@hioa.no [Oslo and Akershus University College, School of business, Faculty of Social Sciences (Norway)

    2015-02-15

    We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples.

  7. 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

  8. Genetic Algorithms for Multiple-Choice Problems

    Aickelin, Uwe

    2010-04-01

    This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of information and the way it is included are important factors for success.Two multiple-choice problems are considered.The first is constructing a feasible nurse roster that considers as many requests as possible.In the second problem, shops are allocated to locations in a mall subject to constraints and maximising the overall income.Genetic algorithms are chosen for their well-known robustness and ability to solve large and complex discrete optimisation problems.However, a survey of the literature reveals room for further research into generic ways to include constraints into a genetic algorithm framework.Hence, the main theme of this work is to balance feasibility and cost of solutions.In particular, co-operative co-evolution with hierarchical sub-populations, problem structure exploiting repair schemes and indirect genetic algorithms with self-adjusting decoder functions are identified as promising approaches.The research starts by applying standard genetic algorithms to the problems and explaining the failure of such approaches due to epistasis.To overcome this, problem-specific information is added in a variety of ways, some of which are designed to increase the number of feasible solutions found whilst others are intended to improve the quality of such solutions.As well as a theoretical discussion as to the underlying reasons for using each operator,extensive computational experiments are carried out on a variety of data.These show that the indirect approach relies less on problem structure and hence is easier to implement and superior in solution quality.

  9. A Monte Carlo evaluation of analytical multiple scattering corrections for unpolarised neutron scattering and polarisation analysis data

    Mayers, J.; Cywinski, R.

    1985-03-01

    Some of the approximations commonly used for the analytical estimation of multiple scattering corrections to thermal neutron elastic scattering data from cylindrical and plane slab samples have been tested using a Monte Carlo program. It is shown that the approximations are accurate for a wide range of sample geometries and scattering cross-sections. Neutron polarisation analysis provides the most stringent test of multiple scattering calculations as multiply scattered neutrons may be redistributed not only geometrically but also between the spin flip and non spin flip scattering channels. A very simple analytical technique for correcting for multiple scattering in neutron polarisation analysis has been tested using the Monte Carlo program and has been shown to work remarkably well in most circumstances. (author)

  10. Electromagnetic imaging of multiple-scattering small objects: non-iterative analytical approach

    Chen, X; Zhong, Y

    2008-01-01

    Multiple signal classification (MUSIC) imaging method and the least squares method are applied to solve the electromagnetic inverse scattering problem of determining the locations and polarization tensors of a collection of small objects embedded in a known background medium. Based on the analysis of induced electric and magnetic dipoles, the proposed MUSIC method is able to deal with some special scenarios, due to the shapes and materials of objects, to which the standard MUSIC doesn't apply. After the locations of objects are obtained, the nonlinear inverse problem of determining the polarization tensors of objects accounting for multiple scattering between objects is solved by a non-iterative analytical approach based on the least squares method

  11. Multiple Scattering Theory for Spectroscopies : a Guide to Multiple Scattering Computer Codes : Dedicated to C. R. Natoli on the Occasion of his 75th Birthday

    Hatada, Keisuke; Ebert, Hubert

    2018-01-01

    This edited book, based on material presented at the EU Spec Training School on Multiple Scattering Codes and the following MSNano Conference, is divided into two distinct parts. The first part, subtitled “basic knowledge”, provides the basics of the multiple scattering description in spectroscopies, enabling readers to understand the physics behind the various multiple scattering codes available for modelling spectroscopies. The second part, “extended knowledge”, presents “state- of-the-art” short chapters on specific subjects associated with improving of the actual description of spectroscopies within the multiple scattering formalism, such as inelastic processes, or precise examples of modelling.

  12. 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)

  13. 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

  14. [Supporting parenting in families with multiple problems].

    Le Foll, Julie

    2015-01-01

    Supporting parenthood in families with multiple problems is a major early prevention challenge. Indeed, the factors of vulnerability, especially if they mount up, expose the child to an increased risk of a somatic pathology, developmental delays, learning difficulties and maltreatment. In order to limit the impact of these vulnerabilities on the health of mothers and infants, it is essential to act early, to adapt the working framework and to collaborate within a network. Copyright © 2015 Elsevier Masson SAS. All rights reserved.

  15. An integral for second-order multiple scattering perturbation theory

    Hoffman, G.G.

    1997-01-01

    This paper presents the closed form evaluation of a six-dimensional integral. The integral arises in the application to many-electron systems of a multiple scattering perturbation expansion at second order when formulated in fourier space. The resulting function can be used for the calculation of both the electron density and the effective one-electron potential in an SCF calculations. The closed form expression derived here greatly facilitates these calculations. In addition, the evaluated integral can be used for the computation of second-order corrections to the open-quotes optimized Thomas-Fermi theory.close quotes 10 refs., 2 figs

  16. Quantum Interference and Entanglement Induced by Multiple Scattering of Light

    Ott, Johan Raunkjær; Mortensen, Asger; Lodahl, Peter

    2010-01-01

    We report on the effects of quantum interference induced by the transmission of an arbitrary number of optical quantum states through a multiple-scattering medium. We identify the role of quantum interference on the photon correlations and the degree of continuous variable entanglement between two...... output modes. It is shown that quantum interference survives averaging over all ensembles of disorder and manifests itself as increased photon correlations due to photon antibunching. Furthermore, the existence of continuous variable entanglement correlations in a volume speckle pattern is predicted. Our...

  17. Sound field reproduction as an equivalent acoustical scattering problem.

    Fazi, Filippo Maria; Nelson, Philip A

    2013-11-01

    Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.

  18. Approximate Coulomb effects in the three-body scattering problem

    Haftel, M.I.; Zankel, H.

    1981-01-01

    From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles

  19. MCRTOF, Multiple Scattering of Resonance Region Neutron in Time of Flight Experiments

    Ohkubo, Mako

    1984-01-01

    1 - Description of program or function: Multiple scattering of neutrons in the resonance energy region impinging on a disk with an arbitrary angle. 2 - Method of solution: The Monte Carlo method is employed to simulate the path of an incident neutron in a medium for which macroscopic cross sections are determined by resonance parameters. By tracing a large number of neutrons, probabilities for capture, transmission, front-face scattering, rear-face scattering and side-face scattering are determined and printed out as function of incident neutron energy. Optionally, the distribution of capture locations in the disk can be printed. The incident neutron energy is swept to fit a situation as encountered in time-of-flight experiments. 3 - Restrictions on the complexity of the problem: The cross section file is constructed from input resonance parameters with a single- level Breit-Wigner formula. The following restrictions and simplifications apply: - The maximum number of resonances is five. - Reactions other than capture and scattering are neglected. - The angular scattering distribution in the center-of-mass system is assumed to be uniform. - Chemical binding effects are neglected

  20. Aethalometer multiple scattering correction Cref for mineral dust aerosols

    Di Biagio, Claudia; Formenti, Paola; Cazaunau, Mathieu; Pangui, Edouard; Marchand, Nicolas; Doussin, Jean-François

    2017-08-01

    In this study we provide a first estimate of the Aethalometer multiple scattering correction Cref for mineral dust aerosols. Cref is an empirical constant used to correct the aerosol absorption coefficient measurements for the multiple scattering artefact of the Aethalometer; i.e. the filter fibres on which aerosols are deposited scatter light and this is miscounted as absorption. The Cref at 450 and 660 nm was obtained from the direct comparison of Aethalometer data (Magee Sci. AE31) with (i) the absorption coefficient calculated as the difference between the extinction and scattering coefficients measured by a Cavity Attenuated Phase Shift Extinction analyser (CAPS PMex) and a nephelometer respectively at 450 nm and (ii) the absorption coefficient from a MAAP (Multi-Angle Absorption Photometer) at 660 nm. Measurements were performed on seven dust aerosol samples generated in the laboratory by the mechanical shaking of natural parent soils issued from different source regions worldwide. The single scattering albedo (SSA) at 450 and 660 nm and the size distribution of the aerosols were also measured. Cref for mineral dust varies between 1.81 and 2.56 for a SSA of 0.85-0.96 at 450 nm and between 1.75 and 2.28 for a SSA of 0.98-0.99 at 660 nm. The calculated mean for dust is 2.09 (±0.22) at 450 nm and 1.92 (±0.17) at 660 nm. With this new Cref the dust absorption coefficient by the Aethalometer is about 2 % (450 nm) and 11 % (660 nm) higher than that obtained by using Cref = 2.14 at both 450 and 660 nm, as usually assumed in the literature. This difference induces a change of up to 3 % in the dust SSA at 660 nm. The Cref seems to be independent of the fine and coarse particle size fractions, and so the obtained Cref can be applied to dust both close to sources and following transport. Additional experiments performed with pure kaolinite minerals and polluted ambient aerosols indicate Cref of 2.49 (±0.02) and 2.32 (±0.01) at 450 and 660 nm (SSA = 0.96-0.97) for

  1. Muon energy estimate through multiple scattering with the MACRO detector

    Ambrosio, M.; Antolini, R.; Auriemma, G.; Bakari, D.; Baldini, A.; Barbarino, G.C.; Barish, B.C.; Battistoni, G.; Becherini, Y.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bloise, C.; Bower, C.; Brigida, M.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Candela, A.; Carboni, M.; Caruso, R.; Cassese, F.; Cecchini, S.; Cei, F.; Chiarella, V.; Choudhary, B.C.; Coutu, S.; Cozzi, M.; De Cataldo, G.; De Deo, M.; Dekhissi, H.; De Marzo, C.; De Mitri, I.; Derkaoui, J.; De Vincenzi, M.; Di Credico, A.; Dincecco, M.; Erriquez, O.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Gray, L.; Grillo, A.; Guarino, F.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Iarocci, E.; Katsavounidis, E.; Katsavounidis, I.; Kearns, E.; Kim, H.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D.S.; Lindozzi, M.; Lipari, P.; Longley, N.P.; Longo, M.J.; Loparco, F.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Margiotta, A.; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M.N.; Michael, D.G.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicolo, D.; Nolty, R.; Orth, C.; Osteria, G.; Palamara, O.; Patera, V.; Patrizii, L.; Pazzi, R.; Peck, C.W.; Perrone, L.; Petrera, S.; Pistilli, P.; Popa, V.; Raino, A.; Reynoldson, J.; Ronga, F.; Rrhioua, A.; Satriano, C.; Scapparone, E. E-mail: eugenio.scapparone@bo.infn.it; Scholberg, K.; Sciubba, A.; Serra, P.; Sioli, M. E-mail: maximiliano.sioli@bo.infn.it; Sirri, G.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J.L.; Sulak, L.R.; Surdo, A.; Tarle, G.; Tatananni, E.; Togo, V.; Vakili, M.; Walter, C.W.; Webb, R

    2002-10-21

    Muon energy measurement represents an important issue for any experiment addressing neutrino-induced up-going muon studies. Since the neutrino oscillation probability depends on the neutrino energy, a measurement of the muon energy adds an important piece of information concerning the neutrino system. We show in this paper how the MACRO limited streamer tube system can be operated in drift mode by using the TDCs included in the QTPs, an electronics designed for magnetic monopole search. An improvement of the space resolution is obtained, through an analysis of the multiple scattering of muon tracks as they pass through our detector. This information can be used further to obtain an estimate of the energy of muons crossing the detector. Here we present the results of two dedicated tests, performed at CERN PS-T9 and SPS-X7 beam lines, to provide a full check of the electronics and to exploit the feasibility of such a multiple scattering analysis. We show that by using a neural network approach, we are able to reconstruct the muon energy for E{sub {mu}}<40 GeV. The test beam data provide an absolute energy calibration, which allows us to apply this method to MACRO data.

  2. Muon energy estimate through multiple scattering with the MACRO detector

    Ambrosio, M; Auriemma, G; Bakari, D; Baldini, A; Barbarino, G C; Barish, B C; Battistoni, G; Becherini, Y; Bellotti, R; Bemporad, C; Bernardini, P; Bilokon, H; Bloise, C; Bower, C; Brigida, M; Bussino, S; Cafagna, F; Calicchio, M; Campana, D; Candela, A; Carboni, M; Caruso, R; Cassese, F; Cecchini, S; Cei, F; Chiarella, V; Choudhary, B C; Coutu, S; Cozzi, M; De Cataldo, G; De Deo, M; Dekhissi, H; De Marzo, C; De Mitri, I; Derkaoui, J; De Vincenzi, M; Di Credico, A; Dincecco, M; Erriquez, O; Favuzzi, C; Forti, C; Fusco, P; Giacomelli, G; Giannini, G; Giglietto, N; Giorgini, M; Grassi, M; Gray, L; Grillo, A; Guarino, F; Gustavino, C; Habig, A; Hanson, K; Heinz, R; Iarocci, E; Katsavounidis, E; Katsavounidis, I; Kearns, E; Kim, H; Kyriazopoulou, S; Lamanna, E; Lane, C; Levin, D S; Lindozzi, M; Lipari, P; Longley, N P; Longo, M J; Loparco, F; Maaroufi, F; Mancarella, G; Mandrioli, G; Margiotta, A; Marini, A; Martello, D; Marzari-Chiesa, A; Mazziotta, M N; Michael, D G; Monacelli, P; Montaruli, T; Monteno, M; Mufson, S; Musser, J; Nicolò, D; Nolty, R; Orth, C; Osteria, G; Palamara, O; Patera, V; Patrizii, L; Pazzi, R; Peck, C W; Perrone, L; Petrera, S; Pistilli, P; Popa, V; Rainó, A; Reynoldson, J; Ronga, F; Rrhioua, A; Satriano, C; Scapparone, E; Scholberg, K; Sciubba, A; Serra, P; Sioli, M; Sirri, G; Sitta, M; Spinelli, P; Spinetti, M; Spurio, M; Steinberg, R; Stone, J L; Sulak, L R; Surdo, A; Tarle, G; Tatananni, E; Togo, V; Vakili, M; Walter, C W; Webb, R

    2002-01-01

    Muon energy measurement represents an important issue for any experiment addressing neutrino-induced up-going muon studies. Since the neutrino oscillation probability depends on the neutrino energy, a measurement of the muon energy adds an important piece of information concerning the neutrino system. We show in this paper how the MACRO limited streamer tube system can be operated in drift mode by using the TDCs included in the QTPs, an electronics designed for magnetic monopole search. An improvement of the space resolution is obtained, through an analysis of the multiple scattering of muon tracks as they pass through our detector. This information can be used further to obtain an estimate of the energy of muons crossing the detector. Here we present the results of two dedicated tests, performed at CERN PS-T9 and SPS-X7 beam lines, to provide a full check of the electronics and to exploit the feasibility of such a multiple scattering analysis. We show that by using a neural network approach, we are able to r...

  3. A new three-dimensional track fit with multiple scattering

    Berger, Niklaus; Kozlinskiy, Alexandr [Physikalisches Institut, Heidelberg University, Heidelberg (Germany); Institut für Kernphysik and PRISMA cluster of excellence, Mainz University, Mainz (Germany); Kiehn, Moritz; Schöning, André [Physikalisches Institut, Heidelberg University, Heidelberg (Germany)

    2017-02-01

    Modern semiconductor detectors allow for charged particle tracking with ever increasing position resolution. Due to the reduction of the spatial hit uncertainties, multiple Coulomb scattering in the detector layers becomes the dominant source for tracking uncertainties. In this case long distance effects can be ignored for the momentum measurement, and the track fit can consequently be formulated as a sum of independent fits to hit triplets. In this paper we present an analytical solution for a three-dimensional triplet(s) fit in a homogeneous magnetic field based on a multiple scattering model. Track fitting of hit triplets is performed using a linearization ansatz. The momentum resolution is discussed for a typical spectrometer setup. Furthermore the track fit is compared with other track fits for two different pixel detector geometries, namely the Mu3e experiment at PSI and a typical high-energy collider experiment. For a large momentum range the triplets fit provides a significantly better performance than a single helix fit. The triplets fit is fast and can easily be parallelized, which makes it ideal for the implementation on parallel computing architectures.

  4. A new three-dimensional track fit with multiple scattering

    Berger, Niklaus; Kozlinskiy, Alexandr; Kiehn, Moritz; Schöning, André

    2017-01-01

    Modern semiconductor detectors allow for charged particle tracking with ever increasing position resolution. Due to the reduction of the spatial hit uncertainties, multiple Coulomb scattering in the detector layers becomes the dominant source for tracking uncertainties. In this case long distance effects can be ignored for the momentum measurement, and the track fit can consequently be formulated as a sum of independent fits to hit triplets. In this paper we present an analytical solution for a three-dimensional triplet(s) fit in a homogeneous magnetic field based on a multiple scattering model. Track fitting of hit triplets is performed using a linearization ansatz. The momentum resolution is discussed for a typical spectrometer setup. Furthermore the track fit is compared with other track fits for two different pixel detector geometries, namely the Mu3e experiment at PSI and a typical high-energy collider experiment. For a large momentum range the triplets fit provides a significantly better performance than a single helix fit. The triplets fit is fast and can easily be parallelized, which makes it ideal for the implementation on parallel computing architectures.

  5. Fining of Red Wine Monitored by Multiple Light Scattering.

    Ferrentino, Giovanna; Ramezani, Mohsen; Morozova, Ksenia; Hafner, Daniela; Pedri, Ulrich; Pixner, Konrad; Scampicchio, Matteo

    2017-07-12

    This work describes a new approach based on multiple light scattering to study red wine clarification processes. The whole spectral signal (1933 backscattering points along the length of each sample vial) were fitted by a multivariate kinetic model that was built with a three-step mechanism, implying (1) adsorption of wine colloids to fining agents, (2) aggregation into larger particles, and (3) sedimentation. Each step is characterized by a reaction rate constant. According to the first reaction, the results showed that gelatin was the most efficient fining agent, concerning the main objective, which was the clarification of the wine, and consequently the increase in its limpidity. Such a trend was also discussed in relation to the results achieved by nephelometry, total phenols, ζ-potential, color, sensory, and electronic nose analyses. Also, higher concentrations of the fining agent (from 5 to 30 g/100 L) or higher temperatures (from 10 to 20 °C) sped up the process. Finally, the advantage of using the whole spectral signal vs classical univariate approaches was demonstrated by comparing the uncertainty associated with the rate constants of the proposed kinetic model. Overall, multiple light scattering technique showed a great potential for studying fining processes compared to classical univariate approaches.

  6. LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

    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.

  7. 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

  8. 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.

  9. Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

    Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

    2013-10-01

    This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

  10. Real space multiple scattering description of alloy phase stability

    Turchi, P.E.A.; Sluiter, M.

    1992-01-01

    This paper presents a brief overview of the advanced methodology which has been recently developed to study phase stability properties of substitutional alloys, including order-disorder phenomena and structural transformations. The approach is based on the real space version of the Generalized Perturbation Method first introduced by Ducastelle and Gautier, within the Korringa-Kohn-Rostoker multiple scattering formulation of the Coherent Potential Approximation. Temperature effects are taken into account with a generalized meanfield approach, namely the Cluster Variation Method. The viability and the predictive power of such a scheme will be illustrated by a few examples, among them: the ground state properties of alloys, in particular the ordering tendencies for a series of equiatomic bcc-based alloys, the computation of alloy phase diagrams with the case of fcc and bcc-based Ni-Al alloys, the calculation of antiphase boundary energies and interfacial energies, and the stability of artificial ordered superlattices

  11. Multiple scattering of slow muons in an electron gas

    Archubi, C.D.; Arista, N.R.

    2017-01-01

    A comparative study of the angular dispersion of slow muons in an electron gas is performed using 3 dielectric models which represent the case of metals (Lindhard model for a free electron gas) and the cases of semiconductors and insulators (Levine and Louie model and Brandt and Reinheimer model for systems with a band gap) and a non-linear model for both cases at very low velocities. The contribution of collective electronic excitations according to the dielectric model are found to be negligible. The results from the calculation using Lindhard expressions for the angular half width are consistent with the result of a multiple scattering model. In particular, the effects produced by the band gap of the material are analyzed in detail. Finally, as the recoil effect is negligible, there is an almost exact scaling, for a given velocity, between the proton and the muon results. (authors)

  12. Study of the multiple scattering effect in TEBENE using the Monte Carlo method

    Singkarat, Somsorn.

    1990-01-01

    The neutron time-of-flight and energy spectra, from the TEBENE set-up, have been calculated by a computer program using the Monte Carlo method. The neutron multiple scattering within the polyethylene scatterer ring is closely investigated. The results show that multiple scattering has a significant effect on the detected neutron yield. They also indicate that the thickness of the scatterer ring has to be carefully chosen. (author)

  13. Characterization of the Lung Parenchyma Using Ultrasound Multiple Scattering.

    Mohanty, Kaustav; Blackwell, John; Egan, Thomas; Muller, Marie

    2017-05-01

    The purpose of the study described here was to showcase the application of ultrasound to quantitative characterization of the micro-architecture of the lung parenchyma to predict the extent of pulmonary edema. The lung parenchyma is a highly complex and diffusive medium for which ultrasound techniques have remained qualitative. The approach presented here is based on ultrasound multiple scattering and exploits the complexity of ultrasound propagation in the lung structure. The experimental setup consisted of a linear transducer array with an 8-MHz central frequency placed in contact with the lung surface. The diffusion constant D and transport mean free path L* of the lung parenchyma were estimated by separating the incoherent and coherent intensities in the near field and measuring the growth of the incoherent diffusive halo over time. Significant differences were observed between the L* values obtained in healthy and edematous rat lungs in vivo. In the control rat lung, L* was found to be 332 μm (±48.8 μm), whereas in the edematous lung, it was 1040 μm (±90 μm). The reproducibility of the measurements of L* and D was tested in vivo and in phantoms made of melamine sponge with varying air volume fractions. Two-dimensional finite difference time domain numerical simulations were carried out on rabbit lung histology images with varying degrees of lung collapse. Significant correlations were observed between air volume fraction and L* in simulation (r = -0.9542, p lung in which edema was simulated by adding phosphate-buffered saline revealed a linear relationship between the fluid volume fraction and L*. These results illustrate the potential of methods based on ultrasound multiple scattering for the quantitative characterization of the lung parenchyma. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

  14. Modified random hinge transport mechanics and multiple scattering step-size selection in EGS5

    Wilderman, S.J.; Bielajew, A.F.

    2005-01-01

    The new transport mechanics in EGS5 allows for significantly longer electron transport step sizes and hence shorter computation times than required for identical problems in EGS4. But as with all Monte Carlo electron transport algorithms, certain classes of problems exhibit step-size dependencies even when operating within recommended ranges, sometimes making selection of step-sizes a daunting task for novice users. Further contributing to this problem, because of the decoupling of multiple scattering and continuous energy loss in the dual random hinge transport mechanics of EGS5, there are two independent step sizes in EGS5, one for multiple scattering and one for continuous energy loss, each of which influences speed and accuracy in a different manner. Further, whereas EGS4 used a single value of fractional energy loss (ESTEPE) to determine step sizes at all energies, to increase performance by decreasing the amount of effort expended simulating lower energy particles, EGS5 permits the fractional energy loss values which are used to determine both the multiple scattering and continuous energy loss step sizes to vary with energy. This results in requiring the user to specify four fractional energy loss values when optimizing computations for speed. Thus, in order to simplify step-size selection and to mitigate step-size dependencies, a method has been devised to automatically optimize step-size selection based on a single material dependent input related to the size of problem tally region. In this paper we discuss the new transport mechanics in EGS5 and describe the automatic step-size optimization algorithm. (author)

  15. Aethalometer multiple scattering correction Cref for mineral dust aerosols

    C. Di Biagio

    2017-08-01

    Full Text Available In this study we provide a first estimate of the Aethalometer multiple scattering correction Cref for mineral dust aerosols. Cref is an empirical constant used to correct the aerosol absorption coefficient measurements for the multiple scattering artefact of the Aethalometer; i.e. the filter fibres on which aerosols are deposited scatter light and this is miscounted as absorption. The Cref at 450 and 660 nm was obtained from the direct comparison of Aethalometer data (Magee Sci. AE31 with (i the absorption coefficient calculated as the difference between the extinction and scattering coefficients measured by a Cavity Attenuated Phase Shift Extinction analyser (CAPS PMex and a nephelometer respectively at 450 nm and (ii the absorption coefficient from a MAAP (Multi-Angle Absorption Photometer at 660 nm. Measurements were performed on seven dust aerosol samples generated in the laboratory by the mechanical shaking of natural parent soils issued from different source regions worldwide. The single scattering albedo (SSA at 450 and 660 nm and the size distribution of the aerosols were also measured. Cref for mineral dust varies between 1.81 and 2.56 for a SSA of 0.85–0.96 at 450 nm and between 1.75 and 2.28 for a SSA of 0.98–0.99 at 660 nm. The calculated mean for dust is 2.09 (±0.22 at 450 nm and 1.92 (±0.17 at 660 nm. With this new Cref the dust absorption coefficient by the Aethalometer is about 2 % (450 nm and 11 % (660 nm higher than that obtained by using Cref  =  2.14 at both 450 and 660 nm, as usually assumed in the literature. This difference induces a change of up to 3 % in the dust SSA at 660 nm. The Cref seems to be independent of the fine and coarse particle size fractions, and so the obtained Cref can be applied to dust both close to sources and following transport. Additional experiments performed with pure kaolinite minerals and polluted ambient aerosols indicate Cref of 2.49 (±0.02 and 2

  16. A DE-Based Scatter Search for Global Optimization Problems

    Kun Li

    2015-01-01

    Full Text Available This paper proposes a hybrid scatter search (SS algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.

  17. Multiple exchange and high-energy fixed-angle scattering

    Halliday, I G; Orzalesi, C A; Tau, M

    1975-01-01

    The application of the eikonal ansatz to fermion fermion elastic scattering with Abelian vector gluon exchanges is discussed. The behaviours of the elastic scattering amplitude and the elastic form factor are considered and an important mechanism for fixed angle high energy elastic scattering is identified. (6 refs).

  18. Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering

    Jeong, Seungwon; Lee, Ye-Ryoung; Choi, Wonjun; Kang, Sungsam; Hong, Jin Hee; Park, Jin-Sung; Lim, Yong-Sik; Park, Hong-Gyu; Choi, Wonshik

    2018-05-01

    The efficient delivery of light energy is a prerequisite for the non-invasive imaging and stimulating of target objects embedded deep within a scattering medium. However, the injected waves experience random diffusion by multiple light scattering, and only a small fraction reaches the target object. Here, we present a method to counteract wave diffusion and to focus multiple-scattered waves at the deeply embedded target. To realize this, we experimentally inject light into the reflection eigenchannels of a specific flight time to preferably enhance the intensity of those multiple-scattered waves that have interacted with the target object. For targets that are too deep to be visible by optical imaging, we demonstrate a more than tenfold enhancement in light energy delivery in comparison with ordinary wave diffusion cases. This work will lay a foundation to enhance the working depth of imaging, sensing and light stimulation.

  19. 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)

  20. Intrinsic acoustical cross sections in the multiple scattering by a pair of rigid cylindrical particles in 2D

    Mitri, F. G.

    2017-08-01

    The multiple scattering effects occurring between two scatterers are described based upon the multipole expansion formalism as well as the addition theorem of cylindrical wave functions. An original approach is presented in which an effective incident acoustic field on a particular object, which includes both the primary and re-scattered waves from the other particle is determined first, and then used with the scattered field to derive closed-form analytical expressions for the inherent (i.e. intrinsic) cross-sections based on the far-field scattering. This method does not introduce any approximation in the calculation of the intrinsic cross-sections since the procedure is reduced to the one-body problem. The mathematical expressions for the intrinsic cross-sections are formulated in partial-wave series expansions (PWSEs) in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. Numerical examples illustrate the analysis for two rigid circular cylindrical cross-sections with different radii immersed in a non-viscous fluid. Computations for the dimensionless extrinsic and intrinsic extinction cross-section factors are evaluated with particular emphasis on varying the angle of incidence, the interparticle distance, as well as the sizes of the particles. A symmetric behavior is observed for the dimensionless extrinsic extinction cross-section, while asymmetry arises for the intrinsic extinction cross-section of each particle with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of the intrinsic (local) scattering, absorption and extinction cross-sections in the multiple acoustic scatterings of plane progressive waves of arbitrary incidence by a pair of scatterers. The results and computational analyses can be used as a priori information for future applications to guide the

  1. Intrinsic acoustical cross sections in the multiple scattering by a pair of rigid cylindrical particles in 2D

    Mitri, F G

    2017-01-01

    The multiple scattering effects occurring between two scatterers are described based upon the multipole expansion formalism as well as the addition theorem of cylindrical wave functions. An original approach is presented in which an effective incident acoustic field on a particular object, which includes both the primary and re-scattered waves from the other particle is determined first, and then used with the scattered field to derive closed-form analytical expressions for the inherent (i.e. intrinsic) cross-sections based on the far-field scattering. This method does not introduce any approximation in the calculation of the intrinsic cross-sections since the procedure is reduced to the one-body problem. The mathematical expressions for the intrinsic cross-sections are formulated in partial-wave series expansions (PWSEs) in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. Numerical examples illustrate the analysis for two rigid circular cylindrical cross-sections with different radii immersed in a non-viscous fluid. Computations for the dimensionless extrinsic and intrinsic extinction cross-section factors are evaluated with particular emphasis on varying the angle of incidence, the interparticle distance, as well as the sizes of the particles. A symmetric behavior is observed for the dimensionless extrinsic extinction cross-section, while asymmetry arises for the intrinsic extinction cross-section of each particle with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of the intrinsic (local) scattering, absorption and extinction cross-sections in the multiple acoustic scatterings of plane progressive waves of arbitrary incidence by a pair of scatterers. The results and computational analyses can be used as a priori information for future applications to guide the

  2. Multiple-scattering analysis of laser-beam propagation in the atmosphere and through obscurants

    Zardecki, A.; Gerstl, S.A.W.

    1983-01-01

    The general purpose, discrete-ordinates transport code TWOTRAN is applied to describe the propagation and multiple scattering of a laser beam in a nonhomogeneous aerosol medium. For the medium composed of smoke, haze, and a rain cloud, the problem of the target detectability in a realistic atmospheric scenario is addressed and solved. The signals reflected from the target vs the signals scattered from the smoke cloud are analyzed as a function of the smoke concentration. By calculating the average intensity and a correction factor in the x-y and r-z geometries, the consistency of the rectangular and cylindrical geometry models is assessed. Received power for a detector with a small field of view is computed on a sphere of 1-km radius around the laser source for the Air Force Geophysics Laboratory rural aerosol model with extinction coefficients of 4 km - 1 and 10 km - 1 . This computation allows us to study the received power as a function of the angle between the detector and source axes. The correction factor describing the multiple-scattering enhancement with respect to the simple Lambert-Beer law is introduced, and its calculation is employed to validate the use of the small-angle approximation for the transmissometer configuration. An outline of the theory for a finite field of view detector is followed by numerical results pertaining to the received power and intensity for various aerosol models. Recommendations regarding future work are also formulated

  3. Wave scattering theory and the absorption problem for a black hole

    Sanchez, N.

    1977-01-01

    The general problem of scattering and absorption of waves from a Schwarzschild black hole is investigated. A scattering absorption amplitude is introduced. The unitarity theorem for this problem is derived from the wave equation and its boundary conditions. The formulation of the problem, within the formal scattering theory approach, is also given. The existence of a singularity in space-time is related explicitly to the presence of a nonzero absorption cross section. Another derivation of the unitarity theorem for our problem is given by operator methods. The reciprocity relation is also proved; that is, for the scattering of waves the black hole is a reciprocal system. Finally, the elastic scattering problem is considered, and the elastic scattering amplitude is calculated for high frequencies and small scattering angles

  4. Measurements and applications of neutron multiple scattering in resonance region

    Ohkubo, Makio

    1977-02-01

    Capture yield of neutrons impinging on a thick material is complicated due to self-shielding and multiple scattering, especially in the resonance region. When the incident neutron energy is equal to a resonance energy of the material, capture probability of the neutron increases with sample thickness and reaches a saturation value P sub(CO). There is a simple relation between P sub(CO) and GAMMA sub(n)/GAMMA and the recoil energy by the Monte-Carlo calculation. To examine validity of the relation, P sub(CO) was measured for 19 resonances in 12 nuclides with thick samples, using a JAERI linac time-of-flight spectrometer with Moxon-Rae type gamma ray detector and transmission type neutron flux monitor. Results of the measurements confirmed the validity. With this relation, the GAMMA sub(n)/GAMMA or GAMMA sub(γ)/GAMMA value can be obtained from the measured P sub(CO), and also the level spins be determined by combining the transmission data. Because of the definition of P sub(CO), determination of the resonance parameters is not sensitive to the sample thickness as far as it is sufficiently thick. (auth.)

  5. Multiple-scattering theory with a truncated basis set

    Zhang, X.; Butler, W.H.

    1992-01-01

    Multiple-scattering theory (MST) is an extremely efficient technique for calculating the electronic structure of an assembly of atoms. The wave function in MST is expanded in terms of spherical waves centered on each atom and indexed by their orbital and azimuthal quantum numbers, l and m. The secular equation which determines the characteristic energies can be truncated at a value of the orbital angular momentum l max , for which the higher angular momentum phase shifts, δ l (l>l max ), are sufficiently small. Generally, the wave-function coefficients which are calculated from the secular equation are also truncated at l max . Here we point out that this truncation of the wave function is not necessary and is in fact inconsistent with the truncation of the secular equation. A consistent procedure is described in which the states with higher orbital angular momenta are retained but with their phase shifts set to zero. We show that this treatment gives smooth, continuous, and correctly normalized wave functions and that the total charge density calculated from the corresponding Green function agrees with the Lloyd formula result. We also show that this augmented wave function can be written as a linear combination of Andersen's muffin-tin orbitals in the case of muffin-tin potentials, and can be used to generalize the muffin-tin orbital idea to full-cell potentals

  6. 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)

  7. 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.

  8. Multilevel fast multipole method based on a potential formulation for 3D electromagnetic scattering problems.

    Fall, Mandiaye; Boutami, Salim; Glière, Alain; Stout, Brian; Hazart, Jerome

    2013-06-01

    A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

  9. Absorption in multiple scattering systems of coated spheres: design applications

    Stout, Brian; Andraud, Christine; Stout, Sophie; Lafait, Jacques

    2003-01-01

    We illustrate the utility of some recently derived transfer matrix methods for electromagnetic scattering calculations in systems composed of coated spherical scatterers. Any of the spherical coatings, cores, or host media may be composed of absorbing materials. Our formulae permit the calculation of local absorption in either orientation fixed or orientation averaged situations. We introduce methods for estimating the macroscopic transport properties of such media, and show how our scattering calculations can permit 'design' optimization of macroscopic properties

  10. Evanescent wave scattering at off-axis incidence on multiple cylinders located near a surface

    Lee, Siu-Chun

    2015-01-01

    The scattering characteristics of an infinite cylinder are strongly influenced by the incidence angle relative to its axis. If the incident wave propagates in the plane normal to the axis of the cylinder, the polarization of the scattered wave remains unchanged and the scattered wave propagates in the same plan as the incident wave. At off-axis incidence such that the incident direction makes an oblique angle with the cylinder axis, the scattered wave is depolarized, and its spatial distribution becomes three-dimensional. This paper presents the scattering solution for oblique incidence on multiple parallel cylinders located near a planar interface by an evanescent wave that is generated by total internal reflection of the source wave propagating in the higher refractive index substrate. Hertz potentials are utilized to formulate the interaction of inhomogeneous waves with the cylinders, scattering at the substrate interface, and near field scattering between the cylinders. Analytic formulas are derived for the electromagnetic fields and Poynting vector of scattered radiation in the near-field and their asymptotic forms in the far-field. Numerical examples are shown to illustrate scattering of evanescent wave by multiple cylinders at off-axis incidence. - Highlights: • Developed an exact solution for off-axis incidence on multiple cylinders. • Included depolarization, near-field scattering, and Fresnel effect in theory. • Derived analytic formulas for scattered radiation in the far field. • Illustrated evanescent scattering at off-axis incidence by numerical data

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. Exact multiple scattering theory of two-nucleus collisions including the Pauli principle

    Gurvitz, S.A.

    1981-01-01

    Exact equations for two-nucleus scattering are derived in which the effects of the Pauli principle are fully included. Our method exploits a modified equation for the scattering of two identical nucleons, which is obtained at the beginning. Considering proton-nucleus scattering we found that the resulting amplitude has two components, one resembling a multiple scattering series for distinguishable particles, and the other a distorted (A-1) nucleon cluster exchange. For elastic pA scattering the multiple scattering amplitude is found in the form of an optical potential expansion. We show that the Kerman-McManus-Thaler theory of the optical potential could be easily modified to include the effects of antisymmetrization of the projectile with the target nucleons. Nucleus-nucleus scattering is studied first for distinguishable target and beam nucleus. Afterwards the Pauli principle is included, where only the case of deuteron-nucleus scattering is discussed in detail. The resulting amplitude has four components. Two of them correspond to modified multiple scattering expansions and the others are distorted (A-1)- and (A-2)- nucleon cluster exchange. The result for d-A scattering is extended to the general case of nucleus-nucleus scattering. The equations are simple to use and as such constitute an improvement over existing schemes

  16. SIMSAS - a window based software package for simulation and analysis of multiple small-angle scattering data

    Jayaswal, B.; Mazumder, S.

    1998-09-01

    Small-angle scattering data from strong scattering systems, e.g. porous materials, cannot be analysed invoking single scattering approximation as specimen needed to replicate the bulk matrix in essential properties are too thick to validate the approximation. The presence of multiple scattering is indicated by invalidity of the functional invariance property of the observed scattering profile with variation of sample thickness and/or wave length of the probing radiation. This article delineates how non accounting of multiple scattering affects the results of analysis and then how to correct the data for its effect. It deals with an algorithm to extract single scattering profile from small-angle scattering data affected by multiple scattering. The algorithm can process the scattering data and deduce single scattering profile in absolute scale. A software package, SIMSAS, is introduced for executing this inversion step. This package is useful both to simulate and to analyse multiple small-angle scattering data. (author)

  17. Elastic and quasielastic scattering of light nuclei in the theory of multiple scattering

    Ismatov, E.I.; Kuterbekov, K.A.; Dzhuraev, Sh.Kh.; Ehsaniyazov, Sh.P.; Zholdasova, S.M.

    2005-01-01

    In the work the calculation method for diffraction scattering amplitudes of light nuclei by heavy nuclei is developed. For A 1 A 2 -scattering effects of pair-, three-fold, and four-fold screenings are estimated. It is shown, that in amplitude calculations for A 1 A 2 elastic scattering it is enough come to nothing more than accounting of total screenings in the first order. Analysis of nucleus-nucleus scattering sensitive characteristics to choice of single-particle nuclear densities parametrization is carried out

  18. The Green Function cellular method and its relation to multiple scattering theory

    Butler, W.H.; Zhang, X.G.; Gonis, A.

    1992-01-01

    This paper investigates techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. The authors derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculation to the problem of solving a nearest neighbor tight-binding problem

  19. Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory.

    Voit, Florian; Hohmann, Ansgar; Schäfer, Jan; Kienle, Alwin

    2012-04-01

    For many research areas in biomedical optics, information about scattering of polarized light in turbid media is of increasing importance. Scattering simulations within this field are mainly performed on the basis of radiative transfer theory. In this study a polarization sensitive Monte Carlo solution of radiative transfer theory is compared to exact Maxwell solutions for all elements of the scattering Müller matrix. Different scatterer volume concentrations are modeled as a multitude of monodisperse nonabsorbing spheres randomly positioned in a cubic simulation volume which is irradiated with monochromatic incident light. For all Müller matrix elements effects due to dependent scattering and multiple scattering are analysed. The results are in overall good agreement between the two methods with deviations related to dependent scattering being prominent for high volume concentrations and high scattering angles.

  20. Multiple pole in the electron--hydrogen-atom scattering amplitude

    Amusia, M.Y.; Kuchiev, M.Y.

    1982-01-01

    It is demonstrated that the amplitude for electron--hydrogen-atom forward scattering has the third-order pole at the point E = -13.6 eV, E being the energy of the incident electron. The coefficients which characterize the pole are calculated exactly. The invalidity of the Born approximation is proved. The contribution of the pole singularity to the dispersion relation for the scattering amplitude is discussed

  1. Generalization of the geometric optical series approach for nonadiabatic scattering problems

    Herman, M.F.

    1982-01-01

    The geometric optical series approach of Bremmer is generalized for multisurface nonadiabatic scattering problems. This method yields the formal solution of the Schroedinger equation as an infinite series of multiple integrals. The zeroth order term corresponds to WKB propagation on a single adiabatic surface, while the general Nth order term involves N reflections and/or transitions between surfaces accompanied by ''free,'' single surface semiclassical propagation between the points of reflection and transition. Each term is integrated over all possible transition and reflection points. The adiabatic and diabatic limits of this expression are discussed. Numerical results, in which all reflections are ignored, are presented for curve crossing and noncrossing problems. These results are compared to exact quantum results and are shown to be highly accurate

  2. A stochastic model of multiple scattering of charged particles: process, transport equation and solutions

    Papiez, L.; Moskvin, V.; Tulovsky, V.

    2001-01-01

    The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)

  3. Observation of spatial quantum correlations induced by multiple scattering of nonclassical light

    Smolka, Stephan; Huck, Alexander; Andersen, Ulrik Lund

    2009-01-01

    and negative spatial quantum correlations are observed when varying the quantum state incident to the multiple scattering medium, and the strength of the correlations is controlled by the number of photons. The experimental results are in excellent agreement with recent theoretical proposals by implementing......We present the experimental realization of spatial quantum correlations of photons that are induced by multiple scattering of squeezed light. The quantum correlation relates photons propagating along two different light paths through the random medium and is infinite in range. Both positive...... the full quantum model of multiple scattering....

  4. THE DECISION OF FORM FOR DIFFRACTIVE STRUCTURES IN THE PROBLEM OF SCATTERING OF RADIO WAVES.

    A. P. Preobrazhensky

    2017-02-01

    Full Text Available This paper considers the problem of scattering of electromagnetic waves in different diffraction structures. The solution of the scattering problem is based on the method of integral equations. On diagrams of backscattering at various frequencies of the incident wave, the decision about the form of the object is carried out.

  5. Density of states calculations and multiple-scattering theory for photons

    Moroz, A.

    1994-05-01

    The density of states for a finite or an infinite cluster of scatterers in the case of both, electrons and photons, can be represented in a general form as the sum over all Krein-Friedel contributions of individual scatterers and a contribution due to the presence of multiple scatterers. The latter is given by the sum over all periodic orbits between different scatterers. General three dimensional multiple-scattering theory for electromagnetic waves in the presence of scatterers of arbitrary shape is presented. Vector structure constants are calculated and general rules for obtaining them from known scalar structure constants are given. The KKR equations for photons are explicitly written down. (author). 22 refs., 2 figs

  6. Parallel time domain solvers for electrically large transient scattering problems

    Liu, Yang; Yucel, Abdulkadir; Bagcý , Hakan; Michielssen, Eric

    2014-01-01

    scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary

  7. Multiple scattering of elliptically polarized light in two-dimensional medium with large inhomogeneities

    Gorodnichev, E. E., E-mail: gorodn@theor.mephi.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (Russian Federation)

    2016-12-15

    For elliptically polarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.

  8. Localization of a small change in a multiple scattering environment without modeling of the actual medium

    Rakotonarivo , Sandrine; Walker , S.C.; Kuperman , W. A.; Roux , Philippe

    2011-01-01

    International audience; A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference between the measured signals then reveals all field components that have interact...

  9. Solution of neutron slowing down equation including multiple inelastic scattering

    El-Wakil, S.A.; Saad, A.E.

    1977-01-01

    The present work is devoted the presentation of an analytical method for the calculation of elastically and inelastically slowed down neutrons in an infinite non absorbing homogeneous medium. On the basis of the Central limit theory (CLT) and the integral transform technique the slowing down equation including inelastic scattering in terms of the Green function of elastic scattering is solved. The Green function is decomposed according to the number of collisions. A formula for the flux at any lethargy O (u) after any number of collisions is derived. An equation for the asymptotic flux is also obtained

  10. Optimum track fitting in the presence of multiple scattering

    Lutz, G.

    1987-06-01

    A method for track fitting is proposed which attempts to be as close as possible to the real track along the full path length. This is done by the introduction of scattering planes in which the particle is allowed to change its direction. A fit over the full track length includes the probability of direction change by scattering. Using matrix notation a fairly simple formalism for error estimation has been developed. Results of this method are compared to those of more widely used procedures for 'typical' examples of High Energy Spectrometers. (orig.)

  11. Eikonal multiple scattering model within the framework of Feynman's positron theory

    Tekou, A.

    1986-07-01

    The Bethe Salpeter equation for nucleon-nucleon, nucleon-nucleus and nucleus-nucleus scattering is eikonalized. Multiple scattering series is obtained. Contributions of three body interations are included. The model presented below may be used to investigate atomic collisions. (author)

  12. Multiple-scattering formalism beyond the quasistatic approximation: Analyzing resonances in plasmonic chains

    de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper

    2012-01-01

    We present a multiple-scattering formalism for simulating scattering of electromagnetic waves on spherical inhomogeneities in 3D. The formalism is based on the Lippmann-Schwinger equation and the electromagnetic Green's tensor and applies an expansion of the electric field on spherical...

  13. Multiple scattering theory for non-local and multichannel potentials

    Natoli, C.R.; Krüger, P.; Hatada, K.; Hayakawa, K.; Sébilleau, D.; Šipr, Ondřej

    2012-01-01

    Roč. 24, č. 36 (2012), s. 1-20 ISSN 0953-8984 Institutional research plan: CEZ:AV0Z10100521 Keywords : multichannel scattering * correlation s * density matrix Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.355, year: 2012

  14. Application of multiple scattering theory in electron dosimetry

    Oliveira, M.J.G.S. de.

    1984-01-01

    A theoretical model, based on the Fermi-Eyges scattering theory, which takes into account the different heterogeneous media, is proposed. Heterogeneous phantoms were built in order to obtain curves of distribution of the absorbed dose. The agreement between the theoretical and experimental data prove that presented theory model is useful to describe the absorbed dose in homogeneous media. (M.A.C.) [pt

  15. Continuum and bound electronic wavefunctions for anisotropic multiple-scattering potentials

    Siegel, J.; Dill, D.; Dehmer, J.L.

    1975-01-01

    Standard multiple-scattering treatments of bound and continuum one-electron states are restricted to a monopole potential in each of the various spherical regions. We have extended the treatment within these regions to a general potential. The corresponding multiple-scattering equations should facilitate accurate treatment of effects of the build-up of charge due to bonding, of the dipole character of polar molecules, and of external fields

  16. Multiple scattering corrections to the Beer-Lambert law. 1: Open detector.

    Tam, W G; Zardecki, A

    1982-07-01

    Multiple scattering corrections to the Beer-Lambert law are analyzed by means of a rigorous small-angle solution to the radiative transfer equation. Transmission functions for predicting the received radiant power-a directly measured quantity in contrast to the spectral radiance in the Beer-Lambert law-are derived. Numerical algorithms and results relating to the multiple scattering effects for laser propagation in fog, cloud, and rain are presented.

  17. 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

  18. 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.

  19. 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

  20. Effects of multiple scattering and atmospheric aerosol on the polarization of the twilight sky

    Ugolnikov, Oleg S.; Postylyakov, Oleg V.; Maslov, Igor A.

    2004-01-01

    The paper presents a review of a number of wide-angle polarization CCD-measurements of the twilight sky in V and R color bands with effective wavelengths 550 and 700nm. The basic factors affecting (usually decreasing) the polarization of the twilight sky are the atmospheric aerosol scattering and multiple scattering. These effects were distinguished from each other, and a method of multiple-scattering separation is discussed. The results are compared with the data of numerical simulation of radiative transfer in the atmosphere for different aerosol models. The whole twilight period is divided into different stages with different mechanisms forming the twilight-sky polarization properties

  1. [Multiple scattering of visible and infrared light by sea fog over wind driving rough sea surface].

    Sun, Xian-Ming; Wang, Hai-Hua; Lei, Cheng-Xin; Shen, Jin

    2013-08-01

    The present paper is concerned with computing the multiple scattering characteristics of a sea fog-sea surface couple system within this context. The single scattering characteristics of sea fog were studied by Mie theory, and the multiple scattering of sunlight by single sea fog layer was studied by radiative transfer theory. The reflection function of a statistically rough ocean surface was obtained using the standard Kirchhoff formulation, with shadowing effects taken into account. The reflection properties of the combined sea fog and ocean surface were obtained employing the adding method, and the results indicated that the reflected light intensity of sea fog increased with the sea background.

  2. Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

    Viard, Nicolas; Giammarinaro, Bruno; Derode, Arnaud; Barrière, Christophe

    2013-08-01

    We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

  3. Multiple scattering in closely packed systems of arbitrary non-overlapping shapes

    Keister, B.D.

    1982-11-01

    It has long been known that the multiple scattering of waves from a system of obstacles of finite extent can be described completely with a knowledge of the on-shell amplitudes of the individual scatterers, provided that the minimally enclosing spheres concentric with the scattering centers do not overlap. In this paper, it is shown that on-shell amplitudes alone suffice for a wider class of scattering configurations, in which the individual scatterers do not overlap, but their geometries do not satisfy the above condition. These extended geometries require a careful treatment of certain partial wave sums. An example is also discussed in which a pair of non-overlapping scatterers requires more than the on-shell amplitudes for a solution

  4. 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

  5. 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

  6. 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)

  7. Comparison of Geant4 multiple Coulomb scattering models with theory for radiotherapy protons.

    Makarova, Anastasia; Gottschalk, Bernard; Sauerwein, Wolfgang

    2017-07-06

    Usually, Monte Carlo models are validated against experimental data. However, models of multiple Coulomb scattering (MCS) in the Gaussian approximation are exceptional in that we have theories which are probably more accurate than the experiments which have, so far, been done to test them. In problems directly sensitive to the distribution of angles leaving the target, the relevant theory is the Molière/Fano/Hanson variant of Molière theory (Gottschalk et al 1993 Nucl. Instrum. Methods Phys. Res. B 74 467-90). For transverse spreading of the beam in the target itself, the theory of Preston and Koehler (Gottschalk (2012 arXiv:1204.4470)) holds. Therefore, in this paper we compare Geant4 simulations, using the Urban and Wentzel models of MCS, with theory rather than experiment, revealing trends which would otherwise be obscured by experimental scatter. For medium-energy (radiotherapy) protons, and low-Z (water-like) target materials, Wentzel appears to be better than Urban in simulating the distribution of outgoing angles. For beam spreading in the target itself, the two models are essentially equal.

  8. Inelastic multiple scattering of interacting bosons in weak random potentials

    Geiger, Tobias

    2013-01-01

    Within the present thesis we develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. Based on a microscopic N-body scattering theory, we identify the relevant diagrams including elastic and inelastic collision processes that are sufficient to describe quantum transport in the regime of weak disorder. By taking advantage of the statistical properties of the weak disorder potential, we demonstrate how the N-body dynamics can be reduced to a nonlinear integral equation of Boltzmann type for the single-particle diffusive flux. A presently available alternative description - based on the Gross-Pitaevskii equation - only includes elastic collisions. In contrast, we show that far from equilibrium the presence of inelastic collisions - even for weak interaction strength - must be accounted for and can induce the full thermalization of the single-particle current. In addition, we also determine the coherent corrections to the incoherent transport, leading to the effect of coherent backscattering. For the first time, we are able to analyze the influence of inelastic collisions on the coherent backscattering signal, which lead to an enhancement of the backscattered cone in a narrow spectral window, even for increasing non-linearity. With a short recollection of the presently available experimental techniques we furthermore show how an immediate implementation of our suggested setup with confined Bose-Einstein condensates can be accomplished. Thereby, the emergence of collective and/or thermodynamic behavior from fundamental, microscopic constituents can also be assessed experimentally. In a second part of this thesis, we present first results for light scattering off strongly interacting Rydberg atoms trapped in a one-dimensional, chain-like configuration. In order to monitor the time-dependence of this interacting many-body system, we devise a weak measurement scenario for which we derive a master equation for the

  9. Schwinger variational principle in scattering problems of charged particles on mesic atoms and atoms

    Belyaev, V.B.; Zubarev, A.L.; Podkopaev, A.P.

    1978-01-01

    The Schwinger variational principle is applied to solve the problems of atomic physics. A separable approximation for a Hamiltonian of a bound subsystem is used. The length of e + H-scattering and the elastic p(dμ)-scattering cross section are calculated in the second Born approximation

  10. 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

  11. In vivo diagnosis of skin cancer using polarized and multiple scattered light spectroscopy

    Bartlett, Matthew Allen

    This thesis research presents the development of a non-invasive diagnostic technique for distinguishing between skin cancer, moles, and normal skin using polarized and multiple scattered light spectroscopy. Polarized light incident on the skin is single scattered by the epidermal layer and multiple scattered by the dermal layer. The epidermal light maintains its initial polarization while the light from the dermal layer becomes randomized and multiple scattered. Mie theory was used to model the epidermal light as the scattering from the intercellular organelles. The dermal signal was modeled as the diffusion of light through a localized semi-homogeneous volume. These models were confirmed using skin phantom experiments, studied with in vitro cell cultures, and applied to human skin for in vivo testing. A CCD-based spectroscopy system was developed to perform all these experiments. The probe and the theory were tested on skin phantoms of latex spheres on top of a solid phantom. We next extended our phantom study to include in vitro cells on top of the solid phantom. Optical fluorescent microscope images revealed at least four distinct scatterers including mitochondria, nucleoli, nuclei, and cell membranes. Single scattering measurements on the mammalian cells consistently produced PSD's in the size range of the mitochondria. The clinical portion of the study consisted of in vivo measurements on cancer, mole, and normal skin spots. The clinical study combined the single scattering model from the phantom and in vitro cell studies with the diffusion model for multiple scattered light. When parameters from both layers were combined, we found that a sensitivity of 100% and 77% can be obtained for detecting cancers and moles, respectively, given the number of lesions examined.

  12. Coherence effects and average multiplicity in deep inelastic scattering at small χ

    Kisselev, A.V.; Petrov, V.A.

    1988-01-01

    The average hadron multiplicity in deep inelastic scattering at small χ is calculated in this paper. Its relationship with the average multiplicity in e + e - annihilation is established. As shown the results do not depend on a choice of the gauge vector. The important role of coherence effects in both space-like and time-like jet evolution is clarified. (orig.)

  13. Suppression of Stimulated Brillouin Scattering in multiple-ion species inertial confinement fusion Hohlraum Plasmas

    Neumayer, P

    2007-01-01

    A long-standing problem in the field of laser-plasma interactions is to successfully employ multiple-ion species plasmas to reduce stimulated Brillouin scattering (SBS) in inertial confinement fusion (ICF) hohlraum conditions. Multiple-ion species increase significantly the linear Landau damping for acoustic waves. Consequently, recent hohlraum designs for indirect-drive ignition on the National Ignition Facility investigate wall liner material options so that the liner gain for parametric instabilities will be below threshold for the onset SBS. Although the effect of two-ion species plasmas on Landau damping has been directly observed with Thomson scattering, early experiments on SBS in these plasmas have suffered from competing non-linear effects or laser beam filamentation. In this study, a reduction of SBS scattering to below the percent level has been observed in hohlraums at Omega that emulate the plasma conditions in an indirect drive ICF experiments. These experiments have measured the laser-plasma interaction processes in ignition-relevant high-electron temperature regime demonstrating Landau damping as a controlling process for SBS. The hohlraums have been filled with various fractions of CO 2 and C 3 H 8 varying the ratio of the light (H) to heavy (C and O) ion density from 0 to 2.6. They have been heated by 14.5 kJ of 351-nm light, thus increasing progressively Landau damping by an order of magnitude at constant electron density and temperature. A delayed 351-nm interaction beam, spatially smoothed to produce a 200-(micro)m laser spot at best focus, has propagated along the axis of the hohlraum. The backscattered light, both into the lens and outside, the transmitted light through the hohlraum plasma and the radiation temperature of the hohlraum has been measured. For ignition relevant laser intensities (3-9 10 14 Wcm -2 ), we find that the SBS reflectivity scales as predicted with Landau damping from >30% to <1%. Simultaneously, the hohlraum radiation

  14. Continuous-wave spatial quantum correlations of light induced by multiple scattering

    Smolka, Stephan; Ott, Johan Raunkjær; Huck, Alexander

    2012-01-01

    and reflectance. Utilizing frequency-resolved quantum noise measurements, we observe that the strength of the spatial quantum correlation function can be controlled by changing the quantum state of an incident bright squeezed-light source. Our results are found to be in excellent agreement with the developed......We present theoretical and experimental results on spatial quantum correlations induced by multiple scattering of nonclassical light. A continuous-mode quantum theory is derived that enables determining the spatial quantum correlation function from the fluctuations of the total transmittance...... theory and form a basis for future research on, e. g., quantum interference of multiple quantum states in a multiple scattering medium....

  15. Multiple and dependent scattering by densely packed discrete spheres: Comparison of radiative transfer and Maxwell theory

    Ma, L.X.; Tan, J.Y.; Zhao, J.M.; Wang, F.Q.; Wang, C.A.

    2017-01-01

    The radiative transfer equation (RTE) has been widely used to deal with multiple scattering of light by sparsely and randomly distributed discrete particles. However, for densely packed particles, the RTE becomes questionable due to strong dependent scattering effects. This paper examines the accuracy of RTE by comparing with the exact electromagnetic theory. For an imaginary spherical volume filled with randomly distributed, densely packed spheres, the RTE is solved by the Monte Carlo method combined with the Percus–Yevick hard model to consider the dependent scattering effect, while the electromagnetic calculation is based on the multi-sphere superposition T-matrix method. The Mueller matrix elements of the system with different size parameters and volume fractions of spheres are obtained using both methods. The results verify that the RTE fails to deal with the systems with a high-volume fraction due to the dependent scattering effects. Apart from the effects of forward interference scattering and coherent backscattering, the Percus–Yevick hard sphere model shows good accuracy in accounting for the far-field interference effects for medium or smaller size parameters (up to 6.964 in this study). For densely packed discrete spheres with large size parameters (equals 13.928 in this study), the improvement of dependent scattering correction tends to deteriorate. The observations indicate that caution must be taken when using RTE in dealing with the radiative transfer in dense discrete random media even though the dependent scattering correction is applied. - Highlights: • The Muller matrix of randomly distributed, densely packed spheres are investigated. • The effects of multiple scattering and dependent scattering are analyzed. • The accuracy of radiative transfer theory for densely packed spheres is discussed. • Dependent scattering correction takes effect at medium size parameter or smaller. • Performance of dependent scattering correction

  16. THE MULTIPLE CHOICE PROBLEM WITH INTERACTIONS BETWEEN CRITERIA

    Luiz Flavio Autran Monteiro Gomes

    2015-12-01

    Full Text Available ABSTRACT An important problem in Multi-Criteria Decision Analysis arises when one must select at least two alternatives at the same time. This can be denoted as a multiple choice problem. In other words, instead of evaluating each of the alternatives separately, they must be combined into groups of n alternatives, where n = 2. When the multiple choice problem must be solved under multiple criteria, the result is a multi-criteria, multiple choice problem. In this paper, it is shown through examples how this problemcan be tackled on a bipolar scale. The Choquet integral is used in this paper to take care of interactions between criteria. A numerical application example is conducted using data from SEBRAE-RJ, a non-profit private organization that has the mission of promoting competitiveness, sustainable developmentand entrepreneurship in the state of Rio de Janeiro, Brazil. The paper closes with suggestions for future research.

  17. Scaling laws governing the multiple scattering of diatomic molecules under Coulomb explosion

    Sigmund, P.

    1992-01-01

    The trajectories of fast molecules during and after penetration through foils are governed by Coulomb explosion and distorted by multiple scattering and other penetration phenomena. A scattering event may cause the energy available for Coulomb explosion to increase or decrease, and angular momentum may be transferred to the molecule. Because of continuing Coulomb explosion inside and outside the target foil, the transmission pattern recorded at a detector far away from the target is not just a linear superposition of Coulomb explosion and multiple scattering. The velocity distribution of an initially monochromatic and well-collimated, but randomly oriented, beam of molecular ions is governed by a generalization of the standard Bothe-Landau integral that governs the multiple scattering of atomic ions. Emphasis has been laid on the distribution in relative velocity and, in particular, relative energy. The statistical distributions governing the longitudinal motion (i.e., the relative motion along the molecular axis) and the rotational motion can be scaled into standard multiple-scattering distributions of atomic ions. The two scaling laws are very different. For thin target foils, the significance of rotational energy transfer is enhanced by an order of magnitude compared to switched-off Coulomb explosion. A distribution for the total relative energy (i.e., longitudinal plus rotational motion) has also been found, but its scaling behavior is more complex. Explicit examples given for all three distributions refer to power-law scattering. As a first approximation, scattering events undergone by the two atoms in the molecule were assumed uncorrelated. A separate section has been devoted to an estimate of the effect of impact-parameter correlation on the multiple scattering of penetrating molecules

  18. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

    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

  19. Broadband electromagnetic dipole scattering by coupled multiple nanospheres

    Jing, Xufeng; Ye, Qiufeng; Hong, Zhi; Zhu, Dongshuo; Shi, Guohua

    2017-11-01

    With the development of nanotechnology, the ability to manipulate light at the nanoscale is critical to future optical functional devices. The use of high refractive index dielectric single silicon nanoparticle can achieve electromagnetic dipole resonant properties. Compared with single nanosphere, the use of dimer and trimer introduces an additional dimension (gap size) for improving the performance of dielectric optical devices through the coupling between closely connected silicon nanospheres. When changing the gap size between the nanospheres, the interaction between the particles can be from weak to strong. Compared with single nanospheres, dimerized or trimeric nanospheres exhibit more pronounced broadband scattering properties. In addition, by introducing more complex interaction, the trimericed silicon nanospheres exhibit a more significant increase in bandwidth than expected. In addition, the presence of the substrate will also contribute to the increase in the bandwidth of the nanospheres. The broadband response in dielectric nanostructures can be effectively applied to broadband applications such as dielectric nanoantennas or solar cells.

  20. 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.

  1. Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation

    Zardecki, A.; Gerstl, S.A.W.; Embury, J.F.

    1983-01-01

    The discrete-ordinates finite-element radiation transport code twotran is applied to describe the multiple scattering of a laser beam from a reflecting target. For a model scenario involving a 99% relative humidity rural aerosol we compute the average intensity of the scattered radiation and correction factors to the Beer-Lambert law arising from multiple scattering. As our results indicate, 2-D x-y and r-z geometry modeling can reliably describe a realistic 3-D scenario. Specific results are presented for the two visual ranges of 1.52 and 0.76 km which show that, for sufficiently high aerosol concentrations (e.g., equivalent to V = 0.76 km), the target signature in a distant detector becomes dominated by multiply scattered radiation from interactions of the laser light with the aerosol environment. The merits of the scaling group and the delta-M approximation for the transfer equation are also explored

  2. Multiple scattering formulation of two-dimensional acoustic and electromagnetic metamaterials

    Torrent, Daniel; Sanchez-Dehesa, Jose, E-mail: datorma1@upvnet.upv.es, E-mail: jsdehesa@upvnet.upv.es [Grupo de Fenomenos Ondulatorios, Departamento de IngenierIa Electronica, Universitat Politecnica de Valencia, Camino de Vera s/n (Edificio 7F), ES-46022 Valencia (Spain)

    2011-09-15

    A multiple scattering formulation of two-dimensional (2D) acoustic metamaterials is presented. This approach is comprehensive and can lead to frequency-dependent effective parameters (scalar bulk modulus and tensorial mass density), as it is possible to have not only positive or negative ellipsoidal refractive index, but also positive or negative hyperbolic refractive index. The correction due to multiple scattering interactions is included in the theory and it is demonstrated that its contribution is important only for lattices with high filling fractions. Since the surface fields on the scatterers are mainly responsible for the anomalous behavior of the resulting effective medium, complex scatterers can be used to engineer the frequency response. Anisotropic effects are also discussed within this formulation and some numerical examples are reported. A homogenization theory is also extended to electromagnetic wave propagation in 2D lattices of dielectric structures, where Mie resonances are found to be responsible for the metamaterial behavior.

  3. Parallel time domain solvers for electrically large transient scattering problems

    Liu, Yang

    2014-09-26

    Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.

  4. Effects of multiple scattering on radiative properties of soot fractal aggregates

    Yon, Jérôme; Liu, Fengshan; Bescond, Alexandre; Caumont-Prim, Chloé; Rozé, Claude; Ouf, François-Xavier; Coppalle, Alexis

    2014-01-01

    The in situ optical characterization of smokes composed of soot particles relies on light extinction, angular static light scattering (SLS), or laser induced incandescence (LII). These measurements are usually interpreted by using the Rayleigh–Debye–Gans theory for Fractal Aggregates (RDG-FA). RDG-FA is simple to use but it completely neglects the impact of multiple scattering (MS) within soot aggregates. In this paper, based on a scaling approach that takes into account MS effects, an extended form of the RDG-FA theory is proposed in order to take into account these effects. The parameters of this extended theory and their dependency on the number of primary sphere inside the aggregate (1 p <1006) and on the wavelength (266nm<λ<1064nm) are evaluated thanks to rigorous calculations based on discrete dipole approximation (DDA) and generalized multi-sphere Mie-solution (GMM) calculations. This study shows that size determination by SLS is not distorted by MS effect. On the contrary, it is shown that fractal dimension can be misinterpreted by light scattering experiments, especially at short wavelengths. MS effects should be taken into account for the interpretation of absorption measurements that are involved in LII or extinction measurements. -- Highlights: • We incorporate multiple scattering effects in a scaling approach for fractal aggregates. • A generalized structure factor is introduced for implementation in RDG-FA theory. • Forward scattering is affected by multiple scattering as well as power law regime. • Absorption cross sections are affected by multiple scattering. • Absorption cross sections are 11% higher than that for forward scattering

  5. Multiple scattering expansion of the self-energy at finite temperature

    Jeon, S.; Ellis, P.J.

    1998-01-01

    An often used rule that the thermal correction to the self-energy is the thermal phase-space times the forward scattering amplitude from target particles is shown to be the leading term in an exact multiple scattering expansion. Starting from imaginary-time finite-temperature field theory, a rigorous expansion for the retarded self-energy is derived. The relationship to the thermodynamic potential is briefly discussed. copyright 1998 The American Physical Society

  6. Multiple Scattering Expansion of the Self-Energy at Finite Temperature

    Jeon, Sangyong; Ellis, Paul J.

    1998-01-01

    An often used rule that the thermal correction to the self-energy is the thermal phase-space times the forward scattering amplitude from target particles is shown to be the leading term in an exact multiple scattering expansion. Starting from imaginary-time finite-temperature field theory, a rigorous expansion for the retarded self-energy is derived. The relationship to the thermodynamic potential is briefly discussed.

  7. Taking apart the enhanced backscattering cone: Interference fringes from reciprocal paths in multiple light scattering

    Bret, Boris P. J.; Ferreira, Flavio P.; Nunes-Pereira, Eduardo J.; Belsley, Michael

    2010-01-01

    We report the decomposition of the enhanced backscattering cone into its constitutive interference fringes. These fringes are due to the constructive interference between reciprocal paths of any multiply scattered wave after ensemble averaging. An optical setup combining a two-point continuous-wave illumination and matching detection allows the observation of the fringes and, therefore, the quantitative characterization of the Green's function for light propagation between the two points in a multiple-scattering media.

  8. Analytical calculations of multiple scattering for high energy photons and neutrons

    Thoe, R.S.

    1994-04-01

    Radiography of large dense objects often require the use of highly penetrating radiation. For example, a couple of centimeters of steel attenuates 50 keV x-rays by a factor of approximately 10 -14 whereas this same amount of steel would attenuate a 500 keV photon beam by only a factor of about 0.25. However, this increase in penetrating power comes with a price. In the case of x-radiation there are two bills to pay: (1) For projection radiography, this increase in penetration directly causes a corresponding decrease in resolution. (2) This increase in penetration occurs in a region where the interaction of radiation and matter is changing from absorption to scattering. In the above example the fraction of scattering goes from about 0.1 at 50 keV to over 0.99 at 500 keV. These scattered photons can significantly degrade contrast. In order to overcome some of these difficulties, radiography using scattered photons has been studied by myself and numerous other authors. In all the above cases, calculation of the intensity of scattered radiation is of primary importance. In cases where scattering is probable, multiple scattering can also be probable. Calculations of multiple scattering are generally very difficult and usually require the use of extremely sophisticated Monte Carlo simulations. It is not unusual for these calculations to require several hours of CPU time on some of the worlds largest and fastest supercomputers. In this paper I will present an alternative approach. I will present an analytical solution to the equations of double scattering, and show how this solution can extended to the case of higher order scattering. Finally, I will give numerical examples of these solutions and compare them to solutions obtained by Monte Carlo simulations

  9. The Multiple Pendulum Problem via Maple[R

    Salisbury, K. L.; Knight, D. G.

    2002-01-01

    The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

  10. Multiple scattering of electromagnetic waves by a collection of plasma drift turbulent vortices

    Resendes, D.

    1995-01-01

    An application of the self-consistent multiple-scattering theory of electro-magnetic waves to drift turbulent vortices is presented. Using the known single-vortex solution, the integral equation describing the scattering from a finite density of drift turbulent vortices is obtained. Rather than solving this equation and then averaging, the averaging operation is taken first to obtain statistical moment equations, from which the coherent and incoherent scattering follow. These results are expressed in a Fourier basis, and the cross-section is evaluated. Limiting forms of the theory and straightforward generalizations are discussed. (Author)

  11. Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

    Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph

    2015-08-01

    Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

  12. Two-dimensional phononic crystals with time-varying properties: a multiple scattering analysis

    Wright, D W; Cobbold, R S C

    2010-01-01

    Multiple scattering theory is a versatile two- and three-dimensional method for characterizing the acoustic wave transmission through many scatterers. It provides analytical solutions to wave propagation in scattering structures, and its computational complexity grows logarithmically with the number of scatterers. In this paper we show how the 2D method can be adapted to include the effects of time-varying material parameters. Specifically, a new T-matrix is defined to include the effects of frequency modulation that occurs in time-varying phononic crystals. Solutions were verified against finite difference time domain (FDTD) simulations and showed excellent agreement. This new method enables fast characterization of time-varying phononic crystals without the need to resort to lengthy FDTD simulations. Also, the method of combining T-matrices to form the T-supermatrix remains unchanged provided that the new matrix definitions are used. The method is quite compatible with existing implementations of multiple scattering theory and could be readily extended to three-dimensional multiple scattering theory

  13. 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.

  14. On multiple level-set regularization methods for inverse problems

    DeCezaro, A; Leitão, A; Tai, X-C

    2009-01-01

    We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels

  15. MULTIPLE-PLANET SCATTERING AND THE ORIGIN OF HOT JUPITERS

    Beaugé, C.; Nesvorný, D.

    2012-01-01

    Doppler and transit observations of exoplanets show a pile-up of Jupiter-size planets in orbits with a 3 day period. A fraction of these hot Jupiters have retrograde orbits with respect to the parent star's rotation, as evidenced by the measurements of the Rossiter-McLaughlin effect. To explain these observations we performed a series of numerical integrations of planet scattering followed by the tidal circularization and migration of planets that evolved into highly eccentric orbits. We considered planetary systems having three and four planets initially placed in successive mean-motion resonances, although the angles were taken randomly to ensure orbital instability in short timescales. The simulations included the tidal and relativistic effects, and precession due to stellar oblateness. Our results show the formation of two distinct populations of hot Jupiters. The inner population (Population I) is characterized by semimajor axis a 1 Gyr and fits nicely the observed 3 day pile-up. A comparison between our three-planet and four-planet runs shows that the formation of hot Jupiters is more likely in systems with more initial planets. Due to the large-scale chaoticity that dominates the evolution, high eccentricities and/or high inclinations are generated mainly by close encounters between the planets and not by secular perturbations (Kozai or otherwise). The relative proportion of retrograde planets seems of be dependent on the stellar age. Both the distribution of almost aligned systems and the simulated 3 day pile-up also fit observations better in our four-planet simulations. This may suggest that the planetary systems with observed hot Jupiters were originally rich in the number of planets, some of which were ejected. In a broad perspective, our work therefore hints on an unexpected link between the hot Jupiters and recently discovered free floating planets.

  16. Point spread function due to multiple scattering of light in the atmosphere

    Pękala, J.; Wilczyński, H.

    2013-01-01

    The atmospheric scattering of light has a significant influence on the results of optical observations of air showers. It causes attenuation of direct light from the shower, but also contributes a delayed signal to the observed light. The scattering of light therefore should be accounted for, both in simulations of air shower detection and reconstruction of observed events. In this work a Monte Carlo simulation of multiple scattering of light has been used to determine the contribution of the scattered light in observations of a point source of light. Results of the simulations and a parameterization of the angular distribution of the scattered light contribution to the observed signal (the point spread function) are presented. -- Author-Highlights: •Analysis of atmospheric scattering of light from an isotropic point source. •Different geometries and atmospheric conditions were investigated. •A parameterization of scattered light distribution has been developed. •The parameterization allows one to easily account for the light scattering in air. •The results will be useful in analyses of observations of extensive air shower

  17. A fast calculating two-stream-like multiple scattering algorithm that captures azimuthal and elevation variations

    Fiorino, Steven T.; Elmore, Brannon; Schmidt, Jaclyn; Matchefts, Elizabeth; Burley, Jarred L.

    2016-05-01

    Properly accounting for multiple scattering effects can have important implications for remote sensing and possibly directed energy applications. For example, increasing path radiance can affect signal noise. This study describes the implementation of a fast-calculating two-stream-like multiple scattering algorithm that captures azimuthal and elevation variations into the Laser Environmental Effects Definition and Reference (LEEDR) atmospheric characterization and radiative transfer code. The multiple scattering algorithm fully solves for molecular, aerosol, cloud, and precipitation single-scatter layer effects with a Mie algorithm at every calculation point/layer rather than an interpolated value from a pre-calculated look-up-table. This top-down cumulative diffusivity method first considers the incident solar radiance contribution to a given layer accounting for solid angle and elevation, and it then measures the contribution of diffused energy from previous layers based on the transmission of the current level to produce a cumulative radiance that is reflected from a surface and measured at the aperture at the observer. Then a unique set of asymmetry and backscattering phase function parameter calculations are made which account for the radiance loss due to the molecular and aerosol constituent reflectivity within a level and allows for a more accurate characterization of diffuse layers that contribute to multiple scattered radiances in inhomogeneous atmospheres. The code logic is valid for spectral bands between 200 nm and radio wavelengths, and the accuracy is demonstrated by comparing the results from LEEDR to observed sky radiance data.

  18. Scattering integral equations and four nucleon problem. Four nucleon bound states and scattering

    Narodetskij, I.M.

    1981-01-01

    Existing results from the application of integral equation technique four-nucleon bound states and scattering are reviewed. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. Developments in the actual numerical solutions of Faddeev-Yakubovsky type equations are such that a detailed comparison can be made with experiment. Bound state calculations indicate that a nonrelativistic description with pairwise nuclear forces does not suffice and additional degrees of freedom are noted [ru

  19. Development of multiple scattering lidar to retrieve cloud extinction and size information

    Kim, Dukhyeon; Cheong, Hai Du; Kim, Young Gi; Park, Sun Ho

    2008-01-01

    Traditional Mie scattering cloud lidar have some limitations because of multiple scattering effects. Because this multiple scattering effects induce depolarization of spherical particle and enhancement of extinction coefficient. We cannot measure the phase of water with depolarization lidar, and also cannot measure the extinction coefficient with single FOV(Field Of View)Mie cloud lidar system. In the study, we have developed a multiple field of view Mie cloud liar system which can give many information about the cloud droplet such as cloud effective size, cloud number density, extinction coefficient of cloud, and phase of water through the correction of multiple scattering effects. For this purpose, we have developed a multiple field of view lidar system which composed of 32 different pinholes. Figure 1 shows the schematic diagram and picture of pinholes which start from 100μm to 8mm. Pihole is located at the focal plane of the parabolic mirror, in this case the minimum FOV is 67μrad, maximum FOV is 5.3 mrad. Figure 2 shows Monte Carlo simulation of the multiple scattering photons vs. cloud depth. In this calculation we assumed that wavelength normalized aerosol size(x)is 100, and density of cloud (extinction efficiency)is 0.01m"-1". By measuring FOV dependent signals and aerosol extinction coefficient we can extract effective droplet size through following equations. Here θ"d"is aerosol effective size, and z"j", f, Θ(z)are height, aerosol density dependent function, and angular size of lidar signal at the height z. Finally. f(z)depends on the light mean free path and number of scattering

  20. Removal of divergences in the problem of scattering of a particle beam by a medium

    Kuz'min, V.L.

    1977-01-01

    Scattering of a beam of particles (neutrons) by a medium is considered. After the averaging according to the statistical mechanics rules, the cross-section of the process is represented in the form of the series including many-particle distribution functions. The series describes the scattering processes of arbitrary multiplicity. Disconnected parts of the distribution functions give rise to divergences. A method of the re-summation of the original series is proposed, which removes all the divergences completely

  1. Resonant Rayleigh scattering of exciton-polaritons in multiple quantum wells

    Malpuech, Guillaume; Kavokin, Alexey; Langbein, Wolfgang Werner

    2000-01-01

    A theoretical concept of resonant Rayleigh scattering (RRS) of exciton-polaritons in multiple quantum wells (QWs) is presented. The optical coupling between excitons in different QWs can strongly affect the RRS dynamics, giving rise to characteristic temporal oscillations on a picosecond scale....... Bragg and anti-Bragg arranged QW structures with the same excitonic parameters are predicted to have drastically different RRS spectra. Experimental data on the RRS from multiple QWs show the predicted strong temporal oscillations at small scattering angles, which are well explained by the presented...

  2. Comparison of multiplicity distributions to the negative binomial distribution in muon-proton scattering

    Arneodo, M.; Ferrero, M.I.; Peroni, C.; Bee, C.P.; Bird, I.; Coughlan, J.; Sloan, T.; Braun, H.; Brueck, H.; Drees, J.; Edwards, A.; Krueger, J.; Montgomery, H.E.; Peschel, H.; Pietrzyk, U.; Poetsch, M.; Schneider, A.; Dreyer, T.; Ernst, T.; Haas, J.; Kabuss, E.M.; Landgraf, U.; Mohr, W.; Rith, K.; Schlagboehmer, A.; Schroeder, T.; Stier, H.E.; Wallucks, W.

    1987-01-01

    The multiplicity distributions of charged hadrons produced in the deep inelastic muon-proton scattering at 280 GeV are analysed in various rapidity intervals, as a function of the total hadronic centre of mass energy W ranging from 4-20 GeV. Multiplicity distributions for the backward and forward hemispheres are also analysed separately. The data can be well parameterized by binomial distributions, extending their range of applicability to the case of lepton-proton scattering. The energy and the rapidity dependence of the parameters is presented and a smooth transition from the binomial distribution via Poissonian to the ordinary binomial is observed. (orig.)

  3. Lloyd's formula in multiple-scattering calculations with finite temperature

    Zeller, Rudolf

    2005-01-01

    Lloyd's formula is an elegant tool to calculate the number of states directly from the imaginary part of the logarithm of the Korringa-Kohn-Rostoker (KKR) determinant. It is shown how this formula can be used at finite electronic temperatures and how the difficult problem to determine the physically significant correct phase of the complex logarithm can be circumvented by working with the single-valued real part of the logarithm. The approach is based on contour integrations in the complex energy plane and exploits the analytical properties of the KKR Green function and the Fermi-Dirac function. It leads to rather accurate results, which is illustrated by a local-density functional calculation of the temperature dependence of the intrinsic Fermi level in zinc-blende GaN

  4. A Hybrid Genetic Algorithm for the Multiple Crossdocks Problem

    Zhaowei Miao

    2012-01-01

    Full Text Available We study a multiple crossdocks problem with supplier and customer time windows, where any violation of time windows will incur a penalty cost and the flows through the crossdock are constrained by fixed transportation schedules and crossdock capacities. We prove this problem to be NP-hard in the strong sense and therefore focus on developing efficient heuristics. Based on the problem structure, we propose a hybrid genetic algorithm (HGA integrating greedy technique and variable neighborhood search method to solve the problem. Extensive experiments under different scenarios were conducted, and results show that HGA outperforms CPLEX solver, providing solutions in realistic timescales.

  5. Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

    Houfek, Karel

    2008-01-01

    Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

  6. Problem in quasi-free scattering at high missing energy $sup 40$Ca as an example

    Frullani, S

    1972-12-29

    From symposium on prescnt status and novel developments in the nuclear many-body problem; Rome, Italy (19 Sep 1972). Experimental data on the knocking- out of deep-bound protons in /sup 40/Ca in quasi-free scattering experiments and some open problems in the interpretation of this type of reactions are reviewed. (auth)

  7. Positive energy Weinberg states for the solution of scattering problems

    Rawitscher, G.

    1982-01-01

    Positive energy Weinberg states are defined and numerically calculated in the presence of a general complex Woods-Saxon potential. The numerical procedure is checked for the limit of a square well potential for which the Weinberg states and the corresponding eigenvalues are known. A finite number M of these (auxiliary) positive energy Weinberg states are then use as a set of basis functions in order to provide a separable approximation of rank M, V/sub M/, to a potential V, and also to the scattering matrix element S which obtains as a result of the presence of V, S/sub M/. Both V/sub M/ and S/sub M/ are obtained by means of algebraic manipulations which involve the matrix elements of V calculated in terms of the auxiliary postive energy Weinberg states Next, expressions are derived which enable one to iteratively correct for the error in V--V/sub M/. These expressions are a modified version of the quasi-particle method of Weinberg. The convergence of S/sub M/ to S, as well as the first order interation of the error in S/sub M/ is examined as a function M for a numerical example which uses a complex Woods-Saxon potential for V and assumes zero angular momentum. With M = 5 and one iteration an error of less than 10% in S is achieved; for M = 8 the error is less than 1%. The method is expected to be useful for the solution of large systems of coupled equations by matrix techniques or when a part of the potential is non-local

  8. Localization of a small change in a multiple scattering environment without modeling of the actual medium.

    Rakotonarivo, S T; Walker, S C; Kuperman, W A; Roux, P

    2011-12-01

    A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference between the measured signals then reveals all field components that have interacted with the perturbation. A simple single scatter filter (that ignores the presence of the medium scatterers) is matched to the earliest change of the coherent difference to localize the perturbation. Using a multi-source/receiver laboratory setup in air, the technique has been successfully tested with experimental data at frequencies varying from 30 to 60 kHz (wavelength ranging from 0.5 to 1 cm) for cm-scale scatterers in a scattering medium with a size two to five times bigger than its transport mean free path. © 2011 Acoustical Society of America

  9. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

    Zhao, Yingfeng; Liu, Sanyang

    2016-01-01

    We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

  10. Is there an Ay problem in low-energy neutron-proton scattering?

    Gross, Franz; Stadler, Alfred

    2008-01-01

    We calculate Ay in neutron-proton scattering for the interactions models WJC-1 and WJC-2 in the Covariant Spectator Theory. We find that the recent 12 MeV measurements performed at TUNL are in better agreement with our results than with the Nijmegen Phase Shift Analysis of 1993, and after reviewing the low energy data, conclude that there is no Ay problem in low-energy np scattering.

  11. Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target

    Adolph, C.; Aghasyan, M.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anfimov, N. V.; Anosov, V.; Augsten, K.; Augustyniak, W.; Austregesilo, A.; Azevedo, C.; Badelek, B.; Balestra, F.; Ball, M.; Barth, J.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bodlák, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Capozza, L.; Chang, W.-C.; Chatterjee, C.; Chiosso, M.; Choi, A.; Chung, S. U.; Cicuttin, A.; Crespo, M.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O.; Dhara, L.; Donskov, S. V.; Doshita, N.; Dreisbach, Ch.; Duic, V.; Dünnweber, W.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Faessler, M.; Ferrero, A.; Finger, M.; Finger jr., M.; Fischer, H.; Franco, C.; Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse-Perdekapm, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; Hamar, G.; von Harrach, D.; Heinsius, F. H.; Heitz, R.; Herrmann, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.-Yu.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jarý, V.; Joosten, R.; Jörg, P.; Kabuss, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Y.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kulinich, Y.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lian, Y.-S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.; Marianski, B.; Martin, A.; Marzec, J.; Matoušek, R.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, M.; Meyer, W.; Mikhailov, Yu. V.; Mikhasenko, M.; Mitrofanov, E.; Mitrofanov, N.; Miyachi, Y.; Nagaytsev, A.; Nerling, F.; Neyret, D.; Nový, J.; Nowak, W. D.; Nukazuka, G.; Nunes, A.S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pešek, M.; Peshekhonov, D. V.; Pierre, N.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Roskot, M.; Rossiyskaya, N. S.; Ryabchikov, D.; Rybnikov, A.; Rychter, A.; Salač, R.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sawada, H.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Seder, E.; Selyunin, A.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Smolík, J.; Sozzi, F.; Srnka, Aleš; Steffen, D.; Stolarski, M.; Subrt, O.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Tasevsky, M.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Thiel, A.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Vondra, J.; Wallner, S.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Ter Wolbeek, J.; Zaremba, K.; Závada, P.; Zavertyaev, M.; Zemlyanichkina, E.; Zhuravlev, N.; Ziembicki, M.; Zink, A.

    2017-01-01

    Roč. 767, 10 APRIL (2017), s. 133-141 ISSN 0370-2693 R&D Projects: GA MŠk(CZ) LO1212 Institutional support: RVO:68081731 Keywords : deep inelastic scattering * kaon multiplicities * quark fragmentation functions * strange quark Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Nuclear physics Impact factor: 4.807, year: 2016

  12. Coulomb correction to the screening angle of the Moliere multiple scattering theory

    Kuraev, E.A.; Voskresenskaya, O.O.; Tarasov, A.V.

    2012-01-01

    Coulomb correction to the screening angular parameter of the Moliere multiple scattering theory is found. Numerical calculations are presented in the range of nuclear charge 4 ≤ Z ≤ 82. Comparison with the Moliere result for the screening angle reveals up to 30% deviation from it for sufficiently heavy elements of the target material

  13. Multiple scattering in electron fluid and energy loss in multi-ionic targets

    Deutsch, C., E-mail: claude.deutsch@u-psud.fr [LPGP, UParis-Sud, 91405-Orsay (France); Tahir, N.A. [GSI, 1Planck Str., 64291-Darmstadt (Germany); Barriga-Carrasco, M. [ETSII, UCastilla-la-Mancha, 13071 Ciudad-Real (Spain); Ceban, V. [LPGP, UParis-Sud, 91405-Orsay (France); Fromy, P. [CRI, UParis-Sud, 91405-Orsay (France); Gilles, D. [CEA/Saclay/DSM/IRFU/SAP, 91191-Gif-s-Yvette (France); Leger, D. [Laboratoire Monthouy, UValenciennes-Hainaut Cambresis (France); Maynard, G. [LPGP, UParis-Sud, 91405-Orsay (France); Tashev, B. [Department of Physics, KazNu, Tole Bi82, Almaty (Kazakhstan); Volpe, L. [Department of Physics, UMilano-Bicocca, Milano 20126 (Italy)

    2014-01-01

    Extensions of the standard stopping model (SSM) for ion projectiles interacting with dense targets of timely concern for ICF and WDM are reviewed. They include multiple scattering on partially degenerate electrons, low velocity ion slowing down in demixing H–He mixtures within Jovian planets core or multiionic target such as Kapton.

  14. Multiple scattering in electron fluid and energy loss in multi-ionic targets

    Deutsch, C.; Tahir, N.A.; Barriga-Carrasco, M.; Ceban, V.; Fromy, P.; Gilles, D.; Leger, D.; Maynard, G.; Tashev, B.; Volpe, L.

    2014-01-01

    Extensions of the standard stopping model (SSM) for ion projectiles interacting with dense targets of timely concern for ICF and WDM are reviewed. They include multiple scattering on partially degenerate electrons, low velocity ion slowing down in demixing H–He mixtures within Jovian planets core or multiionic target such as Kapton

  15. A method for the generation of random multiple Coulomb scattering angles

    Campbell, J.R.

    1995-06-01

    A method for the random generation of spatial angles drawn from non-Gaussian multiple Coulomb scattering distributions is presented. The method employs direct numerical inversion of cumulative probability distributions computed from the universal non-Gaussian angular distributions of Marion and Zimmerman. (author). 12 refs., 3 figs

  16. Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

    Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

    2018-03-01

    The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

  17. Multiobjective scatter search approach with new combination scheme applied to solve environmental/economic dispatch problem

    Athayde Costa e Silva, Marsil de; Klein, Carlos Eduardo; Mariani, Viviana Cocco; Santos Coelho, Leandro dos

    2013-01-01

    The environmental/economic dispatch (EED) is an important daily optimization task in the operation of many power systems. It involves the simultaneous optimization of fuel cost and emission objectives which are conflicting ones. The EED problem can be formulated as a large-scale highly constrained nonlinear multiobjective optimization problem. In recent years, many metaheuristic optimization approaches have been reported in the literature to solve the multiobjective EED. In terms of metaheuristics, recently, scatter search approaches are receiving increasing attention, because of their potential to effectively explore a wide range of complex optimization problems. This paper proposes an improved scatter search (ISS) to deal with multiobjective EED problems based on concepts of Pareto dominance and crowding distance and a new scheme for the combination method. In this paper, we have considered the standard IEEE (Institute of Electrical and Electronics Engineers) 30-bus system with 6-generators and the results obtained by proposed ISS algorithm are compared with the other recently reported results in the literature. Simulation results demonstrate that the proposed ISS algorithm is a capable candidate in solving the multiobjective EED problems. - Highlights: ► Economic dispatch. ► We solve the environmental/economic economic power dispatch problem with scatter search. ► Multiobjective scatter search can effectively improve the global search ability

  18. Heuristic for Solving the Multiple Alignment Sequence Problem

    Roman Anselmo Mora Gutiérrez

    2011-03-01

    Full Text Available In this paper we developed a new algorithm for solving the problem of multiple sequence alignment (AM S, which is a hybrid metaheuristic based on harmony search and simulated annealing. The hybrid was validated with the methodology of Julie Thompson. This is a basic algorithm and and results obtained during this stage are encouraging.

  19. Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs

    Marco Calahorrano

    2004-04-01

    Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$

  20. Four-nucleon problem in terms of scattering of Hilbert-Schmidt resonances

    Narodetsky, I.M.

    1974-01-01

    The four-body integral equations are written in terms of the scattering amplitudes for the Hilbert-Schmidt resonances corresponding to the 3*1 and 2*2 subsystems. As a result, the four-body problem is reduced to the many channel two-body problem. A simple diagram technique is introduced which is the generalization of the usual time-ordered nonrelativistic one. The connection between the amplitudes of the two-body reactions and the scattering amplitudes for the resonances is obtained

  1. Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schroedinger problem and the KPI equation

    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

  2. Influence of Number Size, Problem Structure and Response Mode on Children's Solutions of Multiplication Word Problems.

    De Corte, E.; And Others

    One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…

  3. Multiple scattering effects with cyclical terms in active remote sensing of vegetated surface using vector radiative transfer theory

    The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical t...

  4. Problem-solving with multiple interdependent criteria: better solution to complex problems

    Carlsson, C.; Fuller, R.

    1996-01-01

    We consider multiple objective programming (MOP) problems with additive interdependencies, this is when the states of some chosen objective are attained through supportive or inhibitory feed-backs from several other objectives. MOP problems with independent objectives (when the cause-effect relations between the decision variables and the objectives are completely known) will be treated as special cases of the MOP in which we have interdependent objectives. We illustrate our ideas by a simple three-objective real-life problem

  5. 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.

  6. A multiple scattering theory for EM wave propagation in a dense random medium

    Karam, M. A.; Fung, A. K.; Wong, K. W.

    1985-01-01

    For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

  7. 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)

  8. Analysis of the spectrum of a Cartesian Perfectly Matched Layer (PML) approximation to acoustic scattering problems

    Kim, Seungil; Pasciak, Joseph E.

    2010-01-01

    is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a

  9. The scattering problem in X-ray adsorptiometry using an MWPC; and its solution

    Bateman, J.E.

    1978-03-01

    It is shown that a large aperture imaging X-ray absorptiometric system (in this case a xenon filled MWPC) suffers very badly from scattering in the water bath and soft tissue components of the imaged system in the bone mass measuring case. Applications of a fine focused collimator provides a satisfactory solution to the problem. (author)

  10. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    Bramble, James H.; Pasciak, Joseph E.

    2013-01-01

    to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given

  11. Neutrino-electron scattering and the choice between different MSW solutions of the solar neutrino problem

    Rosen, S.P.; Gelb, J.M.

    1987-01-01

    We consider the scattering of solar neutrinos by electrons as a means for distinguishing between MSW solutions of the solar neutrino problem. In terms of the ratio R between the observed cross-section and that for pure electron-type neutrinos, we find that some correlation between the value R and the appropriate solution. 9 refs., 3 figs

  12. On the method of inverse scattering problem and Baecklund transformations for supersymmetric equations

    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)

  13. Multiple scattering of electromagnetic waves in disordered magnetic media localization parameter, energy transport velocity and diffusion constant

    Pinheiro, F A; Martínez, A S

    2001-01-01

    We review some of our recent results concerning the single and multiple electromagnetic scattering by magnetic spherical particles. For a single electromagnetic scattering we show that the magnetic contribution alters, when compared to nonmagnetic scattering, the behavior of the cross sections and mean cosine of the scattering angle (cos omega). For ferromagnetic particles, resonances may occur even in the small-particle limit when the particle radius is much smaller than the wavelength. The resonances increase the cross sections while (cos omega) is diminished , and even may become negative. Several quantities such the Ioffe-Regel parameter for localization are calculated for the multiple scattering regime. We show that magnetic scattering favors the observation of localization of electromagnetic waves in three dimensions. Further, this is also verified for dynamical experiments, where we show that the diffusion constant can be very small. Since the magnetic permeability of the scatterers can vary significan...

  14. Experimental investigations of multiple scattering of 662 keV gamma photons in elements and binary alloys

    Singh, Gurvinderjit; Singh, Manpreet; Sandhu, B.S.; Singh, Bhajan

    2008-01-01

    The energy, intensity and angular distributions of multiple scattering of 662 keV gamma photons, emerging from targets of pure elements and binary alloys, are observed as a function of target thickness in reflection and transmission geometries. The observed spectra recorded by a properly shielded NaI (Tl) scintillation detector, in addition to singly scattered events, consist of photons scattered more than once for thick targets. To extract the contribution of multiply scattered photons from the measured spectra, a singly scattered distribution is reconstructed analytically. We observe that the numbers of multiply scattered events increase with increase in target thickness, and saturate for a particular thickness called saturation thickness. The saturation thickness decreases with increasing atomic number. The multiple scattering, an interfering background noise in Compton profiles and Compton cross-section measurements, has been successfully used as a new technique to assign the 'effective atomic number' to binary alloys. Monte Carlo calculations support the present experimental results

  15. A NEW HEURISTIC ALGORITHM FOR MULTIPLE TRAVELING SALESMAN PROBLEM

    F. NURIYEVA

    2017-06-01

    Full Text Available The Multiple Traveling Salesman Problem (mTSP is a combinatorial optimization problem in NP-hard class. The mTSP aims to acquire the minimum cost for traveling a given set of cities by assigning each of them to a different salesman in order to create m number of tours. This paper presents a new heuristic algorithm based on the shortest path algorithm to find a solution for the mTSP. The proposed method has been programmed in C language and its performance analysis has been carried out on the library instances. The computational results show the efficiency of this method.

  16. Multiple regression for physiological data analysis: the problem of multicollinearity.

    Slinker, B K; Glantz, S A

    1985-07-01

    Multiple linear regression, in which several predictor variables are related to a response variable, is a powerful statistical tool for gaining quantitative insight into complex in vivo physiological systems. For these insights to be correct, all predictor variables must be uncorrelated. However, in many physiological experiments the predictor variables cannot be precisely controlled and thus change in parallel (i.e., they are highly correlated). There is a redundancy of information about the response, a situation called multicollinearity, that leads to numerical problems in estimating the parameters in regression equations; the parameters are often of incorrect magnitude or sign or have large standard errors. Although multicollinearity can be avoided with good experimental design, not all interesting physiological questions can be studied without encountering multicollinearity. In these cases various ad hoc procedures have been proposed to mitigate multicollinearity. Although many of these procedures are controversial, they can be helpful in applying multiple linear regression to some physiological problems.

  17. Multiple scattering of low energy rare gas ions: a comparison of experiment and computer simulation

    Heiland, W.; Taglauer, E.; Robinson, M.T.

    1976-01-01

    Some aspects of ion scattering below a few keV have been interpreted by multiple scattering. This can partly be simulated by chain or string models, where the single crystal surface is replaced by a chain of atoms. The computer program MARLOWE allows a simulation of solid-ion interaction, which is much closer to reality, e.g. the crystal is three-dimensional, includes lattice vibrations, electronic stopping power, different scattering potentials, etc. It is shown that the energy of the reflected ions as a function of the primary energy, lattice constant, impact angle and scattering angle can be understood within the string model. These results of the string model are confirmed by the MARLOWE calculations. For an interpretation of the measured intensities the simple string model is insufficient, whereas with MARLOWE reasonable agreement with experimental data may be achieved, if the thermal vibrations of the lattice atoms are taken into account. The experimental data include Ne + →Ni, Ne + →Ag and preliminary data on Ne + →W. The screening parameters of the scattering potentials are estimated for these ion-atom combinations. The results allow some conclusions about surface Debye temperatures. (Auth.)

  18. The potential influence of multiple scattering on longwave flux and heating rate simulations with clouds

    Kuo, C. P.; Yang, P.; Huang, X.; Feldman, D.; Flanner, M.; Kuo, C.; Mlawer, E. J.

    2017-12-01

    Clouds, which cover approximately 67% of the globe, serve as one of the major modulators in adjusting radiative energy on the Earth. Since rigorous radiative transfer computations including multiple scattering are costly, only absorption is considered in the longwave spectral bands in the radiation sub-models of the general circulation models (GCMs). Quantification of the effect of ignoring longwave scattering for flux and heating rate simulations is performed by using the GCM version of the Longwave Rapid Radiative Transfer Model (RRTMG_LW) with an implementation with the 16-stream Discrete Ordinates Radiative Transfer (DISORT) Program for a Multi-Layered Plane-Parallel Medium in conjunction with the 2010 CCCM products that merge satellite observations from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), the CloudSat, the Clouds and the Earth's Radiant Energy System (CERES) and the Moderate Resolution Imaging Spectrometer (MODIS). One-year global simulations show that neglecting longwave scattering overestimates upward flux at the top of the atmosphere (TOA) and underestimates downward flux at the surface by approximately 2.63 and 1.15 W/m2, respectively. Furthermore, when longwave scattering is included in the simulations, the tropopause is cooled by approximately 0.018 K/day and the surface is heated by approximately 0.028 K/day. As a result, the radiative effects of ignoring longwave scattering and doubling CO2 are comparable in magnitude.

  19. On the representation of electron multiple elastic-scattering distributions for Monte Carlo calculations

    Kawrakow, I.; Bielajew, A.F.

    1998-01-01

    A new representation of elastic electron-nucleus (Coulomb) multiple-scattering distributions is developed. Using the screened Rutherford cross section with the Moliere screening parameter as an example, a simple analytic angular transformation of the Goudsmit-Saunderson multiple-scattering distribution accounts for most of the structure of the angular distribution leaving a residual 3-parameter (path-length, transformed angle and screening parameter) function that is reasonably slowly varying and suitable for rapid, accurate interpolation in a computer-intensive algorithm. The residual function is calculated numerically for a wide range of Moliere screening parameters and path-lengths suitable for use in a general-purpose condensed-history Monte Carlo code. Additionally, techniques are developed that allow the distributions to be scaled to account for energy loss. This new representation allows ''''on-the-fly'''' sampling of Goudsmit-Saunderson angular distributions in a screened Rutherford approximation suitable for class II condensed-history Monte Carlo codes. (orig.)

  20. UAV remote sensing atmospheric degradation image restoration based on multiple scattering APSF estimation

    Qiu, Xiang; Dai, Ming; Yin, Chuan-li

    2017-09-01

    Unmanned aerial vehicle (UAV) remote imaging is affected by the bad weather, and the obtained images have the disadvantages of low contrast, complex texture and blurring. In this paper, we propose a blind deconvolution model based on multiple scattering atmosphere point spread function (APSF) estimation to recovery the remote sensing image. According to Narasimhan analytical theory, a new multiple scattering restoration model is established based on the improved dichromatic model. Then using the L0 norm sparse priors of gradient and dark channel to estimate APSF blur kernel, the fast Fourier transform is used to recover the original clear image by Wiener filtering. By comparing with other state-of-the-art methods, the proposed method can correctly estimate blur kernel, effectively remove the atmospheric degradation phenomena, preserve image detail information and increase the quality evaluation indexes.

  1. Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target

    Adolph, C.

    2017-04-10

    Precise measurements of charged-kaon multiplicities in deep inelastic scattering were performed. The results are presented in three-dimensional bins of the Bjorken scaling variable x, the relative virtual-photon energy y, and the fraction z of the virtual-photon energy carried by the produced hadron. The data were obtained by the COMPASS Collaboration by scattering 160 GeV muons off an isoscalar 6 LiD target. They cover the kinematic domain 1 (GeV/c)2 5 GeV/c^2 in the invariant mass of the hadronic system. The results from the sum of the z-integrated K+ and K- multiplicities at high x point to a value of the non-strange quark fragmentation function larger than obtained by the earlier DSS fit.

  2. Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target

    C. Adolph

    2017-04-01

    Full Text Available Precise measurements of charged-kaon multiplicities in deep inelastic scattering were performed. The results are presented in three-dimensional bins of the Bjorken scaling variable x, the relative virtual-photon energy y, and the fraction z of the virtual-photon energy carried by the produced hadron. The data were obtained by the COMPASS Collaboration by scattering 160 GeV muons off an isoscalar 6LiD target. They cover the kinematic domain 1(GeV/c25 GeV/c2 in the invariant mass of the hadronic system. The results from the sum of the z-integrated K+ and K− multiplicities at high x point to a value of the non-strange quark fragmentation function larger than obtained by the earlier DSS fit.

  3. Multiple scattering wavelength dependent backscattering of kaolin dust in the IR: Measurements and theory

    Ben-David, Avishai

    1992-01-01

    Knowing the optical properties of aerosol dust is important for designing electro-optical systems and for modeling the effect on propagation of light in the atmosphere. As CO2 lidar technology becomes more advanced and is used for multiwavelength measurements, information on the wavelength dependent backscattering of aerosol dust particles is required. The volume backscattering coefficient of aerosols in the IR is relatively small. Thus, only a few field measurements of backscattering, usually at only a few wavelengths, are reported in the literature. We present spectral field measurements of backscattering of kaolin dust in the 9-11 micron wavelength range. As the quantity of dust increases, multiple scattering contributes more to the measured backscattered signal. The measurements show the effect of the dust quantity of the spectral backscatter measurements. A simple analytical two stream radiative transfer model is applied to confirm the measurements and to give insight to the multiple scattering spectra of backscattering.

  4. Atmospheric neutrino oscillations from upward throughgoing muon multiple scattering in MACRO

    Ambrosio, M.; Antolini, R.; Bakari, D.; Baldini, A.; Barbarino, G.C.; Barish, B.C.; Battistoni, G.; Becherini, Y.; Bellotti, R.; Bemporad, C.; Bernardini, P.; Bilokon, H.; Bloise, C.; Bower, C.; Brigida, M.; Bussino, S.; Cafagna, F.; Calicchio, M.; Campana, D.; Carboni, M.; Caruso, R.; Cecchini, S.; Cei, F.; Chiarella, V.; Chiarusi, T.; Choudhary, B.C.; Coutu, S.; Cozzi, M.; De Cataldo, G.; Dekhissi, H.; De Marzo, C.; De Mitri, I.; Derkaoui, J.; De Vincenzi, M.; Di Credico, A.; Favuzzi, C.; Forti, C.; Fusco, P.; Giacomelli, G.; Giannini, G.; Giglietto, N.; Giorgini, M.; Grassi, M.; Grillo, A.; Gustavino, C.; Habig, A.; Hanson, K.; Heinz, R.; Iarocci, E.; Katsavounidis, E.; Katsavounidis, I.; Kearns, E.; Kim, H.; Kumar, A.; Kyriazopoulou, S.; Lamanna, E.; Lane, C.; Levin, D.S.; Lipari, P.; Longo, M.J.; Loparco, F.; Maaroufi, F.; Mancarella, G.; Mandrioli, G.; Manzoor, S.; Margiotta, A.; Marini, A.; Martello, D.; Marzari-Chiesa, A.; Mazziotta, M.N.; Michael, D.G.; Mikheyev, S.; Monacelli, P.; Montaruli, T.; Monteno, M.; Mufson, S.; Musser, J.; Nicolo, D.; Nolty, R.; Orth, C.; Osteria, G.; Palamara, O.; Patera, V.; Patrizii, L.; Pazzi, R.; Peck, C.W.; Perrone, L.; Petrera, S.; Popa, V.; Raino, A.; Reynoldson, J.; Ronga, F.; Rrhioua, A.; Satriano, C.; Scapparone, E.; Scholberg, K.; Sciubba, A.; Serra, P.; Sioli, M.; Sirri, G.; Sitta, M.; Spinelli, P.; Spinetti, M.; Spurio, M.; Steinberg, R.; Stone, J.L.; Sulak, L.R.; Surdo, A.; Tarle, G.; Togo, V.; Vakili, M.; Walter, C.W.; Webb, R

    2003-07-24

    The energy of atmospheric neutrinos detected by MACRO was estimated using multiple Coulomb scattering of upward throughgoing muons. This analysis allows a test of atmospheric neutrino oscillations, relying on the distortion of the muon energy distribution. These results have been combined with those coming from the upward throughgoing muon angular distribution only. Both analyses are independent of the neutrino flux normalization and provide strong evidence, above the 4{sigma} level, in favour of neutrino oscillations.

  5. All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

    Fillion-Gourdeau, F.; Gagnon, J.-S.; Jeon, S.

    2007-01-01

    We summarize our main findings in deriving the Boltzmann collision term from the Kadanoff-Baym relativistic transport equation and the multiple scattering expansion of the self-energy within a quasi-particle approximation. Our collision term is valid to all orders in perturbation theory and contains processes with any number of participating particles. This work completes a program initiated by Carrington and Mrowczynski and developed further by present authors and Weinstock in recent literature

  6. Exploitation of Microdoppler and Multiple Scattering Phenomena for Radar Target Recognition

    2006-08-24

    progress on the reserach grant "Exploitation of MicroDoppler and Multiple Scattering Phenomena for Radar Target Recognition" during the period 1...paper describes a methodology of modeling A number of ray-based EM techniques have been interferometric synthetic aperture radar (IFSAR) images...modes including the single present an IFSAR simulation methodology to simulate the antenna transmit mode, the ping-pong mode or the repeat interferogram

  7. Quantum theory of dynamic multiple light scattering in fluctuating disordered media

    Skipetrov, S. E.

    2007-01-01

    We formulate a quantum theory of dynamic multiple light scattering in fluctuating disordered media and calculate the fluctuation and the autocorrelation function of the photon number operator for light transmitted through a disordered slab. The effect of disorder on the information capacity of a quantum communication channel operating in a disordered environment is estimated, and the use of squeezed light in diffusing-wave spectroscopy is discussed

  8. SCATTER

    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)

  9. Multiple scattering theory and applications for intermediate energy reactions of nuclei

    Ludeking, L.D.

    1979-01-01

    Interactions of two composite clusters are treated in a multiple scattering framework whereby many-particle operators are decomposed into a systematic and finite series such that there is an ordered sequestering according to particle rank. Thus, an N-body operator is written as the superposition of all distinct groupings of interactions that occur between particle pairs, triplets, quartets, etc., such that all groupings contain at least one particle from each of the composite systems. It is demonstrated how the transition operator, a reaction operator, and an optical potential may be described in this context. The general structure of such decompositions is shown, and the connection to the standard multiple-scattering prescriptions, delineated. The direct reaction amplitude for stripping and pickup is described, and the two potential formula of Gell-Mann and Goldberger is derived. The multiple scattering formalism for direct reactions is constructed in the eikonal approximation. The sensitivity of the transition cross section to the target density and nucleon-nucleon density correlations are examined in this framework. The limitations of the zero-range approximation to the deuteron vertex function are examined by comparison with the finite-range vertex function at a range of energies. 25 figures, 5 tables

  10. The hybrid model for sampling multiple elastic scattering angular deflections based on Goudsmit-Saunderson theory

    Wasaye Muhammad Abdul

    2017-01-01

    Full Text Available An algorithm for the Monte Carlo simulation of electron multiple elastic scattering based on the framework of SuperMC (Super Monte Carlo simulation program for nuclear and radiation process is presented. This paper describes efficient and accurate methods by which the multiple scattering angular deflections are sampled. The Goudsmit-Saunderson theory of multiple scattering has been used for sampling angular deflections. Differential cross-sections of electrons and positrons by neutral atoms have been calculated by using Dirac partial wave program ELSEPA. The Legendre coefficients are accurately computed by using the Gauss-Legendre integration method. Finally, a novel hybrid method for sampling angular distribution has been developed. The model uses efficient rejection sampling method for low energy electrons (500 mean free paths. For small path lengths, a simple, efficient and accurate analytical distribution function has been proposed. The later uses adjustable parameters determined from the fitting of Goudsmith-Saunderson angular distribution. A discussion of the sampling efficiency and accuracy of this newly developed algorithm is given. The efficiency of rejection sampling algorithm is at least 50 % for electron kinetic energies less than 500 keV and longer path lengths (>500 mean free paths. Monte Carlo Simulation results are then compared with measured angular distributions of Ross et al. The comparison shows that our results are in good agreement with experimental measurements.

  11. Double parton scattering in the ultraviolet. Addressing the double counting problem

    Diehl, Markus [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gaunt, Jonathan R. [Nikhef Theory Group, Amsterdam (Netherlands); Amsterdam VU Univ. (Netherlands)

    2016-11-15

    An important question in the theory of double parton scattering is how to incorporate the possibility of the parton pairs being generated perturbatively via 1→ 2splitting into the theory, whilst avoiding double counting with single parton scattering loop corrections. Here, we describe a consistent approach for solving this problem, which retains the notion of double parton distributions (DPDs) for individual hadrons. Further, we discuss the construction of appropriate model DPDs in our framework, and the use of these to compute the DPS part, presenting DPS 'luminosities' from our model DPDs for a few sample cases.

  12. Correlations in multiple production on nuclei and Glauber model of multiple scattering

    Zoller, V.R.; Nikolaev, N.N.

    1982-01-01

    Critical analysis of possibility for describing correlation phenomena during multiple production on nuclei within the framework of the Glauber multiple seattering model generalized for particle production processes with Capella, Krziwinski and Shabelsky has been performed. It was mainly concluded that the suggested generalization of the Glauber model gives dependences on Ng(Np) (where Ng-the number of ''grey'' tracess, and Np-the number of protons flying out of nucleus) and, eventually, on #betta# (where #betta#-the number of intranuclear interactions) contradicting experience. Independent of choice of relation between #betta# and Ng(Np) in the model the rapidity corrletor Rsub(eta) is overstated in the central region and understated in the region of nucleus fragmentation. In mean multiplicities these two contradictions of experience are disguised with random compensation and agreement with experience in Nsub(S) (function of Ng) cannot be an argument in favour of the model. It is concluded that eiconal model doesn't permit to quantitatively describe correlation phenomena during the multiple production on nuclei

  13. The finite element solution of two-dimensional transverse magnetic scattering problems on the connection machine

    Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.

    1990-01-01

    A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems

  14. Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

    Bramble, James H.

    2010-01-01

    We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.

  15. Dual wavelength multiple-angle light scattering system for cryptosporidium detection

    Buaprathoom, S.; Pedley, S.; Sweeney, S. J.

    2012-06-01

    A simple, dual wavelength, multiple-angle, light scattering system has been developed for detecting cryptosporidium suspended in water. Cryptosporidium is a coccidial protozoan parasite causing cryptosporidiosis; a diarrheal disease of varying severity. The parasite is transmitted by ingestion of contaminated water, particularly drinking-water, but also accidental ingestion of bathing-water, including swimming pools. It is therefore important to be able to detect these parasites quickly, so that remedial action can be taken to reduce the risk of infection. The proposed system combines multiple-angle scattering detection of a single and two wavelengths, to collect relative wavelength angle-resolved scattering phase functions from tested suspension, and multivariate data analysis techniques to obtain characterizing information of samples under investigation. The system was designed to be simple, portable and inexpensive. It employs two diode lasers (violet InGaN-based and red AlGaInP-based) as light sources and silicon photodiodes as detectors and optical components, all of which are readily available. The measured scattering patterns using the dual wavelength system showed that the relative wavelength angle-resolved scattering pattern of cryptosporidium oocysts was significantly different from other particles (e.g. polystyrene latex sphere, E.coli). The single wavelength set up was applied for cryptosporidium oocysts'size and relative refractive index measurement and differential measurement of the concentration of cryptosporidium oocysts suspended in water and mixed polystyrene latex sphere suspension. The measurement results showed good agreement with the control reference values. These results indicate that the proposed method could potentially be applied to online detection in a water quality control system.

  16. Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

    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.

  17. Solution of the neutron transport problem with anisotropic scattering in cylindrical geometry by the decomposition method

    Goncalves, G.A.; Bogado Leite, S.Q.; Vilhena, M.T. de

    2009-01-01

    An analytical solution has been obtained for the one-speed stationary neutron transport problem, in an infinitely long cylinder with anisotropic scattering by the decomposition method. Series expansions of the angular flux distribution are proposed in terms of suitably constructed functions, recursively obtainable from the isotropic solution, to take into account anisotropy. As for the isotropic problem, an accurate closed-form solution was chosen for the problem with internal source and constant incident radiation, obtained from an integral transformation technique and the F N method

  18. Three-body scattering problem in the fixed center approximation: The case of attraction

    Kudryavtsev, Alexander E. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Gani, Vakhid A. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Romanov, Alexander I. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)

    2016-12-15

    We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors. (orig.)

  19. Heuristic geometric ''eigenvalue universality'' in a one-dimensional neutron transport problem with anisotropic scattering

    Goncalves, G.A.; Vilhena, M.T. de; Bodmann, B.E.J.

    2010-01-01

    In the present work we propose a heuristic construction of a transport equation for neutrons with anisotropic scattering considering only the radial cylinder dimension. The eigenvalues of the solutions of the equation correspond to the positive values for the one dimensional case. The central idea of the procedure is the application of the S N method for the discretisation of the angular variable followed by the application of the zero order Hankel transformation. The basis the construction of the scattering terms in form of an integro-differential equation for stationary transport resides in the hypothesis that the eigenvalues that compose the elementary solutions are independent of geometry for a homogeneous medium. We compare the solutions for the cartesian one dimensional problem for an infinite cylinder with azimuthal symmetry and linear anisotropic scattering for two cases. (orig.)

  20. Electromagnetic scattering problems -Numerical issues and new experimental approaches of validation

    Geise, Robert; Neubauer, Bjoern; Zimmer, Georg [University of Braunschweig, Institute for Electromagnetic Compatibility, Schleinitzstrasse 23, 38106 Braunschweig (Germany)

    2015-03-10

    Electromagnetic scattering problems, thus the question how radiated energy spreads when impinging on an object, are an essential part of wave propagation. Though the Maxwell’s differential equations as starting point, are actually quite simple,the integral formulation of an object’s boundary conditions, respectively the solution for unknown induced currents can only be solved numerically in most cases.As a timely topic of practical importance the scattering of rotating wind turbines is discussed, the numerical description of which is still based on rigorous approximations with yet unspecified accuracy. In this context the issue of validating numerical solutions is addressed, both with reference simulations but in particular with the experimental approach of scaled measurements. For the latter the idea of an incremental validation is proposed allowing a step by step validation of required new mathematical models in scattering theory.

  1. The importance of anisotropic scattering in high energy neutron transport problems

    Prillinger, G.; Mattes, M.

    1984-01-01

    To describe the highly anisotropic scattering of very fast neutrons adequately the transport code ANISN has been improved. Fokker-Planck terms have been introduced into the transport equation which accurately describe the small changes in energy and angle. The new code has been tested for a d(50)-Be neutron source in a deep penetration iron problem. The influence of the forward peaked elastic scattering on the fast neutron spectrum is shown to be significant and can be handled efficiently in the new ANISN version. Since common cross-section libraries are limited by Legendre expansion, or by their upper energy boundary, or exclude elastic scattering above 20 MeV a special library has been created. (Auth.)

  2. Method of interior boundaries in a mixed problem of acoustic scattering

    P. A. Krutitskii

    1999-01-01

    Full Text Available The mixed problem for the Helmholtz equation in the exterior of several bodies (obstacles is studied in 2 and 3 dimensions. The Dirichlet boundary condition is given on some obstacles and the impedance boundary condition is specified on the rest. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called ‘Method of interior boundaries’, because additional boundaries are introduced inside scattering bodies, where impedance boundary condition is given. The solution of the problem is obtained in the form of potentials on the whole boundary. The density in the potentials satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann, Dirichlet, impedance problems and mixed Dirichlet–Neumann problem are particular cases of our problem.

  3. Multiple scattering effects in fast neutron polarization experiments using high-pressure helium-xenon gas scintillators as analyzers

    Tornow, W.; Mertens, G.

    1977-01-01

    In order to study multiple scattering effects both in the gas and particularly in the solid materials of high-pressure gas scintillators, two asymmetry experiments have been performed by scattering of 15.6 MeV polarized neutrons from helium contained in stainless steel vessels of different wall thicknesses. A monte Carlo computer code taking into account the polarization dependence of the differential scattering cross sections has been written to simulate the experiments and to calculate corrections for multiple scattering on helium, xenon and the gas containment materials. Besides the asymmetries for the various scattering processes involved, the code yields time-of-flight spectra of the scattered neutrons and pulse height spectra of the helium recoil nuclei in the gas scintillator. The agreement between experimental results and Monte Carlo calculations is satisfactory. (Auth.)

  4. Preliminary results on application of the multiple-scattering technique to electron--molecule scattering and molecular photoionization: the PI/sub g/ resonance in e-N2 scattering

    Dehmer, J.L.; Dill, D.

    1974-01-01

    A prototype calculation of the well-known 2.5-eV shape resonance in e-N 2 scattering was performed to test the usefulness of the multiple-scattering method for electronic continuum molecular wavefunctions. The results of this demanding test are very encouraging. (U.S.)

  5. Discrete ordinates transport methods for problems with highly forward-peaked scattering

    Pautz, S.D.

    1998-04-01

    The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method

  6. Quantum trajectories in complex space: One-dimensional stationary scattering problems

    Chou, C.-C.; Wyatt, Robert E.

    2008-01-01

    One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems

  7. A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

    S.I. Zaman

    2000-12-01

    Full Text Available This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz. Green’s representation formula, and the Layer-theoretic formulation utilizing either a simple-layer or a double-layer potential. The review presents and expounds the major contributions in this area over the last four decades. The need for a robust and improved formulation of the exterior scattering problem (Neumann or Dirichlet arose due to the fact that the classical formulation failed to yield a unique solution at (acoustic wave-numbers which correspond to eigenvalues (eigenfrequencies of the corresponding interior scattering problem. Moreover, this correlation becomes more pronounced as the wave-numbers become larger i.e. as the (acoustic frequency increases. The robust integral formulations which are discussed here yield Fredholms integral equations of the second kind which are more amenable to computation than the first kind. However, the integral equation involves a hypersingular kernel which creates ill-conditioning in the final matrix representation. This is circumvented by a regularisation technique. An extensive useful list of references is also presented here for researchers in this area.

  8. Several problems of the theory of transition radiation and transition scattering

    Ginzburg, V.L.; Tsytovich, V.N.

    1979-01-01

    The process of transition radiation is a very general one. It appears if some source, which does not have a proper frequency (for example a point charge, multipole etc), is moving with a constant velocity in an inhomogeneous and/or nonstationary medium. In the case of a periodic medium the transition radiation has some special peculiarities and is called the resonance transition radiation or transition scattering. Transition scattering occurs particularly in the case when some wave of dielectric permittivity acts on a nonmoving (fixed) charge. The processes of transition radiation and transition scattering have analogies outside electrodynamics similarly to the Vavilov-Cherenkov emission. The latter occurs also for a source moving with a constant velocity but in a homogeneous medium (and only if the velocity of the source exceeds the wave phase velocity in the medium). The present review is dealing with several problems of the theory of transition radiation and transition scattering. Attention is paid mainly to the formulation of the problems and to revealing characterisic features and peculiarities of the phenomena described. (Auth.)

  9. 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

  10. Characterisation of ultrasonic structural noise in multiple scattering media using phased arrays

    Bedetti, T; Dorval, V; Jenson, F; Derode, A

    2013-01-01

    The ultrasonic inspection of multiple scattering media gives rise to structural noise which makes it difficult to detect potential damage or crack inside the component. In order to predict the performances of ultrasonic inspection over such complex media, scattering models can be used. Such models rely on specific key parameters describing the multiple scattering process, which can be determined by specific measurements and post-processing techniques. Such experiments were carried out on stainless steel plates using linear phased-arrays. They consist in recording the response matrix constituted by impulse responses between all the elements of the array. By conducting post-processing on this matrix, we measure the elastic mean free path l e and the correlation distance d c of the recorded noise. Additionally, the dynamic behaviour of the coherent backscattering effect was studied in order to measure the diffusion constant D. Plane-wave beamforming has been applied to the response matrix to improve the angular resolution and the signal-to-noise ratio of the backscattered intensity. Details of postprocessing techniques will be shown

  11. Image Based Solution to Occlusion Problem for Multiple Robots Navigation

    Taj Mohammad Khan

    2012-04-01

    Full Text Available In machine vision, occlusions problem is always a challenging issue in image based mapping and navigation tasks. This paper presents a multiple view vision based algorithm for the development of occlusion-free map of the indoor environment. The map is assumed to be utilized by the mobile robots within the workspace. It has wide range of applications, including mobile robot path planning and navigation, access control in restricted areas, and surveillance systems. We used wall mounted fixed camera system. After intensity adjustment and background subtraction of the synchronously captured images, the image registration was performed. We applied our algorithm on the registered images to resolve the occlusion problem. This technique works well even in the existence of total occlusion for a longer period.

  12. Compton scatter correction in case of multiple crosstalks in SPECT imaging.

    Sychra, J J; Blend, M J; Jobe, T H

    1996-02-01

    A strategy for Compton scatter correction in brain SPECT images was proposed recently. It assumes that two radioisotopes are used and that a significant portion of photons of one radioisotope (for example, Tc99m) spills over into the low energy acquisition window of the other radioisotope (for example, Tl201). We are extending this approach to cases of several radioisotopes with mutual, multiple and significant photon spillover. In the example above, one may correct not only the Tl201 image but also the Tc99m image corrupted by the Compton scatter originating from the small component of high energy Tl201 photons. The proposed extension is applicable to other anatomical domains (cardiac imaging).

  13. Scattering by multiple parallel radially stratified infinite cylinders buried in a lossy half space.

    Lee, Siu-Chun

    2013-07-01

    The theoretical solution for scattering by an arbitrary configuration of closely spaced parallel infinite cylinders buried in a lossy half space is presented in this paper. The refractive index and permeability of the half space and cylinders are complex in general. Each cylinder is radially stratified with a distinct complex refractive index and permeability. The incident radiation is an arbitrarily polarized plane wave propagating in the plane normal to the axes of the cylinders. Analytic solutions are derived for the electric and magnetic fields and the Poynting vector of backscattered radiation emerging from the half space. Numerical examples are presented to illustrate the application of the scattering solution to calculate backscattering from a lossy half space containing multiple homogeneous and radially stratified cylinders at various depths and different angles of incidence.

  14. Algebraic realization of the resonating group method for multichannel scattering problem in an eight nucleon system

    Badalov, S.A.; Filippov, G.F.

    1983-01-01

    All the basic calculation formulas of an algebraic version of the resonating-group method for a pultichannel problem of the scattering of a nucleon by 7 Li and 7 Be taking into account α+α channel are derived. The spin-orbital and the Coulomb interactions are taken into consideration. The procedure enabling an exact projection into the states with the given values of the channel quantum numbers is proposed

  15. Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

    Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

    2010-05-12

    We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

  16. Analysis of the spectrum of a Cartesian Perfectly Matched Layer (PML) approximation to acoustic scattering problems

    Kim, Seungil

    2010-01-01

    In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication. © 2009 Elsevier Inc. All rights reserved.

  17. Integrated Production-Distribution Scheduling Problem with Multiple Independent Manufacturers

    Jianhong Hao

    2015-01-01

    Full Text Available We consider the nonstandard parts supply chain with a public service platform for machinery integration in China. The platform assigns orders placed by a machinery enterprise to multiple independent manufacturers who produce nonstandard parts and makes production schedule and batch delivery schedule for each manufacturer in a coordinate manner. Each manufacturer has only one plant with parallel machines and is located at a location far away from other manufacturers. Orders are first processed at the plants and then directly shipped from the plants to the enterprise in order to be finished before a given deadline. We study the above integrated production-distribution scheduling problem with multiple manufacturers to maximize a weight sum of the profit of each manufacturer under the constraints that all orders are finished before the deadline and the profit of each manufacturer is not negative. According to the optimal condition analysis, we formulate the problem as a mixed integer programming model and use CPLEX to solve it.

  18. Analysis of a Cartesian PML approximation to acoustic scattering problems in and

    Bramble, James H.

    2013-08-01

    We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.

  19. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    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

  20. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    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.

  1. 11Li-12C scattering as a four-body problem

    Formanek, J.; Lombard, R.J.

    1995-01-01

    11 Li- 12 C scattering is described as a four-body problem. The succession of approximations required to obtain the simplified approach of Yabana et al(1992) is examined in detail. We found that whereas their simple model is roughly acceptable for total cross sections (with discrepancies of the order of a few per cent), it has dramatic effects on the differential cross section. Beyond the very forward angles, the problem has to be treated in its full complexity; the various possible intermediate approximations generate differential cross sections which deviate noticeably from the correct calculation. (author)

  2. Measurement of hadron multiplicities in deep inelastic scattering and extraction of quark fragmentation functions

    Curiel-Garcia, Quiela-Marina

    2014-01-01

    One of the goals of the COMPASS experience is the study of the nucleon spin structure. Data were taken from a polarized muon beam (160 GeV/c) scattering off a polarized target ( 6 LiD or NH 3 ). In this context, the need of a precise knowledge of quark Fragmentation Functions (final-state hadronization of quarks q into hadrons h, FFs) was raised. The FFs can be extracted from hadron multiplicities produced in Semi-Inclusive Deep Inelastic Scattering (SIDIS). This thesis presents the measurement of charged hadrons (pions and kaons) multiplicities from SIDIS data collected in 2006. The data cover a large kinematical range: Q 2 ≥1 (GeV/c)2, y belongs to [0.1,0.9], x belongs to [0.004,0.7] and W belongs to [5,17] GeV. These multiplicities provide an important input for global QCD analyses of world data at NLO, aiming at the FFs determination. (author) [fr

  3. Learning of Rule Ensembles for Multiple Attribute Ranking Problems

    Dembczyński, Krzysztof; Kotłowski, Wojciech; Słowiński, Roman; Szeląg, Marcin

    In this paper, we consider the multiple attribute ranking problem from a Machine Learning perspective. We propose two approaches to statistical learning of an ensemble of decision rules from decision examples provided by the Decision Maker in terms of pairwise comparisons of some objects. The first approach consists in learning a preference function defining a binary preference relation for a pair of objects. The result of application of this function on all pairs of objects to be ranked is then exploited using the Net Flow Score procedure, giving a linear ranking of objects. The second approach consists in learning a utility function for single objects. The utility function also gives a linear ranking of objects. In both approaches, the learning is based on the boosting technique. The presented approaches to Preference Learning share good properties of the decision rule preference model and have good performance in the massive-data learning problems. As Preference Learning and Multiple Attribute Decision Aiding share many concepts and methodological issues, in the introduction, we review some aspects bridging these two fields. To illustrate the two approaches proposed in this paper, we solve with them a toy example concerning the ranking of a set of cars evaluated by multiple attributes. Then, we perform a large data experiment on real data sets. The first data set concerns credit rating. Since recent research in the field of Preference Learning is motivated by the increasing role of modeling preferences in recommender systems and information retrieval, we chose two other massive data sets from this area - one comes from movie recommender system MovieLens, and the other concerns ranking of text documents from 20 Newsgroups data set.

  4. Multiple X-ray tomography using transmitted, scattered and fluorescent radiation

    Cesareo, R.; Brunetti, A.; Golosio, B.; Lopes, R.T.; Barroso, R.C.; Donativi, M.; Castellano, A.; Quarta, S.

    2003-01-01

    A multiple CT-scanner is described, which contemporaneously uses transmitted, scattered and fluorescent X-rays for Imaging. The scanner is characterized by a small size X-ray tube and by four detectors: a ''pencil'' X-ray NaI(Tl) for transmitted tomography, a larger size NaI(Tl) for 90 C o Compton tomography, a thermoelectrically cooled Si-PIN or CdZnTe for fluorescent imaging and a CdZnTe for Rayleigh (or diffraction) tomography. Examples of applications are shown

  5. Multiple-scattering and DV-Xα analyses of a Cl-passivated Ge(111) surface

    Cao, S; Tang, J-C; Shen, S-L

    2003-01-01

    The multiple-scattering cluster and DV-Xα methods have been employed to analyse the chlorine 1s near edge x-ray absorption fine structure (NEXAFS) of a Cl-passivated Ge(111) surface. Our detailed analysis demonstrates how the chlorine atoms form a perfect monochloride structure with Cl bonding to the topmost Ge atom. Our calculation reveals the interaction in the chlorine layer is multipolar electrostatic forces. Furthermore, the DV-Xα cluster calculation shows that the orbital contour of the sharp Cl-Ge resonance exhibits a global symmetry, which confirms it to be σ * -like. The above studies are found to enrich previous experimental NEXAFS investigations

  6. Topological cross sections in hadron-nucleus collisions and multiple scattering theory

    Zoller, V.R.

    1987-01-01

    The multiple scattering theory supplemented with cutting rules of Abramovsky, V.A., Gribov, V.N., Kancheli, O.V. is applied to calculation of the hadron-nucleus interaction cross sections. In contrast to standard Glauber approach neither smalness of the interaction radius compared to the nuclear radii nor Gaussian form of the hN-interaction profile function are assumed. The theory of the supercritical pomeron are used. However all the results are more general and do not depend on the parametrization of the pomeron pole amplitude. The region of validity of the widely used approximate formulae for topological and total hA-interaction cross sections are discussed

  7. The Multiple-Minima Problem in Protein Folding

    Scheraga, Harold A.

    1991-10-01

    The conformational energy surface of a polypeptide or protein has many local minima, and conventional energy minimization procedures reach only a local minimum (near the starting point of the optimization algorithm) instead of the global minimum (the multiple-minima problem). Several procedures have been developed to surmount this problem, the most promising of which are: (a) build up procedure, (b) optimization of electrostatics, (c) Monte Carlo-plus-energy minimization, (d) electrostatically-driven Monte Carlo, (e) inclusion of distance restraints, (f) adaptive importance-sampling Monte Carlo, (g) relaxation of dimensionality, (h) pattern-recognition, and (i) diffusion equation method. These procedures have been applied to a variety of polypeptide structural problems, and the results of such computations are presented. These include the computation of the structures of open-chain and cyclic peptides, fibrous proteins and globular proteins. Present efforts are being devoted to scaling up these procedures from small polypeptides to proteins, to try to compute the three-dimensional structure of a protein from its amino sequence.

  8. Multiple Choice Knapsack Problem: example of planning choice in transportation.

    Zhong, Tao; Young, Rhonda

    2010-05-01

    Transportation programming, a process of selecting projects for funding given budget and other constraints, is becoming more complex as a result of new federal laws, local planning regulations, and increased public involvement. This article describes the use of an integer programming tool, Multiple Choice Knapsack Problem (MCKP), to provide optimal solutions to transportation programming problems in cases where alternative versions of projects are under consideration. In this paper, optimization methods for use in the transportation programming process are compared and then the process of building and solving the optimization problems is discussed. The concepts about the use of MCKP are presented and a real-world transportation programming example at various budget levels is provided. This article illustrates how the use of MCKP addresses the modern complexities and provides timely solutions in transportation programming practice. While the article uses transportation programming as a case study, MCKP can be useful in other fields where a similar decision among a subset of the alternatives is required. Copyright 2009 Elsevier Ltd. All rights reserved.

  9. Multiple scattering modeling pipeline for spectroscopy and photometry of airless Solar System objects

    Penttilä, Antti; Väisänen, Timo; Markkanen, Johannes; Martikainen, Julia; Gritsevich, Maria; Muinonen, Karri

    2017-10-01

    We combine numerical tools to analyze the reflectance spectra of granular materials. Our motivation comes from the lack of tools when it comes to intimate mixing of materials and modeling space-weathering effects with nano- or micron-sized inclusions. The current practice is to apply a semi-physical models such as the Hapke models (e.g., Icarus 195, 2008). These are expressed in a closed form so that they are fast to apply. The problem is that the validity of the model is not guaranteed, and the derived properties related to particle scattering can be unrealistic (JQSRT 113, 2012).Our pipeline consists of individual scattering simulation codes and a main program that chains them together. The chain for analyzing a macroscopic target with space-weathered mineral would go as: (1) Scattering properties of small inclusions inside a host matrix are derived using exact Maxwell equation solvers. From the scattering properties, we use the so-called incoherent fields and Mueller matrices as input for the next step; (2) Scattering by a regolith grain is solved using a geometrical optics method with surface reflections, internal absorption, and internal diffuse scattering; (3) The radiative transfer simulation is executed inputting the regolith grains from the previous step as the scatterers in a macroscopic planar volume element.For the most realistic asteroid reflectance model, the chain would produce the properties of a planar surface element. Then, a shadowing simulation over the surface elements would be considered, and finally the asteroid phase function would be solved by integrating the bidirectional reflectance distribution function of the planar element over the object's realistic shape model.The tools in the proposed chain already exist, and practical task for us is to tie these together into an easy-to-use public pipeline. We plan to open the pipeline as a web-based open service a dedicated server, using Django application server and Python environment for the

  10. Multiple and double scattering contributions to depth resolution and low energy background in hydrogen elastic recoil detection

    Wielunski, L S [Commonwealth Scientific and Industrial Research Organisation (CSIRO), Lindfield, NSW (Australia). Div. of Applied Physics

    1997-12-31

    The sensitivity of hydrogen elastic recoil detection ( ERD ) is usually limited by the low energy background in the ERD spectrum. A number of 4.5 MeV He{sup ++} hydrogen ERD spectra from different hydrogen implanted samples are compared. The samples are chosen with different atomic numbers from low Z (carbon) to high Z (tungsten carbide) to observe the effects of multiple scattering and double scattering within the sample material. The experimental depth resolution and levels of the low energy background in ERD spectra are compared with theoretical predictions from multiple and double scattering. 10 refs., 2 tabs., 5 figs.

  11. Multiple and double scattering contributions to depth resolution and low energy background in hydrogen elastic recoil detection

    Wielunski, L.S. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), Lindfield, NSW (Australia). Div. of Applied Physics

    1996-12-31

    The sensitivity of hydrogen elastic recoil detection ( ERD ) is usually limited by the low energy background in the ERD spectrum. A number of 4.5 MeV He{sup ++} hydrogen ERD spectra from different hydrogen implanted samples are compared. The samples are chosen with different atomic numbers from low Z (carbon) to high Z (tungsten carbide) to observe the effects of multiple scattering and double scattering within the sample material. The experimental depth resolution and levels of the low energy background in ERD spectra are compared with theoretical predictions from multiple and double scattering. 10 refs., 2 tabs., 5 figs.

  12. Symmetry relationships for multiple scattering of polarized light in turbid spherical samples: theory and a Monte Carlo simulation.

    Otsuki, Soichi

    2016-02-01

    This paper presents a theory describing totally incoherent multiple scattering of turbid spherical samples. It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in spherical samples. Monte Carlo simulations generate a reduced effective scattering Mueller matrix, which virtually satisfies reciprocity and mirror symmetry. The scattering matrix was factorized by using the symmetric decomposition in a predefined form, as well as the Lu-Chipman polar decomposition, approximately into a product of a pure depolarizer and vertically oriented linear retarding diattenuators. The parameters of these components were calculated as a function of the polar angle. While the turbid spherical sample is a pure depolarizer at low polar angles, it obtains more functions of the retarding diattenuator with increasing polar angle.

  13. Collision-induced Raman scattering and the peculiar case of neon: Anisotropic spectrum, anisotropy, and the inverse scattering problem

    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

  14. A MULTIPLE SCATTERING POLARIZED RADIATIVE TRANSFER MODEL: APPLICATION TO HD 189733b

    Kopparla, Pushkar; Yung, Yuk L. [Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA (United States); Natraj, Vijay; Swain, Mark R. [Jet Propulsion Laboratory (NASA-JPL), Pasadena, CA (United States); Zhang, Xi [Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ (United States); Wiktorowicz, Sloane J., E-mail: pkk@gps.caltech.edu [Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA (United States)

    2016-01-20

    We present a multiple scattering vector radiative transfer model that produces disk integrated, full phase polarized light curves for reflected light from an exoplanetary atmosphere. We validate our model against results from published analytical and computational models and discuss a small number of cases relevant to the existing and possible near-future observations of the exoplanet HD 189733b. HD 189733b is arguably the most well observed exoplanet to date and the only exoplanet to be observed in polarized light, yet it is debated if the planet’s atmosphere is cloudy or clear. We model reflected light from clear atmospheres with Rayleigh scattering, and cloudy or hazy atmospheres with Mie and fractal aggregate particles. We show that clear and cloudy atmospheres have large differences in polarized light as compared to simple flux measurements, though existing observations are insufficient to make this distinction. Futhermore, we show that atmospheres that are spatially inhomogeneous, such as being partially covered by clouds or hazes, exhibit larger contrasts in polarized light when compared to clear atmospheres. This effect can potentially be used to identify patchy clouds in exoplanets. Given a set of full phase polarimetric measurements, this model can constrain the geometric albedo, properties of scattering particles in the atmosphere, and the longitude of the ascending node of the orbit. The model is used to interpret new polarimetric observations of HD 189733b in a companion paper.

  15. Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

    Wang, Zuowei; Biwa, Shiro

    2018-03-01

    A numerical procedure is proposed for the multiple scattering analysis of flexural waves on a thin plate with circular holes based on the Kirchhoff plate theory. The numerical procedure utilizes the wave function expansion of the exciting as well as scattered fields, and the boundary conditions at the periphery of holes are incorporated as the relations between the expansion coefficients of exciting and scattered fields. A set of linear algebraic equations with respect to the wave expansion coefficients of the exciting field alone is established by the numerical collocation method. To demonstrate the applicability of the procedure, the stop band characteristics of flexural waves are analyzed for different arrangements and concentrations of circular holes on a steel plate. The energy transmission spectra of flexural waves are shown to capture the detailed features of the stop band formation of regular and random arrangements of holes. The increase of the concentration of holes is found to shift the dips of the energy transmission spectra toward higher frequencies as well as deepen them. The hexagonal hole arrangement can form a much broader stop band than the square hole arrangement for flexural wave transmission. It is also demonstrated that random arrangements of holes make the transmission spectrum more complicated.

  16. Multiple Coulomb scattering of high-energy heavy charged particle beams used in biology and medicine

    Wong, M.; Schimmerling, W.; Ludewigt, B.; Phillips, M.; Curtis, S.; Tobias, C.A.

    1987-01-01

    The authors measured lateral displacement and angular distributions of high-energy heavy charged particles emerging from a target at the Lawrence Berkeley Laboratory BEVALAC with beams used in radiobiology experiments. Multiple Coulomb scattering occurring in the target material generally spreads the beam laterally and increases its divergence. The apparatus consists of four sets of position-sensitive semiconductor detectors located along the beam line. Each providing two position signals and one energy signal. The difference between the two position signals is used to determine the particle position in one dimension. The two position signals are constrained to add up to the energy deposition signal in order to reject multiple-particle traversals. The vector directions for the incident and emerging particles are reconstructed in three dimensions from their measured coordinated positions. Lateral and angular distributions are reported for beams of high-energy neon, iron and uranium ions incident on targets of aluminum, cooper, lead and water

  17. Energy dependence of the charged multiplicity in deep inelastic scattering at HERA

    Chekanov, S.; Derrick, M.; Magill, S. [Argonne National Laboratory, Argonne, IL (US)] (and others)

    2008-03-15

    The charged multiplicity distributions and the mean charged multiplicity have been investigated in inclusive neutral current deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of 38.6 pb{sup -1}. The measurements were performed in the current region of the Breit frame, as well as in the current fragmentation region of the hadronic centre-of-mass frame. The KNO-scaling properties of the data were investigated and the energy dependence was studied using different energy scales. The data are compared to results obtained in e{sup +}e{sup -} collisions and to previous DIS measurements as well as to leading-logarithm parton-shower Monte Carlo predictions. (orig.)

  18. Energy dependence of the charged multiplicity in deep inelastic scattering at HERA

    Chekanov, S.; Derrick, M.; Magill, S.

    2008-03-01

    The charged multiplicity distributions and the mean charged multiplicity have been investigated in inclusive neutral current deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of 38.6 pb -1 . The measurements were performed in the current region of the Breit frame, as well as in the current fragmentation region of the hadronic centre-of-mass frame. The KNO-scaling properties of the data were investigated and the energy dependence was studied using different energy scales. The data are compared to results obtained in e + e - collisions and to previous DIS measurements as well as to leading-logarithm parton-shower Monte Carlo predictions. (orig.)

  19. Multiple solutions to dense systems in radar scattering using a preconditioned block GMRES solver

    Boyse, W.E. [Advanced Software Resources, Inc., Santa Clara, CA (United States)

    1996-12-31

    Multiple right-hand sides occur in radar scattering calculations in the computation of the simulated radar return from a body at a large number of angles. Each desired angle requires a right-hand side vector to be computed and the solution generated. These right-hand sides are naturally smooth functions of the angle parameters and this property is utilized in a novel way to compute solutions an order of magnitude faster than LINPACK The modeling technique addressed is the Method of Moments (MOM), i.e. a boundary element method for time harmonic Maxwell`s equations. Discretization by this method produces general complex dense systems of rank 100`s to 100,000`s. The usual way to produce the required multiple solutions is via LU factorization and solution routines such as found in LINPACK. Our method uses the block GMRES iterative method to directly iterate a subset of the desired solutions to convergence.

  20. Vehicle Routing Problem with Backhaul, Multiple Trips and Time Window

    Johan Oscar Ong

    2011-01-01

    Full Text Available Transportation planning is one of the important components to increase efficiency and effectiveness in the supply chain system. Good planning will give a saving in total cost of the supply chain. This paper develops the new VRP variants’, VRP with backhauls, multiple trips, and time window (VRPBMTTW along with its problem solving techniques by using Ant Colony Optimization (ACO and Sequential Insertion as initial solution algorithm. ACO is modified by adding the decoding process in order to determine the number of vehicles, total duration time, and range of duration time regardless of checking capacity constraint and time window. This algorithm is tested by using set of random data and verified as well as analyzed its parameter changing’s. The computational results for hypothetical data with 50% backhaul and mix time windows are reported.

  1. Functional analysis screening for multiple topographies of problem behavior.

    Bell, Marlesha C; Fahmie, Tara A

    2018-04-23

    The current study evaluated a screening procedure for multiple topographies of problem behavior in the context of an ongoing functional analysis. Experimenters analyzed the function of a topography of primary concern while collecting data on topographies of secondary concern. We used visual analysis to predict the function of secondary topographies and a subsequent functional analysis to test those predictions. Results showed that a general function was accurately predicted for five of six (83%) secondary topographies. A specific function was predicted and supported for a subset of these topographies. The experimenters discuss the implication of these results for clinicians who have limited time for functional assessment. © 2018 Society for the Experimental Analysis of Behavior.

  2. Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions.

    Reichardt, J; Hess, M; Macke, A

    2000-04-20

    Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

  3. 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

  4. 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.

  5. Effects of dependence in high-dimensional multiple testing problems

    van de Wiel Mark A

    2008-02-01

    Full Text Available Abstract Background We consider effects of dependence among variables of high-dimensional data in multiple hypothesis testing problems, in particular the False Discovery Rate (FDR control procedures. Recent simulation studies consider only simple correlation structures among variables, which is hardly inspired by real data features. Our aim is to systematically study effects of several network features like sparsity and correlation strength by imposing dependence structures among variables using random correlation matrices. Results We study the robustness against dependence of several FDR procedures that are popular in microarray studies, such as Benjamin-Hochberg FDR, Storey's q-value, SAM and resampling based FDR procedures. False Non-discovery Rates and estimates of the number of null hypotheses are computed from those methods and compared. Our simulation study shows that methods such as SAM and the q-value do not adequately control the FDR to the level claimed under dependence conditions. On the other hand, the adaptive Benjamini-Hochberg procedure seems to be most robust while remaining conservative. Finally, the estimates of the number of true null hypotheses under various dependence conditions are variable. Conclusion We discuss a new method for efficient guided simulation of dependent data, which satisfy imposed network constraints as conditional independence structures. Our simulation set-up allows for a structural study of the effect of dependencies on multiple testing criterions and is useful for testing a potentially new method on π0 or FDR estimation in a dependency context.

  6. Multiple-scattering formalism for correlated systems: A KKR-DMFT approach

    Minar, J.; Perlov, A.; Ebert, H.; Chioncel, L.; Katsnelson, M. I.; Lichtenstein, A.I.

    2005-01-01

    We present a charge and self-energy self-consistent computational scheme for correlated systems based on the Korringa-Kohn-Rostoker (KKR) multiple scattering theory with the many-body effects described by the means of dynamical mean field theory (DMFT). The corresponding local multiorbital and energy dependent self-energy is included into the set of radial differential equations for the single-site wave functions. The KKR Green's function is written in terms of the multiple scattering path operator, the later one being evaluated using the single-site solution for the t-matrix that in turn is determined by the wave functions. An appealing feature of this approach is that it allows to consider local quantum and disorder fluctuations on the same footing. Within the coherent potential approximation (CPA) the correlated atoms are placed into a combined effective medium determined by the DMFT self-consistency condition. Results of corresponding calculations for pure Fe, Ni, and Fe x Ni 1-x alloys are presented

  7. The Over-Barrier Resonant States and Multi-Channel Scattering in Multiple Quantum Wells

    A Polupanov

    2016-09-01

    Full Text Available We demonstrate an explicit numerical method for accurate calculation of the scattering matrix and its poles, and apply this method to describe the multi-channel scattering in the multiple quantum-wells structures. The S-matrix is continued analytically to the unphysical region of complex energy values. Results of calculations show that there exist one or more S-matrix poles, corresponding to the over-barrier resonant states critical for the effect of the absolute reflection of holes in the energy range where only the heavy ones may propagate over barriers in a structure. Light- and heavy-hole states are described by the Luttinger Hamiltonian matrix. In contrast to the single quantum-well case, at some parameters of a multiple quantum-wells structure the number of S-matrix poles may exceed that of the absolute reflection peaks, and at different values of parameters the absolute reflection peak corresponds to different resonant states. The imaginary parts of the S-matrix poles and hence the lifetimes of resonant states as well as the widths of resonant peaks of absolute reflection depend drastically on the quantum-well potential depth. In the case of shallow quantum wells there is in fact a long-living over-barrier resonant hole state.

  8. 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

  9. Spectrometer for Particle Characterization With a New Multiple-Scattering Theory, Phase I

    National Aeronautics and Space Administration — There are two major commercial types of light-scattering particle size analyzers: Static Light Scattering and Dynamic Light Scattering. They are expensive, delicate,...

  10. Semiclassical expansion of quantum characteristics for many-body potential scattering problem

    Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.

    2007-01-01

    In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  11. The nodal discrete-ordinate transport calculation of anisotropy scattering problem in three-dimensional cartesian geometry

    Wu Hongchun; Xie Zhongsheng; Zhu Xuehua

    1994-01-01

    The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained

  12. Track reconstruction for the Mu3e experiment based on a novel Multiple Scattering fit

    Kozlinskiy Alexandr

    2017-01-01

    Full Text Available The Mu3e experiment is designed to search for the lepton flavor violating decay μ+ → e+e+e−. The aim of the experiment is to reach a branching ratio sensitivity of 10−16. In a first phase the experiment will be performed at an existing beam line at the Paul-Scherrer Institute (Switzerland providing 108 muons per second, which will allow to reach a sensitivity of 2 · 10−15. The muons with a momentum of about 28 MeV/c are stopped and decay at rest on a target. The decay products (positrons and electrons with energies below 53MeV are measured by a tracking detector consisting of two double layers of 50 μm thin silicon pixel sensors. The high granularity of the pixel detector with a pixel size of 80 μm × 80 μm allows for a precise track reconstruction in the high multiplicity environment of the Mu3e experiment, reaching 100 tracks per reconstruction frame of 50 ns in the final phase of the experiment. To deal with such high rates and combinatorics, the Mu3e track reconstruction uses a novel fit algorithm that in the simplest case takes into account only the multiple scattering, which allows for a fast online tracking on a GPU based filter farm. An implementation of the 3-dimensional multiple scattering fit based on hit triplets is described. The extension of the fit that takes into account energy losses and pixel size is used for offline track reconstruction. The algorithm and performance of the offline track reconstruction based on a full Geant4 simulation of the Mu3e detector are presented.

  13. The Problem of Scattering by a Mixture of Cracks and Obstacles

    Yan Guozheng

    2009-01-01

    Full Text Available Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack and a bounded domain in as cross section. We assume that the crack is divided into two parts, and one of the two parts is (possibly coated on one side by a material with surface impedance . Different boundary conditions are given on and . Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory.

  14. On increasing stability in the two dimensional inverse source scattering problem with many frequencies

    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.

  15. Relativistic Inverse Scattering Problem for a Superposition of a Nonlocal Separable and a Local Quasipotential

    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

  16. Anomalous small-angle scattering as a way to solve the Babinet principle problem

    Boiko, M. E.; Sharkov, M. D.; Boiko, A. M.; Bobyl, A. V.

    2013-01-01

    X-ray absorption spectra (XAS) have been used to determine the absorption edges of atoms present in a sample under study. A series of small-angle X-ray scattering (SAXS) measurements using different monochromatic X-ray beams at different wavelengths near the absorption edges is performed to solve the Babinet principle problem. The sizes of clusters containing atoms determined by the method of XAS were defined in SAXS experiments. In contrast to differential X-ray porosimetry, anomalous SAXS makes it possible to determine sizes of clusters of different atomic compositions

  17. Anomalous small-angle scattering as a way to solve the Babinet principle problem

    Boiko, M. E., E-mail: m.e.boiko@mail.ioffe.ru; Sharkov, M. D.; Boiko, A. M.; Bobyl, A. V. [Russian Academy of Sciences, Ioffe Physicotechnical Institute (Russian Federation)

    2013-12-15

    X-ray absorption spectra (XAS) have been used to determine the absorption edges of atoms present in a sample under study. A series of small-angle X-ray scattering (SAXS) measurements using different monochromatic X-ray beams at different wavelengths near the absorption edges is performed to solve the Babinet principle problem. The sizes of clusters containing atoms determined by the method of XAS were defined in SAXS experiments. In contrast to differential X-ray porosimetry, anomalous SAXS makes it possible to determine sizes of clusters of different atomic compositions.

  18. Anomalous small-angle scattering as a way to solve the Babinet principle problem

    Boiko, M. E.; Sharkov, M. D.; Boiko, A. M.; Bobyl, A. V.

    2013-12-01

    X-ray absorption spectra (XAS) have been used to determine the absorption edges of atoms present in a sample under study. A series of small-angle X-ray scattering (SAXS) measurements using different monochromatic X-ray beams at different wavelengths near the absorption edges is performed to solve the Babinet principle problem. The sizes of clusters containing atoms determined by the method of XAS were defined in SAXS experiments. In contrast to differential X-ray porosimetry, anomalous SAXS makes it possible to determine sizes of clusters of different atomic compositions.

  19. Analysis of multiple scattering contributions in electron-impact ionization of molecular hydrogen

    Ren, Xueguang; Hossen, Khokon; Wang, Enliang; Pindzola, M. S.; Dorn, Alexander; Colgan, James

    2017-10-01

    We report a combined experimental and theoretical study on the low-energy (E 0 = 31.5 eV) electron-impact ionization of molecular hydrogen (H2). Triple differential cross sections are measured for a range of fixed emission angles of one outgoing electron between {θ }1=-70^\\circ and -130° covering the full 4π solid angle of the second electron. The energy sharing of the outgoing electrons varies from symmetric ({E}1={E}2=8 eV) to highly asymmetric (E 1 = 1 eV and E 2 = 15 eV). In addition to the binary and recoil lobes, a structure is observed perpendicular to the incoming beam direction which is due to multiple scattering of the projectile inside the molecular potential. The absolutely normalized experimental cross sections are compared with results from the time-dependent close-coupling (TDCC) calculations. Molecular alignment dependent TDCC results demonstrate that these structures are only present if the molecule axis is lying in the scattering plane.

  20. Angular distribution of diffuse reflectance from incoherent multiple scattering in turbid media.

    Gao, M; Huang, X; Yang, P; Kattawar, G W

    2013-08-20

    The angular distribution of diffuse reflection is elucidated with greater understanding by studying a homogeneous turbid medium. We modeled the medium as an infinite slab and studied the reflection dependence on the following three parameters: the incident direction, optical depth, and asymmetry factor. The diffuse reflection is produced by incoherent multiple scattering and is solved through radiative transfer theory. At large optical depths, the angular distribution of the diffuse reflection with small incident angles is similar to that of a Lambertian surface, but, with incident angles larger than 60°, the angular distributions have a prominent reflection peak around the specular reflection angle. These reflection peaks are found originating from the scattering within one transport mean free path in the top layer of the medium. The maximum reflection angles for different incident angles are analyzed and can characterize the structure of angular distributions for different asymmetry factors and optical depths. The properties of the angular distribution can be applied to more complex systems for a better understanding of diffuse reflection.

  1. Measurement of Hadron Multiplicities in Deep Inelastic Muon-Nucleon Scattering

    du Fresne von Hohenesche, Nicolas

    2016-06-02

    In deep-inelastic muon-nucleon scattering, a single quark can be ejected out of the nucleon by the absorption of a high-energy photon. Such a free isolated quark has never been observed in nature. In quantum chromodynamics (QCD), coloured objects, such as a single quark, create additional quark anti-quark pairs out of the colour field and the final state comprises a jet of hadrons. The hadronisation process can be described by fragmentation functions D_q^h, the probability that a quark with the flavour q turns into a hadron of the type h. Similar to the parton distribution function, the fragmentation functions are fundamental, universal and process-independent quantities. The fragmentation functions are measured with the COM- PASS spectrometer in muon-nucleon scattering. The observables are the hadron multiplicities M_h. The COMPASS experiment consists of a two-stage magnetic spectrometer located at the M2 beam line of the Super Proton Synchrotron at CERN and uses a polarised muon beam on a nuclear fixed targ...

  2. Modified Moliere's screening parameter and its impact on multiple coulomb scattering

    Striganov, Sergei

    2015-01-01

    The Moliere approximation of elastic Coulomb scattering cross-sections plays an important role in accurate description of multiple scattering, non-ionisation energy, DPA radiation damage etc. The cross-section depends only on a single parameter that describes the atomic screening. Moliere calculated the screening angle for the Tomas-Fermi distribution of electrons in atoms. In this paper, the screening parameter was recalculated using a more accurate atomic form-factor obtained from the self-consistent Dirac-Hartree-Fock-Slater computations. For relativistic particles, the new screening angle can differ from the Moliere approximation by up to 50%. At the same time, it is rather close to other independent calculations. At low energies, the new screening angle is different for positrons and electrons. The positron screening parameter is much larger than the electron one for heavy nuclei at energies of ∼Z keV. The impact of the screening angle on particle transport and calculated quantities is discussed. (authors)

  3. The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory

    Layton, E.G.

    1993-01-01

    The Fourier-grid (FG) method is a recent L 2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions; it is rather a discrete variable representation approach. In this article we restate the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. (author)

  4. Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

    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

  5. Diffusion equations and hard collisions in multiple scattering of charged particles

    Papiez, Lech; Tulovsky, Vladimir

    1998-01-01

    The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities

  6. Hydrogen Balmer alpha intensity distributions and line profiles from multiple scattering theory using realistic geocoronal models

    Anderson, D. E., Jr.; Meier, R. R.; Hodges, R. R., Jr.; Tinsley, B. A.

    1987-01-01

    The H Balmer alpha nightglow is investigated by using Monte Carlo models of asymmetric geocoronal atomic hydrogen distributions as input to a radiative transfer model of solar Lyman-beta radiation in the thermosphere and atmosphere. It is shown that it is essential to include multiple scattering of Lyman-beta radiation in the interpretation of Balmer alpha airglow data. Observations of diurnal variation in the Balmer alpha airglow showing slightly greater intensities in the morning relative to evening are consistent with theory. No evidence is found for anything other than a single sinusoidal diurnal variation of exobase density. Dramatic changes in effective temperature derived from the observed Balmer alpha line profiles are expected on the basis of changing illumination conditions in the thermosphere and exosphere as different regions of the sky are scanned.

  7. Diffusion equations and hard collisions in multiple scattering of charged particles

    Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States); Tulovsky, Vladimir [Department of Mathematics, St. John' s College, Staten Island, New York, NY (United States)

    1998-09-01

    The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities.

  8. Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis

    Chomaz, L; Corman, L; Yefsah, T; Desbuquois, R; Dalibard, J

    2012-01-01

    Absorption imaging with quasi-resonant laser light is a commonly used technique for probing ultra-cold atomic gases in various geometries. In this paper, we investigate some non-trivial aspects of this method when applying the method to in situ diagnosis of a quasi-two-dimensional (2D) gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known 3D result (the Beer-Lambert law) and outline the specific features of the 2D case. (paper)

  9. Multiple Scattering Analysis of Cu - K EXAFS in Bi2Sr1.5 Cu2O8+δ

    Roehler, J.; Cruesemann, R.

    1995-01-01

    We have analyzed the Cu K-EXAFS of Bi 2 Sr 1.5 Ca 1.5 Cu 2 O 8+δ using a full multiple scattering analysis in a cluster with diameter d∼ 7.6 A. The layered structure has numerous quasi one-dimensional structural elements which give rise to significant multiple scattering contributions in the EXAFS. We confirm the Sr/Ca ratio of the sample is 1:1, and one Ca atom is located close to a nominal Sr-site. At 40 K the dimpling angle in the CuO 2 -plane is found to be ≤ 3.5 . (author)

  10. Multiple Scattering Approach to Polarization Dependence of F K-Edge XANES Spectra for Highly Oriented Polytetrafluoroethylene (PTFE) Thin Film

    Nagamatsu, S.; Ono, M.; Kera, S.; Okudaira, K. K.; Fujikawa, T.; Ueno, N.

    2007-01-01

    The polarization dependence of F K-edge X-ray absorption near edge structure (XANES) spectra of highly-oriented thin-film of polytetrafluoroethylene (PTFE) has been analyzed by using multiple scattering theory. The spectra show clear polarization dependence due to the highly-oriented structure. The multiple scattering calculations reflects a local structure around an absorbing atom. The calculated results obtained by considering intermolecular-interactions are in good agreement with the observed polarization-dependence. We have also analyzed structural models of the radiation damaged PTFE films

  11. Prize for Industrial Applications of Physics Talk: The Inverse Scattering Problem and the role of measurements in its solution

    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.

  12. Coherent light scattering of heterogeneous randomly rough films and effective medium in the theory of electromagnetic wave multiple scattering

    Berginc, G [THALES, 2 avenue Gay-Lussac 78995 ELANCOURT (France)

    2013-11-30

    We have developed a general formalism based on Green's functions to calculate the coherent electromagnetic field scattered by a random medium with rough boundaries. The approximate expression derived makes it possible to determine the effective permittivity, which is generalised for a layer of an inhomogeneous random medium with different types of particles and bounded with randomly rough interfaces. This effective permittivity describes the coherent propagation of an electromagnetic wave in a random medium with randomly rough boundaries. We have obtained an expression, which contains the Maxwell – Garnett formula at the low-frequency limit, and the Keller formula; the latter has been proved to be in good agreement with experiments for particles whose dimensions are larger than a wavelength. (coherent light scattering)

  13. Half-space albedo problem with modified F{sub N} method for linear and quadratic anisotropic scattering

    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.

  14. Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

    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.

  15. 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.

  16. 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

  17. 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

  18. Neutrino-electron scattering and the choice between different MSW solutions of the solar neutrino problem

    Rosen, S.P.; Gelb, J.M.

    1989-01-01

    This paper considers the scattering of solar neutrinos by electrons as a means for distinguishing between different MSW solutions of the solar neutrino problem. In terms of the ratio R between the observed cross-section and that for pure electron-type neutrinos, some correlation between the value of R and each solution is found. A value of R ≤ 1/3 implies that the adiabatic solution is correct, while values between 1/3 and 3/5 are consistent with the large angle solution. A value close to 1/2 is also consistent with the non-adiabatic solution, and a value less than (1/6 - 1/7) implies oscillations into sterile neutrinos

  19. Memory function approach to the line shape problem in collision-induced light scattering

    Balucani, U.; Tognetti, V.; Vallauri, R.

    1980-01-01

    This article mainly deals with the problem of the shape of the spectrum due to interacting pairs of atoms at low and moderate densities. A memory function approach is used which permits to obtain in a consistent way the shape of the scattered spectrum. In order to obtain 'exact' time correlation functions and spectral shapes, molecular-dynamics 'experiments' in Lennard-Jones argon at two different densities were also performed. The dipole-induced dipole (DID) polarizabilities have been used to ascertain the validity of the theoretical approach in a well-defined physical model. The theoretical shapes and correlation functions can be then directly compared with computer simulations. Finally, a comparison with the data of real experiments clarifies the relevance of other-than-DID polarizability mechanisms as far as the spectrum is concerned. (KBE)

  20. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

    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.

  1. Influence of multiple well defined conformations on small-angle scattering of proteins in solution.

    Heller, William T

    2005-01-01

    A common structural motif for many proteins comprises rigid domains connected by a flexible hinge or linker. The flexibility afforded by these domains is important for proper function and such proteins may be able to adopt more than one conformation in solution under equilibrium conditions. Small-angle scattering of proteins in solution samples all conformations that exist in the sampled volume during the time of the measurement, providing an ensemble-averaged intensity. In this paper, the influence of sampling an ensemble of well defined protein structures on the small-angle solution scattering intensity profile is examined through common analysis methods. Two tests were performed using simulated data: one with the extended and collapsed states of the bilobal calcium-binding protein calmodulin and the second with the catalytic subunit of protein kinase A, which has two globular domains connected by a glycine hinge. In addition to analyzing the simulated data for the radii of gyration Rg, distance distribution function P(r) and particle volume, shape restoration was applied to the simulated data. Rg and P(r) of the ensemble profiles could be easily mistaken for a single intermediate state. The particle volumes and models of the ensemble intensity profiles show that some indication of multiple conformations exists in the case of calmodulin, which manifests an enlarged volume and shapes that are clear superpositions of the conformations used. The effect on the structural parameters and models is much more subtle in the case of the catalytic subunit of protein kinase A. Examples of how noise influences the data and analyses are also presented. These examples demonstrate the loss of the indications of multiple conformations in cases where even broad distributions of structures exist. While the tests using calmodulin show that the ensemble states remain discernible from the other ensembles tested or a single partially collapsed state, the tests performed using the

  2. Multiplicities of charged pions and charged hadrons from deep-inelastic scattering of muons off an isoscalar target

    Adolph, C.; Aghasyan, M.; Akhunzyanov, R.; Alexeev, G. D.; Alexeev, M.; Amoroso, A.; Andrieux, V.; Anfimov, N. V.; Anosov, V.; Augsten, K.; Augustyniak, W.; Austregesilo, A.; Azevedo, C.; Badelek, B.; Balestra, F.; Barth, J.; Beck, D.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bisplinghoff, J.; Bodlák, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Capozza, L.; Chang, W.-C.; Chatterjee, C.; Chiosso, M.; Choi, I.; Chung, S.U.; Cicuttin, A.; Crespo, M.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O.; Dhara, L.; Donskov, S. V.; Doshita, N.; Duic, V.; Dünnweber, W.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Faessler, M.; Ferrero, A.; Finger, M.; Finger jr., M.; Fischer, H.; Franco, C.; Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse-Perdekapm, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F. H.; Heitz, R.; Herrmann, E.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.-Yu.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jarý, V.; Joosten, R.; Jörg, P.; Kabuss, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Y.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kuhn, R.; Kulinich, Y.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lian, Y.-S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G. K.; Marchand, C.; Marianski, B.; Martin, A.; Marzec, J.; Matoušek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, M.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Mikhasenko, M.; Mitrofanov, E.; Mitrofanov, N.; Miyachi, Y.; Montuenga, P.; Nagaytsev, A.; Nerling, F.; Neyret, D.; Nikolaenko, V. I.; Nový, J.; Nowak, W. D.; Nukazuka, G.; Nunes, A.S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pešek, M.; Peshekhonov, D. V.; Pierre, N.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Roskot, M.; Rossiyskaya, N. S.; Ryabchikov, D.; Rybnikov, A.; Rychter, A.; Salač, R.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sawada, T.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Schopferer, S.; Seder, E.; Selyunin, A.; Shevchenko, O. Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Smolík, J.; Sozzi, F.; Srnka, Aleš; Steffen, D.; Stolarski, M.; Šulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Tasevsky, M.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Vondra, J.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Ter Wolbeek, J.; Zaremba, K.; Závada, P.; Zavertyaev, M.; Zemlyanichkina, E.; Zhuravlev, N.; Ziembicki, M.; Zink, A.

    2017-01-01

    Roč. 764, JAN (2017), s. 1-10 ISSN 0370-2693 R&D Projects: GA MŠk(CZ) LO1212 Institutional support: RVO:68081731 Keywords : deep inelastic scattering * pion multiplicities * fragmentation functions Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Nuclear physics Impact factor: 4.807, year: 2016

  3. Nonparametric estimation of the heterogeneity of a random medium using compound Poisson process modeling of wave multiple scattering.

    Le Bihan, Nicolas; Margerin, Ludovic

    2009-07-01

    In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material. Our approach is based on the modeling of forward multiple scattering using compound Poisson processes on compact Lie groups. The estimation technique is validated through numerical simulations based on radiative transfer theory.

  4. Study of problems met in muon pattern recognition for a deep inelastic scattering experiment at the S.P.S

    Besson, C.

    1976-01-01

    The problems of the muon pattern recognition are studied for a muon-proton deep inelastic scattering experiment at the S.P.S. The pattern recognition program is described together with the problems caused by some characteristics of the apparatus of the European muon collaboration. Several reconstruction technics are compared, and a way of handling big drift chamber problems is found. Some results on Monte-Carlo tracks are given [fr

  5. Analogue of Pontryagin's maximum principle for multiple integrals minimization problems

    Mikhail, Zelikin

    2016-01-01

    The theorem like Pontryagin's maximum principle for multiple integrals is proved. Unlike the usual maximum principle, the maximum should be taken not over all matrices, but only on matrices of rank one. Examples are given.

  6. Measurement of through-going particle momentum by means of multiple scattering with the ICARUS T600 TPC

    Ankowski, A.; Graczyk, K.; Nowak, J.; Sobczyk, J.; Antonello, M.; Cavanna, F.; Piano Mortari, G.; Segreto, E.; Aprili, P.; Arneodo, F.; Palamara, O.; Badertscher, A.; Ge, Y.; Laffranchi, M.; Messina, M.; Rubbia, A.; Baiboussinov, B.; Baldo Ceolin, M.; Centro, S.; Gibin, D.; Guglielmi, A.; Meng, G.; Pietropaolo, F.; Varanini, F.; Ventura, S.; Battistoni, G.; Muraro, S.; Sala, P.R.; Benetti, P.; Borio di Tigliole, A.; Brunetti, R.; Calligarich, E.; De Vecchi, C.; Dolfini, R.; Gigli Berzolari, A.; Grandi, L.; Mauri, F.; Menegolli, A.; Montanari, C.; Piazzoli, A.; Prata, M.; Prata, M.C.; Przewlocki, P.; Rappoldi, A.; Raselli, G.L.; Rossella, M.; Rubbia, C.; Scannicchio, D.; Vignoli, C.; Bueno, A.; Carmona, M.C.; Garcia-Gamez, D.; Lozano, J.; Martinez de la Ossa, A.; Melgarejo, A.J.; Navas, S.; Carbonara, F.; Cocco, A.G.; Di Cicco, A.; Ereditato, A.; Fiorillo, G.; Rossi, B.; Cennini, P.; Ferrari, A.; Cesana, A.; Terrani, M.; Cline, D.B.; Lisowski, B.; Matthey, C.; Otwinowski, S.; Seo, Y.; Wang, H.; Yang, X.; Cieslik, K.; Dabrowska, A.; Markiewicz, M.; Stefan, D.; Szarska, M.; Wachala, T.; Zalewska, A.; Gil-Botella, I.; Holeczek, J.; Kisiel, J.; Kielczewska, D.; Lagoda, J.; Posiadala, M.; Kozlowski, T.; Mijakowski, P.; Rondio, E.; Stepaniak, J.; Szeptycka, M.; Periale, L.; Picchi, P.; Polchlopek, W.; Sergiampietri, F.; Sulej, R.

    2006-01-01

    The ICARUS collaboration has demonstrated, following the operation of a 600 ton (T600) detector at shallow depth, that the technique based on liquid argon time projection chambers is now mature. The study of rare events, not contemplated in the standard model, can greatly benefit from the use of this kind of detectors. In particular, a deeper understanding of atmospheric neutrino properties will be obtained thanks to the unprecedented quality of the data ICARUS provides. However if we concentrate on the T600 performance, most of the ν μ charged current sample will be partially contained, due to the reduced dimensions of the detector. In this article, we address the problem of how well we can determine the kinematics of events having partially contained tracks. The analysis of a large sample of atmospheric muons collected during the T600 test run demonstrates that, in case the recorded track is at least one meter long, the muon momentum can be reconstructed by an algorithm that measures the multiple Coulomb scattering along the particle's path. Moreover, we show that momentum resolution can be improved by almost a factor two using an algorithm based on the Kalman filtering technique. (orig.)

  7. Solving Multiple Timetabling Problems at Danish High Schools

    Kristiansen, Simon

    name; Elective Course Student Sectioning. The problem is solved using ALNS and solutions are proven to be close to optimum. The algorithm has been implemented and made available for the majority of the high schools in Denmark. The second Student Sectioning problem presented is the sectioning of each...... high schools. Two types of consultations are presented; the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Problem (SCTP). One mathematical model containing both consultation types has been created and solved using an ALNS approach. The received solutions...... problems as mathematical models and solve them using operational research techniques. Two of the models and the suggested solution methods have resulted in implementations in an actual decision support software, and are hence available for the majority of the high schools in Denmark. These implementations...

  8. Studying time of flight imaging through scattering media across multiple size scales (Conference Presentation)

    Velten, Andreas

    2017-05-01

    Light scattering is a primary obstacle to optical imaging in a variety of different environments and across many size and time scales. Scattering complicates imaging on large scales when imaging through the atmosphere when imaging from airborne or space borne platforms, through marine fog, or through fog and dust in vehicle navigation, for example in self driving cars. On smaller scales, scattering is the major obstacle when imaging through human tissue in biomedical applications. Despite the large variety of participating materials and size scales, light transport in all these environments is usually described with very similar scattering models that are defined by the same small set of parameters, including scattering and absorption length and phase function. We attempt a study of scattering and methods of imaging through scattering across different scales and media, particularly with respect to the use of time of flight information. We can show that using time of flight, in addition to spatial information, provides distinct advantages in scattering environments. By performing a comparative study of scattering across scales and media, we are able to suggest scale models for scattering environments to aid lab research. We also can transfer knowledge and methodology between different fields.

  9. Multiple parton interactions in deep inelastic ep-scattering at HERA

    Osman, Sakar

    2008-12-15

    The production of jets with low transverse momenta (mini-jets) in deep inelastic electron-proton scattering is studied. The analyses uses data taken with the H1 detector at HERA during the years 1999 to 2000. The events are required to contain either at least one leading jet of P{sub T}>5 GeV (the inclusive 1-jet sample) or at least two hard jets where one of them has to be at an angle larger than 140 degrees with respect to the leading jet (inclusive 2-jet sample). Mini-jet multiplicities and their average transverse momenta are presented as a function of Q{sup 2}, in two regions of psuedo-rapidity and for two bins in the hadronic mass, W for the inclusive 1-jet sample. For the inclusive 2-jet sample the results are shown for direct and resolved photon interactions in two bins of W. The results are compared to various QCD based models. A new method for calibrating jet energy measurements up to 10 GeV has been developed and its performance has been studied. (orig.)

  10. Band structures in a two-dimensional phononic crystal with rotational multiple scatterers

    Song, Ailing; Wang, Xiaopeng; Chen, Tianning; Wan, Lele

    2017-03-01

    In this paper, the acoustic wave propagation in a two-dimensional phononic crystal composed of rotational multiple scatterers is investigated. The dispersion relationships, the transmission spectra and the acoustic modes are calculated by using finite element method. In contrast to the system composed of square tubes, there exist a low-frequency resonant bandgap and two wide Bragg bandgaps in the proposed structure, and the transmission spectra coincide with band structures. Specially, the first bandgap is based on locally resonant mechanism, and the simulation results agree well with the results of electrical circuit analogy. Additionally, increasing the rotation angle can remarkably influence the band structures due to the transfer of sound pressure between the internal and external cavities in low-order modes, and the redistribution of sound pressure in high-order modes. Wider bandgaps are obtained in arrays composed of finite unit cells with different rotation angles. The analysis results provide a good reference for tuning and obtaining wide bandgaps, and hence exploring the potential applications of the proposed phononic crystal in low-frequency noise insulation.

  11. Multiple parton interactions in deep inelastic ep-scattering at HERA

    Osman, Sakar

    2008-12-01

    The production of jets with low transverse momenta (mini-jets) in deep inelastic electron-proton scattering is studied. The analyses uses data taken with the H1 detector at HERA during the years 1999 to 2000. The events are required to contain either at least one leading jet of P T >5 GeV (the inclusive 1-jet sample) or at least two hard jets where one of them has to be at an angle larger than 140 degrees with respect to the leading jet (inclusive 2-jet sample). Mini-jet multiplicities and their average transverse momenta are presented as a function of Q 2 , in two regions of psuedo-rapidity and for two bins in the hadronic mass, W for the inclusive 1-jet sample. For the inclusive 2-jet sample the results are shown for direct and resolved photon interactions in two bins of W. The results are compared to various QCD based models. A new method for calibrating jet energy measurements up to 10 GeV has been developed and its performance has been studied. (orig.)

  12. Multiple parton scattering in nuclei: heavy quark energy loss and modified fragmentation functions

    Zhang Benwei; Wang, Enke; Wang Xinnian

    2005-01-01

    Multiple scattering, induced radiative energy loss and modified fragmentation functions of a heavy quark in nuclear matter are studied within the framework of generalized factorization in perturbative QCD. Modified heavy quark fragmentation functions and energy loss are derived in detail with illustration of the mass dependencies of the Landau-Pomeranchuk-Migdal interference effects and heavy quark energy loss. Due to the quark mass dependence of the gluon formation time, the nuclear size dependencies of nuclear modification of the heavy quark fragmentation function and heavy quark energy loss are found to change from a linear to a quadratic form when the initial energy and momentum scale are increased relative to the quark mass. The radiative energy loss of the heavy quark is also significantly suppressed due to limited cone of gluon radiation imposed by the mass. Medium modification of the heavy quark fragmentation functions is found to be limited to the large z region due to the form of heavy quark fragmentation functions in vacuum

  13. Contributions to the theory of electron spectroscopy. Applications of the relativistic multiple-scattering theory

    Henk, J.

    2004-01-01

    Electron spectroscopy provides access to fundamental properties of solids, such as the geometric, electronic, and the magnetic structure. The latter are necessary for the understanding of a variety of basic but nevertheless important effects. The present work outlines recently developed theoretical approaches to electron spectroscopies. Most of the collected results rely on first-principles calculations, as formulated in multiple-scattering theory, and are contrasted with experimental findings. One topic involves spin- and angle-resolved photoelectron spectroscopy which is addressed for magnetic surfaces and ultrathin films. Exemplary results comprise magnetic dichroism in both valence-band and core-level photoemission as well as the temperature dependence of magnetic properties of ultrathin films. Another topic is spin-dependent ballistic transport through planar tunnel junctions, focusing here on the zero-bias anomaly. In most of the cases, spin-orbit coupling (SOC) is an essential ingredient and, hence, favors a relativistic description. Prominent effects of SOC are illustrated by means of the electronic structure of rare gases adsorbed on a substrate and by the splitting of surface states on Au(111). Concerning magnetism, the magnetic anisotropy of Ni films on Cu(001) is discussed, focusing in particular on the spin reorientation transition induced by lattice distortions in ultrathin films. (orig.)

  14. Active probing of cloud multiple scattering, optical depth, vertical thickness, and liquid water content using wide-angle imaging lidar

    Love, Steven P.; Davis, Anthony B.; Rohde, Charles A.; Tellier, Larry; Ho, Cheng

    2002-09-01

    At most optical wavelengths, laser light in a cloud lidar experiment is not absorbed but merely scattered out of the beam, eventually escaping the cloud via multiple scattering. There is much information available in this light scattered far from the input beam, information ignored by traditional 'on-beam' lidar. Monitoring these off-beam returns in a fully space- and time-resolved manner is the essence of our unique instrument, Wide Angle Imaging Lidar (WAIL). In effect, WAIL produces wide-field (60-degree full-angle) 'movies' of the scattering process and records the cloud's radiative Green functions. A direct data product of WAIL is the distribution of photon path lengths resulting from multiple scattering in the cloud. Following insights from diffusion theory, we can use the measured Green functions to infer the physical thickness and optical depth of the cloud layer, and, from there, estimate the volume-averaged liquid water content. WAIL is notable in that it is applicable to optically thick clouds, a regime in which traditional lidar is reduced to ceilometry. Here we present recent WAIL data on various clouds and discuss the extension of WAIL to full diurnal monitoring by means of an ultra-narrow magneto-optic atomic line filter for daytime measurements.

  15. Active probing of cloud multiple scattering, optical depth, vertical thickness, and liquid water content using wide-angle imaging LIDAR

    Love, Steven P.; Davis, Anthony B.; Rohde, Charles A.; Tellier, Larry L.; Ho, Cheng

    2002-01-01

    At most optical wavelengths, laser light in a cloud lidar experiment is not absorbed but merely scattered out of the beam, eventually escaping the cloud via multiple scattering. There is much information available in this light scattered far from the input beam, information ignored by traditional 'on-beam' lidar. Monitoring these off-beam returns in a fully space- and time-resolved manner is the essence of our unique instrument, Wide Angle Imaging Lidar (WAIL). In effect, WAIL produces wide-field (60-degree full-angle) 'movies' of the scattering process and records the cloud's radiative Green functions. A direct data product of WAIL is the distribution of photon path lengths resulting from multiple scattering in the cloud. Following insights from diffusion theory, we can use the measured Green functions to infer the physical thickness and optical depth of the cloud layer, and, from there, estimate the volume-averaged liquid water content. WAIL is notable in that it is applicable to optically thick clouds, a regime in which traditional lidar is reduced to ceilometry. Here we present recent WAIL data oti various clouds and discuss the extension of WAIL to full diurnal monitoring by means of an ultra-narrow magneto-optic atomic line filter for daytime measurements.

  16. The Scatter Search Based Algorithm to Revenue Management Problem in Broadcasting Companies

    Pishdad, Arezoo; Sharifyazdi, Mehdi; Karimpour, Reza

    2009-09-01

    The problem under question in this paper which is faced by broadcasting companies is how to benefit from a limited advertising space. This problem is due to the stochastic behavior of customers (advertiser) in different fare classes. To address this issue we propose a mathematical constrained nonlinear multi period model which incorporates cancellation and overbooking. The objective function is to maximize the total expected revenue and our numerical method performs it by determining the sales limits for each class of customer to present the revenue management control policy. Scheduling the advertising spots in breaks is another area of concern and we consider it as a constraint in our model. In this paper an algorithm based on Scatter search is developed to acquire a good feasible solution. This method uses simulation over customer arrival and in a continuous finite time horizon [0, T]. Several sensitivity analyses are conducted in computational result for depicting the effectiveness of proposed method. It also provides insight into better results of considering revenue management (control policy) compared to "no sales limit" policy in which sooner demand will served first.

  17. 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.

  18. Application of hot neutron scattering to the problem of 3d metallic paramagnetism

    Brown, P.J.; Capellmann, H.; Deportes, J.; Givord, D.; Johnson, S.M.; Ziebeck, K.R.A.

    1984-01-01

    The authors report in this paper on experiments performed in Fe and Ni in their paramagnetic state. Scattering of polarized neutrons with polarization analysis has been used to separate out the magnetic scattering from other sources of scattering. Large quasi-elastic scattering is observed which characterizes ferromagnetic correlations over several inter-atomic distances. The large-Q component of the scattering is fairly small as expected for itinerant electrons in which the energy of magnetic excitations may be of the order of the bandwidth. These should help discriminate between the itinerant and localized models

  19. High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

    Pérez-Arancibia, Carlos; Bruno, Oscar P

    2014-08-01

    This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

  20. Multiple Scattering Principal Component-based Radiative Transfer Model (PCRTM) from Far IR to UV-Vis

    Liu, X.; Wu, W.; Yang, Q.

    2017-12-01

    Modern satellite hyperspectral satellite remote sensors such as AIRS, CrIS, IASI, CLARREO all require accurate and fast radiative transfer models that can deal with multiple scattering of clouds and aerosols to explore the information contents. However, performing full radiative transfer calculations using multiple stream methods such as discrete ordinate (DISORT), doubling and adding (AD), successive order of scattering order of scattering (SOS) are very time consuming. We have developed a principal component-based radiative transfer model (PCRTM) to reduce the computational burden by orders of magnitudes while maintain high accuracy. By exploring spectral correlations, the PCRTM reduce the number of radiative transfer calculations in frequency domain. It further uses a hybrid stream method to decrease the number of calls to the computational expensive multiple scattering calculations with high stream numbers. Other fast parameterizations have been used in the infrared spectral region reduce the computational time to milliseconds for an AIRS forward simulation (2378 spectral channels). The PCRTM has been development to cover spectral range from far IR to UV-Vis. The PCRTM model have been be used for satellite data inversions, proxy data generation, inter-satellite calibrations, spectral fingerprinting, and climate OSSE. We will show examples of applying the PCRTM to single field of view cloudy retrievals of atmospheric temperature, moisture, traces gases, clouds, and surface parameters. We will also show how the PCRTM are used for the NASA CLARREO project.

  1. Multiple-instance learning as a classifier combining problem

    Li, Yan; Tax, David M. J.; Duin, Robert P. W.

    2013-01-01

    In multiple-instance learning (MIL), an object is represented as a bag consisting of a set of feature vectors called instances. In the training set, the labels of bags are given, while the uncertainty comes from the unknown labels of instances in the bags. In this paper, we study MIL with the ass...

  2. A hybrid approach to simulate multiple photon scattering in X-ray imaging

    Freud, N.; Letang, J.-M.; Babot, D.

    2005-01-01

    A hybrid simulation approach is proposed to compute the contribution of scattered radiation in X- or γ-ray imaging. This approach takes advantage of the complementarity between the deterministic and probabilistic simulation methods. The proposed hybrid method consists of two stages. Firstly, a set of scattering events occurring in the inspected object is determined by means of classical Monte Carlo simulation. Secondly, this set of scattering events is used as a starting point to compute the energy imparted to the detector, with a deterministic algorithm based on a 'forced detection' scheme. For each scattering event, the probability for the scattered photon to reach each pixel of the detector is calculated using well-known physical models (form factor and incoherent scattering function approximations, in the case of Rayleigh and Compton scattering respectively). The results of the proposed hybrid approach are compared to those obtained with the Monte Carlo method alone (Geant4 code) and found to be in excellent agreement. The convergence of the results when the number of scattering events increases is studied. The proposed hybrid approach makes it possible to simulate the contribution of each type (Compton or Rayleigh) and order of scattering, separately or together, with a single PC, within reasonable computation times (from minutes to hours, depending on the number of pixels of the detector). This constitutes a substantial benefit, compared to classical simulation methods (Monte Carlo or deterministic approaches), which usually requires a parallel computing architecture to obtain comparable results

  3. A hybrid approach to simulate multiple photon scattering in X-ray imaging

    Freud, N. [CNDRI, Laboratory of Nondestructive Testing using Ionizing Radiations, INSA-Lyon Scientific and Technical University, Bat. Antoine de Saint-Exupery, 20, avenue Albert Einstein, 69621 Villeurbanne Cedex (France)]. E-mail: nicolas.freud@insa-lyon.fr; Letang, J.-M. [CNDRI, Laboratory of Nondestructive Testing using Ionizing Radiations, INSA-Lyon Scientific and Technical University, Bat. Antoine de Saint-Exupery, 20, avenue Albert Einstein, 69621 Villeurbanne Cedex (France); Babot, D. [CNDRI, Laboratory of Nondestructive Testing using Ionizing Radiations, INSA-Lyon Scientific and Technical University, Bat. Antoine de Saint-Exupery, 20, avenue Albert Einstein, 69621 Villeurbanne Cedex (France)

    2005-01-01

    A hybrid simulation approach is proposed to compute the contribution of scattered radiation in X- or {gamma}-ray imaging. This approach takes advantage of the complementarity between the deterministic and probabilistic simulation methods. The proposed hybrid method consists of two stages. Firstly, a set of scattering events occurring in the inspected object is determined by means of classical Monte Carlo simulation. Secondly, this set of scattering events is used as a starting point to compute the energy imparted to the detector, with a deterministic algorithm based on a 'forced detection' scheme. For each scattering event, the probability for the scattered photon to reach each pixel of the detector is calculated using well-known physical models (form factor and incoherent scattering function approximations, in the case of Rayleigh and Compton scattering respectively). The results of the proposed hybrid approach are compared to those obtained with the Monte Carlo method alone (Geant4 code) and found to be in excellent agreement. The convergence of the results when the number of scattering events increases is studied. The proposed hybrid approach makes it possible to simulate the contribution of each type (Compton or Rayleigh) and order of scattering, separately or together, with a single PC, within reasonable computation times (from minutes to hours, depending on the number of pixels of the detector). This constitutes a substantial benefit, compared to classical simulation methods (Monte Carlo or deterministic approaches), which usually requires a parallel computing architecture to obtain comparable results.

  4. Application of a multiple scattering model to estimate optical depth, lidar ratio and ice crystal effective radius of cirrus clouds observed with lidar.

    Gouveia Diego

    2018-01-01

    Full Text Available Lidar measurements of cirrus clouds are highly influenced by multiple scattering (MS. We therefore developed an iterative approach to correct elastic backscatter lidar signals for multiple scattering to obtain best estimates of single-scattering cloud optical depth and lidar ratio as well as of the ice crystal effective radius. The approach is based on the exploration of the effect of MS on the molecular backscatter signal returned from above cloud top.

  5. Application of a multiple scattering model to estimate optical depth, lidar ratio and ice crystal effective radius of cirrus clouds observed with lidar.

    Gouveia, Diego; Baars, Holger; Seifert, Patric; Wandinger, Ulla; Barbosa, Henrique; Barja, Boris; Artaxo, Paulo; Lopes, Fabio; Landulfo, Eduardo; Ansmann, Albert

    2018-04-01

    Lidar measurements of cirrus clouds are highly influenced by multiple scattering (MS). We therefore developed an iterative approach to correct elastic backscatter lidar signals for multiple scattering to obtain best estimates of single-scattering cloud optical depth and lidar ratio as well as of the ice crystal effective radius. The approach is based on the exploration of the effect of MS on the molecular backscatter signal returned from above cloud top.

  6. On the solution of the inverse scattering problem for the quadratic bundle of the one-dimensional Schroedinger operators of the whole axis

    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

  7. Time and multiple objectives in scheduling and routing problems

    Dabia, S.

    2012-01-01

    Many optimization problems encountered in practice are multi-objective by nature, i.e., different objectives are conflicting and equally important. Many times, it is not desirable to drop some of them or to optimize them in a composite single objective or hierarchical manner. Furthermore, cost

  8. The collapsed cone algorithm for (192)Ir dosimetry using phantom-size adaptive multiple-scatter point kernels.

    Tedgren, Åsa Carlsson; Plamondon, Mathieu; Beaulieu, Luc

    2015-07-07

    The aim of this work was to investigate how dose distributions calculated with the collapsed cone (CC) algorithm depend on the size of the water phantom used in deriving the point kernel for multiple scatter. A research version of the CC algorithm equipped with a set of selectable point kernels for multiple-scatter dose that had initially been derived in water phantoms of various dimensions was used. The new point kernels were generated using EGSnrc in spherical water phantoms of radii 5 cm, 7.5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm. Dose distributions derived with CC in water phantoms of different dimensions and in a CT-based clinical breast geometry were compared to Monte Carlo (MC) simulations using the Geant4-based brachytherapy specific MC code Algebra. Agreement with MC within 1% was obtained when the dimensions of the phantom used to derive the multiple-scatter kernel were similar to those of the calculation phantom. Doses are overestimated at phantom edges when kernels are derived in larger phantoms and underestimated when derived in smaller phantoms (by around 2% to 7% depending on distance from source and phantom dimensions). CC agrees well with MC in the high dose region of a breast implant and is superior to TG43 in determining skin doses for all multiple-scatter point kernel sizes. Increased agreement between CC and MC is achieved when the point kernel is comparable to breast dimensions. The investigated approximation in multiple scatter dose depends on the choice of point kernel in relation to phantom size and yields a significant fraction of the total dose only at distances of several centimeters from a source/implant which correspond to volumes of low doses. The current implementation of the CC algorithm utilizes a point kernel derived in a comparatively large (radius 20 cm) water phantom. A fixed point kernel leads to predictable behaviour of the algorithm with the worst case being a source/implant located well within a patient

  9. Child outcomes of home-visiting for families with complex and multiple problems

    van Assen, Arend; Dickscheit, Jana; Post, Wendy; Grietens, Hans

    2016-01-01

    Introduction Families with complex and multiple problems are faced with an accumulation of problems across multiple areas of life. Furthermore, these families are often considered to be ‘difficult to treat’. Children and teenagers growing up in these families are exposed to an accumulation of risks

  10. The difference between the classical and quantum mechanical definitions of scattering cross sections and the problem of the classical limit

    Sen, D.; Basu, A.N.; Sengupta, S.

    1994-01-01

    A critical analysis of the difference between the classical and quantum mechanical definitions of scattering cross sections for particles is presented. This leads to a clarification of the classical limit problem and suggests precise criteria for its validity. In particular these criteria are derived for both finite and infinite range potentials. (orig.)

  11. Classical scattering theory of waves from the view point of an eigenvalue problem and application to target identification

    Bottcher, C.; Strayer, M.R.; Werby, M.F.

    1993-01-01

    The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWE's. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can by obtained in matrix form be expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways to long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented

  12. 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)

  13. Solving very large scattering problems using a parallel PWTD-enhanced surface integral equation solver

    Liu, Yang

    2013-07-01

    The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(NtNs(log 2)Ns) and O(Ns 1.5); here N t and Ns denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to Ns ≈ 0.5 × 106 and Nt ≈ 10 3. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. © 2013 IEEE.

  14. Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts

    Nefedov, Nikolay

    2016-06-01

    In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.

  15. Multiple scattering of a zero-order Bessel beam with arbitrary incidence by an aggregate of uniaxial anisotropic spheres

    Li, Z.J.; Wu, Z.S.; Qu, T.; Shang, Q.C.; Bai, L.

    2016-01-01

    Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO 2 , SiO 2 , or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation. - Highlights: • Scattering of Bessel beam by an aggregate of uniaxial anisotropic spheres is studied. • The zero-order Bessel beam propagates and polarizes along arbitrary direction. • The accuracy of expansion coefficients, the scattering theory and codes is verified. • Effects of various parameters on scattering properties are numerically discussed. • Scattering properties of several type of periodical array are numerically analyzed.

  16. Performance analysis of 2D asynchronous hard-limiting optical code-division multiple access system through atmospheric scattering channel

    Zhao, Yaqin; Zhong, Xin; Wu, Di; Zhang, Ye; Ren, Guanghui; Wu, Zhilu

    2013-09-01

    Optical code-division multiple access (OCDMA) systems usually allocate orthogonal or quasi-orthogonal codes to the active users. When transmitting through atmospheric scattering channel, the coding pulses are broadened and the orthogonality of the codes is worsened. In truly asynchronous case, namely both the chips and the bits are asynchronous among each active user, the pulse broadening affects the system performance a lot. In this paper, we evaluate the performance of a 2D asynchronous hard-limiting wireless OCDMA system through atmospheric scattering channel. The probability density function of multiple access interference in truly asynchronous case is given. The bit error rate decreases as the ratio of the chip period to the root mean square delay spread increases and the channel limits the bit rate to different levels when the chip period varies.

  17. Some applications of the multiple scattering theory to the study of the hadron-nucleus interactions at intermediate energies

    Dedonder, J.-P.

    1979-01-01

    This work is devoted to the study of elastic hadron nucleus scattering. At first, an asymptotic evaluation leads to a closed, analytic expression of the eikonal amplitude. This approximate expression displays the role and the influence of the nuclear paremeters in, e.g., p-nucleus scattering around 1 GeV. Pion-nucleus scattering around the 3-3 resonance is then studied. A 3 body model calculation (pion, bound nucleon and residual nucleus represented by a potential) allows to study the importance of binding effects in this problem dominated by the strong energy dependence of the elementary amplitude. The last part is devoted to the construction in momentum space of a realistic optical potential and its comparison with experimental data. The scalling of π + and π - on neighbouring isotopes should allow the measure of the differences between the proton and neutron distributions in nuclei [fr

  18. Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

    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.

  19. The slab albedo problem for the triplet scattering kernel with modified F{sub N} method

    Tuereci, Demet [Ministry of Education, 75th year Anatolia High School, Ankara (Turkey)

    2016-12-15

    One speed, time independent neutron transport equation for a slab geometry with the quadratic anisotropic scattering kernel is considered. The albedo and transmission factor are calculated by the modified F{sub N} method. The obtained numerical results are listed for different scattering coefficients.

  20. The problem of scattering in fibre-fed VPH spectrographs and possible solutions

    Ellis, S. C.; Saunders, Will; Betters, Chris; Croom, Scott

    2014-07-01

    All spectrographs unavoidably scatter light. Scattering in the spectral direction is problematic for sky subtraction, since atmospheric spectral lines are blurred. Scattering in the spatial direction is problematic for fibre fed spectrographs, since it limits how closely fibres can be packed together. We investigate the nature of this scattering and show that the scattering wings have both a Lorentzian component, and a shallower (1/r) component. We investigate the causes of this from a theoretical perspective, and argue that for the spectral PSF the Lorentzian wings are in part due to the profile of the illumination of the pupil of the spectrograph onto the diffraction grating, whereas the shallower component is from bulk scattering. We then investigate ways to mitigate the diffractive scattering by apodising the pupil. In the ideal case of a Gaussian apodised pupil, the scattering can be significantly improved. Finally we look at realistic models of the spectrograph pupils of fibre fed spectrographs with a centrally obstructed telescope, and show that it is possible to apodise the pupil through non-telecentric injection into the fibre.

  1. Effective potential in the problem of scattering of three charged particles

    Kvitsinskii, A.A.; Merkur'ev, S.P.

    1988-01-01

    We study the effective interaction potential in the scattering of a charged particle by a bound state of two other charged particles. Scattering by both the ground and excited states of the target is considered. Explicit representations describing the asymptotic structure of effective potentials are proved

  2. Multiple scattering of MeV ions: Comparison between the analytical theory and Monte-Carlo and molecular dynamics simulations

    Mayer, M.; Arstila, K.; Nordlund, K.; Edelmann, E.; Keinonen, J.

    2006-01-01

    Angular and energy distributions due to multiple small angle scattering were calculated with different models, namely from the analytical Szilagyi theory, the Monte-Carlo code MCERD in binary collision approximation and the molecular dynamics code MDRANGE, for 2 MeV 4 He in Au at backscattering geometry and for 20 MeV 127 I recoil analysis of carbon. The widths and detailed shapes of the distributions are compared, and reasons for deviations between the different models are discussed

  3. Protective factors associated with fewer multiple problem behaviors among homeless/runaway youth.

    Lightfoot, Marguerita; Stein, Judith A; Tevendale, Heather; Preston, Kathleen

    2011-01-01

    Although homeless youth exhibit numerous problem behaviors, protective factors that can be targeted and modified by prevention programs to decrease the likelihood of involvement in risky behaviors are less apparent. The current study tested a model of protective factors for multiple problem behavior in a sample of 474 homeless youth (42% girls; 83% minority) ages 12 to 24 years. Higher levels of problem solving and planning skills were strongly related to lower levels of multiple problem behaviors in homeless youth, suggesting both the positive impact of preexisting personal assets of these youth and important programmatic targets for further building their resilience and decreasing problem behaviors. Indirect relationships between the background factors of self-esteem and social support and multiple problem behaviors were significantly mediated through protective skills. The model suggests that helping youth enhance their skills in goal setting, decision making, and self-reliant coping could lessen a variety of problem behaviors commonly found among homeless youth.

  4. Bilevel formulation of a policy design problem considering multiple objectives and incomplete preferences

    Hawthorne, Bryant; Panchal, Jitesh H.

    2014-07-01

    A bilevel optimization formulation of policy design problems considering multiple objectives and incomplete preferences of the stakeholders is presented. The formulation is presented for Feed-in-Tariff (FIT) policy design for decentralized energy infrastructure. The upper-level problem is the policy designer's problem and the lower-level problem is a Nash equilibrium problem resulting from market interactions. The policy designer has two objectives: maximizing the quantity of energy generated and minimizing policy cost. The stakeholders decide on quantities while maximizing net present value and minimizing capital investment. The Nash equilibrium problem in the presence of incomplete preferences is formulated as a stochastic linear complementarity problem and solved using expected value formulation, expected residual minimization formulation, and the Monte Carlo technique. The primary contributions in this article are the mathematical formulation of the FIT policy, the extension of computational policy design problems to multiple objectives, and the consideration of incomplete preferences of stakeholders for policy design problems.

  5. A Path Loss Model for Non-Line-of-Sight Ultraviolet Multiple Scattering Channels

    2010-01-01

    scattering is self -governed, and the distances and angles for different scattering events are conditioned on previous quantities. Therefore, the arrival...solid angle of the receiver determined by the receiver area and distance rn. Note that no integration over rn is needed because it is a function of...www.eurasip.org). This year edition will take place in Barcelona, capital city of Catalonia (Spain), and will be jointly organized by the Centre Tecnològic de

  6. Exact and approximate multiple diffraction calculations

    Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

    1976-08-01

    A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

  7. An algorithm to compute a rule for division problems with multiple references

    Sánchez Sánchez, Francisca J.

    2012-01-01

    Full Text Available In this paper we consider an extension of the classic division problem with claims: Thedivision problem with multiple references. Hinojosa et al. (2012 provide a solution for this type of pro-blems. The aim of this work is to extend their results by proposing an algorithm that calculates allocationsbased on these results. All computational details are provided in the paper.

  8. Light focusing through a multiple scattering medium: ab initio computer simulation

    Danko, Oleksandr; Danko, Volodymyr; Kovalenko, Andrey

    2018-01-01

    The present study considers ab initio computer simulation of the light focusing through a complex scattering medium. The focusing is performed by shaping the incident light beam in order to obtain a small focused spot on the opposite side of the scattering layer. MSTM software (Auburn University) is used to simulate the propagation of an arbitrary monochromatic Gaussian beam and obtain 2D distribution of the optical field in the selected plane of the investigated volume. Based on the set of incident and scattered fields, the pair of right and left eigen bases and corresponding singular values were calculated. The pair of right and left eigen modes together with the corresponding singular value constitute the transmittance eigen channel of the disordered media. Thus, the scattering process is described in three steps: 1) initial field decomposition in the right eigen basis; 2) scaling of decomposition coefficients for the corresponding singular values; 3) assembling of the scattered field as the composition of the weighted left eigen modes. Basis fields are represented as a linear combination of the original Gaussian beams and scattered fields. It was demonstrated that 60 independent control channels provide focusing the light into a spot with the minimal radius of approximately 0.4 μm at half maximum. The intensity enhancement in the focal plane was equal to 68 that coincided with theoretical prediction.

  9. A Path Loss Model for Non-Line-of-Sight Ultraviolet Multiple Scattering Channels

    Sadler BrianM

    2010-01-01

    Full Text Available An ultraviolet (UV signal transmission undergoes rich scattering and strong absorption by atmospheric particulates. We develop a path loss model for a Non-Line-of-Sight (NLOS link. The model is built upon probability theory governing random migration of photons in free space, undergoing scattering, in terms of angular direction and distance. The model analytically captures the contributions of different scattering orders. Thus it relaxes the assumptions of single scattering theory and provides more realistic results. This allows us to assess the importance of high-order scattering, such as in a thick atmosphere environment, where short range NLOS UV communication is enhanced by hazy or foggy weather. By simulation, it is shown that the model coincides with a previously developed Monte Carlo model. Additional numerical examples are presented to demonstrate the effects of link geometry and atmospheric conditions. The results indicate the inherent tradeoffs in beamwidth, pointing angles, range, absorption, and scattering and so are valuable for NLOS communication system design.

  10. Meromorphic extension of the scattering matrix for long range two-body problems

    Gerard, C.; Martinez, A.

    1989-01-01

    We prove the existence of a meromorphic extension of the scattering matrix for long range potentials analytic at infinity. This extension exists as a bounded operator on some Gevrey spaces on S n-1 , with critical depending on the rate of decay of the potential at infinity. We use a semi-stationary definition of the scattering operator due to Isozaki-Kitada, using time independent modifiers. We show that the poles of the scattering matrix coincide with the resonances of the Hamiltonian [fr

  11. [AIDS in Chile: a problem with multiple facets].

    Ormazabal, B

    1991-03-01

    Chile's 1st case of AIDS was diagnosed in 1984. Some 250 AIDS cases and 1600 HIV positive persons have since been reported, although the actual number by some estimates may reach 5000. Chile, although in the initial stages of the epidemic, already has a serious problem which at present can only be combatted through education. It will be necessary to convince the population that significant modifications of sexual behavior are needed to control the spread of the disease. Education for AIDS prevention is a priority of the National Commission on AIDS (CONASIDA), which is basing its program on the premise that stable monogamy is the most natural form of expression of a couple. Manuals for prevention are under development, and the 1st, for health workers and the general population, is in process of publication. A series of pamphlets and educational videos for workers in sexually transmitted disease clinics are under development. Educational materials are also being created for specific groups such as university students and agricultural workers and for groups at high risk. A social communications campaign has been prepared and approved by the authorities, and is awaiting funding for dissemination. Education of the population is also a concern for the Catholic Church, which views reinforcement of the family and its mission of providing sex education as a primary means of preventing AIDS. CONASIDA is also responsible for epidemiological study of AIDS in Chile through surveillance of sentinel groups and in quality control of the blood supply. Condoms are to be distributed in sexually transmitted disease clinics for the purpose of AIDS prevention.

  12. Structural dynamics of surfaces by ultrafast electron crystallography: experimental and multiple scattering theory.

    Schäfer, Sascha; Liang, Wenxi; Zewail, Ahmed H

    2011-12-07

    Recent studies in ultrafast electron crystallography (UEC) using a reflection diffraction geometry have enabled the investigation of a wide range of phenomena on the femtosecond and picosecond time scales. In all these studies, the analysis of the diffraction patterns and their temporal change after excitation was performed within the kinematical scattering theory. In this contribution, we address the question, to what extent dynamical scattering effects have to be included in order to obtain quantitative information about structural dynamics. We discuss different scattering regimes and provide diffraction maps that describe all essential features of scatterings and observables. The effects are quantified by dynamical scattering simulations and examined by direct comparison to the results of ultrafast electron diffraction experiments on an in situ prepared Ni(100) surface, for which structural dynamics can be well described by a two-temperature model. We also report calculations for graphite surfaces. The theoretical framework provided here allows for further UEC studies of surfaces especially at larger penetration depths and for those of heavy-atom materials. © 2011 American Institute of Physics

  13. Solving very large scattering problems using a parallel PWTD-enhanced surface integral equation solver

    Liu, Yang; Bagci, Hakan; Michielssen, Eric

    2013-01-01

    numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from

  14. Scattering of particles with inclusions. Modeling and inverse problem solution in the Rayleigh-Gans approximation

    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.

  15. Local normal vector field formulation for periodic scattering problems formulated in the spectral domain

    van Beurden, M.C.; Setija, Irwan

    2017-01-01

    We present two adapted formulations, one tailored to isotropic media and one for general anisotropic media, of the normal vector field framework previously introduced to improve convergence near arbitrarily shaped material interfaces in spectral simulation methods for periodic scattering geometries.

  16. Spin-lattice interactions studied by polarised and unpolarised inelastic scattering application to the invar problem

    Brown, P J [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1996-11-01

    A semi-quantitative analysis is given of some of the ways in which spin-lattice interactions can modify the cross-sections observable in neutron scattering experiments. This analysis is applied to the scattering from the invar alloy Fe{sub 65}Ni{sub 35} using a model in which the magnetic moment is a function of the near neighbour separation. This model has been applied to clarify the results of inelastic scattering experiments carried out on Fe{sub 65}Ni{sub 35} using both polarised and unpolarised neutrons. The extra information obtainable using polarised neutrons as well as the difficulties and limitations of the technique for inelastic scattering are discussed. (author) 8 figs., 14 refs.

  17. Problems of phenomenological description of elastic pp scattering at the LHC predictions of contemporary models

    Kundrát, Vojtech; Kaspar, Jan; Procházka, Jirí

    2010-01-01

    The standard description of common influence of both the Coulomb and hadronic elastic scattering in the proton - proton elastic collisions at high energies with the help of West and Yennie complete amplitude is shown to be theoretically inconsistent. The approach being based on the eikonal model amplitude removes these troubles. The preference of its applica- tion to the analysis of experimental data and in obtaining the predictions of contemporary models for proton - proton high energy elastic hadronic scattering are discussed.

  18. Quantum multiple scattering: Eigenmode expansion and its applications to proximity resonance

    Li Sheng; Heller, Eric J.

    2003-01-01

    We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In other words, the T matrix of the system is of rank N, and the eigenmodes are eigenvectors corresponding to nonzero eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano line shape of sharp proximity resonance peaks based on the high-energy tail of a broadband; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular-momentum eigenstates

  19. Analysis of pp scattering at the CERN ISR energies in the multiple Regge pole model

    Bugrij, A.I.; Kobylinsky, N.A.

    1976-01-01

    The simple Regge model is suggested for describing data on proton-proton elastic scattering at high energies. The simplest variant of the Regge model can be formulated as a sum of two pomerons, the first being a moving double pole and the second - a fixed simple pole. Comparison with known data is given. The model gives an infinite rise of the total cross section of pp-scattering. The differential cross section changes slowly with energy. The models of two pomerons reproduce many features of the geometric scaling, in particular, the shift of the dip and rise of scattering total cross section at the second maximum. The considered model is rather simple and is well consistent with experiment

  20. Second-order multiple-scattering theory associated with backscattering enhancement for a millimeter wavelength weather radar with a finite beam width

    Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood

    2005-01-01

    Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time-independent vector theory, including up to second-order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross-polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.

  1. Solving protein nanocrystals by cryo-EM diffraction: Multiple scattering artifacts

    Subramanian, Ganesh [Department of Materials Science and Engineering, Arizona State University, Tempe, AZ (United States); Basu, Shibom [Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ (United States); Liu, Haiguang [Department of Physics, Arizona State University, Tempe, AZ 85287-1504 (United States); Zuo, Jian-Min [Department of Materials Science and Engineering, University of Illinois, Urbana, IL (United States); Spence, John C.H., E-mail: spence@asu.edu [Department of Physics, Arizona State University, Tempe, AZ 85287-1504 (United States)

    2015-01-15

    The maximum thickness permissible within the single-scattering approximation for the determination of the structure of perfectly ordered protein microcrystals by transmission electron diffraction is estimated for tetragonal hen-egg lysozyme protein crystals using several approaches. Multislice simulations are performed for many diffraction conditions and beam energies to determine the validity domain of the required single-scattering approximation and hence the limit on crystal thickness. The effects of erroneous experimental structure factor amplitudes on the charge density map for lysozyme are noted and their threshold limits calculated. The maximum thickness of lysozyme permissible under the single-scattering approximation is also estimated using R-factor analysis. Successful reconstruction of density maps is found to result mainly from the use of the phase information provided by modeling based on the protein data base through molecular replacement (MR), which dominates the effect of poor quality electron diffraction data at thicknesses larger than about 200 Å. For perfectly ordered protein nanocrystals, a maximum thickness of about 1000 Å is predicted at 200 keV if MR can be used, using R-factor analysis performed over a subset of the simulated diffracted beams. The effects of crystal bending, mosaicity (which has recently been directly imaged by cryo-EM) and secondary scattering are discussed. Structure-independent tests for single-scattering and new microfluidic methods for growing and sorting nanocrystals by size are reviewed. - Highlights: • Validity domain of single-scattering approximation for protein electron diffraction is assessed • Electron Diffraction for tetragonal hen-egg lysozyme is simulated using multislice. • Bias from the use of phase information in modeling by molecular replacement (MR) is evaluated. • We find an approximate upper thickness limit, if MR is used, of 100 nm. • A 35% error in structure factor magnitudes may be

  2. The Core Problem within a Linear Approximation Problem $AX/approx B$ with Multiple Right-Hand Sides

    Hnětynková, Iveta; Plešinger, Martin; Strakoš, Z.

    2013-01-01

    Roč. 34, č. 3 (2013), s. 917-931 ISSN 0895-4798 R&D Projects: GA ČR GA13-06684S Grant - others:GA ČR(CZ) GA201/09/0917; GA MŠk(CZ) EE2.3.09.0155; GA MŠk(CZ) EE2.3.30.0065 Program:GA Institutional support: RVO:67985807 Keywords : total least squares problem * multiple right-hand sides * core problem * linear approximation problem * error-in-variables modeling * orthogonal regression * singular value decomposition Subject RIV: BA - General Mathematics Impact factor: 1.806, year: 2013

  3. Comparison of approximate methods for multiple scattering in high-energy collisions. II

    Nolan, A.M.; Tobocman, W.; Werby, M.F.

    1976-01-01

    The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass

  4. Light scattering by multiple spheres: comparison between Maxwell theory and radiative-transfer-theory calculations.

    Voit, Florian; Schäfer, Jan; Kienle, Alwin

    2009-09-01

    We present a methodology to compare results of classical radiative transfer theory against exact solutions of Maxwell theory for a high number of spheres. We calculated light propagation in a cubic scattering region (20 x 20 x 20 microm(3)) consisting of different concentrations of polystyrene spheres in water (diameter 2 microm) by an analytical solution of Maxwell theory and by a numerical solution of radiative transfer theory. The relative deviation of differential as well as total scattering cross sections obtained by both approaches was evaluated for each sphere concentration. For the considered case, we found that deviations due to radiative transfer theory remain small, even for concentrations up to ca. 20 vol. %.

  5. Multiple refraction switches realized by stretching elastomeric scatterers in sonic crystals

    Y. Huang

    2015-02-01

    Full Text Available The effect of out-of-plane pre-stretch on the 2D sonic crystal with stretchable elastomeric scatterers is explored. The hyperelastic scatterers are characterized by a compressible neo-Hookean model. The Dirichlet-to-Neumann (DtN map is adopted to obtain the band structure and equi-frequency contours. We focus on the first passband and find that a variety of switching functionalities for refraction behaviors can be realized in selected frequencies under a specific pre-stretch range. These refraction switches enable an active control of wave propagation and are applicable in advanced technologies where switchable and multifunctional sonic crystals are required.

  6. Multiple Problem-Solving Strategies Provide Insight into Students' Understanding of Open-Ended Linear Programming Problems

    Sole, Marla A.

    2016-01-01

    Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students' unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex,…

  7. Integral transform method for solving neutron transport problems with general anisotropic scattering in a cylinder of finite height

    Kumar, V.; Sahni, D.C.

    1983-01-01

    In this paper, the authors present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a homogeneous cylinder of finite height with general anisotropic scattering. They present the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the S/sub N/ method of TWOTRAN

  8. Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron

    Airapetian, A. [Giessen Univ. (Germany). Physikalisches Inst.; Michigan Univ., Ann Arbor, MI (United States). Randall Lab. of Physics; Akopov, N. [Yerevan Physics Institute (Armenia); Akopov, Z. [DESY Hamburg (Germany)] [and others; Collaboration: HERMES Collaboration

    2012-12-15

    Multiplicities in semi-inclusive deep-inelastic scattering are presented for each charge state of {pi}{sup {+-}} and K{sup {+-}} mesons. The data were collected by the HERMES experiment at the HERA storage ring using 27.6 GeV electron and positron beams incident on a hydrogen or deuterium gas target. The results are presented as a function of the kinematic quantities x{sub B}, Q{sup 2}, z, and P{sub h} {sub perpendicular} {sub to}. They represent a unique data set for identified hadrons that will significantly enhance our understanding of the fragmentation of quarks into final-state hadrons in deep-inelastic scattering.

  9. Influence of multiple small-angle neutron scattering on diffraction peak broadening in ferritic steel

    Woo, W.; Em, V.; Shin, E.; Mikula, Pavol; Ryukhtin, Vasyl

    2015-01-01

    Roč. 48, APR (2015), s. 350-356 ISSN 0021-8898 R&D Projects: GA ČR GB14-36566G; GA MŠk(CZ) LM2011019 Institutional support: RVO:61389005 Keywords : peak broadening * small-angle neutron scattering * neutron diffraction * magnetic domain Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.720, year: 2014

  10. The double travelling salesman problem with multiple stacks - Formulation and heuristic solution approaches

    Petersen, Hanne Løhmann; Madsen, Oli B.G.

    2009-01-01

    This paper introduces the double travelling salesman problem with multiple stacks and presents four different metaheuristic approaches to its solution. The double TSP with multiple stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks...

  11. Multiple scattering in grazing-incidence X-ray diffraction: impact on lattice-constant determination in thin films

    Resel, Roland, E-mail: roland.resel@tugraz.at; Bainschab, Markus; Pichler, Alexander [Graz University of Technology, Graz (Austria); Dingemans, Theo [Delft University of Technology, Delft (Netherlands); Simbrunner, Clemens [Johannes Kepler University, Linz (Austria); University of Bremen, Bremen (Germany); Stangl, Julian [Johannes Kepler University, Linz (Austria); Salzmann, Ingo [Humboldt University, Berlin (Germany)

    2016-04-20

    The use of grazing-incidence X-ray diffraction to determine the crystal structure from thin films requires accurate positions of Bragg peaks. Refraction effects and multiple scattering events have to be corrected or minimized. Dynamical scattering effects are observed in grazing-incidence X-ray diffraction experiments using an organic thin film of 2,2′:6′,2′′-ternaphthalene grown on oxidized silicon as substrate. Here, a splitting of all Bragg peaks in the out-of-plane direction (z-direction) has been observed, the magnitude of which depends both on the incidence angle of the primary beam and the out-of-plane angle of the scattered beam. The incident angle was varied between 0.09° and 0.25° for synchrotron radiation of 10.5 keV. This study reveals comparable intensities of the split peaks with a maximum for incidence angles close to the critical angle of total external reflection of the substrate. This observation is rationalized by two different scattering pathways resulting in diffraction peaks at different positions at the detector. In order to minimize the splitting, the data suggest either using incident angles well below the critical angle of total reflection or angles well above, which sufficiently attenuates the contributions from the second scattering path. This study highlights that the refraction of X-rays in (organic) thin films has to be corrected accordingly to allow for the determination of peak positions with sufficient accuracy. Based thereon, a reliable determination of the lattice constants becomes feasible, which is required for crystallographic structure solutions from thin films.

  12. Designing and using multiple-possibility physics problems in physics courses

    Shekoyan, Vazgen

    2012-02-01

    One important aspect of physics instruction is helping students develop better problem solving expertise. Besides enhancing the content knowledge, problems help students develop different cognitive abilities and skills. This presentation focuses on multiple-possibility problems (alternatively called ill-structured problems). These problems are different from traditional ``end of chapter'' single-possibility problems. They do not have one right answer and thus the student has to examine different possibilities, assumptions and evaluate the outcomes. To solve such problems one has to engage in a cognitive monitoring called epistemic cognition. It is an important part of thinking in real life. Physicists routinely use epistemic cognition when they solve problems. I have explored the instructional value of using such problems in introductory physics courses.

  13. The generalized PN synthetic acceleration method for linear transport problems with highly anisotropic scattering

    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

  14. The generalized PN synthetic acceleration method for linear transport problems with highly anisotropic scattering

    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

  15. Visual Attention for Solving Multiple-Choice Science Problem: An Eye-Tracking Analysis

    Tsai, Meng-Jung; Hou, Huei-Tse; Lai, Meng-Lung; Liu, Wan-Yi; Yang, Fang-Ying

    2012-01-01

    This study employed an eye-tracking technique to examine students' visual attention when solving a multiple-choice science problem. Six university students participated in a problem-solving task to predict occurrences of landslide hazards from four images representing four combinations of four factors. Participants' responses and visual attention…

  16. On Solution of Total Least Squares Problems with Multiple Right-hand Sides

    Hnětynková, I.; Plešinger, Martin; Strakoš, Zdeněk

    2008-01-01

    Roč. 8, č. 1 (2008), s. 10815-10816 ISSN 1617-7061 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : total least squares problem * multiple right-hand sides * linear approximation problem Subject RIV: BA - General Mathematics

  17. The computer-aided design of a servo system as a multiple-criteria decision problem

    Udink ten Cate, A.J.

    1986-01-01

    This paper treats the selection of controller gains of a servo system as a multiple-criteria decision problem. In contrast to the usual optimization-based approaches to computer-aided design, inequality constraints are included in the problem as unconstrained objectives. This considerably simplifies

  18. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

    Salazar, Daniel; Rocco, Claudio M.; Galvan, Blas J.

    2006-01-01

    This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature

  19. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

    Salazar, Daniel [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain) and Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: danielsalazaraponte@gmail.com; Rocco, Claudio M. [Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: crocco@reacciun.ve; Galvan, Blas J. [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain)]. E-mail: bgalvan@step.es

    2006-09-15

    This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.

  20. Step by Step: Biology Undergraduates’ Problem-Solving Procedures during Multiple-Choice Assessment

    Prevost, Luanna B.; Lemons, Paula P.

    2016-01-01

    This study uses the theoretical framework of domain-specific problem solving to explore the procedures students use to solve multiple-choice problems about biology concepts. We designed several multiple-choice problems and administered them on four exams. We trained students to produce written descriptions of how they solved the problem, and this allowed us to systematically investigate their problem-solving procedures. We identified a range of procedures and organized them as domain general, domain specific, or hybrid. We also identified domain-general and domain-specific errors made by students during problem solving. We found that students use domain-general and hybrid procedures more frequently when solving lower-order problems than higher-order problems, while they use domain-specific procedures more frequently when solving higher-order problems. Additionally, the more domain-specific procedures students used, the higher the likelihood that they would answer the problem correctly, up to five procedures. However, if students used just one domain-general procedure, they were as likely to answer the problem correctly as if they had used two to five domain-general procedures. Our findings provide a categorization scheme and framework for additional research on biology problem solving and suggest several important implications for researchers and instructors. PMID:27909021

  1. Experimental characterization of a prototype secondary spectrometer for vertically scattering multiple energy analysis at cold-neutron triple axis spectrometers

    Toft-Petersen, Rasmus; Groitl, Felix; Kure, Mathias

    2016-01-01

    A thorough experimental characterization of a multiplexing backend with multiple energy analysis on a cold-neutron triple axis spectrometer (cTAS) is presented. The prototype employs two angular segments (2 theta-segments) each containing five vertically scattering analyzers (energy channels...... to the energy resolution of a standard cTAS. The dispersion relation of the antiferromagnetic excitations in MnF2 has been mapped out by performing constant energy transfer maps. These results show that the tested setup is virtually spurion free. In addition, focusing effects due to (mis...

  2. High-efficiency γ-ray flash generation via multiple-laser scattering in ponderomotive potential well.

    Gong, Z; Hu, R H; Shou, Y R; Qiao, B; Chen, C E; He, X T; Bulanov, S S; Esirkepov, T Zh; Bulanov, S V; Yan, X Q

    2017-01-01

    γ-ray flash generation in near-critical-density target irradiated by four symmetrical colliding laser pulses is numerically investigated. With peak intensities about 10^{23} W/cm^{2}, the laser pulses boost electron energy through direct laser acceleration, while pushing them inward with the ponderomotive force. After backscattering with counterpropagating laser, the accelerated electron is trapped in the electromagnetic standing waves or the ponderomotive potential well created by the coherent overlapping of the laser pulses, and emits γ-ray photons in a multiple-laser-scattering regime, where electrons act as a medium transferring energy from the laser to γ rays in the ponderomotive potential valley.

  3. All orders transport theory from the multiple scattering expansion of the self-energy. The central cuts

    Gagnon, J.S.; Fillion-Gourdeau, F.; Sangyong Jeong; RIKEN Research Center, Upton, NY

    2006-01-01

    We use the full multiple scattering expansion of the retarded self-energy to obtain the gain and loss rates present in the Kadanoff-Baym relativistic transport equation. The rates we obtain include processes with any number of particles. As a first approximation, we only consider central cuts in the self-energies, but otherwise our results are general. We specialize to the case of scalar field theory to compare with lowest order results. The main application of this work is relativistic transport theory of very dense systems, such as the quark-gluon plasma or the early universe, where multi-particle interactions are important. (author)

  4. Sum of ratios of products forα-μ random variables in wireless multihop relaying and multiple scattering

    Wang, Kezhi; Wang, Tian; Chen, Yunfei; Alouini, Mohamed-Slim

    2014-01-01

    The sum of ratios of products of independent 2642 2642α-μ random variables (RVs) is approximated by using the Generalized Gamma ratio approximation (GGRA) with Gamma ratio approximation (GRA) as a special case. The proposed approximation is used to calculate the outage probability of the equal gain combining (EGC) or maximum ratio combining (MRC) receivers for wireless multihop relaying or multiple scattering systems considering interferences. Numerical results show that the newly derived approximation works very well verified by the simulation, while GRA has a slightly worse performance than GGRA when outage probability is below 0.1 but with a more simplified form.

  5. Sum of ratios of products forα-μ random variables in wireless multihop relaying and multiple scattering

    Wang, Kezhi

    2014-09-01

    The sum of ratios of products of independent 2642 2642α-μ random variables (RVs) is approximated by using the Generalized Gamma ratio approximation (GGRA) with Gamma ratio approximation (GRA) as a special case. The proposed approximation is used to calculate the outage probability of the equal gain combining (EGC) or maximum ratio combining (MRC) receivers for wireless multihop relaying or multiple scattering systems considering interferences. Numerical results show that the newly derived approximation works very well verified by the simulation, while GRA has a slightly worse performance than GGRA when outage probability is below 0.1 but with a more simplified form.

  6. Revisit the spin-FET: Multiple reflection, inelastic scattering, and lateral size effects

    Xu, Luting; Li, Xin-Qi; Sun, Qing-feng

    2014-01-01

    We revisit the spin-injected field effect transistor (spin-FET) by simulating a lattice model based on recursive lattice Green's function approach. In the one-dimensional case and coherent regime, the simulated results reveal noticeable differences from the celebrated Datta-Das model, which motivate thus an improved treatment and lead to analytic and generalized result. The simulation also allows us to address inelastic scattering (using B\\"uttiker's fictitious reservoir approach) and lateral...

  7. Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

    Torrini, M.

    1983-01-01

    The exponential nature of the translation matrix G of spherical free waves has been set forth in a previous paper.The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectros and the eigenvalues of G have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centered at a different point is solved

  8. Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

    Hnětynková, Iveta; Plešinger, M.; Sima, D.M.

    2016-01-01

    Roč. 37, č. 3 (2016), s. 861-876 ISSN 0895-4798 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : total least squares (TLS) problem * multiple right-hand sides * core problem * linear approximation problem * error-in-variables modeling * orthogonal regression * classical TLS algorithm Subject RIV: BA - General Mathematics Impact factor: 2.194, year: 2016

  9. Multiple Scattering of Gamma Radiation in a Spherical Concrete Wall Room

    Leimdoerfer, M

    1962-12-15

    The Monte Carlo method has been applied for the calculation of the energy flux of scattered gamma radiation in a spherical room surrounded by an infinitely thick spherical wall and with a point source at the centre. Source energies were I, 2, 4, 6, and 10 MeV. The main investigation was carried out at a room radius of 500 cm but, for the 1 MeV source, the influence of varying the room radius down to 1 cm was analysed. The results contain energy distributions of the first four successive reflection components at the centre of the room and at the wall surface, as well as spatial distributions of the successive energy flux components. The neglect of reflection contributions of order five and higher was estimated to introduce an error of less than 0. 2 % of the total scattered energy flux. An analytical approximation is shown to produce a useful and easily applicable method of predicting the amount of scattered radiation in a spherical room.

  10. Multiple Scattering of Gamma Radiation in a Spherical Concrete Wall Room

    Leimdoerfer, M.

    1962-12-01

    The Monte Carlo method has been applied for the calculation of the energy flux of scattered gamma radiation in a spherical room surrounded by an infinitely thick spherical wall and with a point source at the centre. Source energies were I, 2, 4, 6, and 10 MeV. The main investigation was carried out at a room radius of 500 cm but, for the 1 MeV source, the influence of varying the room radius down to 1 cm was analysed. The results contain energy distributions of the first four successive reflection components at the centre of the room and at the wall surface, as well as spatial distributions of the successive energy flux components. The neglect of reflection contributions of order five and higher was estimated to introduce an error of less than 0. 2 % of the total scattered energy flux. An analytical approximation is shown to produce a useful and easily applicable method of predicting the amount of scattered radiation in a spherical room

  11. High-energy gravitational scattering and the general relativistic two-body problem

    Damour, Thibault

    2018-02-01

    A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys. Rev. D 94, 104015 (2016), 10.1103/PhysRevD.94.104015]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the two-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.

  12. Simultaneous distribution between the deflection angle and the lateral displacement under the Moliere theory of multiple scattering

    Nakatsuka, Takao [Okayama Shoka University, Laboratory of Information Science, Okayama (Japan); Okei, Kazuhide [Kawasaki Medical School, Dept. of Information Sciences, Kurashiki (Japan); Iyono, Atsushi [Okayama university of Science, Dept. of Fundamental Science, Faculty of Science, Okayama (Japan); Bielajew, Alex F. [Univ. of Michigan, Dept. Nuclear Engineering and Radiological Sciences, Ann Arbor, MI (United States)

    2015-12-15

    Simultaneous distribution between the deflection angle and the lateral displacement of fast charged particles traversing through matter is derived by applying numerical inverse Fourier transforms on the Fourier spectral density solved analytically under the Moliere theory of multiple scattering, taking account of ionization loss. Our results show the simultaneous Gaussian distribution at the region of both small deflection angle and lateral displacement, though they show the characteristic contour patterns of probability density specific to the single and the double scatterings at the regions of large deflection angle and/or lateral displacement. The influences of ionization loss on the distribution are also investigated. An exact simultaneous distribution is derived under the fixed energy condition based on a well-known model of screened single scattering, which indicates the limit of validity of the Moliere theory applied to the simultaneous distribution. The simultaneous distribution will be valuable for improving the accuracy and the efficiency of experimental analyses and simulation studies relating to charged particle transports. (orig.)

  13. Recent trends in the incidence of multiple births and its consequences on perinatal problems in Korea.

    Choi, Sun Hee; Park, Young Sil; Shim, Kye Shik; Choi, Yong Sung; Chang, Ji Young; Hahn, Won Ho; Bae, Chong-Woo

    2010-08-01

    The aim of this study was to survey multiple birth data and to analyze the recent trends of multiple births and its consequences on perinatal problems in Korea from 1991 to 2008. Data were obtained from the Korean Statistical Information Service. The total number of multiple births showed increasing trends. The multiple birth rate was maintained within less than 10.0 for the decade from 1981 to 1990. However, it increased gradually to reach 27.5 in 2008. The maternal age for multiple births was higher than for total live births. The mean birth weight of the total live births was 3.23 kg; for the multiple births it was 2.40 kg in 2008. The incidence of low birth weight infants (LBWI) among total live births was 3.8% in 2000 and 4.9% in 2008. For multiple births it was 49.2% and 53.0% during the same years. The incidence of preterm births among total live births was 3.8% in 2000 and 5.5% in 2008; for the multiple births it was 38.3% and 51.5% during the same years. The incidence of multiple births and its consequences on perinatal problems (preterm, LBWI, and advanced-maternal age) have been increased steadily over the last two decades in Korea.

  14. Multiplicities of charged pions and unidentified charged hadrons from deep-inelastic scattering of muons off an isoscalar target

    Adolph, C.; Aghasyan, M.; Akhunzyanov, R.; Alexeev, M.G.; Alexeev, G.D.; Amoroso, A.; Andrieux, V.; Anfimov, N.V.; Anosov, V.; Augustyniak, W.; Austregesilo, A.; Azevedo, C.D.R.; Badelek, B.; Balestra, F.; Barth, J.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E.R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Buechele, M.; Capozza, L.; Chang, W. -C.; Chatterjee, C.; Chiosso, M.; Choi, I.; Chung, S. -U.; Cicuttin, A.; Crespo, M.L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S.S.; Dasgupta, S.; Denisov, O. Yu.; Dhara, L.; Donskov, S.V.; Doshita, N.; Duic, V.; Duennweber, W.; Dziewiecki, M.; Efremov, A.; Eversheim, P.D.; Eyrich, W.; Faessler, M.; Ferrero, A.; Finger, M.; Fischer, H.; Franco, C.; von Hohenesche, N. du Fresne; Friedrich, J.M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmueller, S.; Grasso, A.; Grosse Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F.H.; Heitz, R.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; dHose, N.; Hsieh, C. -Y.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Joosten, R.; Joerg, P.; Kabuss, E.; Ketzer, B.; Khaustov, G.V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J.H.; Kolosov, V.N.; Kondo, K.; Koenigsmann, K.; Konorov, I.; Konstantinov, V.F.; Kotzinian, A.M.; Kouznetsov, O.M.; Kuhn, R.; Kraemer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z.V.; Kulinich, Y.; Kunne, F.; Kurek, K.; Kurjata, R.P.; Lednev, A.A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G.K.; Marchand, C.; Marianski, B.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.V.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Mikhasenko, M.; Mitrofanov, E.; Mitrofanov, N.; Miyachi, Y.; Montuenga, P.; Nagaytsev, A.; Nerling, F.; Neyret, D.; Nikolaenko, V.I.; Novy, J.; Nowak, W.-D.; Nukazuka, G.; Nunes, A.S.; Olshevsky, A.G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J. -C.; Pereira, F.; Pesek, M.; Peshekhonov, D.V.; Pierre, N.; Platchkov, S.; Pochodzalla, J.; Polyakov, V.A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Roskot, M.; Ryabchikov, D.I.; Rybnikov, A.; Rychter, A.; Salac, R.; Samoylenko, V.D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I.A.; Sawada, T.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schoenning, K.; Schopferer, S.; Seder, E.; Selyunin, A.; Shevchenko, O. Yu.; Steffen, D.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Smolik, J.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Tasevsky, M.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Vondra, J.; Weisrock, T.; Wilfert, M.; Windmolders, R.; ter Wolbeek, J.; Zaremba, K.; Zavada, P.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.

    2017-01-10

    Multiplicities of charged pions and unidentified hadrons produced in deep-inelastic scattering were measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the relative hadron energy $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam and an isoscalar target ($^6$LiD). They cover the kinematic domain in the photon virtuality $Q^2$ > 1(GeV/c$)^2$, $0.004 < x < 0.4$, $0.2 < z < 0.85$ and $0.1 < y < 0.7$. In addition, a leading-order pQCD analysis was performed using the pion multiplicity results to extract quark fragmentation functions.

  15. Multiplicities of charged pions and charged hadrons from deep-inelastic scattering of muons off an isoscalar target

    C. Adolph

    2017-01-01

    Full Text Available Multiplicities of charged pions and charged hadrons produced in deep-inelastic scattering were measured in three-dimensional bins of the Bjorken scaling variable x, the relative virtual-photon energy y and the relative hadron energy z. Data were obtained by the COMPASS Collaboration using a 160GeV muon beam and an isoscalar target (6LiD. They cover the kinematic domain in the photon virtuality Q2>1(GeV/c2, 0.004multiplicity results to extract quark fragmentation functions.

  16. Windows pollution problems of the dust concentration measurement based on scattering method

    Zhao Yanjun; Zhang Yongtao; Shi Xinyue; Xu Chuanlong; Wang Shimin

    2009-01-01

    The windows are separated the measurement system from the dust space in the light Scattering dust concentration measurement system. The windows are polluted unavoidably by the dust and the measurement error is produced. Based on the Mie Scattering theory, the measurement error is researched in this paper. The numerical simulation results show that the measurement error is related to the particles diameter distribution and the refractive index, but is independent of the particles average diameter. A novel photoelectricity sensor is developed in this paper in order to solve the measurement error by the windows pollution. The calculated method is brought out which can amend the measurement errors by the windows pollution and improve the measurement accuracy.

  17. Statistics of α-μ Random Variables and Their Applications inWireless Multihop Relaying and Multiple Scattering Channels

    Wang, Kezhi

    2015-06-01

    Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-To-interference ratio (SIR) in a multiple scattering system with interference. © 1967-2012 IEEE.

  18. Statistics of α-μ Random Variables and Their Applications inWireless Multihop Relaying and Multiple Scattering Channels

    Wang, Kezhi; Wang, Tian; Chen, Yunfei; Alouini, Mohamed-Slim

    2015-01-01

    Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-To-interference ratio (SIR) in a multiple scattering system with interference. © 1967-2012 IEEE.

  19. WKB approach to evaluate series of Mathieu functions in scattering problems

    Hubert, Maxime; Dubertrand, Remy

    2017-01-01

    The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when the wavelength is comparable to the obstacle size, when the most standard approximations fail. The approximations of the radial (or modified) Mathieu functions using WKB method are shown to be especially efficient, in order to precisely evaluate series of suc...

  20. Towards a Resolution of the Proton Form Factor Problem: New Electron and Positron Scattering Data

    Adikaram, D.; Rimal, D.; Weinstein, L. B.; Raue, B.; Khetarpal, P.; Bennett, R. P.; Arrington, J.; Brooks, W. K.; Adhikari, K. P.; Afanasev, A. V.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Avakian, H.; Ball, J.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Burkert, V. D.; Carman, D. S.; Careccia, S.; Celentano, A.; Chandavar, S.; Charles, G.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Dodge, G. E.; Dupre, R.; Egiyan, H.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Eugenio, P.; Fedotov, G.; Fegan, S.; Filippi, A.; Fleming, J. A.; Fradi, A.; Garillon, B.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Goetz, J. T.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guegan, B.; Guidal, M.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Holtrop, M.; Hughes, S. M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jiang, H.; Jo, H. S.; Joo, K.; Joosten, S.; Kalantarians, N.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Livingston, K.; Lu, H. Y.; MacGregor, I. J. D.; Markov, N.; Mattione, P.; Mayer, M.; McKinnon, B.; Mestayer, M. D.; Meyer, C. A.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moody, C. I.; Moutarde, H.; Movsisyan, A.; Camacho, C. Munoz; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Osipenko, M.; Ostrovidov, A. I.; Park, K.; Pasyuk, E.; Peña, C.; Pisano, S.; Pogorelko, O.; Price, J. W.; Procureur, S.; Prok, Y.; Protopopescu, D.; Puckett, A. J. R.; Ripani, M.; Rizzo, A.; Rosner, G.; Rossi, P.; Roy, P.; Sabatié, F.; Salgado, C.; Schott, D.; Schumacher, R. A.; Seder, E.; Sharabian, Y. G.; Simonyan, A.; Skorodumina, I.; Smith, E. S.; Smith, G. D.; Sober, D. I.; Sokhan, D.; Sparveris, N.; Stepanyan, S.; Stoler, P.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tian, Ye; Trivedi, A.; Ungaro, M.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Wei, X.; Wood, M. H.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.; CLAS Collaboration

    2015-02-01

    There is a significant discrepancy between the values of the proton electric form factor, GEp, extracted using unpolarized and polarized electron scattering. Calculations predict that small two-photon exchange (TPE) contributions can significantly affect the extraction of GEp from the unpolarized electron-proton cross sections. We determined the TPE contribution by measuring the ratio of positron-proton to electron-proton elastic scattering cross sections using a simultaneous, tertiary electron-positron beam incident on a liquid hydrogen target and detecting the scattered particles in the Jefferson Lab CLAS detector. This novel technique allowed us to cover a wide range in virtual photon polarization (ɛ ) and momentum transfer (Q2) simultaneously, as well as to cancel luminosity-related systematic errors. The cross section ratio increases with decreasing ɛ at Q2=1.45 GeV2 . This measurement is consistent with the size of the form factor discrepancy at Q2≈1.75 GeV2 and with hadronic calculations including nucleon and Δ intermediate states, which have been shown to resolve the discrepancy up to 2 - 3 GeV2 .

  1. Fluorescence lifetime spectroscopy in multiple-scattering environments: an application to biotechnology

    Cerussi, Albert E.; Gratton, Enrico; Fantini, Sergio

    1999-07-01

    Over the past few years, there has been significant research activity devoted to the application of fluorescence spectroscopy to strongly scattering media, where photons propagate diffusely. Much of this activity focused on fluorescence as a source of contrast enhancement in optical tomography. Our efforts have emphasized the quantitative recovery of fluorescence parameters for spectroscopy. Using a frequency-domain diffusion-based model, we have successfully recovered the lifetime, the absolute quantum yield, the fluorophore concentration, and the emission spectrum of the fluorophore, as well as the absorption and the reduced scattering coefficients at the emission wavelength of the medium in different measurements. In this contribution, we present a sensitive monitor of the binding between ethidium bromide and bovine cells in fresh milk. The spectroscopic contrast was the approximately tenfold increase in the ethidium bromide lifetime upon binding to DNA. The measurement clearly demonstrated that we could quantitatively measure the density of cells in the milk, which is an application vital to the tremendous economic burden of bovine subclinical mastitis detection. Furthermore, we may in principle use the spirit of this technique as a quantitative monitor of the binding of fluorescent drugs inside tissues. This is a first step towards lifetime spectroscopy in tissues.

  2. Studies on laser beam propagation and stimulated scattering in multiple beam experiments

    Labaune, C.; Lewis, K.; Bandulet, H.; Lewis, K.; Depierreux, S.; Huller, S.; Masson-Laborde, P.E.; Pesme, D.; Riazuelo, G.

    2006-01-01

    The propagation and stimulated scattering of intense laser beams interacting with underdense plasmas are two important issues for inertial confinement fusion (ICF). The purpose of this work was to perform experiments under well-controlled interaction conditions and confront them with numerical simulations to test the physics included in the codes. Experimental diagnostics include time and space resolved images of incident and SBS light and of SBS-ion acoustic activity. New numerical diagnostics, including similar constraints as the experimental ones and the treatment of the propagation of the light between the emitting area and the detectors, have been developed. Particular care was put to include realistic plasma density and velocity profiles, as well as laser pulse shape in the simulations. In the experiments presented in this paper, the interaction beam was used with a random phase plate (RPP) to produce a statistical distribution of speckles in the focal volume. Stimulated Brillouin Scattering (SBS) was described using a decomposition of the spatial scales which provides a predictive modeling of SBS in an expanding mm-scale plasma. Spatial and temporal behavior of the SBS-ion acoustic waves was found to be in good agreement with the experimental ones for two laser intensities. (authors)

  3. Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods

    Capolei, Andrea; Jørgensen, John Bagterp

    2012-01-01

    of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent...... algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution...... discontinuities on each shooting interval are present. The ESDIRK methods are implemented using an inexact Newton method that reuses the factorization of the iteration matrix for the integration as well as the sensitivity computation. Numerical experiments are provided to demonstrate the algorithm....

  4. Finding Multiple Optimal Solutions to Optimal Load Distribution Problem in Hydropower Plant

    Xinhao Jiang

    2012-05-01

    Full Text Available Optimal load distribution (OLD among generator units of a hydropower plant is a vital task for hydropower generation scheduling and management. Traditional optimization methods for solving this problem focus on finding a single optimal solution. However, many practical constraints on hydropower plant operation are very difficult, if not impossible, to be modeled, and the optimal solution found by those models might be of limited practical uses. This motivates us to find multiple optimal solutions to the OLD problem, which can provide more flexible choices for decision-making. Based on a special dynamic programming model, we use a modified shortest path algorithm to produce multiple solutions to the problem. It is shown that multiple optimal solutions exist for the case study of China’s Geheyan hydropower plant, and they are valuable for assessing the stability of generator units, showing the potential of reducing occurrence times of units across vibration areas.

  5. A Multiple Period Problem in Distributed Energy Management Systems Considering CO2 Emissions

    Muroda, Yuki; Miyamoto, Toshiyuki; Mori, Kazuyuki; Kitamura, Shoichi; Yamamoto, Takaya

    Consider a special district (group) which is composed of multiple companies (agents), and where each agent responds to an energy demand and has a CO2 emission allowance imposed. A distributed energy management system (DEMS) optimizes energy consumption of a group through energy trading in the group. In this paper, we extended the energy distribution decision and optimal planning problem in DEMSs from a single period problem to a multiple periods one. The extension enabled us to consider more realistic constraints such as demand patterns, the start-up cost, and minimum running/outage times of equipment. At first, we extended the market-oriented programming (MOP) method for deciding energy distribution to the multiple periods problem. The bidding strategy of each agent is formulated by a 0-1 mixed non-linear programming problem. Secondly, we proposed decomposing the problem into a set of single period problems in order to solve it faster. In order to decompose the problem, we proposed a CO2 emission allowance distribution method, called an EP method. We confirmed that the proposed method was able to produce solutions whose group costs were close to lower-bound group costs by computational experiments. In addition, we verified that reduction in computational time was achieved without losing the quality of solutions by using the EP method.

  6. Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

    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.

  7. Continuity of the direct and inverse problems in one-dimensional scattering theory and numerical solution of the inverse problem

    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

  8. The nucleon axial mass and the MiniBooNE quasielastic neutrino-nucleus scattering problem

    Nieves, J.; Ruiz Simo, I.; Vicente Vacas, M.J.

    2012-01-01

    The charged-current double differential neutrino cross section, measured by the MiniBooNE Collaboration, has been analyzed using a microscopical model that accounts for, among other nuclear effects, long range nuclear (RPA) correlations and multinucleon scattering. We find that MiniBooNE data are fully compatible with the world average of the nucleon axial mass in contrast with several previous analyses which have suggested an anomalously large value. We also discuss the reliability of the algorithm used to estimate the neutrino energy.

  9. Regularization methods for ill-posed problems in multiple Hilbert scales

    Mazzieri, Gisela L; Spies, Ruben D

    2012-01-01

    Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed. (paper)

  10. Localization and Poincaré catastrophe in the problem of a photon scattering on a pair of Rayleigh particles

    Maksimenko, V. V.; Zagaynov, V. A.; Agranovski, I. E.

    2013-11-01

    It is shown that complexities in a problem of elastic scattering of a photon on a pair of Rayleigh particles (two small metallic spheres) are similar to the complexities of the classic problem of three bodies in celestial mechanics. In the latter problem, as is well known, the phase trajectory of a system becomes a nonanalytical function of its variables. In our problem, the trajectory of a virtual photon at some frequency could be considered such as the well-known Antoine set (Antoine's necklace) or a chain with interlaced sections having zero topological dimension and fractal structure. Such a virtual “zero-dimensional” photon could be localized between the particles of the pair. The topology suppresses the photon's exit to the real world with dimensional equal-to-or-greater-than units. The physical reason for this type of photon localization is related to the “mechanical rigidity” of interlaced sections of the photon trajectory due to a singularity of energy density along these sections. Within the approximations used in this paper, the effect is possible if the frequency of the incident radiation is equal to double the frequency of the dipole surface plasmon in an isolated particle, which is the only character frequency in the problem. This condition and transformation of the photon trajectory to the zero-dimensional Antoine set reminds of some of the simplest variants of Poincaré's catastrophe in the dynamics of some nonintegrable systems. The influence of the localization on elastic light scattering by the pair is investigated.

  11. Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming

    Rauff Lind Christensen, Tue; Klose, Andreas; Andersen, Kim Allan

    important aspects of supplier selection, an important application of the SSFCTP, this does not reflect the real life situation. First, transportation costs faced by many companies are in fact piecewise linear. Secondly, when suppliers offer discounts, either incremental or all-unit discounts, such savings......The Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem (SSFCMCTP) is a problem with versatile applications. This problem is a generalization of the Single-Sink, Fixed-Charge Transportation Problem (SSFCTP), which has a fixed-charge, linear cost structure. However, in at least two...... are neglected in the SSFCTP. The SSFCMCTP overcome this problem by incorporating a staircase cost structure in the cost function instead of the usual one used in SSFCTP. We present a dynamic programming algorithm for the resulting problem. To enhance the performance of the generic algorithm a number...

  12. Solving Minimal Covering Location Problems with Single and Multiple Node Coverage

    Darko DRAKULIĆ

    2016-12-01

    Full Text Available Location science represents a very attractiveresearch field in combinatorial optimization and it is in expansion in last five decades. The main objective of location problems is determining the best position for facilities in a given set of nodes.Location science includes techniques for modelling problemsand methods for solving them. This paper presents results of solving two types of minimal covering location problems, with single and multiple node coverage, by using CPLEX optimizer and Particle Swarm Optimization method.

  13. The Relationship Between Problem Size and Fixation Patterns During Addition, Subtraction, Multiplication, and Division

    Evan T. Curtis

    2016-08-01

    Full Text Available Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8 and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6. Participants (N = 109 solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

  14. Step by Step: Biology Undergraduates' Problem-Solving Procedures during Multiple-Choice Assessment.

    Prevost, Luanna B; Lemons, Paula P

    2016-01-01

    This study uses the theoretical framework of domain-specific problem solving to explore the procedures students use to solve multiple-choice problems about biology concepts. We designed several multiple-choice problems and administered them on four exams. We trained students to produce written descriptions of how they solved the problem, and this allowed us to systematically investigate their problem-solving procedures. We identified a range of procedures and organized them as domain general, domain specific, or hybrid. We also identified domain-general and domain-specific errors made by students during problem solving. We found that students use domain-general and hybrid procedures more frequently when solving lower-order problems than higher-order problems, while they use domain-specific procedures more frequently when solving higher-order problems. Additionally, the more domain-specific procedures students used, the higher the likelihood that they would answer the problem correctly, up to five procedures. However, if students used just one domain-general procedure, they were as likely to answer the problem correctly as if they had used two to five domain-general procedures. Our findings provide a categorization scheme and framework for additional research on biology problem solving and suggest several important implications for researchers and instructors. © 2016 L. B. Prevost and P. P. Lemons. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  15. Nonlinear coupled mode approach for modeling counterpropagating solitons in the presence of disorder-induced multiple scattering in photonic crystal waveguides

    Mann, Nishan; Hughes, Stephen

    2018-02-01

    We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.

  16. Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

    Zhi-Wei Lv

    2010-06-01

    Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

  17. Exact Solutions to the Double Travelling Salesman Problem with Multiple Stacks

    Petersen, Hanne L.; Archetti, Claudia; Speranza, M. Grazia

    2010-01-01

    In this paper we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region...

  18. Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

    Zhao, Ying; Shi, Luoyi

    2017-01-01

    This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

  19. Emotional and Behavioural Problems in Children with Visual Impairment, Intellectual and Multiple Disabilities

    Alimovic, S.

    2013-01-01

    Background: Children with multiple impairments have more complex developmental problems than children with a single impairment. Method: We compared children, aged 4 to 11 years, with intellectual disability (ID) and visual impairment to children with single ID, single visual impairment and typical development on "Child Behavior Check…

  20. Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols

    Wang Hai-Hua; Sun Xian-Ming

    2012-01-01

    The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing models. The internal mixing model is modeled with a two-layered sphere (water cloud droplets containing black carbon (BC) inclusions), and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 μm by using the Lorenz—Mie theory. The external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets externally. The multiple scattering characteristics are computed by using the Monte Carlo method. The results show that when the size of the BC aerosol is small, the reflection intensity of the internal mixing model is bigger than that of the external mixing model. However, if the size of the BC aerosol is big, the absorption of the internal mixing model will be larger than that of the external mixing model. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)