Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.     

Inverse scattering problem in the relativistic quasiclassical approximation

We apply the quasipotential approach of quantum field theory to solve the inverse scattering problem in the relativistic quasiclassical approximation. We obtain expressions for reconstructing the quasipotential from the phase shifts and consider both nonrelativistic and ultrarelativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No-5, pp. 11–17, May, 1987.The authors are deeply grateful to Yu. S. Vernov and N. B. Skachkov for their interest and helpful discussion of the results.     

Reconstruction of the characteristics of a light-scattering layer from its reflectance and transmittance: The neural network method

The problem of reconstructing the probability of photon survival, the optical layer thickness, and the parameter of asymmetry of the scattering indicatrix of an elementary volume from the dependence of the reflectance and the transmittance on the angle of incidence of radiation onto a layer of a medium with Fresnel reflection from the boundaries is considered. To solve this problem, a method based on the use of correlation neural networks is proposed. For training and control of the operation of neural networks, the reflectance and the transmittance of the layer calculated within the framework of the radiation transfer theory were used. For the simulation of the scattering characteristics of an elementary volume, the Mie theory was used. Estimates of errors in the reconstruction of the characteristics of the medium were performed.     

X-ray diffraction scattering and determination of the structural parameters of a film with a variable strain gradient

Characteristics of the x-ray diffraction field in structures with a variable strain gradient are analyzed using a model with an exponential profile. It is shown that the problem of reconstructing the structural parameters of the strained layer from the angular positions of the principal maximum and the oscillations is generally multivalued even when the strain varies monotonically over depth. Conditions are determined for which this problem can be solved. An analogy is identified with the results of an approach to determine the parameters of the strained layer based on using the integral characteristics of the diffraction reflection curve. Zh. Tekh. Fiz. 69, 67–70 (June 1999)     

Reconstruction of the stiffness of an inhomogeneous elastic plate

The paper discusses the problem of reconstructing the inhomogeneous cylindrical, symmetric stiffness distribution of a round plate using information on the bias function for established oscillations, which is measured at a certain point. A solution is constructed to the direct problem using the Galerkin method and to the inverse problem of reconstructing the stiffness using an iterative approach based on the regularized linearization method. We present the results of calculation experiments on reconstructing different types of functions that show the efficiency of the proposed approach and make it possible to estimate changes in stiffness.     

An inverse algorithm for reconstructing the acoustic parameters of layered medium

I.IntroductionThcinvcrsescattcringprob1cmisbasicinarcassuchasradar,sonar,geophysica1explora-honandnondestructivctesting.Whenthescatteringobjectisaconstitutiveparametersvaryinacontinuousmannerandtheinvcrseproblcmistodctcrmineoneormoreoftheseparametcrsfromtheobserveddata.Muchofthcpreviousworkonthisproblcmforthecaseofp1anewaveatnormalincidencchasconsistcdofderivingaSchr6dingerequationfromthebasicacousticandstrcss-straincquations,andthenreconstruchngthepotentialappearinginthisequationbyusingtheGe…     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Electromagnetic-Wave Diffraction by a Grating with a Chiral Layer

We consider the vector problem of diffraction of an obliquely incident, elliptically polarized wave by a one-dimensional periodic grating located in a layered medium with a chiral layer. The use of analytical regularization based on the Riemann-Hilbert problem allows us to obtain a rigorous and efficient method for solving such diffraction problems. The performed numerical study reveals certain features of diffraction in the presence of a chiral medium.     

Time series-based bifurcation diagram reconstruction

We consider the problem of reconstructing bifurcation diagrams (BDs) of maps using time series. This study goes along the same line of ideas presented by Tokunaga et al. [Physica D 79 (1994) 348] and Tokuda et al. [Physica D 95 (1996) 380]. The aim is to reconstruct the BD of a dynamical system without the knowledge of its functional form and its dependence on the parameters. Instead, time series at different parameter values, assumed to be available, are used. A three-layer fully-connected neural network is employed in the approximation of the map. The task of the network is to learn the dynamics of the system as function of the parameters from the available time series. We determine a class of maps for which one can always find a linear subspace in the weight space of the network where the network’s bifurcation structure is qualitatively the same as the bifurcation structure of the map. We discuss a scheme in locating this subspace using the time series. We further discuss how to recognize time series generated by this class of maps. Finally, we propose an algorithm in reconstructing the BDs of this class of maps using predictor functions obtained by neural network. This algorithm is flexible so that other classes of predictors, apart from neural networks, can be used in the reconstruction.     

Coherent marine seismoacoustics: New approaches to reconstructing bottom layer structures in shelf water areas

Results from the theoretical development and experimental study of the coherent seismoacoustic sounding of the sea floor under natural conditions are discussed. Ways of solving the inverse problem of estimating the geoacoustic parameters of the bottom layer by layer are proposed, and their effectiveness and robustness are analyzed numerically. Practical means of seismoacoustic profiling and reconstructing the parameters of individual layers at the sea floors of the shallow water areas using coherent hydroacoustic radiating elements of original design are demonstrated.     

Identifying the inhomogeneous properties of an orthotropic elastic layer

A scheme is proposed for reconstructing inhomogeneously thick elasticity modules of an orthotropic layer from acoustic sounding data. The problem of reconstruction has been reduced to stepwise reconstruction of the functions characterizing the elasticity modules, based on iteration regularization and A.N. Tikhonov’s regularization method, which utilize analysis of the averaged characteristics. A computer experiment is performed for different inhomogeneity layers, the effective frequency sounding regions for identification are revealed, and various aspects of numerical realization are discussed.     

Acoustic-Gravity Waves in the Atmosphere with a Piecewise-Linear Temperature Profile

We consider the problem of propagation of acoustic-gravity waves in the atmosphere with a constant temperature gradient in the near-surface layer. The assumption of linear temperature dependence on height allowed us to reduce the wave equation to the hypergeometric form, regardless of the compressibility of the medium. The solution of this equation is represented in terms of degenerate hypergeometric functions. To analyze the obtained solution, we consider a two-layer model of a half-bounded atmosphere with a height-independent background temperature in the upper layer. The results are studied in detail under the approximation of an incompressible medium. For the model specified above, we find analytical expressions for the perturbation fields and obtain a characteristic equation whose solution allows us to calculate wave dispersion characteristics at frequencies close to the Brunt-Väisälä frequency for large horizontal scales as compared to the layer thickness.     

Ambiguity of the Reconstruction of Plasma Frequency Profiles from a Given Height-Frequency Characteristic and Their Discernibility for Oblique Propagation of HF Radio Waves in an Isotropic Ionosphere

We specify the formulation of the problem of reconstructing the plasma frequency height distribution from a given height-frequency characteristic (HFC) for a spherically symmetric isotropic ionosphere. We propose a numerical algorithm for solving the problem of correctly processing the region of near-critical frequencies of ionospheric layers. On this basis, we study the discernibility of plasma frequency profiles (PFPs) satisfying a given HFC when the properties of an obliquely propagating HF signal are analyzed.     

A new method for solving the problem of diffraction by a compact obstacle in a layered medium

We propose a new method for solving the two-dimensional problem of diffraction by a cylindrical body in a layered medium. Unlike the traditional methods, the boundary-value problem is reduced to solving the integral equation for the scattering pattern of the body. As an illustration of this method, we consider the problem of scattering by a round cylinder located in a dielectric layer between two homogeneous half-spaces. Technical University of Communication and Information Science, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 874–888, July, 1998.     

Layer-edge conditions for multislab atmospheric radiative transfer problems

We derive nonstandard layer-edge conditions for efficient solution of multislab atmospheric radiative transfer problems. We begin by defining a local radiative transfer problem on the lowermost layer of a multislab model atmosphere and we consider a standard discrete ordinates version of this local problem. We then make use of a recently developed computational method in order to derive layer-edge conditions involving incident, reflected and transmitted radiation. These layer-edge conditions for the lowermost layer are given in terms of inherent optical properties of the layer, the solar zenith angle and the quadrature set used in the discrete ordinates approach. They can be used to increase the efficiency of our computational method in solving practical problems in atmospheric radiative transfer. Moreover, they are amenable to incorporation into other discrete ordinates methods. To illustrate, we report numerical results for two atmospheric model problems.     

Motion predicted online dynamic MRI reconstruction from partially sampled k-space data

In this work we address the problem of reconstructing dynamic MRI sequences in an online fashion, i.e. reconstructing the current frame given that the previous frames have been already reconstructed. The reconstruction consists of a prediction and a correction step. The prediction step is based on an Auto-Regressive AR(1) model. Assuming that the prediction is good, the difference between the predicted frame and the actual frame (to be reconstructed) will be sparse. In the correction step, the difference between the predicted frame and the actual frame is estimated from partially sampled K-space data via a sparsity promoting least squares minimization problem. We have compared the proposed method with state-of-the-art methods in online dynamic MRI reconstruction. The experiments have been carried out on 2D and 3D Dynamic Contrast Enhanced (DCE) MRI datasets. Results show that our method yields the least reconstruction error.     

Using short curved vertical arrays in ocean acoustic tomography

We consider the possibility of reconstructing the ocean mode structure based on measurements with short (not covering the entire ocean waveguide) arrays curved in an unknown way by ocean currents, which corresponds to the conditions of a real experiment. We have developed an algorithm for estimating the arrival times of various mode signals by solving a system of linear equations. The mode reconstruction accuracy as a function of the array length and profile curvature is investigated. The cases of using both the ocean noise field and deterministic signals as a sound source are considered. Comparison with the commonly used mode filtering method is made.     

The interpretation of x-ray interferometer moiré patterns

In most experiments the x-ray-interferometer moire bands take the form of curves which complicate the problem of reconstructing the distribution pattern of deformations in single-crystal blocks giving rise to such moirés. In the paper we consider the regularities in the variation of the interplane distances and relative rotations of these planes for which moiré lines close in form to the experimental ones are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 8–12, April, 1984.     

Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

The paper focuses on the determination of statistical characteristics of photon distributions in a semi-infinite turbid medium, specifically the photon average trajectory and the root-mean-square deviation of photons from the average trajectory, with an approach based on the diffusion approximation to the radiative transfer equation. We show that the Dirichlet and Robin boundary conditions used for this purpose give close results. We derive exact analytical expressions for the case of the Dirichlet boundary condition. To demonstrate the practical value of our results we consider approximate solution of the inverse problem of time-domain diffuse optical tomography with the flat layer transmission geometry. The problem is solved with the method of photon average trajectories which are constructed with analytical expressions derived for a semi-infinite medium.     

Thermonuclear Instabilities and Fueling in a Tokamak Reactor

The problem of fueling is of primary importance in the conceptual design of a fusion reactor. We consider a possible mechanism of supplying fresh fuel from a cold-plasma layer at the surface of the plasma. The existence of an energetic component of ions, viz, the alpha particles, may excite unstable collective oscillations of the plasma (called the thermonuclear instabilities). Such instabilities could give rise to microscopic processes which, in principle, would allow influx of fresh fuel while helping efflux of reaction products. A three-regime model is used to understand the nature of such fueling mechanisms and the possibility of using a cold-plasma layer as a surface fueling source.