Two-dimensional Inhomogeneous Media Research Articles

Research on recovering scattering obstacles in inhomogeneous medium based on Bayesian method

ABSTRACT In this paper, the problem of acoustic wave scattering by obstacles in the two-dimensional inhomogeneous medium is considered. When the refractive index is a binary function, a hybrid method for reconstructing multiple impenetrable obstacles is proposed. The obstacle number is predicted based on the measured far-field data by using the neural network method. And then, it is used as the prior information of Bayesian method, the shape and position parameters of multiple obstacles are reconstructed using Markov chain Monte Carlo algorithm. The results of numerical experiments show that this method can effectively reconstruct the number, shape and position of obstacles in the inhomogeneous medium.

Temporal evolution of sound pulse in shallow water under conditions of horizontal refraction. Vertical modes and space-time horizontal rays

As is known, to describe horizontal refraction in a shallow water waveguide, the “vertical modes and horizontal rays” approach (Burridge & Weinberg, 1974) is used, within which the two-dimensional eikonal equation for the modal amplitude includes the refractive index determined by the eigenvalues depending on the horizontal coordinates (x,y) and frequency (f). In other words, we have an effective two-dimensional inhomogeneous dispersive medium, to describe the propagation of signals in which, the authors propose to use the so-called space-time rays (Rytov, 1940, Connor & Felsen, 1974, Hillion, 1993) applied for the horizontal plane (STHR). The set of STHRs in a given situation is constructed for each mode. Within the framework of this approach, it is possible to obtain the evolution of the pulses of each mode from the solution of the nonstationary eikonal equation in the horizontal plane or from the corresponding Hamilton-Jacobi equations, obtained using non-local integral wave equation. Examples of constructing STHR in some typical situations (in particular in a wedge) are considered, some specific effects during signal propagation are considered, in particular, the so-called the pulse front tilt, previously discovered in laser optics (Bor & Rasz, 1985). Work was supported by ISF, grant 946/20.

Semiclassical theory for plasmons in two-dimensional inhomogeneous media

Semiclassical theory for plasmons in two-dimensional inhomogeneous media

Analytical study of SH wave scattering by a cylindrical cavity in the two-dimensional and approximately linear inhomogeneous medium

Based on the complex function method, shear horizontal wave scattering in the two-dimensional and approximately linear inhomogeneous medium is investigated analytically in this work. A new pair of transformation is proposed to normalize the governing equation of the two-dimensional inhomogeneous medium. Then wave fields and the corresponding stresses are expressed by complex variables. With the help of the boundary condition at the cavity, the undetermined coefficients are determined. By controlling the ratio of two inhomogeneous parameters, the medium can be modeled as two-dimensional inhomogeneous and approximately linear inhomogeneous. Finally, the parametric study presents that wave number and inhomogeneous parameters have significant influences on dynamic stress concentration factor around the cavity in different kinds of inhomogeneous media.

Numerical Simulation of Acoustic Waves Propagation in an “Atmosphere–Forestland–Ground” System

Under study is the problem of numerical simulation of acoustic waves propagation in a two-dimensional inhomogeneous medium represented by the “atmosphere–forestland–ground” model. A specific feature of the simulation is the introduction into the basic equations of acoustics of a linear damping function that characterizes the energy loss of the acoustic wave with respect to afforestation. The problem is considered of interaction between the acoustic waves incident at a given angle from the atmosphere to the “forestland–ground” boundary and the seismic waves arising in the ground. The issue of the forestland influence on the levels of acoustic and seismic waves is investigated. In particular, the impact of the friction coefficient on the attenuation rate of acoustic oscillations in the forestland is estimated. The algorithm and software are developed and implemented for calculating the acoustic pressure levels in various media, by using the wave equation for the atmosphere, Euler’s gas dynamics equations for the forestland, and the elasticity equation for the ground. The results of numerical experiments are presented as instantaneous images of the wave field.

Method for choosing the variable of integration on numerical construction of ray paths in inhomogeneous dielectric media

An algorithm for choosing the variable of integration providing a specified accuracy in each variable when solving the problem of electromagnetic-wave propagation in a two-dimensional inhomogeneous medium by the geometrical optics method is presented, and the accuracy of the algorithm is estimated.

Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

AbstractBased on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.

Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation

Simultaneous reconstruction of the radiative parameter distributions in participating media, based on the transient radiative transfer equation (TRTE), was investigated. The discrete ordinate method was employed to solve the direct TRTE for two-dimensional participating media. A multi-start iterative technique, based on the conjugate gradient (CG) method, was proposed to accelerate the convergence speed of the inverse procedure. The maximum a posteriori (MAP) estimation was used to overcome the retrieval difficulties resulting from the ill-posed nature of the inverse problem. The gradient of the objective function was obtained using adjoint differentiation. All the simulation results show that MAP combined with the multi-start iterative CG technique is effective in simultaneously reconstructing the distributions of absorption and scattering coefficients in two-dimensional inhomogeneous media, even with noisy data.

Modelling and analysis of the dynamic behavior of inhomogeneous continuum containing a circular inclusion

Based on the complex function theory, an universal approach of solving the dynamic stress concentration around a circular inclusion in two-dimensional (2D) inhomogeneous medium is presented. The inhomogeneous Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by using the general conformal transformation technique analytically. An inhomogeneity with the density varying as a smooth function of two spatial coordinates and the constant elastic modulus is established to verify the accuracy of analytical results. As a typical example, an exponential variation of the density is introduced for analyzing the dynamic stress concentration factor (DSCF) around the inclusion. Numerical results show the efficiency of the method and the effects of the medium inhomogeneity, reference wave number of the background medium, the reference wave number and shear modulus ratios between the background medium and inclusion.

Reciprocity relations in the problem of nonlinear conductivity of two-dimensional inhomogeneous systems

The symmetry transformation proposed by A.M. Dykhne is applied to a nonlinear problem of the conductivity of two-dimensional inhomogeneous media. A number of relations are obtained between the local and effective nonlinear characteristics of the original system and its reciprocal. Reciprocity relations for even partial moments of electric field strength of arbitrary order are established for two-component two-dimensional composites.

Efficient scalar and vectorial singular beam shaping using homogeneous anisotropic media

We propose and demonstrate a global and efficient approach for scalar and vectorial beam shaping based on the interaction of circularly polarized light with a single piece of homogeneous anisotropic medium. The main idea is to mimic the behavior of a two-dimensional inhomogeneous birefringent medium with a radial distribution of its optical axis. This is done by transforming an incident Gaussian beam into a conical nipple of light that further propagates along the optical axis of a c-cut uniaxial crystal.

Propagation of graphs in two-dimensional inhomogeneous media

We consider the propagation of a front in a two-dimensional striated medium. In the case of a front that can be written as a graph over the real line we are led to an Eikonal equation for the height function which contains a possibly discontinuous coefficient. We prove existence and uniqueness of a viscosity solution in the sense of Ishii. Furthermore, we obtain an O ( h ) -error bound for a monotone and consistent finite difference scheme. We conclude with some numerical tests.

Inversion of Resistivity and Permittivity Using Phase Induction Logging Data

AbstractAn inverse method is presented to estimate the permittivity and resistivity profile of formation in a two‐dimensional axisymmetric inhomogeneous medium, the measured data of phase induction logging are the phase difference and amplitude ratio of the two receiving coils. The initial value of formation geometrical parameter is taken by using phase difference and amplitude ratio logging curves. The inverse equation is derived from the logging response equation and the variation principle, the conjugate gradient (CG) method is used to solve this inverse equation. The simultaneous inversion of multi‐layer formation resistivity, permittivity and geometrical parameter is obtained, the numerical results show the validity of this method.

Simultaneous Inversion of Formation Resistivity and Geometric Boundary Location from Phase Induction Logging Data

In this paper, the inversion method is used to simultaneously reconstruct formation resistivity and boundary location per bed from the phase induction logging data. The inversion equation is obtained by applying the variation principal and the phase difference response equation in a two-dimensional axisymmetrical inhomogeneous medium. The inversion result of synthetic data shows the validity of this inversion method.

An efficient, preconditioned, high-order solver for scattering by two-dimensional inhomogeneous media

We consider the problem of evaluating the scattering of TE polarized electromagnetic waves by two-dimensional penetrable inhomogeneities: building upon previous work [IEEE Trans. Antennas Propag. 48 (2000) 1862] we present a practical and general fast integral equation algorithm for this problem. The contributions introduced in this text include: (1) a preconditioner that significantly reduces the number of iterations required by the algorithm in the treatment of electrically large scatterers, (2) a new radial integration scheme based on Chebyshev polynomial approximation, which gives rise to increased accuracy, efficiency and stability, and (3) an efficient and stable method for the evaluation of scaled high-order Bessel functions, which extends the capabilities of the method to arbitrarily high frequencies. These enhancements give rise to an algorithm that is much more accurate and efficient than its previous counterpart, and that allows for treatment of much larger problems than permitted by the previous approach. In one test case, for example, the present algorithm results in far-field errors of 8.9×10 −13 in a 2.12 s calculation (on a 1.7 GHz PC) whereas the original algorithm gave rise to far-field errors of 1.1×10 −8 in 88.91 s on a 400 MHz PC. In another example, the present algorithm evaluates accurately the scattering by a cylinder of acoustical size κR=256, which is of the order of 20 times larger (400 times larger in square wavelengths) than the largest scatterers that could be treated by the previous approach. Yielding, at worst, third-order far field accuracy (or substantially better, for smooth scatterers) in fast computing times ( O(N logN) operations for an N point mesh) even for discontinuous and complex refractive index distributions (possibly containing severe geometric singularities such as corners and cusps), the proposed approach is the highest-order O(N logN) solver in existence for the problem under consideration.

Use of Wavelets for Analyzing Transient Radiative Heat Transfer in an Inhomogeneous Medium

Abstract Transient radiative heat transfer in a two-dimensional inhomogeneous rectangular medium is considered. The medium is gray, absorbing, emitting and strongly scattering, and bounded by cold, black walls. Inhomogeneous zones of various sizes are placed at different locations within the medium. The incident radiant energy due to a short laser pulse produces a highly transient and unique transmittance, which is investigated. The discrete wavelets method is used to solve the corresponding equation of transient radiative transfer. The time dependent transmittance for various inhomogeneous areas and the significance of the size and location of the inhomogeneous zones are computed.

Antiplane shear wave propagation in fiber-reinforced composites.

A self-consistent method for analyzing antiplane shear wave propagation in two-dimensional inhomogeneous media is presented. For applications in the high-frequency range, the self-consistent condition for the effective medium is solved being supplemented with the theory of quasidynamic effective density. Comparisons with other theoretical calculations and experimental data for fiber-reinforced composites demonstrate the merits of using the present method.

Method of transfer relations in the theory of multiple resonant scattering of waves as applied to diffraction gratings and photonic crystals

An approach is proposed in the theory of multiple scattering of wave fields in two-dimensional inhomogeneous media, which provides a universal description for wave scattering from one-dimensional periodic interfaces between two dielectric media (optical gratings) and from two-dimensional periodic dielectric structures (photonic crystals). The approach is based on the transfer matrix methodology, which involves sub-dividing the scattering medium into elementary layers with gaps; however, in contrast to the transfer matrix method, it leads to invariant imbedding equations for the matrix coefficients of reflection and transmission of an inhomogeneous medium. The developed approach is applied in a quantitative analysis of two optical effects: resonant decrease in the light reflection coefficient from the grating, associated with the profile depth effect, and exponential-power decay of optical radiation in the forbidden band of a 2D photonic crystal upon an increase in the number of its layers starting from one layer. The frequency spectrum for the electromagnetic radiation power transmission through a 2D photonic crystal formed by parallel layers of infinitely long cylinders is interpreted taking into account the spectral dependence of the total cross section of scattering from a single cylinder. Such an interpretation of the frequency spectrum with two forbidden gaps combined with the analysis of layer-by-layer dynamics of its formation makes it possible to reveal the role of microscopic resonant scattering of waves from a single cylinder and of macroscopic Bragg-type resonant scattering from a periodic system of cylinders during the formation of the spectrum of radiation transmission through a photonic crystal. A physical explanation is given for the transparency peaks in one of the forbidden gaps in the spectra of radiation transmission through a perfectly ordered system of cylinders in terms of multipole resonances of scattering from a single cylinder.

Geometrooptical Representation of the Field Produced by an Extended Source in a Two-Dimensional Inhomogeneous Medium

Geometrooptical Representation of the Field Produced by an Extended Source in a Two-Dimensional Inhomogeneous Medium

Solving the propagation of electromagnetic wave in a simple two-dimensional inhomogeneous medium based on symplectic geometrical theory

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic waves in the two-dimensional inhomogeneous media is presented in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining the geometrical optics. The drawback that the solution in the caustic region can't be obtained with geometrical optics is overcome by this method. The results are compared with those obtained by finite elements method; it proves to be satisfactory.