Search results for: inverse scattering theory

Authors: Abdon Choque-Rivero

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The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: S. S. Sathiesh

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The aim of this project is to study the radiation mechanism synchrotron and Inverse Compton scattering. Theoretically, we discussed spectral energy distribution for both. Programming is done for plotting the graph of Power-law spectrum for synchrotron Radiation using fortran90. The importance of power law spectrum was discussed and studied to infer its physical parameters from the model fitting. We also discussed how to infer the physical parameters from the theoretically drawn graph, we have seen how one can infer B (magnetic field of the source), γ min, γ max, spectral indices (p1, p2) while fitting the curve to the observed data.

Keywords: blazars/quasars, beaming, synchrotron radiation, Synchrotron Self Compton, inverse Compton scattering, mrk421

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Authors: A.R. Eskandari, M.R. Eskandari

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A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.

Keywords: inverse scattering, microwave imaging, two-dimensional objects, Linear Sampling Method (LSM)

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Muhammad Hassan Khalil, Xu Jiadong

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Early detection through screening is the best tool short of a perfect treatment against the malignant tumor inside the breast of a woman. By detecting cancer in its early stages, it can be recognized and treated before it has the opportunity to spread and change into potentially dangerous. Microwave tomography is a new imaging method based on contrast in dielectric properties of materials. The mathematical theory of microwave tomography involves solving an inverse problem for Maxwell’s equations. In this paper, we present designed antenna for breast cancer detection, which will use in microwave tomography configuration.

Keywords: microwave imaging, inverse scattering, breast cancer, malignant tumor detection

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

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This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: kinematics, degree of freedom, optimization, robot manipulator

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Mahasen M. Abdel Mageed, H. S. Zaghloul

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Annihilations, phase shifts, scattering lengths, and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wavefunction is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical, and experimental results. Especially, the estimated positive scattering length supports the possibility of positron-magnesium bound state system that was confirmed in previous experimental and theoretical work.

Keywords: bound wavefunction, positron annihilation, scattering phase shift, scattering length

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Authors: Prerana Sharma

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Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.

Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

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We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: Sumei Cai, Hong Li

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Either during water or gas injection into reservoir, in order to understand the areal flow pressure distribution underground, associated bounding deformation is prevalently monitored by ground or downhole tiltmeters. In this paper, an inverse solution to elastic response of far field displacements induced by reservoir pressure change due to flow injection was studied. Furthermore, the fundamental theory on inverse solution to elastic problem as well as its spatial smoothing approach is presented. Taking advantage of source code development based on Boundary Element Method, numerical analysis on the monitoring data of ground surface displacements to further understand the behavior of reservoir process was developed. Numerical examples were also conducted to verify the effectiveness.

Keywords: remote displacement, inverse problem, boundary element method, BEM, reservoir process

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Jaehyug Lee, Tae-Ho Song

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Vacuum insulation panel (VIP) can achieve very low thermal conductivity by evacuating its inner space. Heat transfer in the core materials of highly-evacuated VIP occurs by conduction through the solid structure and radiation through the pore. The effect of various scattering modes in combined conduction-radiation in VIP is investigated through numerical analysis. The discrete ordinates interpolation method (DOIM) incorporated with the commercial code FLUENT® is employed. It is found that backward scattering is more effective in reducing the total heat transfer while isotropic scattering is almost identical with pure absorbing/emitting case of the same optical thickness. For a purely scattering medium, the results agree well with additive solution with diffusion approximation, while a modified term is added in the effect of optical thickness to backward scattering is employed. For other scattering phase functions, it is also confirmed that backwardly scattering phase function gives a lower effective thermal conductivity. Thus, the materials with backward scattering properties, with radiation shields are desirable to lower the thermal conductivity of VIPs.

Keywords: combined conduction and radiation, discrete ordinates interpolation method, scattering phase function, vacuum insulation panel

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Authors: Yassine Ait-El-Aoud, Michael Okomoto, Andrew M. Luce, Alkim Akyurtlu, Richard M. Osgood III

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Light scattering of metal nanoparticles (NPs) has a unique, and technologically important effect on enhancing light absorption in substrates because most of the light scatters into the substrate near the localized plasmon resonance of the NPs. The optical response, such as the resonant frequency and forward- and backward-scattering, can be tuned to trap light over a certain spectral region by adjusting the nanoparticle material size, shape, aggregation state, Metallic vs. insulating state, as well as local environmental conditions. In this work, we examined the light scattering characteristics of ordered arrays of metal nanoparticles and the light trapping, in order to enhance absorption, by measuring the forward- and backward-scattering using a UV/VIS/NIR spectrophotometer. Samples were fabricated using the popular self-assembly process method: dip coating, combined with nanosphere lithography.

Keywords: dip coating, light-scattering, metal nanoparticles, nanosphere lithography

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Authors: Sergey Svita, Valeriy Astapenko

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The presentation is devoted to the theoretical analysis of ultrashort electromagnetic pulses (USP) scattering on metallic nanospheres in a dielectric medium in the vicinity of surface plasmon resonance due to excitation of dipole and quadrupole surface plasmons.

Keywords: surface plasmon, scattering, metallic nanosphere

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Ionel D. Craiu, Mihai Nedelcu

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Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: damage detection, generalized beam theory, inverse finite element method, shape sensing

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Authors: Hidouri Sami, Aguili Taoufik

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We consider fast and accurate solutions of scattering problems by large perfectly conducting objects (PEC) formulated by an optimization of the Method of Auxiliary Sources (MAS). We present various techniques used to reduce the total computational cost of the scattering problem. The first technique is based on replacing the object by an array of finite number of small (PEC) object with the same shape. The second solution reduces the problem on considering only the half of the object.These two solutions are compared to results from the reference bibliography.

Keywords: method of auxiliary sources, scattering, large object, RCS, computational resources

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Authors: A. Elsariti, T. Evans

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An understanding of the interaction between acoustic waves and cancellous bone is needed in order to realize the full clinical potential of ultrasonic bone measurements. Scattering is likely to be of central importance but has received little attention to date. Few theoretical approaches have been described to explain scattering of ultrasound from bone. In this study, a scattering model based on velocity and density fluctuations in a binary mixture (marrow fat and cortical matrix) was used to estimate the ultrasonic attenuation in cancellous bone as a function of volume fraction. Predicted attenuation and backscatter coefficient were obtained for a range of porosities and scatterer size. At 600 kHZ and for different scatterer size the effect of velocity and density fluctuations in the predicted attenuation was approximately 60% higher than velocity fluctuations.

Keywords: ultrasound scattering, sound speed, density fluctuations, attenuation coefficient

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Authors: Mor Diama L. O., Matthieu Davy, Laurent Ferro-Famil

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In this article, inverse synthetic aperture radar (ISAR) is combined with compressive imaging techniques in order to perform 3D interferometric imaging. Interferometric ISAR (InISAR) imaging relies on a two-dimensional antenna array providing diversities in the elevation and azimuth directions. However, the signals measured over several antennas must be acquired by coherent receivers resulting in costly and complex hardware. This paper proposes to use a chaotic cavity as a compressive device to encode the signals arising from several antennas into a single output port. These signals are then reconstructed by solving an inverse problem. Our approach is demonstrated experimentally with a 3-elements L-shape array connected to a metallic compressive enclosure. The interferometric phases estimated from a unique broadband signal are used to jointly estimate the target’s effective rotation rate and the height of the dominant scattering centers of our target. Our experimental results show that the use of the compressive device does not adversely affect the performance of our imaging process. This study opens new perspectives to reduce the hardware complexity of high-resolution ISAR systems.

Keywords: interferometric imaging, inverse synthetic aperture radar, compressive device, computational imaging

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Authors: Tatiana A. Dolenko, Sergey A. Burikov, Alexander O. Efitorov, Sergey A. Dolenko

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In this study, a comparative analysis of the approaches associated with the use of neural network algorithms for effective solution of a complex inverse problem – the problem of identifying and determining the individual concentrations of inorganic salts in multicomponent aqueous solutions by the spectra of Raman scattering of light – is performed. It is shown that application of artificial neural networks provides the average accuracy of determination of concentration of each salt no worse than 0.025 M. The results of comparative analysis of input data compression methods are presented. It is demonstrated that use of uniform aggregation of input features allows decreasing the error of determination of individual concentrations of components by 16-18% on the average.

Keywords: inverse problems, multi-component solutions, neural networks, Raman spectroscopy

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: H. Duggal, G. Singh, G. Singh, A. Bhalla, S. Kumar, J. S. Shahi, D. Mehta

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The total differential cross section for scattering of the 5.895 keV photons by various polymers has been measured at scattering angle of 135o. The experimental measurements were carried out using the energy dispersive setup involving annular source of the 55Fe radioisotope and a low energy germanium (LEGe) detector. The cross section values are measured for 20 polymer targets namely, Paraffin Wax, Polytetrafluoro ethylene (PTFE), Cellulose, Silicone oil, Polyvinyl alcohol (PVA), Polyvinyl purrolidone (PVP), Polymethyl methacrylate (PMMA), Kapton, Mylar, Chitosan, Polyvinyl chloride (PVC), Bakelite, Carbopol, Chlorobutyl rubber (CBR), Polyetylene glycol (PEG), Polysorbate-20, Nylon-6, Cetyl alcohol, Carboxyl methyl sodium cellulose and Sodium starch glucolate. The measurements were performed in vacuum so as to avoid scattering contribution due to air and strong absorption of low energy photons in the air column. In the present investigations, the geometrical factor and efficiency of the detector were determined by measuring the K x-rays emitted from the 22Ti and 23V targets excited by the Mn K x-rays in the same experimental set up. The measured scattering cross sections have been compared with the sum of theoretically calculated elastic and inelastic scattering cross sections. The theoretical elastic (Rayleigh) scattering cross sections based on the various form factor approximations, namely, non-relativistic form factor (NF), relativistic form factor (RF), modified form factor (MF), and MF with anomalous scattering factor (ASF) as well as the second order S-matrix formalisms, and the inelastic scattering differential cross sections based on the Klein-Nishina formula after including the inelastic scattering function (KN+ISF) have been calculated. The experimental results show fairly good agreement with theoretical cross sections.

Keywords: photon, polymers, elastic and inelastic, scattering cross sections

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Authors: Sh. Hamada

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The current work aims to study the rainbow like-structure observed in the elastic scattering of alpha particles on both ¹²C and ¹⁶O nuclei. We reanalyzed the experimental elastic scattering angular distributions data for α+¹²C and α+¹⁶O nuclear systems at different energies using both optical model and double folding potential of different interaction models such as: CDM3Y1, DDM3Y1, CDM3Y6 and BDM3Y1. Potential created by BDM3Y1 interaction model has the shallowest depth which reflects the necessity to use higher renormalization factor (N_r). Both optical model and double folding potential of different interaction models fairly reproduce the experimental data.

Keywords: density distribution, double folding, elastic scattering, nuclear rainbow, optical model

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Authors: Hongbin Yang, Mingxue Liao, Changwen Zheng, Mengyao Kong, Chaohui Liu

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Microfacet-based reflection models are widely used to model light reflections for rough surfaces. Microfacet models have become the standard surface material building block for describing specular components with varying roughness; and yet, while they possess many desirable properties as well as produce convincing results, their design ignores important sources of scattering, which can cause a significant loss of energy. Specifically, they only simulate the single scattering on the microfacets and ignore the subsequent interactions. As the roughness increases, the interaction will become more and more important. So a multiple-scattering microfacet model based on specular V-cavity is presented for this important open problem. However, it spends much unnecessary rendering time because of setting the same number of scatterings for different roughness surfaces. In this paper, we design a geometric attenuation term G to compute the BRDF (Bidirectional reflection distribution function) of multiple scattering of rough surfaces. Moreover, we consider determining the number of scattering by deterministic heuristics for different roughness surfaces. As a result, our model produces a similar appearance of the objects with the state of the art model with significantly improved rendering efficiency. Finally, we derive a multiple scattering BRDF based on the original microfacet framework.

Keywords: bidirectional reflection distribution function, BRDF, geometric attenuation term, multiple scattering, V-cavity model

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