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A scattering matrix technique is used to calculate the longitudinal and transverse energy dependence of the transmission probability through various heterostructures using both the BenDaniel–Duke (BD) and the lesser known Zhu–Kroemer (ZK) boundary conditions to take into account the spatial dependence of the effective mass. We first illustrate the large difference in the transmission probabilities calculated using both boundary conditions for the simple problems of tunneling through a potential step, a single rectangular barrier, and a resonant tunneling device. Then, we present numerical calculations of the external electric field dependence of the field emission (FE) current from a n-doped GaAs semiconductor/vacuum interface using both boundary conditions, showing that the BD boundary conditions underestimate the FE current for large values of the applied external electrostatic field. A comparison of calculated FE characteristics with FE data may be a way to determine the appropriate boundary conditions to solve tunneling problems through heterostructures with spatially varying effective mass. [ABSTRACT FROM AUTHOR]

Hafnia (HfO2) is a potential candidate for the high-k gate dielectrics in next-generation high-power electronics. Its thermal transport properties, which determine the performance of these related high-power electronics, are critical while rarely investigated. Here, the thermal transport properties of HfO2 in a wide temperature range of 300–2000 K with a phase transition between monoclinic and tetragonal phases at ∼1765 K, are systematically studied based on the temperature-dependent effective potential landscapes with both propagating and coherence thermal transport considered. It is found that the cage-like structure of monoclinic HfO2 results in the avoid crossing in the phonon band structures, which increases the three-phonon scattering largely. Some phonon modes with significant scattering matrix can have relatively larger 3ph and 4ph scattering rates in tetragonal HfO2. Consequently, the thermal conductivity of HfO2 is only 11.95–1.72 W/mK at 300–2000 K. Our results further show that propagating phonon channels dominate the thermal transport in HfO2 and contribute at least 70% to the total thermal conductivity. The rest of the thermal conductivity of HfO2 results from the coherence thermal transport channels, which is caused by the overlap of phonons. Four-phonon scatterings are found to be significant for the thermal transport in tetragonal HfO2, which can result in a thermal conductivity reduction of ∼50%. Our results here advance the understanding of the thermal transport in HfO2, which may benefit the performance optimization of HfO2-related electronics. [ABSTRACT FROM AUTHOR]

In this work, we have studied the spin-dependent ballistic transport and anomalous quantum tunneling in bilayer graphene horizontally placed in between two Rashba–Zeeman (RZ) leads under external electric biasing. We investigated the transmission and conductance for the proposed system using scattering matrix formalism and the Landauer–Büttiker formula considering a double delta-like barrier under a set of experimentally viable parameters. We found that the transmission characteristics are notably different for up- and down-spin incoming electrons depending upon the strength of magnetization. Moreover, the transmission of up- and down-spin electrons is found to be magnetization orientation dependent. The maximum tunneling conductance can be achieved by tuning biasing energy and magnetization strength and choosing a material with suitable Rashba spin–orbit coupling (RSOC). This astonishing property of our system can be utilized in fabricating devices, such as spin filters. We found that the Fano factor of our system is 0.4 under strong magnetization conditions, while it reduces to 0.3 under low magnetization conditions. Moreover, we also noticed that the transmission and conductance significantly depend on the Rashba–Zeeman effect. Therefore, considering a suitable RZ material, the tunneling of the electrons can be tuned and controlled. Our result suggests that considering suitable strength and orientation of magnetization with moderate RSOC, one can obtain a different transmission probability for spin species under suitable biasing energy. These results indicate the suitability of the proposed system in fabrication of spintronic devices, such as spin filter, spin transistor, etc. [ABSTRACT FROM AUTHOR]

Within aerosol-rich environments, efficient simulation of frequency-modulated continuous wave (FMCW) laser detector echo characteristics is crucial. Conventional methods often need more efficiency. To address this, we propose a photon matrix-based approach for simulating intricate photon scattering processes, enhancing simulation accuracy. This study focuses on short-range FMCW laser detection under aerosol interference, assessing performance via signal-to-noise ratio (SNR). We analyze the impact of amplitude modulation coefficient and photon count on SNR. Surprisingly, the photon count minimally affects SNR, while the amplitude modulation coefficient significantly influences it. These findings shed light on optimizing FMCW laser detection in aerosol-laden environments. Attention to the amplitude modulation coefficient can notably enhance SNR and overall detection efficiency. [ABSTRACT FROM AUTHOR]

Parity-time (PT) symmetry has enabled the demonstration of fascinating wave phenomena in non-Hermitian systems characterized by precisely balanced gain and loss. Until now, the exploration and observation of PT symmetry in scattering settings have largely been limited to propagating waves. Here, we demonstrate a versatile coupled-resonator acoustic waveguide (CRAW) system that enables the observation of PT-symmetric scattering responses for evanescent waves within a bandgap. By examining the generalized scattering matrix in the evanescent wave regime, we observe hallmark PT-symmetric phenomena—including phase transitions at an exceptional point, anisotropic transmission resonances, and laser-absorber modes—in systems that do not require balanced distributions of gain and loss. Owing to the peculiar energy transfer features of evanescent waves, our results not only demonstrate a distinct pathway for observing PT symmetry, but also enable strategies for exotic energy tunneling mechanisms, paving fresh directions for wave engineering grounded in non-Hermitian physics. Non-Hermitian physics and parity-time (PT) symmetry are of broad interest in classical wave systems. This work demonstrates evanescent wave manipulation and scattering control based on PT symmetry in a versatile coupled-resonator acoustic waveguide (CRAW) system, which not only extends the framework of non-Hermitian physics but also offers strategies for near-field manipulation and control. [ABSTRACT FROM AUTHOR]

Previous modeling studies have not properly explained the measured mass absorption cross section (MAC) at 550 nm, the linear backscattering depolarization ratio (LDR) at 355 and 532 nm, and the scattering matrix of soot at 532 nm. In this work, we attempt to use a black carbon (BC) model with an intrinsic organic carbon (OC) coating to explain the large MAC, large LDR, and measured scattering matrix. Our results show that the bare fractal BC model is not able to explain MAC, LDR, and scattering matrix simultaneously and that the modeling values do not cover the measurement range. This study shows that the modeled LDR and scattering matrix can cover the measurement range if we constrain the MAC of the BC in the measurement range by the intrinsic OC coating when we consider the effects of monomer radius, monomer number, and monomer overlap simultaneously. Therefore, intrinsic OC coating can be a significant source of uncertainty in the optical properties of fresh soot. Plain Language Summary: Since soot is the most important absorbing particle in the atmosphere, an accurate calculation of the optical properties of soot is of great importance for climate assessment and remote sensing. However, some of the observed optical properties of soot are difficult to explain with current models. In this study, a black carbon (BC) model with an intrinsic organic carbon (OC) coating is used to explain these difficult‐to‐explain optical properties. The results show that the simulated mass absorption cross section (MAC), linear backscattering depolarization ratio (LDR), and scattering matrix are difficult to explain when only the influence of BC is considered, although the effects of monomer size, monomer number, and monomer overlap are taken into account. Range of observation. However, after accounting for the intrinsic OC coating, the model is able to account for the range of realistic optical observations. Therefore, the intrinsic OC coating may be responsible for some optical properties that are difficult to explain with the current models. Key Points: The model of pure black carbon (BC) has difficulty explaining some optical observations of sootWe have proposed a soot model consisting of a BC core and an intrinsic organic carbon (OC) shellThe intrinsic OC coating may be a cause of some unexplained optical properties in current models [ABSTRACT FROM AUTHOR]

A family of quasi-1D Schrödinger operators is investigated through scattering theory. The continuous spectrum of these operators exhibits changes of multiplicity, and some of these operators possess resonances at thresholds. It is shown that the corresponding wave operators belong to an explicitly constructed C∗-algebra. The quotient of this algebra by the ideal of compact operators is studied, and an index theorem is deduced from these investigations. This result corresponds to a topological version of Levinson’s theorem in the presence of embedded thresholds, resonances, and changes of multiplicity of the scattering matrices. In the last two sections of the paper, the K-theory of the main C∗-algebra and the dependence on an external parameter are carefully analyzed. In particular, a surface of resonances is exhibited, probably for the first time. The contents of these two sections are of independent interest, and the main result does not depend on them. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) is a well-known supervised method that can perform dimensionality reduction and feature extraction effectively. However, traditional LDA-based methods need to be turned into the trace ratio form to compute the closed-form solution, in which the within-class scatter matrix should be nonsingular. In this article, we design a new model named generalized robust linear discriminant analysis (GRLDA) method to tackle this disadvantage and improve the robustness. GRLDA uses L 2 , 1 -norm on both loss functions to reduce the influence of outliers and on regularization term to obtain joint sparsity simultaneously. The intrinsic graph and the penalty graph are constructed to characterize the intraclass similarity and interclass separability, respectively. A novel optimization method is proposed to solve the proposed model, in which a quadratic problem on the Stiefel manifold is involved to avoid the inverse computation on a singular matrix. We also analyze the computational complexity rigorously. Finally, the experimental results on face, object, and medical images exhibit the superiority of GRLDA. [ABSTRACT FROM AUTHOR]

Three-body bound, virtual and resonant states in the dtμ− and ddμ− systems were found by solving homogeneous Faddeev equations on the real and complex energy planes. The formalism of searching is conducted for the scattering matrix poles on both physical and nonphysical energy sheets with an analytical continuation of the corresponding Lippmann–Schwinger equations for t-matrix. Some benchmark tests have been done with model and realistic two-body potentials to verify the analytical continuation procedure. Direct calculations revealed five resonant states in the dtμ− and ddμ− systems, as well as two virtual states in the dtμ− system in the strong coupling mode. The key influence of short-range dt and dd interactions was found on the appearance of dtμ− and ddμ− bound states in the energy range of 1–20keV, which disappeared when such interactions were turned off. [ABSTRACT FROM AUTHOR]

String theory on AdS3 × S3 × T4 geometries supported by a combination of NS-NS and R-R charges is believed to be integrable. We elucidate the kinematics and analytic structure of worldsheet excitations in mixed charge and pure NS-NS backgrounds, when expressed in momentum, Zhukovsky variables and the rapidity u which appears in the quantum spectral curve. We discuss the relations between fundamental and bound state excitations and the role of fusion in constraining and determining the S matrices of these theories. We propose a scalar dressing factor consistent with a novel u-plane periodicity and comment on its close relation to the XXZ model at roots of unity. We solve the odd part of crossing and show that our solution is consistent with fusion and reduces in the relativistic limit to dressing phases previously found in the literature. [ABSTRACT FROM AUTHOR]

Non-Hermitian optics has revealed a series of counterintuitive phenomena with profound implications for sensing, lasing, and light manipulation. While the non-Hermiticity of Hamiltonians has been intensively investigated, recent advancements in the non-Hermitian scattering matrix have given birth to a lot of unique phenomena, such as simultaneous lasing and anti-lasing, reflectionless scattering modes (RSMs), and coherent chaos control. Despite these developments, the investigation has predominantly focused on static and symmetric configurations, leaving the dynamic properties of non-Hermitian scattering in detuned systems, which is essential for applications in sensing and beyond, largely unexplored. Here, we extend the stationary behaviors associated with the RSMs to resonant detuned systems. Contrary to the common belief of exceptional point (EP) sensors as being susceptible to parametric disturbances, we induce an RSM EP in a one-dimensional optical cavity and demonstrate its robustness in displacement sensing against laser frequency drifts up to 10 MHz. Our findings not only contribute to the broader understanding of non-Hermitian scattering phenomena but also pave the way for the next generation of non-Hermitian sensors. [ABSTRACT FROM AUTHOR]

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solutions, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-order ODEs. Because of the half-range boundary conditions for incoming particles, however, full-range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively. [ABSTRACT FROM AUTHOR]

We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients, refining methods used in (J. Differential Equations 137(2) (1997) 251–272) and (J. Funct. Anal. 178(2) (2000) 396–420). [ABSTRACT FROM AUTHOR]

Density fluctuation potential induced by a screening of the photohole scatters the photoelectron and generally causes its emission delay from the scattering matrix in the photoemission spectroscopy, where the photoemission delay usually quantifies the extrinsic loss of the photoelectron depending on the atomic orbital. Without the potential scattering, however, the photoemission from the coherent two-state mixture created by the laser driving is found to undergo the unexpected photoemission delay, which originates from the mixed photoemission matrix. Using the Haldane model, we analytically calculate such coherent mixing induced photoemission delay in an angle-resolved mode, which is found to reveal the local Berry curvature structure as long as the coherent mixing is sustained. This finding is confirmed through the streaking computation for the photoemission delay by solving the time-dependent Schrödinger equation and suggests that the photoemission delay be a new spectroscopic diagnosis of the material topology of two-dimensional semiconductors. [ABSTRACT FROM AUTHOR]

The main goal of the SPASCHARM experiment is the systematic study of spin phenomena at intermediate energies. For this purpose, it is planned to create a beam of polarized protons and antiprotons. The research includes, among other things, the study of elastic scattering. Some of the required equipment for polarimetry is planned to be also used to study elastic scattering immediately after the creation of such a channel. In this work, a set of observables necessary for model-free reconstruction of elastic proton–proton scattering amplitudes is investigated and determined. [ABSTRACT FROM AUTHOR]

The transmission characteristics of terahertz (THz) waves in a non-uniform microplasma are investigated by using the scattering matrix method. The electron density distribution in microplasma is simulated by Epstein and parabolic models. The effects of physical parameters, such as the incidence angle of THz waves, microplasma size, electron density, and collision frequency, on the propagation of THz waves are numerically analyzed. The results show that lower frequency THz waves are difficult to penetrate the microplasma with high electron density and high collision frequency. The microplasma density distribution, especially the gradient variation of the density in the first layer, has a large effect on the reflection of THz waves. Thus, THz waves can be used to diagnose the physical parameters of microplasmas. [ABSTRACT FROM AUTHOR]

We apply subspace migration (SM) for fast identification of a small object in microwave imaging. Most research in this area is performed under the assumption that the diagonal elements of the scattering matrix can be easily measured if the transmitter and the receiver are in the same location. Unfortunately, it is very difficult to measure such elements in most real-world microwave imaging. To address this issue, several studies have been conducted with the unknown diagonal elements set to zero. In this paper, we generalize the imaging problem by using SM to set the diagonal elements of the scattering matrix to a constant. To demonstrate the applicability of SM and its dependence on the constant, we show that the imaging function of SM can be represented by an infinite series of Bessel functions of integer order, antenna number and arrangement, and the applied constant. This result allows us to discover additional properties, such as the unique determination of the object. We also demonstrated simulation results using synthetic data to back up the theoretical result. [ABSTRACT FROM AUTHOR]

Manipulating orthogonally polarized waves independently in a single metasurface is pivotal. However, independently controlling the phase shifts of orthogonally polarized waves is difficult, especially in the same frequency bands. Here, we propose a receiver-phase shift-transmitter transmitarray with independent control of arbitrary polarization states in the same frequency bands, in which transmission rates reach more than 90% in the frequency bands 4.2~4.9 GHz and 5.3~5.5 GHz. By introducing a phase-regulation structure to each element, phases covering 360 ° for different polarized incident waves can be independently controlled by different geometric parameters, and two-bit coding phases can be obtained. The design principle based on the two-port network's scattering matrix has been analyzed. To verify the independent tuning abilities of the proposed transmitarray for different polarization incidences in the same frequency bands, a multifunctional receive-phase shift-radiation coding transmitarray (RPRCT), which is composed of 16 × 16 elements, with functions of anomalous refraction (for example, orbital angular momentum wave) and focusing transmission for different polarized incident waves was simulated and measured. The measured results agree reasonably well with the simulated ones. Our findings provide a simple method for obtaining a multifunctional metasurface with orthogonal polarization in the same frequency bands, which greatly improves the capacity and spectral efficiency of communication channels. [ABSTRACT FROM AUTHOR]

Light scattering holds immense significance in various applications, including LED lighting, display enhancement, and solar cell optimization, emphasizing the critical role of understanding scattering mechanisms, especially light–matter interactions, achieving effective optical diffusion. Consequently, the influence of stimuli on material properties, including refractive indices and thermal expansion behavior, has emerged as a pivotal consideration, leading to the development of stimuli‐responsive light scattering modifier. Here, a temperature‐sensitive light scattering modifier composed of poly(methyl methacrylate‐co‐styrene) and poly(ethylene‐co‐vinyl acetate) is presented as scattering particles and matrix, respectively, using a melt‐blending process. Optical properties are evaluated across controlled temperatures 0–70 °C. These findings demonstrate an increasing trend in diffuse transmission and haze as temperatures increased across all light scattering modifiers. Significantly, the optimized light scattering modifier, integrating a dual particle system, showcased uniform reduction gaps in parallel transmission and adjustable haze characteristics across the visible spectrum under temperature control. This optical modifier achieved a total transmission of 92% and adjustable haze levels ranging from 35% to 90% under temperature control. Furthermore, this fabrication of three‐layer films incorporating the light scattering modifier exhibited identical characteristics to the developed light scattering modifier, emphasizing their potential for seamless integration across diverse technological domains. [ABSTRACT FROM AUTHOR]

In recent years, much attention has been paid to integrated photonics devices based on nonlinear media. A generalization of the transfer matrix method to problems in plane-parallel layered media with quadratic and cubic nonlinearity is proposed. The incident radiation can be either a monochromatic wave or a non-monochromatic pulse. Previously, such problems could only be solved using grid methods. The proposed approaches significantly expand the range of applicability of matrix methods and are drastically superior in efficiency to the well-known grid methods. [ABSTRACT FROM AUTHOR]

The exact expressions for scattering matrix and transmission coefficient in open multi-cascade nanostructure are obtained. The theory of spectral characteristics of electron quasi-stationary states is developed in two approaches. For the nanostructure with GaAs wells and AlGaAs barriers, it is established that resonance bands appear in the N-cascade structure. Each one is formed by the energies of N states. Only the scattering matrix allows to unambiguously determine the resonance energies and resonance widths of all electron states in the multi-cascade structure. The approach of transmission coefficient, due to the collapse of resonances, gives the incomplete information about the spectral characteristics. [ABSTRACT FROM AUTHOR]

Non‐Hermitian metasurfaces with chiral exceptional points (EPs) in their scattering matrices have garnered significant attention due to their potential for optical polarization manipulation and wavefront control. However, existing approaches predominantly operate under normal incidence conditions, limiting their application in the manipulation of chiral EPs in momentum space. Here, the wavelength‐fixed manipulation of the chiral EPs across a wide‐range momentum space using a polyatomic metasurface is realized, which is attributed to the effective modulation of the collective interference of guided‐mode resonances excited by oblique transverse magnetic (TM) and transverse electric (TE) illuminations. Further, both theoretical and experimental analyses are conducted to explore the potential applications of the proposed design in the wavevector‐ and spin‐selective manipulation of reflection intensity and optical encryption. This work provides a straightforward method to realize and manipulate chiral EPs in momentum space at a fixed operational wavelength, paving the way for designing polarization‐selective and wavevector‐selective devices. [ABSTRACT FROM AUTHOR]

The estimation of signal dimension under heavy-tailed latent variable models is studied. As a primary contribution, robust extensions of an earlier estimator based on Gaussian Stein's unbiased risk estimation are proposed. These novel extensions are based on the framework of elliptical distributions and robust scatter matrices. Extensive simulation studies are conducted in order to compare the novel methods with several well-known competitors in both estimation accuracy and computational speed. The novel methods are applied to a financial asset return data set. [ABSTRACT FROM AUTHOR]

In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied. [ABSTRACT FROM AUTHOR]

New SPICE-compatible circuit models of a multiport are presented here that are suitable for the frequency-domain and time-domain analyses of hybrid systems containing linear distributed elements and possibly non-linear lumped elements. Distributed elements models are based on scattering parameters with potentially complex reference impedances, which are not necessarily equal for all ports. Both exact and approximated (lumped) models are proposed. The scattering parameters are directly taken as the model element values in the former case. In the latter case, the model element values are equal to the real and imaginary parts of the poles and residues of the rational approximation. The models comprise a multiport (with an admittance matrix numerically equal to the modeled scattering matrix or approximating it) equipped with a pair of coupled impedances at each port. A few examples validate the proposed approach and prove its efficiency in terms of matrix size and analysis time compared to some selected commercial counterparts. [ABSTRACT FROM AUTHOR]

Speckle reduction is a key preprocessing approach for the applications of Synthetic Aperture Radar (SAR) data. For many interpretation tasks, high-quality SAR images with a rich texture and structure information are useful. Therefore, a satisfactory SAR image filter should retain this information well after processing. Some quantitative assessment indicators have been presented to evaluate the edge-preservation capability of single-polarization SAR filters, among which the non-clean-reference-based (i.e., blind) ones are attractive. However, most of these indicators are derived based only on the basic fact that the speckle is a kind of multiplicative noise, and they do not take into account the detailed statistical distribution traits of SAR data, making the assessment not robust enough. Moreover, to our knowledge, there are no specific blind assessment indicators for fully Polarimetric SAR (PolSAR) filters up to now. In this paper, a blind assessment indicator based on an SAR Ratio Gradient Operator (RGO) and Confidence Interval Estimation (CIE) is proposed. The RGO is employed to quantify the edge gradient between two neighboring image patches in both the speckled and filtered data. A decision is then made as to whether the ratio gradient value in the filtered image is close to that in the unobserved clean image by considering the statistical traits of speckle and a CIE method. The proposed indicator is also extended to assess the PolSAR filters by transforming the polarimetric scattering matrix into a scalar which follows a Gamma distribution. Experiments on the simulated SAR dataset and three real-world SAR images acquired by ALOS-PALSAR, AirSAR, and TerraSAR-X validate the robustness and reliability of the proposed indicator. [ABSTRACT FROM AUTHOR]

The optimal absorption of flexural energy by the critical coupling of a locally resonant grating embedded in a thin plate is reported in this work for the reflection and transmission problems. The grating is made of a 1D-periodic array of local resonators. A viscoelastic coating is also placed on top of each resonator to control the intrinsic losses of the system. The scattering matrices for the propagative waves of both problems are obtained by means of the Layered Multiple Scattering Theory and validated by the Finite Element Method. In this work, we find that the perfect absorption can be obtained in the reflection problem and the maximal absorption in the transmission problem is limited to 50% by tuning the losses only. These results agree with the theoretical predictions since the eigenvalues reduce to the reflection coefficient in the reflection problem and only one of the two eigenvalues of the scattering matrix is critically coupled in the transmission problem. These results highlight the adaptability of the critical coupling method to optimize the absorption of locally resonant materials for flexural waves in 2D transmission and reflection problems, and pave the way to the design of resonators for efficient flexural wave absorption. [ABSTRACT FROM AUTHOR]

A Landau–Zener-type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a 2 × 2 system of first-order h-differential operator with O (ε) off-diagonal part is considered in 1D. Asymptotic behavior as ε h m / (m + 1) → 0 + of the local scattering matrix near an avoided-crossing is given, where m stands for the contact order of two curves of the characteristic set. A generalization including the cases with vanishing off-diagonals and non-Hermitian symbols is also given. [ABSTRACT FROM AUTHOR]

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix without diagonal elements, whose elements are measured scattering parameters, is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies some of its properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with realdata are conducted. [ABSTRACT FROM AUTHOR]

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules. [ABSTRACT FROM AUTHOR]

Electromagnetic (EM) metasurfaces comprising artificially designed subwavelength unit cells have drawn considerable attention due to the EM properties beyond the limits of natural materials. As one of the representative structures, active polarization conversion metasurface (APCM) is switchable by loading active components. It provides great freedom to manipulate the polarization state of EM waves. However, the current research mainly focused on the application of communication and paid less attention to the radar effect of APCM. APCM redistributes electromagnetic wave energy in multi-polarization channels, so it will have great application potential in polarimetric radar. Herein, based on the fully polarimetric radar one-dimensional high resolution range profile, the radar effect of time-modulated metasurface is studied. For this purpose, a method of target scattering mechanisms manipulation and a polarization-insensitive structure of APCM are proposed. The amplitude-phase joint modulation method is specifically analyzed in detail. The distance transformation and virtual multi-target phenomena are further discovered. Virtual targets along the distance dimension are generated in multi-polarization channels, while the scattering mechanisms of k-order targets are effectively manipulated. The relationship between the target scattering matrix and the modulation parameters is obtained. It may provide an effective method for the application of active metasurface in fully polarimetric radars. [ABSTRACT FROM AUTHOR]

Transfer matrix formalism is widely used in modeling periodic heat diffusion in layered structures. Due to an intrinsic numerical instability issue, this formalism fails at high heating frequencies and/or in thick structures. Inspired by its success in modeling wave propagation, we develop a numerically stable scattering matrix framework to model periodic heat diffusion in stratified solid media. As a concrete example, we apply this scattering matrix methodology to the 3ω method. We first validate our framework using various well-known solutions. Next, we demonstrate the numerical stability of the framework using a configuration that resembles the three-dimensional stacked architecture for chip packing. Last, we propose synthetic "experiments" to exhibit, under certain circumstances, the merits of the scattering matrix formalism in extracting thermal properties. [ABSTRACT FROM AUTHOR]

In this paper, a study of the coupled Schrödinger Maxwell-Bloch equations, which described the propagation of two optical pulses in an optical medium with coherent three-level atoms, is presented via the Riemann-Hilbert approach. First, we performed a spectral analysis on the basis of Lax pair with the negative flow, and then the Jost function, scattering matrix, and their analytic and symmetric properties are given. Second, the Riemann-Hilbert problem is established successfully through a standard dressing procedure via the Riemann-Hilbert approach, and then the potential function related to the solution of the Riemann-Hilbert problem is reconstructed. By introducing the special matrix functions, we can transform the irregular Riemann-Hilbert problem into the regular one, which can be solved by the Plemelj formula. Finally, some applications are given to solve the Riemann-Hilbert problem without reflection for the coupled Schrödinger Maxwell-Bloch equation, and the multi-soliton solutions are obtained explicitly. Moreover, the dynamic behaviors of some soliton solutions are discussed graphically by choosing appropriate parameters. [ABSTRACT FROM AUTHOR]

In this paper we consider time-harmonic acoustic wave propagation in a half-plane filled by inhomogeneous periodic medium. If the refractive index depends on the horizontal coordinate only, we define upward and downward radiating modes by solving a one-dimensional Sturm-Liouville eigenvalue problem with a complex-valued periodic coefficient. The upward and downward radiation conditions are introduced based on a generalized Rayleigh series. Using the variational method, we then prove uniqueness and existence for the scattering of an incoming wave mode by a grating located between an upper and lower half plane with such inhomogeneous periodic media. The solution operator of the quasiperiodic boundary value problem yields a well-defined scattering operator, the numerical approximation of which is nothing else but the S-matrix in scattering matrix algorithms like Rigorous Coupled Wave Analysis (RCWA) or Fourier Modal Method (FMM). [ABSTRACT FROM AUTHOR]

Measuring the orientation, mass and body length of migratory insects through entomological radar is crucial for early warnings of migratory pests. The fully polarized entomological radar is an efficient device for observing migratory insects by calculating insect parameters through the scattering matrix obtained from the target. However, the measured target scattering matrix will be affected by system polarization measurement errors, leading to errors in insect parameter calculation, while the related analysis is currently relatively limited. Therefore, the scattering matrix measurement process is modeled, followed by an analysis of the effects of different errors on orientation, mass and body length estimation. The influence of polarization measurement errors on insect scattering characteristics is also analyzed. The results present that for fixed polarization measurement errors, the measurement errors of insect orientation, mass and body length will vary with insect orientation in specific patterns, and the distribution of measured insect parameters will be drastically distorted compared to the true parameter distribution. In addition, polarization measurement errors could seriously disrupt the reciprocity and bilateral symmetry of the measured insect scattering matrix. These analyses and conclusions provide a good basis for eliminating the effects of polarization measurement errors and improving the accuracy of insect parameter measurement. [ABSTRACT FROM AUTHOR]

The propagation characteristics of sub-terahertz (sub-THz) waves through the sharp-coned plasma sheath are investigated, revealing a frequency selection phenomenon. Two significant electron density gradients within the sharp-coned plasma sheath, which result in high reflection coefficients, are identified. These strong reflective interfaces divide the plasma into distinct regions, and the frequency selection mechanism is analyzed using the improved scattering matrix method. This research finds that the combination of these reflective interfaces and the intervening plasma forms a "resonator structure," leading to the observed frequency selection. A quantitative relationship between plasma parameters and the frequency selection phenomenon is analyzed. The results indicate that the reflection coefficients of the reflective interfaces increase, making the frequency selection more pronounced, when the thickness of the interfaces decreases or the peak electron density increases. In addition, a lower collision frequency leads to reduced absorption effects and a more pronounced frequency selection. The phenomenon suggests that enhancing transmissivity at lower frequencies may be feasible, providing a theoretical insight into the application of sub-THz waves in mitigating communication blackouts. [ABSTRACT FROM AUTHOR]

Several researches have confirmed the possibility of localizing small anomalies via Kirchhoff migration (KM); however, when the background information is unknown, small anomalies cannot be satisfactorily retrieved. This fact can be examined through the simulation results; however, related theoretical result to explain the reason of such phenomenon has not yet been investigated. In this contribution, we show that the imaging function of the KM can be expressed by an infinite series of the Bessel function of the first kind, material properties, and antenna arrangement, and applied alternative value of the background wavenumber. Based on the theoretical result, we explain why the exact location and shape of anomalies cannot be retrieved. The simulation results with synthetic data exhibited to support the theoretical result. [ABSTRACT FROM AUTHOR]

The scattering matrix method is applied to investigate the propagation characteristics of obliquely incident terahertz (THz) waves in inhomogeneous fully ionized dusty plasma. The propagation coefficients of THz waves are analyzed with different physical parameters in the case of parabolic electron density distribution. The results show that the transmissivity of lower frequency THz waves have a noticeable variation with the change of physical parameters. However, the transmissivity values can rapidly approach 1 in higher frequency band. We notice that there is a critical value f c ≈ 0.045 THz. When f > f c , the transmissivity increases as the dust particles density and radius increase. However, it is somewhat opposite when f < f c . Significantly, the THz waves exhibit a greater propensity for penetrating fully ionized dusty plasma compared with the weakly ionized dusty plasma. To a certain degree, the investigation results provide new ideas for addressing the issue of "blackout". [ABSTRACT FROM AUTHOR]

Clarifying China's position in the global system is an important logical basis for developing national diplomacy. Although much research has been done on China's development status, most studies have been based on country comparisons or institutional environment. In today's networked era in which the global economy, trade, personnel, and information are closely connected, studies on China's global position and its status changes and influencing factors in multiple contact networks are still insufficient. In this study, from the perspective of diverse global contact networks, we constructed economic, cultural, and political influence indices to explore the changes and influencing factors on China's status in the global system from 2005 to 2018. The results show that during the study period, China's global influence in the fields of economic ties, cultural exchanges, and political contacts increased significantly, but its influence in the fields of cultural exchanges and political contacts lagged far economic ties. The pattern of China's economic influence on various economies around the world has shown a transformation from an 'upright pyramid' to an 'inverted pyramid' structure. The proportion of these economies in low-influence zones has decreased from more than 60% in 2005 to less than 20% in 2018. China's cultural and political influence on various economies around the world has increased significantly; however, for the former, the percentage of high-influence areas is still less than 20%, whereas for the latter the percentage of these economies in medium- and high-influence areas is still less than 50%. Analyses such as a scatter plot matrix show that geographical proximity, economic globalization, close cooperation with developing countries, and a proactive and peaceful foreign policy are important factors in improving China's status in the diverse global network system. [ABSTRACT FROM AUTHOR]

Most domain adaptive methods enhance the classification performance of target domain via overcoming the distribution difference between source and target domains while ignoring the nature of classifier, i.e., the data being correctly classified by classifier is due to the high separability of data. Therefore, inspired by this, we propose a simple yet effective domain adaptive method in accordance with the property of classifier, namely cross-domain Fisher discrimination criterion (CFDC). CDFC is intended to upgrade the inter-class discrimination and intra-class compactness of samples for the scenario where the target domain has few labeled samples. Specifically, we reconstruct the intra- and inter- class scatter matrices of Fisher's criterion from a geometrically intuitive perspective, enabling it to extract highly discriminative features from cross-domain samples. The reconstructed between-class scatter matrix aims to maximize the class separation of target samples, while the redefined within-class scatter matrix seeks to have samples from different domains densely clustered around the class center of target samples. Six widely used image datasets are involved to verify the effectiveness and efficiency of CFDC. Experimental results demonstrate that the performance of CFDC is significantly superior to similar methods and conventional unsupervised domain adaptation methods, comparable to non-deep semi-supervised domain adaptation methods, but with a significantly lower time consumption. Even compared with state-of-the-art deep semi-supervised domain adaptation methods, CFDC exhibits performance advantages on certain datasets. [ABSTRACT FROM AUTHOR]

We study the two-particle form-factors for the relativistic limit of the integrable S-matrix of the mixed-flux AdS3 × S3 × T4 string theory. The S-matrix theory was formally constructed in two distinct ways by two different teams. We focus on the massive theory built up by Frolov, Polvara and Sfondrini, and derive expressions for the minimal solutions to the axioms, in both integral and manifestly meromorphic form, and then proceed to apply the off-shell Bethe ansatz method of Babujian et al. We obtain the integral formulas for the two-particle complete form-factors and check the axioms at this particle number. [ABSTRACT FROM AUTHOR]

In a recent paper, it has been shown that, if an N‐port network fulfills the condition of (geometrical) unconditional stability at a given frequency, then its scattering parameters will also necessarily satisfy N easily computable bounds, one per port. In order to complete that picture, this contribution investigates whether a tighter bound can be obtained by combining the N$$ N $$ bounds into just one. The answer is in general negative, except that the 3‐port case does indeed exhibit a peculiar behavior: this can be exploited to reduce the upper bound when the diagonal elements of the scattering matrix are limited in magnitude up to some α$$ \alpha $$, and in particular for α=0$$ \alpha =0 $$ (simultaneous conjugate match). [ABSTRACT FROM AUTHOR]

The multichannel scattering problem for the stationary Schrödinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the Jost solutions as functions of the spectral parameter is described. Unitarity of the scattering matrix is proved in the general case when some of the scattering channels can be closed and the thresholds can be different at left and right infinities on the line. The symmetry relations of the S -matrix are established. The condition determining the bound states is obtained. The asymptotics of the Jost functions and of the transition matrix are derived for a large spectral parameter. [ABSTRACT FROM AUTHOR]

This document is a correction notice for a paper titled "The Asymmetric Dynamical Casimir Effect" published in the journal Physics. The correction addresses an error in the calculation of the DCE spectrum from time-dependent perturbations. The matching conditions computed in the original paper were solved incorrectly, and it appears that these conditions cannot be generally solved by any known method. The correction provides revised content for Section 2.4 and adds a paragraph to the end of Section 2.3. It also corrects erroneous inclusions in equations and modifies the discussion of fluctuations in Section 6. Appendix A is added to highlight the difficulties in calculating the time-dependent perturbations. The author contributions have been corrected to include Patrick M. Brown and Jacob A. Matulevich as authors. [Extracted from the article]

We study the two-particle form-factors for the relativistic limit of the integrable S-matrix of the mixed-flux AdS3 × S3 × T4 string theory. The S-matrix theory was formally constructed in two distinct ways by two different teams. We focus on the massive theory built up by Frolov, Polvara and Sfondrini, and derive expressions for the minimal solutions to the axioms, in both integral and manifestly meromorphic form, and then proceed to apply the off-shell Bethe ansatz method of Babujian et al. We obtain the integral formulas for the two-particle complete form-factors and check the axioms at this particle number. [ABSTRACT FROM AUTHOR]

Charge Transfer (CT) has enjoyed continuous interest due to increasing experimental control over molecular structures, leading to applications in, for example, photovoltaics and hydrogen production. In this paper, we investigate the effect of CT states on the absorption spectrum of linear molecular aggregates using a scattering matrix technique that allows us to deal with arbitrarily large systems. The presented theory performs well for both strong and weak mixing of exciton and CT states, bridging the gap between previously employed methods, which are applicable in only one of these limits. In experimental spectra, the homogeneous linewidth is often too large to resolve all optically allowed transitions individually, resulting in a characteristic two-peak absorption spectrum in both the weak- and strong-coupling regime. Using the scattering matrix technique, we examine the contributions of free and bound states in detail. We conclude that the skewness of the high-frequency peak may be used as a new way to identify the exciton–CT-state coupling strength. [ABSTRACT FROM AUTHOR]

Background: Ultrasound's real-time, high-resolution imaging, and accessibility at the point of care make it a valuable tool for diagnosing clavicle fractures, with growing evidence supporting its diagnostic accuracy compared to other imaging modalities. Objective: To assess the diagnostic utility of ultrasound in detecting clavicle fractures. Methods: A systematic review and meta-analysis were conducted by performing a comprehensive literature search in PubMed, Scopus, Web of Science, and Embase databases up to March 10, 2023, following established guidelines. Eligible studies that reported outcomes of interest were included, relevant data elements were extracted, and data analysis was performed using STATA software version 17.0. Results: Meta-analysis of seven included studies showed high-pooled sensitivity (0.94) and specificity (0.98) values for ultrasonography in diagnosing clavicle fractures, with low to moderate heterogeneity for sensitivity and high heterogeneity for specificity. Meta-regression and subgroup analyses revealed that pediatric studies had higher sensitivity but significantly lower specificity (P=0.01) compared to mixed or adult studies. Additional subgroup analysis in the pediatric group indicated decreased heterogeneity for specificity. Fagan plot analysis demonstrated favorable post-test probabilities for both positive and negative results across varying pre-test probabilities. Additionally, the likelihood ratio scatter matrix showed moderate to high test performance for both exclusion and confirmation purposes. Conclusion: The current literature supports ultrasound as a reliable imaging modality for detecting clavicle fractures. It offers accurate diagnosis without exposing patients, especially children, to radiation. [ABSTRACT FROM AUTHOR]

Studies have found that matrix metalloproteinase-9 (MMP-9) plays a significant role in cancer cell invasion, metastasis, and tumor growth. But it is a challenge to go for highly sensitive and selective detection and targeting of MMP-9 due to the similar structure and function of the MMP proteins family. Herein, a novel surface-enhanced Raman scattering (SERS) sensing strategy was developed based on the aptamer-induced SERS "hot spot" formation for the extremely sensitive and selective determination of MMP-9. To develop the nanosensor, one group of gold nanospheres was modified with MMP-9 aptamer and its complementary strand DNA1, while DNA2 (complementary to DNA1) and the probe molecule 5,5′-dithiobis-(2-nitrobenzoic acid) (DTNB) were grafted on the surface of the other group of gold nanospheres. In the absence of MMP-9, DTNB located on the 13-nm gold nanospheres has only generated a very weak SERS signal. However, when MMP-9 is present, the aptamer preferentially binds to the MMP-9 to construct MMP-9–aptamer complex. The bare DNA1 can recognize and bind to DNA2, which causes them to move in close proximity and create a SERS hot spot effect. Due to this action, the SERS signal of DTNB located at the nanoparticle gap is greatly enhanced, achieving highly sensitive detection of MMP-9. Since the hot spot effect is caused by the aptamer that specifically recognizes MMP-9, the approach exhibits excellent selectivity for MMP-9 detection. Based on the benefits of both high sensitivity and excellent selectivity, this method was used to distinguish the difference in MMP-9 levels between normal and cancer cells as well as the expression of MMP-9 from cancer cells with different degrees of metastasis. In addition, this strategy can accurately reflect the dynamic changes in intracellular MMP-9 levels, stimulated by the MMP-9 activator and inhibitor. This strategy is expected to be transformed into a new technique for diagnosis of specific cancers related to MMP-9 and assessing the extent of cancer occurrence, development and metastasis. [ABSTRACT FROM AUTHOR]

This paper proposes a new, fast, and efficient method for determining the electromagnetic field distribution in two-port E-plane dielectric-loaded uniform rectangular waveguides. The analysis region is divided into individual blocks in the absence and presence of dielectric obstacles. The non-zero electric and magnetic field components are constructed throughout the system via the proposed method by utilizing the generalized scattering matrix method between blocks for unimodal or multimodal excitation. The resulting field distributions are compared to those obtained from commercial software, with very close agreement achieved, but with a significantly reduced computational time for the proposed method. The method is applicable in a straightforward manner and has been tested on both a filter device with relatively complex geometry and a disjoint system with a modal coupling challenge between its elements. The field components' accuracy is also tested by calculating the Poynting vector along the system. Additionally, this approach provides the global scattering parameters at the physical ports as a co-product. The proposed method has the potential to be applied to various two-port networks by using the proposed method according to the considered problem. [ABSTRACT FROM AUTHOR]