Inhomogeneous Research Articles

Verification of effect of interference between multiple scatterers on the evaluation of backscattering coefficient

Backscatter coefficient analysis methods for biological tissues have been clinically applied but assume a homogeneous scattering medium. In addition, there are few examples of actual measurement studies in the HF band, and the consistency with theory has not been sufficiently confirmed. In this paper, the effect of correlations among scatterer positions on backscattering was investigated by performing experiments on inhomogeneous media having two types of scattering source with different structural and acoustic properties. In the echo data of phantoms containing two types of scatterer acquired by multiple sensors, the power and frequency dependence of the backscatter coefficient were different from theoretical calculations due to the interference effects of each scatterer. The effect of interference between the two types of scatterer was confirmed to be particularly strong for echoes acquired by the sensor at high intensity and HF, or for a higher number density of strong scatterers.

Switching Between Whistler‐Mode Waves on Inhomogeneities of the Plasma Density and Magnetic Field

AbstractWe present results from the investigation of a transition between two whistler‐mode waves with the same frequency and the parallel wavelength but different perpendicular wavenumbers in the inhomogeneous media consisting of the plasma density and the background magnetic field. We consider transverse inhomogeneities of these quantities. We demonstrate that there are critical values of the plasma density and the magnetic field (which depend on the wave frequency and the parallel wavelength) and the switching between two whistler‐mode waves occurs in the vicinity of these values. We analyze this problem assuming that these critical values are reached inside the finite‐size transition layer between two regions where all the background quantities are homogeneous. We found analytical criteria for the mode switching and we confirmed our results with time‐dependent simulations of the electron‐MHD equations describing whistler‐mode waves in the magnetospheric plasma. We also investigate numerically the dependency of various parameters of the wave switching on the size of the transition region containing critical values of the plasma density and the magnetic field.

A novel design methodology for asymmetric coupled line passive devices and its application in impedance transformers

ABSTRACT This article presents a novel design methodology for asymmetric coupled line passive devices. Based on the extraction of distributed parameters of coupled lines from S-parameters, we re-derived modal characteristic parameters and Z matrix of four-port asymmetric coupled lines in inhomogeneous mediums. Then, Z matrices of ten two-port asymmetric coupled line circuits are derived and their frequency responses are analyzed. Inspired by the image parameter method, image impedances are adopted for two-port device designs. Data diagrams which connect geometric parameters with impedances are provided to simplify design processes. Two impedance transformers utilizing the open-ended and short-ended coupled line circuits, respectively, producing high transforming ratios of 100 (50 Ω to 0.5 Ω) and 40 (50 Ω to 2000 Ω) are fabricated to verify the proposed analysis and design method. Excellent agreement between the simulation and measurement result proves the unique superiorities of asymmetric coupled lines with better initial values.

General acoustic Willis media modeled as conventional materials with embedded sources

Willis coupling vectors provide additional degrees of freedom to manipulate acoustic waves unavailable in conventional materials, but the additional material properties make it difficult to simulate the interaction between sound and Willis media especially when inhomogeneous media with arbitrary geometries are involved. To address this challenge, we establish the equivalence between the wave equation inside a three-dimensional, inhomogeneous, and anisotropic Willis medium to the well-known acoustic wave equation in conventional materials with embedded continuous distributions of monopole and dipole sources. We validate the equivalence in numerical simulations showing that conventional materials with embedded sources replace physical Willis metamaterials anisotropic in the Willis and mass density tensors without modifying the scattered sound distribution. Moreover, the equivalence offers insights into the physics of Willis materials. For example, it shows that various combinations of Willis coupling vectors can generate identical sound scattering for any excitation. It also shows whether effective material parameters extracted from single Willis cell simulations remain valid in bulk metamaterials obtained by replicating periodically that cell. These results suggest that the equivalence model can advance the design of Willis metamaterials and provide a tool to better understand the physics of Willis media.

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.

Multiscale modeling and simulation of turbulent flows in porous media

Numerical simulation is an important tool for understanding the physics of flows in porous media and for making predictions. The state of the art of multiscale modeling and simulation of turbulent flows in porous media is reviewed in this paper. Numerical simulations of flows in porous media can be classified as microscopic simulations, in which both macroscopic and pore-scale flows are directly resolved, and macroscopic simulations, in which the pore-scale motions are modeled while the volume-averaged equations are solved. Studies in the past few years have shown that microscopic simulations improve the understanding of turbulent flows in porous media considerably; this motivates the development of more efficient and more accurate turbulence models for macroscopic simulations. On the basis of this review, we believe that simulation of flows with higher Reynolds numbers, understanding the transport of macroscopic turbulence, modeling of turbulent flows in inhomogeneous and anisotropic porous media, simulation of compressible and multiphase turbulent flows in porous media, and fluid–structure interaction in deformable porous matrices are important topics to be studied in the future.

Solving Surface-volume Integral Equations for PEC and Inhomogeneous/Anisotropic Materials with Multibranch Basis Functions

Multibranch basis functions have been confirmed to be effective for local refinement of domain decomposition methods in the application of solving surface and volume integral equations. Surface-volume integral equations (SVIEs) are applied for solving the hybrid electromagnetic scattering problems involving perfect electric conductors (PEC) and dielectrics, especially inhomogeneous and anisotropic media. In this paper, multibranch Rao-Wilton-Glisson basis functions (MB-RWGs) are applied in conjunction with multibranch Schaubert-Wilton-Glisson basis functions (MB-SWGs) for solving the SVIEs. Block diagonal preconditioners (BDPs) are used to accelerate the iteration convergence based on generalized minimum residual (GMRES) algorithms. The numerical results demonstrate the accuracy of the multibranch basis functions in solving SVIEs, and also show that proper BDPs can accelerate the iteration convergency.

Chirped self-similar optical solitons with cubic–quintic–septic–nonic form of self-phase modulation

This study investigates the dynamics of ultrashort light pulses in an inhomogeneous optical medium exhibiting all orders of nonlinearity up to the ninth order. The research focuses on exploring the existence and properties of self-similar solitons while varying cubic, quintic, septic, and nonic nonlinearities, group velocity dispersion, and loss or gain. It is found that the transmission system supports the existence of novel types of self-similar bright and dark pulses in the presence of various physical processes. Importantly, these self-similar localized waves exhibit a linear chirp, a crucial factor for achieving effective pulse amplification or compression. Based on the chirp property, the dynamical behaviors of these self-similar waveforms are discussed in a periodically distributed amplification system. The findings highlight that the shape and dynamics of these chirped self-similar pulses can be precisely controlled by selecting appropriate profiles for gain or loss, nonlinearity, and dispersion. Additionally, the research numerically discusses the interaction dynamics between two and three adjacent solitons.

Uniform stability of a semilinear coupled Timoshenko beam and an elastodynamic system in an inhomogeneous medium

In this paper, we consider a semilinear coupled Timoshenko beam and an elastodynamic system posed in an inhomogeneous one-dimensional medium subject to localized damping mechanisms acting in the three equations. We show uniform decay rates for the energy of the solutions of such a problem without assuming any restrictions on the non-constant coefficients. To establish these results, refined arguments of the Microlocal Analysis Theory are applied.

An attack-resistant target localization in underwater based on consensus fusion

Target localization has been regarded as one of the most important techniques of underwater sensor networks (USNs). However, the challenges posed by weak communication, inhomogeneous medium, and openness of underwater environment make localization more difficult. With consideration of the asynchronous clock, isogradient sound speed and forging attack, this paper presents a consensus fusion-based target localization solution with USNs. The localization procedure is mainly divided into two phases, i.e., internal position estimation and external information fusion. In the first phase, the received signal strength (RSS) and the time of flight (TOF) measurements are jointly employed to develop an asynchronous localization protocol. Particularly, a ray compensation strategy is incorporated to remove the localization bias from assuming the straight-line transmission. Based on this, a consensus fusion based localization estimator is designed in the second phase to mitigate data falsification attacks introduced by malicious sensor nodes. It is worth mentioning that, the proposed localization solution in this paper can fuse the RSS and TOF measurements by the consensus interaction procedure. Furthermore, it is resistant to data falsification attacks in inhomogeneous water medium. Finally, simulation and experimental results reveal that our solution can reduce the influences of data forging attacks and improve the localization accuracy as compared with the other works.

Broadband acoustic bend composed of homogeneous curved waveguides in quasi-two-dimensional space

By exploring equivalent acoustic path length between inhomogeneous medium and homogenous curved geometry, we present a broadband acoustic bend composed of homogeneous curved waveguides in quasi-two-dimensional space. Simultaneous control of the wavefront and phase accumulation of acoustic waves is achieved by designing the embedding geometry of homogeneous curved waveguides with subwavelength ports, guaranteeing both the bending effect and extremely high transmission. Unlike metamaterials-based wave bends, homogeneous curved waveguides, filled with background air, exhibit promising broadband properties. Moreover, we propose a broadband acoustic splitter by mirroring the acoustic bend. Simulation results demonstrate functionalities of our designs.

Lie symmetries, solitary wave solutions, and conservation laws of coupled KdV‐mKdV equation for internal gravity waves

The propagation of nonlinear solitary and shallow water waves can be examined by nonlinear evolution equations. The dynamics of nonlinear behavior are described by exact solutions having parametric functions. The integrability of nonlinear equation discloses various characteristics of real phenomenon with continuous and fluctuating background. This work aims to generate symmetry reductions and exact solutions of KdV‐mKdV equation, which is a completely integrable system of nonlinear equations and describes combined solitary wave effects in inhomogeneous medium. The infinitesimal generators and their commutative relations are deduced under invariance property of Lie groups. The invariance property provides a symmetry reduction of governing system. Therefore, a continuous process of reductions transmutes the KdV‐mKdV equation to an equivalent system of ODEs. This system of ODEs leads to the exact solutions involving several arbitrary constants and functions. Such obtained results are generalized than earlier works and never reported in literature. Furthermore, adjoint equation and conserved quantities associated with Lagrangian formulation are constructed under Lie symmetries. To reveal the significance of governing phenomenon, the exact solutions are traced via numerical simulation and thus the graphical structures demonstrate line multisoliton, single soliton, lumps, parabolic and stationary wave profiles.

Analytical Solution of Ice–Rock-Model Stress Field and Stress Intensity Factors in Inhomogeneous Media

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies.

Berkovich indentation and the Oliver-Pharr method for shape memory alloys

Advances in instrumentation and interpretation of nanoindentation data with the Oliver-Pharr (O-P) method have fueled the reliable assessment of hardness and elastic modulus. However, shape memory alloys (SMAs) undergo a reversible phase transformation that complicates and challenges the conventional practice. This paper examines through finite element simulations the variation in nanoindentation response with SMA constitutive properties and the deformation regimes underneath a Berkovich indenter. Unique features of phase transformations – including tension-compression asymmetry, limited magnitude of transformation strain compared to plastic strain, and pressure-dependent transformation stress – inject fundamentally different patterns of elastic and inelastic deformation, compared to conventional elastic-plastic indentation. This can generate errors of up to 16% and 40% in hardness and modulus, respectively, when a conventional O-P approach for elastic-plastic materials is used. These errors are decreased if (1) contact stiffness is measured over a reduced (2% or less) portion of the initial unloading response and (2) new material-dependent expressions are used for geometric and correction factors in the O-P nanoindentation analysis. Approximate analytic expressions are obtained for the effective elastic modulus and martensite volume fraction in the inhomogeneous medium created by indentation. This new method is applied to Ni50.5Ti49.5 (at%) wire and for other SMAs, general guidance for selection of geometric and correction factors is provided.

Effect of magnetic field on impedance characteristics in manganese sulfide Mn0.9S

Manganese sulfide with a lack of manganese cations in the lattice is being studied. Samples that are single-phase and have a cubic structure have been certified. The impedance components were measured over a wide range of frequencies and temperatures without a magnetic field and in a magnetic field. The real and imaginary parts of the impedance as a function of temperature are described in the Debye model. The relaxation time of current carriers is found from the impedance hodograph. The change in impedance components in a magnetic field is described in a model of an inhomogeneous electrical medium.

Jet quenching in anisotropic flowing matter

We study the interplay between the flow and hydrodynamic gradients in jet quenching at first order in opacity. We find that the mixed flow-gradient contributions in jet quenching are enhanced by the medium length and survive in the eikonal limit, dominating over other medium evolution effects. The resulting modification to the jet quenching parameter and energy loss rate can be substantial, leading to ample phenomenological implications. We also compute the leading corrections to the jet broadening due to the flow velocity gradients and consider the leading gradient effects in the medium-induced branching for general kinematics, extending the recent considerations of jets in inhomogeneous media. These results can be straightforwardly coupled to matter simulations, providing new opportunities for jet tomography in heavy-ion collisions. Published by the American Physical Society 2024

NSNO: Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium

NSNO: Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium

Compact bright pulse in inhomogeneous and nonlinear medium: Case of the Bose–Einstein Condensate

The extended one-dimensional Gross–Pitaevskii equation which describes the dynamics of localized wave in nonlocal nonlinear media, in particular the Bose–Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms, is investigated. Through analytical methods invoking a modified lens-type transformation, an equivalent nonlocal GP equation with constant coefficients is derived as well as the integrability conditions. In the limit of zero transverse kinetic energy, we show that the nonlocal GP equation exhibits a stationary bright pulse with strictly localized support and with the width independent of the amplitude. However due to the property of conservation of the norm, the BEC amplitude will be a function of both the pulse width and the number of trap atoms. Similarly, the obtained integrability conditions also appear as the conditions under which the compact bright waves describing the BECs can be managed by controlling the parameters of the external potential. Thus, the number of trap atoms can be managed through the functional gain or loss which is not sensitive to the strength of the magnetic trap. It also appears that, in the presence of the nonlocal interaction, the shape of the BEC interpolates between the shape of the compact bright pulse and that of the NLS bright pulse, and the number of condensed atoms participating to the formation of the BEC increases with the strength of the nonlocal interactions.

Fast rapidly convergent penetrable scattering computations

We present a fast high-order scheme for the numerical solution of a volume-surface integro-differential equation. Such equations arise in problems of scattering of time-harmonic acoustic and electromagnetic waves by inhomogeneous media with variable density wherein the material properties jump across the medium interface. The method uses a partition of unity to segregate the interior and the boundary regions of the scattering obstacle, enabling us to make use of specially designed quadratures to deal with the material discontinuities in a high-order manner. In particular, the method uses suitable changes of variables to resolve the singularities present in the integrals in conjunction with a decomposition of Green’s function via the addition theorem. To achieve a reduced computational cost, the method employs a Fast Fourier Transform (FFT) based acceleration strategy to compute the integrals over the boundary region. Moreover, the necessary offgrid evaluation of the density and the inter-grid transfer of data is achieved by applying an FFT-based refined-grid interpolation strategy. We validate the performance of the method through multiple scattering simulations. In particular, the numerical experiments demonstrate that the proposed method can handle high-contrast material properties without any adverse effect on the number of GMRES iterations.

A refined analytical model for reconstruction problems in diffuse reflectance spectroscopy

A refined analytical model of spatially resolved diffuse reflectance with small source-detector separations (SDSs) for the in vivo skin studies is proposed. Compared to the conventional model developed by Farrell et al., it accounts for the limited acceptance angle of the detector fiber. The refined model is validated in the wide range of optical parameters by Monte Carlo simulations of skin diffuse reflectance at SDSs of units of mm. Cases of uniform dermis and two-layered epidermis-dermis structures are studied. Higher accuracy of the refined model compared to the conventional one is demonstrated in the separate, constraint-free reconstruction of absorption and reduced scattering spectra of uniform dermis from the Monte Carlo simulated data. In the case of epidermis-dermis geometry, the recovered values of reduced scattering in dermis are overestimated and the recovered values of absorption are underestimated for both analytical models. Presumably, in the presence of a thin mismatched topical layer, only the effective attenuation coefficient of the bottom layer can be accurately recovered using a diffusion theory-based analytical model while separate reconstruction of absorption and reduced scattering fails due to the inapplicability of the method of images. These findings require implementation of more sophisticated models of light transfer in inhomogeneous media in the recovery algorithms.