scholarly journals Simulation study for cross-sectional absorption distribution in turbid medium using spatially resolved backscattered light with lateral scanning and one-dimensional solution of nonlinear inverse problem

2021 ◽  
Author(s):  
Kazuhiro Nishida ◽  
Yuji Kato ◽  
Nobuki Kudo ◽  
Koichi Shimizu
Keyword(s):  
Inverse Problem ◽  
Simulation Study ◽  
Turbid Medium ◽  
Nonlinear Inverse Problem ◽  
Dimensional Solution ◽  
Cross Sectional ◽  
One Dimensional ◽  
Spatially Resolved

scholarly journals Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem

2021 ◽  
Vol 2092 (1) ◽  
pp. 012022
Author(s):  
Sergey I. Kabanikhin ◽  
Nikita S. Novikov ◽  
Maxim A. Shishlenin
Keyword(s):  
Inverse Problem ◽  
Integral Equations ◽  
Nonlinear Inverse Problem ◽  
Inverse Coefficient Problem ◽  
One Dimensional ◽  
The One ◽  
Linear Integral ◽  
Fast Inversion ◽  
Linear Integral Equations ◽  
Inverse Coefficient

Abstract In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave’s velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.

An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation

2014 ◽  
Vol 6 (4) ◽  
pp. 515-522
Author(s):  
Nobuyuki Higashimori
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Turbid Medium ◽  
Radiative Transport ◽  
One Dimensional ◽  
Propagation Of Light ◽  
Radiative Transport Equation

AbstractWe consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.

scholarly journals Quantitative imaging and automated fuel pin identification for passive gamma emission tomography

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ming Fang ◽  
Yoann Altmann ◽  
Daniele Della Latta ◽  
Massimiliano Salvatori ◽  
Angela Di Fulvio
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Image Resolution ◽  
Emission Tomography ◽  
Nuclear Safeguards ◽  
Activity Levels ◽  
Spent Fuel ◽  
Gamma Emission ◽  
Cross Sectional ◽  
Fuel Rods

AbstractCompliance of member States to the Treaty on the Non-Proliferation of Nuclear Weapons is monitored through nuclear safeguards. The Passive Gamma Emission Tomography (PGET) system is a novel instrument developed within the framework of the International Atomic Energy Agency (IAEA) project JNT 1510, which included the European Commission, Finland, Hungary and Sweden. The PGET is used for the verification of spent nuclear fuel stored in water pools. Advanced image reconstruction techniques are crucial for obtaining high-quality cross-sectional images of the spent-fuel bundle to allow inspectors of the IAEA to monitor nuclear material and promptly identify its diversion. In this work, we have developed a software suite to accurately reconstruct the spent-fuel cross sectional image, automatically identify present fuel rods, and estimate their activity. Unique image reconstruction challenges are posed by the measurement of spent fuel, due to its high activity and the self-attenuation. While the former is mitigated by detector physical collimation, we implemented a linear forward model to model the detector responses to the fuel rods inside the PGET, to account for the latter. The image reconstruction is performed by solving a regularized linear inverse problem using the fast-iterative shrinkage-thresholding algorithm. We have also implemented the traditional filtered back projection (FBP) method based on the inverse Radon transform for comparison and applied both methods to reconstruct images of simulated mockup fuel assemblies. Higher image resolution and fewer reconstruction artifacts were obtained with the inverse-problem approach, with the mean-square-error reduced by 50%, and the structural-similarity improved by 200%. We then used a convolutional neural network (CNN) to automatically identify the bundle type and extract the pin locations from the images; the estimated activity levels finally being compared with the ground truth. The proposed computational methods accurately estimated the activity levels of the present pins, with an associated uncertainty of approximately 5%.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

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