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We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known GW self-energy, as well as the particle–particle and electron–hole T-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory. The performance of these schemes on strongly correlated systems (B2 and C2) is also discussed. [ABSTRACT FROM AUTHOR]

Second–harmonic generation (SHG) is forbidden in centrosymmetric materials. However, a signal is observed from interfaces where the symmetry is broken. Whereas the effect can be phenomenologically accommodated, a qualitative and quantitative description remained elusive, preventing the exploration of questions such as how deep below the surface the second–harmonic is generated. A multi–scale approach to compute the total and layer‐dependent intensity of surface SHG from molecular crystals is thus presented. The microscopic origin of surface SHG is identified in layer‐dependent models with embedding partial charges combined with density functional theory (DFT) showing symmetry‐breaking distortions of the electron cloud as the surface layer is approached. The SHG at the molecular level is determined using time‐dependent DFT and then brought to the macroscopic scale through a rigorous self‐consistent multiple scattering formalism. The intensity of the SHG at the surface layer is two orders of magnitude larger than at the next layer below and three orders of magnitude larger than two layers below. This approach can be used for designing and optimizing optical devices containing nonlinear molecular materials, such as molecular laminates. It is shown that a basic Kretschmann‐like setup can enhance the surface SHG of centrosymmetric molecular material a thousand times. [ABSTRACT FROM AUTHOR]

• Nonlinear multiple scattering method is proposed for modeling thin plates with multiple scatterers. • The method can semi-analytically analyze scattering and transmission properties of harmonic waves. • Stop-bands of fundamental and second-harmonic waves are captured simultaneously. • Nonreciprocal transmission of flexural waves is fulfilled and enhanced by defect modes. Developing nonlinear resonant metamaterial plates requires an effective wave simulation method to analyze the wave interactions between multiple nonlinear scatterers. The multiple scattering method has the advantages of high computational efficiency and closed-form displacement solutions in modeling the finitely periodic scatterer array. However, the multiple scattering method of nonlinear scatterers is absent in the available studies of plate structures. In this paper, a nonlinear multiple scattering approach is formulated and analyzed for thin plates with nonlinear resonant scatterers. The resonant scatterer consists of an inner plate with a local resonator modeled by the nonlinear mass-spring system. The motion equation of resonant scatterers is solved using the perturbation technology and wave expansion method. The T-matrix of the resonant scatterer of each order is then derived at the arbitrary harmonic frequency from continuous interfacial conditions of resonant scatterers. Finally, the multiple scattering is formulated for a finitely periodic array of resonant scatterers on a thin plate. Numerical simulations capture the scattering characteristics and stop-band formations of fundamental and second-harmonic waves. Furthermore, the finitely periodic array of nonlinear and linear resonant scatterers achieves the nonreciprocal transmission of flexural waves. These numerical results demonstrate the potential applications of the proposed method in designing metamaterial-based plates with complex transmission properties. [ABSTRACT FROM AUTHOR]

The Frenet–Serret (FS) framework stands as a pivotal tool in shape sensing for various infrastructures. However, this tool suffers from accumulative errors, particularly at inflection points where the normal vector undergoes sign changes. To minimize the error, the traditional FS framework is modified by incorporating the homogeneous matrix transformation (HMT) method for segments containing inflection points. Additionally, inclination information is also used to calculate the unit tangent vector and the unit norm vector at the start point of each segment. This novel approach, termed the FS-HMT method, aims to enhance accuracy. To validate the effectiveness of the proposed method, a simulation of a cantilever column was conducted using finite element software ANSYS 19.2. The numerical results demonstrate the capability of the proposed method to accurately predict curves with inflection points, yielding a maximum error of 1.1%. Subsequently, experimental verification was performed using a 1 m long spring steel sheet, showcasing an error of 4.9%, which is notably lower than that of the traditional FS framework. Our proposed modified FS framework exhibits improved accuracy, especially in scenarios involving inflection points. These findings underscore its potential as a valuable tool for enhanced shape sensing in practical applications. [ABSTRACT FROM AUTHOR]

Continuum robots play the role of end effectors in various surgical robots and endoscopic devices. While soft continuum robots (SCRs) have proven advantages such as safety and compliance, more research and development are required to enhance their capability for specific medical scenarios. This research aims at designing a soft robot, considering the concepts of geometric and kinematic similarities. The chosen application is a semi-invasive medical application known as transesophageal echocardiography (TEE). The feasibility of fabrication of a soft endoscopic device derived from the Chorda dorsalis paragon was shown empirically by producing a three-segment pneumatic SCR. The main novelties include bioinspired design, modeling, and a navigation control strategy presented as a novel algorithm to maintain a kinematic similarity between the soft robot and the rigid counterpart. The kinematic model was derived based on the method of transformation matrices, and an algorithm based on a self-organizing map (SOM) network was developed and applied to realize kinematic similarity. The simulation results indicate that the control method forces the soft robot tip to follow the path of the rigid probe within the prescribed distance error (5 mm). The solution provides a soft robot that can surrogate and succeed the traditional rigid counterpart owing to size, workspace, and kinematics. [ABSTRACT FROM AUTHOR]

We utilize a previously constructed thermodynamic T-matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T-matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results. [ABSTRACT FROM AUTHOR]

In order to fully utilize the control degrees of freedom of a multi-three-phase-star smooth-pole permanent magnet synchronous motor (PMSM), this paper first develops a modeling approach using a new matrix transformation method. The proposed transformation produces decoupled and independent star windings, removing the inductive couplings and preserving the model and torque control's consistency as the number of phases increases. The model, together with a new vector control scheme, is superior for studying the effect of the winding phase angle shift on motor performance. Based on a numerical simulation, this paper focuses on the quality analysis of phase currents, non-sequential currents, and torque ripple with different phase angles for double- and triple-star PMSM drives. The control of a triple-star PMSM is validated, and the behavior analysis is investigated by OPAL-RT. [ABSTRACT FROM AUTHOR]

As an improvement on the traditional model-based Yamaguchi four-component decomposition method, in recent years, to fully utilize the polarization information in the coherency matrix, four-component target decomposition methods Y4R and S4R have been proposed, which are based on the rotation of the coherency matrix and the expansion of the volume model, respectively. At the same time, there is also an improved G4U method proposed based on Y4R and S4R. Although these methods have achieved certain decomposition results, there are still problems with overestimation of volume scattering and insufficient utilization of polarization information. In this paper, a unitary transformation extension to the four-component target decomposition method of PolSAR based on the properties of the Jacobi method is proposed. By analyzing the terms in the basic scattering models, such as volume scattering, in the existing four-component decomposition methods, it is clear that the reason for the existence of the residual matrix in the existing decomposition methods is that the off-diagonal term T 13 and the real part of T 23 of the coherency matrix T do not participate in the four-component decomposition. On this basis, a matrix transformation method is proposed to decouple terms T 13 and Re T 23 , and the residual matrix decomposed based on this method is derived. The performance of the proposed method was validated and evaluated using two datasets. The experimental results indicate that, compared with model-based methods such as Y4R, S4R and G4U, the proposed method can enhance the contribution of double-bounce scattering and odd-bounce scattering power in urban areas in both sets of data. The computational time of the proposed method is equivalent to Y4R, S4R, etc. [ABSTRACT FROM AUTHOR]

In this paper, we give a method for the constructions of Hadamard matrices of composite orders by using suitable T-matrices and known Hadamard matrices. We establish a formula for Tmatrices and Hadamard matrices and discuss under what condition we can get T-matrices from the known Hadamard matrices. [ABSTRACT FROM AUTHOR]

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions A (Z , N) → A (Z ± 2 , N ∓ 2) are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n 2 p − 2 and p 2 n − 2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data. [ABSTRACT FROM AUTHOR]

Quantitative precipitation estimates (QPE) can be further improved using estimation algorithms derived from localized raindrop size distribution (DSD) observations. In this study, DSD measurements from two disdrometer stations within Metro Manila during the Southwest monsoon (SWM) period were used to investigate the microphysical properties of rainfall and develop localized dual-polarimetric relations for different radar bands and rainfall types. Observations show that the DSD in Metro Manila is more distributed to larger diameters compared to Southern Luzon and neighboring countries and regions in the Western Pacific. This is reflected by the relatively higher mass-weighted mean diameter (Dm) and smaller shape (μ) and slope (Λ) parameters measured in the region. The average values of Dm and normalized intercept parameter (Nw) in convective rain samples also suggest that convective rains in Metro Manila are highly influenced by both continental and oceanic convective processes. Dual-polarimetric variables simulated using the T-matrix scattering method showed good agreement with disdrometer-derived reflectivity (ZH) values. The 0.5 dB and 0.3° km−1 thresholds for the differential reflectivity (ZDR) and specific differential phase (KDP) based on the blended algorithm of Cifelli (J Atmos Ocean Technol 28:352-364, 2011) and Thompson et al. (2017) are proven to be useful since the utility of the dual-polarimetric variables as rainfall estimators are shown to have dependencies on the radar band and rainfall type. Evaluation of the QPE products with respect to the C-band shows that R (KDP, ZDR) has the best performance among the dual-pol relations and statistically outperformed the conventional Marshall & Palmer relation [R(ZMP)]. The results show that dual-polarimetric variables such as ZDR and KDP can better represent the DSD properties compared to one-dimensional Z, hence providing more accurate QPE products than the conventional R(Z) relations. [ABSTRACT FROM AUTHOR]

A solution to the electrostatic problem for the spheroidal particle with a spherical core is constructed. To involve the problem geometry in a full manner, in a vicinity of the particle surface the potentials of the fields are represented by their expansions in terms of spheroidal harmonics of Laplace equation, while in a vicinity of the core surface by the expansions in terms of spherical harmonics. Matching of the fields inside the particle shell is made by using the relations between the spheroidal and spherical harmonics. The T-matrix relates the coefficients of expansions of the incident and "scattered" fields. In the present paper, both the particle polarizability related to the main matrix element T11, and the whole T-matrix are considered. The symmetry of the matrix as well as its dependence on the size of the layered particle are shown. A relationship between the T-matrices in the spherical and spheroidal systems was also found. Numerical calculations made for particles of small and large aspect ratios (a/b = 1.5 − 5.0) confirmed high efficiency of the suggested solution in contrast to the methods that use a single spherical basis. [ABSTRACT FROM AUTHOR]

A piecewise-homogeneous medium, consisting of anisotropic layers, is excited by a primary spherical sound wave due to a point source lying in the exterior of the medium or in one of its layers. The direct scattering problem is formulated by means of a modified scalar Helmholtz equation incorporating the anisotropic characteristics of the problem. The T-matrix of the problem is determined analytically by means of a suitable coordinate transformation. Then, the acoustic fields in all layers are obtained. Finally, specific reductions to special cases are presented. [ABSTRACT FROM AUTHOR]

The analysis of nucleon–nucleon elastic and inelastic scattering data is presented by considering the combined interaction of nuclear and electromagnetic potentials of equal range. The exact analytical off-shell solutions of the nonrelativistic Schrödinger equation for the effective potential with the centrifugal term are investigated using ordinary differential equation approach. Numerical results of scattering phase shifts, differential cross-sections and Transition matrices are in sensible conformity with previous works. [ABSTRACT FROM AUTHOR]

While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe–Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems. A comparison with more conventional schemes as well as other wave function methods is also reported. Our results suggest that the T-matrix-based formalism performs best in few-electron systems where the electron density remains low. [ABSTRACT FROM AUTHOR]

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the "t-matrix" model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This "t-matrix" model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts. [ABSTRACT FROM AUTHOR]

This paper proposes a controller synthesis method based on matrix transformation and integer linear programming to address the problem of forbidden state controller design for Petri net systems with uncontrollable transitions. The key idea behind this method involves transforming generalized mutual exclusion constraints (GMEC) that represent the legal states of a Petri net system. Based on the incidence matrix of a Petri net, it divides the set of places into irrelevant places, uncontrollable places, and complementary places. By modifying the weights of complementary places and uncontrollable places in the given GMEC, it then converts the given GMEC into an allowable one by solving integer linear programming problems. Using the allowable GMEC, this paper designs a structural controller for Petri nets based on the principle of place invariants. Finally, it takes a part processing system as an example to show that the application is versatile and efficient, offering an effective solution for the controller design of intelligent manufacturing systems. [ABSTRACT FROM AUTHOR]

In the modern field of microelectronics, the performance of interconnects tends to decrease as the technology node advances. Therefore, Cu-CNT composite TSV interconnects are utilized due to their favorable performance. In this article, Cu-CNT composite TSV interconnects have been studied. The objective of this work was to propose an accurate method for calculating time domain coupling noise in 3D structures based on Cu-CNT composite TSVs. The equivalent lumped element circuit, the NILT method, and the T-matrix were exploited. Throughout the study, the influence of geometric parameters, temperature, and CNT filling ratio were examined. The proposed method has been validated using PSpice results. The obtained results have shown good performance and accuracy. The average percentage error observed is less than 1 %. [ABSTRACT FROM AUTHOR]

The interaction of light with time-varying materials offers intriguing opportunities for controlling light scattering and wavefront manipulation, thereby unlocking fascinating applications in the realm of optics and photonics. In this study, we present an analytical solution for the scattering from a particle made of a material with time-varying permittivity by exploiting the T-matrix approach. Through the manipulation of the active medium's eigenvalues, we demonstrate the pivotal ability to regulate the elements of a dynamically controlled T-matrix, thus enabling precise control over the scattering characteristics of the particle. Crucially, this dynamic control is achieved without resorting to modifying the particle's inherent physical parameters, such as shape, size, and dispersion. We demonstrate that the eigenvalues of the dynamic material can be skillfully manipulated through the adequate choice of the particle's modulation function, resulting in either in-phase or out-of-phase interactions between the magnetic and electric dipole modes, allowing us to satisfy the Kerker conditions at diverse harmonics. The results of the optimal modulation functions are presented in both the near-field and far-field regions, revealing time modulation as a dynamic means of achieving unidirectional scattering. Our findings pave the way for developing time-varying structures comprising dynamic meta-atoms, offering valuable insight into advanced light–matter interactions, and providing lucrative guidance for future research in the realm of dynamic photonic systems. [ABSTRACT FROM AUTHOR]

In this note, we obtain extensions of a theorem of Meyer-König and Zeller and a theorem of Wilansky in that the given results do not require a summability matrix to be a bounded operator from the convergent sequences into themselves. The culmination of the results in this note is that a triangle matrix method T with null columns maps a bounded divergent sequence to a null sequence if and only if the range of T is not closed in the null sequences. [ABSTRACT FROM AUTHOR]

The relations between the T-matrices emerging when solving the problem of light scattering by a spheroid by applying the expansions of the electro-magnetic fields in the employing spheroidal and spherical bases are found. The behavior of the obtained relations is numerically studied, and it is noted that in a wide range of the task parameter values the calculation of the spheroidal T-matrix and its corresponding transformation is the only practical way to derive the spherical T-matrix often used in applications. [ABSTRACT FROM AUTHOR]

In this paper, an improved two‐step method is presented for the sensitivity analysis of vector network analyzer (VNA) S‐parameter measurements due to the non‐ideal line‐reflect‐match (LRM) calibration standards. This improved method is based on the indirect uncertainty propagation mechanism, which is especially suitable for the S‐parameter measurements applying the self‐calibration technique. To further simplify the formula derivation, the deviation matrices [δA] and [δB] are newly defined to represent the uncertainties of the T‐matrices of error boxes. With this definition, formulas for the deviations of device under test (DUT) S‐parameters can be concluded as functions of [δA] and [δB] in a concise form. Eventually, by solving only three linear combinations of the elements from [δA] and [δB], the sensitivity coefficients of DUT S‐parameters due to non‐ideal LRM can be conveniently deduced in an analytical form. Finally, experiments are performed to verify the proposed method. [ABSTRACT FROM AUTHOR]

To improve the imaging accuracy in solving inverse scattering problems with mixed boundary conditions, the authors propose an inverse scattering imaging method based on a physics‐inspired neural network. First, the contrast source inversion and the T‐matrix method are unified to establish a combined parameter model, in which the characteristics of perfect electric conductor and dielectric scatterers are represented by the T‐matrix coefficients t and the dielectric contrast χdie ${\boldsymbol{\chi }}^{die}$ respectively. Considering the influence of singularity of conductor contrast, the PEC region and the DIE contrast are reconstructed separately. Then, an alternative parameter updating neural network method, called APU‐Net, is proposed to update the contrast of dielectric scatterers and the T‐matrix of perfect electric conductor scatterers alternately. The experimental results demonstrate the strong performance of APU‐Net for inverse scattering imaging of PEC‐DIE hybrid targets as well as its improved generalisation ability over existing methods. [ABSTRACT FROM AUTHOR]

The classic formulation of the extended boundary condition method is revisited to inject the regularization operators for the unknown coefficients of the eigen-function expansions for the travelling and standing waves throughout the dielectric scatterer. It is shown that, using the new definitions, the existing algorithm of the scattering field calculation can be kept the same for its well-conditioned version. This is exemplified for scalar 2D problems for both TM and TE polarization under illumination of a line source. The condition numbers of the matrix operators in the new version of the algorithm are drastically reduced when the regularization interfaces are eigen-surfaces of the field expansions, i.e. circles on extended boundaries in the counter null-fields. The arbitrariness of the boundary interface is involved in the calculations, via parameterized contours and effects of elongation and corrugation of the interface boundary contour on the condition of the algorithm is extensively discussed in comparison with the results of the boundary integral equation formulation of the same problem. [ABSTRACT FROM AUTHOR]

The problem of coordinate system alignment must be solved first for the 3D measurement of complex surfaces like turbine blades. Coordinate system alignment is an important prerequisite for path planning and measurement data error analysis in the subsequent measurement process. Due to the complex geometric characteristics of turbine blades, the traditional 3-2-1 method cannot guarantee the accuracy, efficiency and stability of alignment. Therefore, based on the point laser non-contact three-coordinate measuring system, this paper proposes a practical two-step alignment method after the analysis of the advantages and disadvantages of the existing alignment technologies. The proposed method divides the alignment process of complex surface coordinate system into two parts: rough alignment and precise alignment. Rough alignment selects feature points according to local measurement results, and calculates the initial transformation matrix between coordinate systems. On the basis of rough configuration, the improved iterative nearest point algorithm is used to calculate the precise transformation matrix to achieve accurate alignment. The experimental results show that the twostep alignment method proposed in this paper effectively solves the efficiency and accuracy problems of alignment, and has a good robustness. [ABSTRACT FROM AUTHOR]

To meet the fast iteration speed and high computing power requirements of deep learning models, mainstream hardware vendors are increasingly inclined towards heterogeneous systems consisting of general-purpose processors and AI-specific accelerator cores. However, AI-specific accelerator ores only support certain core operators and do not have general programming capabilities. Therefore, how to efficiently deploy deep learning tasks on such heterogeneous architectures is worth further research. Based on the domestically developed FT-Matrix DSP+MatrixZone heterogeneous system platform, this paper designs and implements a deep learning programming framework, called KaiSa. KaiSa analyzes the input parameters of the deep learning model, identifies the operator type, and assigns it to the corresponding computing core. For complex operators, KaiSa automatically completes the optimal search for the block size based on a performance model, improving the performance of dual-core parallel computing. At the same time, KaiSa shields all low-level hardware details to provide users with a friendly programming environment for efficient program development. Experimental results show that KaiSa can achieve performance improvements of up to 39.0%. [ABSTRACT FROM AUTHOR]

The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Padé approximation which interpolates between the known small scattering-rate expansion and the deviation from the Fermi energy. The first two energy-weighted sum rules are shown to be fulfilled independent of the interpolating function for any selfenergy. For various models of one-dimensional Fermions scattering with impurities the quality of the Padé approximation for the spectral function is demonstrated and the reduced density matrix or momentum distribution is reproduced not possessing a jump at the Fermi energy. Though the two-fold expansion is necessary to realize the spectral function and reduced density, the extended quasiparticle approximation itself is sufficient for the description of transport properties due to cancellation of divergent terms under integration. The T-matrix approximation leads to the delay time as the time two particles spend in a correlated state. This contributes to the reduced density matrix and to an additional part in the conductivity which is presented at zero and finite temperatures. Besides a localization at certain impurity concentrations, the conductivity shows a maximum at small temperatures interpreted as onset of superconducting behaviour triggered by impurities. The Tan contact reveals the same universal behaviour as known from electron–electron scattering. [ABSTRACT FROM AUTHOR]

In order to improve the understanding of the microphysical characteristics of raindrop size distribution (DSD) under different rainfall rates (R) classes, and broaden the knowledge of the impact of radar wavelengths and R classes on the QPE of dual-polarization radars in the Tianshan Mountains, a typical arid area in China, we investigated the microphysical characteristics of DSD across R classes and dual-polarimetric radar QPE relationships across radar wavelengths and R classes, based on the DSD data from a PARSIVEL2 disdrometer at Zhaosu in the Tianshan Mountains during the summers of 2020 and 2021. As the R class increased, the DSD became wider and flatter. The mean value of the mass-weighted mean diameters (Dm) increased, while the mean value of logarithm normalized intercept parameters (log10 Nw) decreased after increasing from C1 to C3, as the R class increased. The largest contributions to R and the radar reflectivity factor from large raindrops (diameter > 3 mm) accounted for approximately 50% and 97%, respectively, while 84% of the total raindrops were small raindrops (diameter < 1 mm). Dual-polarization radars—horizontal polarization reflectivity (Zh), differential reflectivity (Zdr), and specific differential phase (Kdp)—were retrieved based on the DSD data using the T-matrix scattering method. The DSD-based polarimetric radar QPE relations of a single-parameter (R(Zh), R(Kdp)), and double-parameters (R(Zh,Zdr), R(Kdp,Zdr)) on the S-, C-, and X-bands were derived and evaluated. Overall, the performance of the R(Kdp) (R(Kdp,Zdr)) scheme was better than that of R(Zh) (R(Zh,Zdr)) for the QPE in the three bands. Furthermore, we have for the first time confirmed and quantified the performance differences in the QPE relationship of dual-polarization radars under different schemes, radar wavelengths, and R classes in typical arid areas of China. Therefore, selecting an appropriate dual-polarization radar band and QPE scheme for different R classes is necessary to improve the QPE ability compared with an independent scheme under all R classes. [ABSTRACT FROM AUTHOR]

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented them as Plithogenic Attributive Subjectively Whole Hyper-Super-Soft-Matrix (PASWHSS-Matrix) and Plithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. [ABSTRACT FROM AUTHOR]

This paper studies the control problem of continuous interval type 2 fuzzy singular fractional-order systems with order 0 < α < 1. A dynamic output feedback control strategy is proposed to solve it. The advantages of our approach with respect to the existing results are threefold. First, the control design allows mismatched membership functions between the controller and the plant, thus enhancing its universality. Second, some specific assumptions on the system matrix are removed, hence improving the generality of our approach. Third, for ease of calculation of the controller gains, the equivalent transformation method and the linear matrix inequality technique are adopted, instead of iterative algorithms or singular value decomposition technique. The simulation results are given to show the effectiveness and the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

The performance of different quantitative precipitation estimation (QPE) relationships is examined using the polarimetric variables from the X-band polarimetric phased-array radars in Guangzhou, China. Three QPE approaches, namely, R(ZH), R(ZH, ZDR) and R(KDP), are developed for horizontal reflectivity, differential reflectivity and specific phase shift rate, respectively. The estimation parameters are determined by fitting the relationships to the observed radar variables using the T-matrix method. The QPE relationships were examined using the data of four heavy precipitation events in southern China. The examination shows that the R(ZH) approach performs better for the precipitation rate less than 5 mm h-1, and R(KDP) is better for the rate higher than 5 mm h-1, while R(ZH, ZDR) has the worst performance. An adaptive approach is developed by taking the advantages of both R(ZH) and R(KDP) approaches to improve the QPE accuracy. [ABSTRACT FROM AUTHOR]

Because of the strong electron–atom interaction, the kinematic theory of diffraction cannot be used to describe the scattering of electrons by an assembly of atoms due to the strong dynamical diffraction that needs to be taken into account. In this paper, the scattering of high‐energy electrons by a regular array of light atoms is solved exactly by applying the T‐matrix formalism to the corresponding Schrödinger's equation in spherical coordinates. The independent atom model is used, where each atom is represented by a sphere with an effective constant potential. The validity of the forward scattering approximation and the phase grating approximation, assumed by the popular multislice method, is discussed, and an alternative interpretation of multiple scattering is proposed and compared with existing interpretations. [ABSTRACT FROM AUTHOR]

In this paper, the temperature dependence of defect modes of several one-dimensional superconducting-dielectrics photonic crystals was studied implementing the matrix transformation method. The thermo-optical effect and the thermal expansion effect were considered for a closer look (to obtain more accurate results). The studied photonic crystals contained SiO2 (L), Bi4Ge3O12 (H), MoSe2 (M) dielectrics, and the YBa2Cu3O7 (S) superconductor. Our results indicated that among the considered photonic crystals, the (HLM)NS(MLH)NL structure had the most temperature sensitivity, which could be applied as a low-temperature sensor and a tunable filter. The thickness of the layers was assumed in the nano-meter range. In order to validate our method, we compared our simulation result with an available experimental data in the literature. [ABSTRACT FROM AUTHOR]

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays produce new materials as 3D lattices of scattering unit cells. Computing the response of objects of arbitrary shape made from such materials is typically computationally prohibitive unless an effective homogeneous medium approximates the discrete material. In here, a homogenization method based on the effective transition (T‐)matrix, Teff${T_{eff}}$ is introduced. Such a matrix captures the exact response of the discrete material, is determined by the T‐matrix of the isolated unit cell and the material lattice vectors, and is free of spatial dispersion. The truncation of Teff${T_{eff}}$ to dipolar order determines the common bi‐anisotropic constitutive relations. When combined with quantum‐chemical and Maxwell solvers, the method allows one to compute the response of arbitrarily‐shaped volumetric patchworks of structured molecular materials and metamaterials. [ABSTRACT FROM AUTHOR]

We discuss the hadron–quark crossover accompanied by the formation of Cooper triples (three-body counterpart of Cooper pairs) by analogy with the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer crossover in two-component fermionic systems. Such a crossover is different from a phase transition, which often involves symmetry breaking. We calculate the in-medium three-body energy from the three-body T-matrix with a phenomenological three-body force characterizing a bound hadronic state in vacuum. With increasing density, the hadronic bound-state pole smoothly undergoes a crossover toward the Cooper triple phase where the in-medium three-body clusters coexist with the quark Fermi sea. The relation to the quarkyonic matter model can also be found in a natural manner. [ABSTRACT FROM AUTHOR]

In this paper, we are devoted to finding Goethals–Seidel sequences by using k-partition, and based on the finite Parseval relation, the construction of Goethals–Seidel sequences could be transformed to the construction of the associated polynomials. Three different structures of Goethals–Seidel sequences will be presented. We first propose a method based on T-matrices directly to obtain a quad of Goethals–Seidel sequences. Next, by introducing the k-partition, we utilize two classes of 8-partitions to obtain a new class of polynomials still remaining the same (anti)symmetrical properties, with which a quad of Goethals–Seidel sequences could be constructed. Moreover, an adoption of the 4-partition together with a quad of four symmetrical sequences can also lead to a quad of Goethals–Seidel sequences. [ABSTRACT FROM AUTHOR]

Several applications of a cylindrical waveguide filled with inhomogeneous materials have been demonstrated. Analytical solutions for modes, an inhomogeneous cylindrical waveguide, are available only for a few material parameters and those are also mostly approximations. We have obtained exact analytical solutions for cylindrical waveguides filled with different inhomogeneous and anisotropic material parameters. Different sets of material parameters are obtained using the geometric transformation method. The analytical and numerical modal field distributions, the value of cutoff frequencies and effective mode indices for different propagating modes are well matched to each other. The inhomogeneity can be used to miniaturize the radial dimensions of the waveguide. This is highly desirable for many applications like sensing, near-field coupling and magnetic resonance imaging (MRI). [ABSTRACT FROM AUTHOR]

Quantitative precipitation estimates (QPE) can be further improved using estimation algorithms derived from localized raindrop size distribution (DSD) observations. In this study, DSD measurements from two disdrometer stations within Metro Manila during the Southwest monsoon (SWM) period were used to investigate the microphysical properties of rainfall and develop localized dual-polarimetric relations for different radar bands and rainfall types. Observations show that the DSD in Metro Manila is more distributed to larger diameters compared to Southern Luzon and neighboring countries and regions in the Western Pacific. This is reflected by the relatively higher mass-weighted mean diameter (Dm) and smaller shape (μ) and slope (Λ) parameters measured in the region. The average values of Dm and normalized intercept parameter (Nw) in convective rain samples also suggest that convective rains in Metro Manila are highly influenced by both continental and oceanic convective processes. Dual-polarimetric variables simulated using the T-matrix scattering method showed good agreement with disdrometer-derived reflectivity (ZH) values. The 0.5 dB and 0.3° km-1 thresholds for the differential reflectivity (ZDR) and specific differential phase (KDP) based on the blended algorithm of Cifelli (J Atmos Ocean Technol 28:352-364, 2011) and Thompson et al. (2017) are proven to be useful since the utility of the dual-polarimetric variables as rainfall estimators are shown to have dependencies on the radar band and rainfall type. Evaluation of the QPE products with respect to the C-band shows that R (KDP, ZDR) has the best performance among the dual-pol relations and statistically outperformed the conventional Marshall & Palmer relation [R(ZMP)]. The results show that dual-polarimetric variables such as ZDR and KDP can better represent the DSD properties compared to one-dimensional Z, hence providing more accurate QPE products than the conventional R(Z) relations. [ABSTRACT FROM AUTHOR]

Visual/Inertial/GNSS (VIG) integrated navigation and positioning systems are widely used in unmanned vehicles and other systems. This VIG system is vulnerable to of GNSS spoofing attacks. Relevant research on the harm that spoofing causes to the system and performance analyses of VIG systems under GNSS spoofing are not sufficient. In this paper, an open-source VIG algorithm, VINS-Fusion, based on nonlinear optimization, is used to analyze the performance of the VIG system under a GNSS spoofing attack. The influence of the visual inertial odometer (VIO) scale estimation error and the transformation matrix deviation in the transition period of spoofing detection is analyzed. Deviation correction methods based on the GNSS-assisted scale compensation coefficient estimation method and optimal pose transformation matrix selection are proposed for VIG-integrated system in spoofing areas. For an area that the integrated system can revisit many times, a global pose map-matching method is proposed. An outfield experiment with a GNSS spoofing attack is carried out in this paper. The experiment result shows that, even if the GNSS measurements are seriously affected by the spoofing, the integrated system still can run independently, following the preset waypoint. The scale compensation coefficient estimation method, the optimal pose transformation matrix selection method and the global pose map-matching method can depress the estimation error under the circumstances of a spoofing attack. [ABSTRACT FROM AUTHOR]

A boundary element modeling for predicting the plasmonic response from a Nanoparticle‐on‐Mirror (NPoM) structure is proposed. The NPoM can be considered as one of the most important platforms in the research on nanophotonics. Instead of using the local response model to describe the optical response of metals, the nonlocal hydrodynamic model is used to account for the dynamics of free electrons in the metallic NP and the metallic mirror beneath. A system of boundary integral equations (BIEs) is derived to describe the interaction of light with the NPoM structure. The BIEs are solved by the boundary element method. To validate the implementation, two exemplary structures are considered: the Nanosphere‐on‐Mirror structure and the Nanocube‐on‐Mirror structure. By contrasting with the results from previous works and the results from a generalized T‐matrix method, both a qualitative and quantitative agreement in the near field and the far field regimes are observed. [ABSTRACT FROM AUTHOR]

The closed-form analytical expressions for the off-shell solutions for Hulthén-distorted Yamaguchi potential are derived to deal with the charged hadron systems. To construct these solutions, the particular integrals of the non-homogeneous Schrödinger equations are utilised in conjunction with the interacting Green’s functions. The Jost functions thus obtained, both on- and off-shell, are exploited to find the half-off-shell T-matrix. The off-shell Jost function exists but off-shell Jost solution for the said potential has not yet been discussed in the literature. The merits of the T-matrix are examined through some model calculations. Exploiting the expressions for on- and half-shell transition matrices, the s-wave elastic and inelastic scattering cross-sections are also estimated. Our results for the proton–proton and proton–oxygen systems are in close agreement with other calculations. [ABSTRACT FROM AUTHOR]

Airborne particulate matter plays an important role in climate change and health impacts, and is generally irregularly shaped and/or forms agglomerates. These particles may be characterized through their light scattering signals. Two-dimensional angular scattering from such particles produce a speckle pattern that is influenced by their morphology (shape and material composition). In what follows, we revisit morphological descriptors obtained from computationally generated light scattering patterns from aggregates of spherical particles. These descriptors are used as inputs to a multivariate statistical algorithm and then classified via supervised machine learning algorithms. The classification results show improved accuracy over previous efforts and demonstrate the utility of the proposed morphological descriptors. [ABSTRACT FROM AUTHOR]

A novel semi-analytical solution is proposed to analyze the consolidation behavior of composite ground with a floating impervious column in unsaturated soil based on the equal-strain hypothesis. The basic governing equations in the reinforced zone and the underlying stratum are first obtained. Using the Laplace transformation and matrix analysis method, a final solution in the Laplace domain is derived. Afterwards, on the basis of Stehfest's method, an inverse Laplace transform is conducted to derive the solution in the time domain. The effectiveness of the proposed solution is then evaluated against the results of finite difference analysis. Moreover, a sensitivity analysis is performed to assess the effects of area replacement ratio, depth improvement ratio, and column stiffness on the dissipation of excess pore-water/air pressure and the average degree of consolidation. Results show that only vertical seepage occurs during the consolidation process of unsaturated composite ground under a condition of equal-strain. The consolidation rate of unsaturated soft ground can be improved by introducing floating impervious columns. The use of larger area replacement ratio, depth improvement ratio, and column stiffness can increase the consolidation speed and reduce the settlement of composite ground with a floating impervious column in unsaturated soil. [ABSTRACT FROM AUTHOR]

The invariant imbedding T-matrix (IIM T-matrix) model is regarded as one of the most promising models for calculating the scattering parameters of non-spherical particles. However, the IIM T-matrix model needs to be iterated along the radial direction when calculating the T-matrix, which involves complex calculations such as matrix inversion and multiplication. Therefore, how to improve its computational efficiency is an important problem to be solved. Focused on particles with N-fold symmetric geometry, this paper deduced the symmetry in the calculation process of the IIM T-matrix model, derived the block iteration scheme of the T-matrix, and contracted the IIM T-matrix program for particles with N-fold symmetric geometry. Discrete Dipole Approximation (DDA) and Geometrical Optics Approximation (IGOA) were employed to verify the accuracy of the improved IIM T-matrix model. The results show that the six phase matrix elements (P11, P12/P11, P22/P11, P33/P11, P34/P11 and P44/P11) calculated by our model are in good agreement with other models. The computational efficiency of the improved IIM T-matrix model was further investigated. As demonstrated by the results, the computational efficiency for the particles with N-fold symmetry improved by nearly 70% with the improvement of the symmetry of U matrix and T matrix. In conclusion, the improved model can remarkably reduce the calculation time while maintaining high accuracy. [ABSTRACT FROM AUTHOR]

Feature extraction of electrical load plays a vital role in providing a reliable basis and guidance for power companies. In this paper, we propose a novel clustering algorithm named the Density-based Matrix Transformation (DBMT) Clustering method to extract features (peaks, valleys and trends) of electrical load curves. The main objective of the algorithm is to reorder the data items until the data items belonging to the same cluster are organized together; that is, the adjacent matrix is rearranged to the type of block diagonal. This method adaptively determines the number of clusters and filters out noise without input global parameters. Moreover, for the specific characteristics of raw electrical load data, we propose a variant of Dynamic Time Warp (DTW) distance, dsDTW, which aligns the peaks, valleys and trends of load curves meanwhile dealing with missing values in different situations. After feeding the dsDTW adjacent matrix to DBMT, the results indicate that our proposal can accurately extract the feature of the load curves compared to different clustering methods. [ABSTRACT FROM AUTHOR]

Multiple scattering of parallel cylinders with arbitrary cross section is computed using the T-matrix of each single scatterer and the general translational matrix for cylindrical waves. Usually, the recommended golden rule to compute the translational matrix is Graf’s addition theorem. However, this approach cannot be properly implemented for some geometries, such as in a two-cylinder case when the center of one of them falls within the minimum circular cylinder that circumscribes the other one. In order to overcome this limitation, a transformation between cylindrical waves and plane waves, followed by propagation of the latter, is proposed. The new approach succeeds due to an adequate truncation of the evanescent plane wave spectrum. This strategy is demonstrated by studying the scattering of three infinite elliptic metallic cylinders for different electrical sizes and observing the convergence of the results as a function of the truncated spectrum. Finally, to conclusively show the interest and applicability of the approach, two more complex problems are treated: a group of infinite elliptic metallic cylinders where two different sizes are combined and a practical real-life filter in substrate integrated waveguide (SIW) technology, including several groups of rectangular dielectric cylinders. [ABSTRACT FROM AUTHOR]

In this article, a unified learning-based approach is introduced to solve inverse scattering problems (ISPs) with mixed boundary conditions (BCs). The scattering behavior of hybrid dielectric and perfect electric conductors (PEC) scatterers is modeled by the T-matrix method. A rough image of the zero-order T-matrix coefficients for unknown scatterers is first reconstructed by the backpropagation (BP) method, which is then refined by an attention-assisted pix2pix generative adversarial network (GAN). The spatial attention mechanism is utilized to enforce the generator network to learn salient features of the unknown scatterers instead of the background. The adversarial training of the generator and the discriminator further enables the reconstructed image to be constrained by high-level features of reference scatterers. Numerical tests on both synthetic and experimental data verify the superior performance of the proposed method for ISP reconstructions with hybrid scatterers. It effectively expands the application scope of learning-based ISP methods to reconstruct scatterers without knowing the BCs of scatterers in advance. [ABSTRACT FROM AUTHOR]

• Impact of fractal dimension on aggregate scattering cross-section predicted by EMA was assessed. • Condition when EMA is more accurate than RDG-FA was proposed with reference to MSTM. • A critical aggregate size parameter value for which EMA is applicable was suggested. Particles within aggregates are commonly in a status of dependent scattering due to the near-field multiple scattering and far-field interferences from neighboring particles. The integral radiative characteristics of fractal aggregates are consequently not only influenced by the monomer size parameter x s , the refractive index n m , and the monomer number N s , but also tied to the fractal dimension D f. The effective-medium approximation (EMA) simplifies the calculation of aggregate radiative characteristics by treating an aggregate and its surrounding medium as a homogeneous sphere with an effective refractive index, and by applying the Lorenz-Mie theory to this equivalent sphere. The study aims to assess the applicability of EMA to predict the scattering cross-section of fractal aggregates consisting of non-absorbing monomers with x s , varying from 0.001 to 1.25, N s ranging from 10 to 500, under different fractal dimensions D f. The accurate results obtained using the multiple spheres T-matrix were used as a reference. In addition, the RDG-FA (Rayleigh-Deybe-Gans Fractal Aggregates) theory, which is widely used for aggregates with monomer size x s ≪ 1, was also evaluated for comparison. The finding reveals that both EMA and RDG-FA provide accurate predictions for aggregates satisfying the equivalent aggregate size parameter χ m less than D f , where the dependent scattering is limited. As the dependent scattering effect increases, the fractal dimension D f emerges as a critical factor influencing EMA's accuracy, with EMA excelling for aggregates with larger fractal dimensions close to 3. Furthermore, 2.1 is a critical value of D f above which EMA outperforms RDG-FA. [ABSTRACT FROM AUTHOR]

The effect of point-like lattice impurities on nanoparticle Raman spectra is studied using both numerical and analytical methods. Particular cases of replacement atoms of various masses, vacancies, and disorder in interatomic bonds are considered. It is shown that the disorder leads not only to the broadening of optical phonon lines but also to the shift of the corresponding Raman peak. The latter can be either positive (i.e., blueshift) or negative (redshift) depending on the type of impurities. Thus there is an additional contribution to the well-known redshift that occurs due to the size-quantization (confinement) effect. Considering nanometer-sized diamond particles as a representative example, we show that the broadening and the shift are, as a rule, of the same order of magnitude. The results are discussed in the framework of the self-consistent T-matrix approach. It is argued that both effects should be considered for accurate treatment of experimental Raman spectra. Simple recipes to do so are formulated for several important cases including NV centers in nanodiamonds. [Display omitted] [ABSTRACT FROM AUTHOR]