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• 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]

• 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]

Relying on the time averaged Poynting vector expressed in terms of beam shape coefficients, dark and superdark theorems are discussed generalizing a previously published dark theorem. The superdark theorem allows one to characterize helical beams (that is to say beams possessing a topological charge) in terms of beam shape coefficients, and to demonstrate that beams with a topological charge equal to ± 2 are not necessarily vortex beams, although it is erroneously traditional to state that helical beams are all vortex beams. • Dark and superdark theorems are established in terms of beam shape coefficients of GLMT. • They allow one to decide on the properties of light intensities (null or not) on the axis of a beam. • And then to decide whether a beam with topological charge is a vortex beam or not. • We may then exhibit examples of beams with topological charges which are not vortex beams. [ABSTRACT FROM AUTHOR]

• A hybrid manipulator for optomechanical modules assembly in an inertial confinement fusion facility is presented. • The analytic inverse kinematics solution is obtained by decomposing the coupled kinematics model into two simple sub-models. • An improved back propagation neural network is proposed to increase the kinematic accuracy. A novel hybrid manipulator is proposed in this work, in order to assemble optomechanical modules in an inertial confinement fusion facility (SG-Ⅲ). Differ from general serial and parallel manipulators, both the inverse and forward kinematics problems of hybrid manipulators are difficult to be solved. Based on an analytic method, the position and orientation mapping functions between the optomechanical module and the parallel manipulators are established, and then the method of transformation matrix is employed to obtain the inverse kinematics solution. The forward kinematics of this hybrid manipulator is highly nonlinear and coupled, so a back propagation neural network using all class one network strategy is trained to approximate the mapping relation. Aiming to improve the accuracy, the network is split into two sub-networks corresponding to the natural property of the outputs. In the end, an improved back propagation neural network is proposed to optimize the network, results illustrate that the kinematic accuracy is increased significantly. [ABSTRACT FROM AUTHOR]

The present paper pursues a fairly usual tradition basically devoted to reviews describing advances in some light scattering theories in which the illuminating beam is described using vector wave function expansions, with expansion coefficients known as beam shape coefficients. After the most recent review dealing with the period 2014–2018, the present review deals with the fiducial period 2019–2023. Relying on about 700 references, it discusses as well other light scattering approaches and applications to optical particle characterization techniques, therefore providing an overview of light scattering approaches and applications during half a decade. • The paper reviews light scattering theories and applications. • It is mainly devoted to T-matrix approaches for structured beams including mainly GLMT. • With about 700 references, it provides the reader with a birdview of advances during the period 2019–2023. [ABSTRACT FROM AUTHOR]

• We study the many-body t-matrix approximation for the weakly interacting bose gas. • We solved the coupled equation for the t-matrix and the condensate density. • This results lead to the correct order of the phase transition. We have proved in the many-body t-matrix approximation for the weakly interacting Bose gas the infrared divergences are exactly removed. We also show that this t-matrix becomes very temperature-dependent and, as the temperature approaches to T c it vanishes at the transition point. This leads to a smooth change of condensate density and compressibility at T c , implying the second order phase transition occurs at T c. [ABSTRACT FROM AUTHOR]

Previous works have been devoted to the symmetry properties of the Poynting vector for longitudinal axisymmetric beams expressed in terms of beam shape coefficients (BSCs). In the present paper, we examine the case of circularly axisymmetric beams. The former is defined as beams whose longitudinal component of the Poynting vector does not depend on the azimuthal angle. The latter is defined as beams whose all components of the Poynting vector do not depend on the azimuthal angle. We establish that two previously studied families of longitudinal axisymmetric beams are actually circularly axisymmetric beams as well. Examples are provided. • Symmetries of Poynting vector may be expressed in terms of beam shape coefficients of the GLMT. • Such symmetries are studied in the case of circularly symmetric beams. • Two families of such circularly symmetric beams are examined. • Examples and counter-examples are provided. [ABSTRACT FROM AUTHOR]

Currently, the majority of publicly raindrop scattering database are calculated with spherical particles. However, as the raindrop grows, the bottom of the raindrop gradually flattens out. The differences of raindrop shape will lead to a difference of the calculated scattering parameters from reality, and further influencing the accuracy of calculations in the fields of radar detection, microwave transmission and satellite remote sensing. In this regard, we developed a non-spherical raindrop scattering parameter database (RP database) with frequencies from 3GHz to 1000GHz. It has been published in an open-access repository. We compared the RP database with the database of Ekelund et al., and found that their difference is basically under 5%; Further the comparisons were also made between the scattering parameters of ellipsoids, spherical raindrops and the non-spherical raindrops, both spherical and ellipsoidal particles have clear difference from non-spherical particles. Finally, we analyzed the group particle attenuation at different frequencies. • A database of the Raindrop Scattering Properties covering the Millimeter and Sub-Millimeter band is established. • The actual shape of the rain droplet is considered in the scattering simulation. • The appicablity of different shape model of rain droplet is systematically analyzed. [ABSTRACT FROM AUTHOR]

• A new method for preparing non spherical particles (burning Ganoderma spores method) has been proposed. • A polarized light simulation transmission model based on T-matrix was established in a smoke simulation environment. • Conducted quantitative and qualitative model validation experiments. In order to deal with the problem of serious pollution caused by non-spherical particles, this study developed and obtained a non-spherical medium based on the theoretical basis of polarized optics and a new non-spherical particle preparation method (burning Ganoderma lucidum spores method). A polarized light simulation transport model based on the T-matrix was established by applying it to the smoke simulation environment. Using this polarization transmission model, simulation experiments were conducted to determine the effects of wavelength, polarization state, optical thickness and various transmission media on the Degree of Polarization (DOP). The simulation results show that both incoming linearly and circularly polarized light undergo depolarization as the optical thickness increases; however, the depolarization of circularly polarized light becomes more severe. In addition, the DOP in the non-spherical particle medium is always larger than that in the spherical particle medium, which indicates that the circularly polarized light is superior to the linearly polarized light in terms of deflection precession. [ABSTRACT FROM AUTHOR]

The T-matrix is a powerful tool that provides the complete description of the linear interaction between the electromagnetic field and a given object. In here, we generalize the usual monochromatic formalism to the case of polychromatic field-matter interaction. The group of transformations of special relativity provides the guidance for building the new formalism, which is inherently polychromatic. The polychromatic T-matrix affords the direct treatment of the interaction of electromagnetic pulses with objects, even when the objects move at constant relativistic speeds. • We expand the T-matrix method to the domain of polychromatic fields. • We put the T-matrix method in the framework of representations of the Poincare group. • We derive the matrix element of the Lorentz boost for the T-matrix in closed form. [ABSTRACT FROM AUTHOR]

Aerodynamic load is one of the important loads that must be considered for wind-wave energy hybrid devices. In this study, the effects of blade angle and foundation structure vibration on aerodynamic loads are considered, and the traditional blade element momentum (BEM) is dynamically modified by the method of coordinate matrix transformation and vibration function analysis, starting from the relative inflow angle and the instantaneous wind speed of the wind turbine, and the aerodynamic loads of the wind turbine were simulated by using the improved BEM theory. The correctness of the proposed method in this study is verified by comparing the data of a large number of researchers and the computational results of OpenFast. A simulation study has been carried out using AQWA, combining the modified aerodynamic load of the wind turbine and the hydrodynamic load of the wave energy device, to analyze the variation trend of the base structure response of the wind-wave hybrid device under general and extreme conditions. The results show that the method developed in this paper can provide theoretical reference for the development and stable operation of wind-wave hybrid device. • In this study, the classical BEM theory was modified based on the blade installation angle and foundation structure vibration. • The load fluctuation rules of the structure under the combined effect of blade angle and foundation vibration were revealed. • The distribution rules of the axial thrust of the blades were obtained by considered the effects of wind shear and fluctuating wind on the aerodynamic loads. • The response change rules of the foundation structure of hybrid devices under general and extreme conditions were analyzed. [ABSTRACT FROM AUTHOR]

Analytical expression for the Hulthén off-shell T -matrix in all partial waves is constructed in its maximal reduced form. As a basic requirement the off-shell solutions and Jost function are first developed by following the differential equation approach to the problem together with judicious exploitation of the properties of certain special functions of mathematical physics. The off-shell T -matrix is found to be in order with respect to its limiting behaviours and off-shell unitarity. [ABSTRACT FROM AUTHOR]

The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the 1-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the 2-D case of Toeplitz-block Toeplitz (TBT) matrices, described a minimal information, which is necessary to recover the inverse matrices, and gave a complete characterisation of the inverse matrices. Now, we develop our approach for the more complicated cases of the block TBT-matrices and of the 3-D Toeplitz matrices. Some important special cases are treated as well. [ABSTRACT FROM AUTHOR]

Due to suffering the thermal and mechanical loadings simultaneously, metamaterials integrating with the customizable coefficient of thermal expansion (CTE) and high mechanical performances are desirable to ensure the thermal and structural stabilities in engineering devices. Hence, various multi-phase metamaterials with programmable CTEs and mechanical performances were developed. Specifically, inspired by the mixture of multiple phases in composites and the rigid rotations of framework structures in materials with negative CTE, a typical pyramid unit was introduced. Additionally, two series of metamaterials were systematically designed, which were constructed in batches from different units through the matrix transformation method. The CTEs of the metamaterials were theoretically established and analyzed. Besides, mechanical performances, including relative density, stiffness and strength were also calculated and discussed. The results suggest that the directionality and magnitude of CTEs are determined by the constructing principle of multi-fold rotations. In addition, the large ranges of programmable CTEs and high load-bearing capacity are available in the devised metamaterials by reasonably modulating the geometrical parameters. The thermal expansion and mechanical performances of the metamaterials could be synchronously programmed. The diversity of the phase configurations and geometrical architectures in the metamaterials offers the opportunity to satisfy manifold requirements in different applications. [ABSTRACT FROM AUTHOR]

The approximation of real non-spherical scatterers by spheroids is used in various applications. It often requires fast massive calculations of the optical properties of spheroids. The most powerful approach to that is known to be a field expansion in terms of spheroidal wave functions, in particular, in the way suggested by Farafonov over 30 years ago. We improve the main shortcomings of such an approach. Our solution is formulated in terms of normalised spheroidal functions, and firstly for their definition given by Meixner & Schäfke, which is computationally favourable and is required by the unique subroutines recently created to compute these functions. By means of T -matrix transformations we solve a long-standing major problem of Farafonov's version, namely the accuracy and time losses for one kind (TE mode) of the incident wave polarisation. Apart from this and other improvements of this solution, for the first time we relate its single particle spheroidal T -matrix to the standard spherical one which is widely employed for particle ensembles. The constructed algorithm has been extensively numerically tested. It is found to be very accurate for dielectric spheroids with the aspect ratio a / b reaching 100 and the diffraction (size) parameter x a = 2 π a / λ as large as 300, where a and b are the major and minor semi-axes, respectively, λ is the wavelength. The algorithm is supplied with a program interface to the free package CosTuuM to perform parallel computations of various optical properties for ensembles of spheroids with different distributions over orientation (alignment) and shape. • The approximation of real scatterers by spheroids is still in use in some fields. • Old codes using the field expansions in spheroidal functions need improvements. • SVM-algorithm to treat spheroids with diffraction parameter up to 300 is suggested. • The code is included in a package to prepare data for polarised radiative transfer. [ABSTRACT FROM AUTHOR]

The accurate calculation of magnetic energy losses for electromagnetic materials directly affects the global optimization design and operating efficiency of electromagnetic devices, especially under high frequency excitation. This study gropes for measurement methods of hysteresis, loss, and temperature rise characteristics for magnetostrictive Tb-Dy-Fe alloys materials under comprehensive operation conditions of high-frequency excitation, compressive stresses, temperature, and DC bias. Based on the measured data, a multiple variables loss matrix that can describe the characteristics of multiple energy fields (electromagnetic-, thermal- and mechanical fields) is established. Using loss matrix transformation method, the variation of hysteresis loss coefficients and generalized eddy current loss coefficients with different energy field characteristic variables are obtained. By establishing a dual statistical framework of sensitivity and deviation degree, the main influence variables which have the greatest impact on loss coefficients are extracted from these variables. Then a loss model for magnetostrictive material considering comprehensive operation conditions is presented which can describe the output characteristics of electromagnetic devices with strong non-linearity and multi-coupling effects among different energy fields. Furthermore, this method allows for the expansion of dimensions of linear or nonlinear variables and considers more energy fields, enabling a comprehensive analysis of interplay between multiple fields and facilitating engineering calculations. • A measurement method for high-frequency magnetic energy losses of magnetostrictive Tb-Dy-Fe alloys under different energy fields is constructed. • A new magnetic loss calculation model is proposed and the loss and hysteresis properties are analysis for magnetostrictive Tb-Dy-Fe alloy under multivariable comprehensive operation conditions. • A new method is proposed to expand the dimensions of linear or nonlinear variables, and to consider more energy fields related to Tb-Dy-Fe alloys. [ABSTRACT FROM AUTHOR]

The Radiative transfer coherent backscattering (RT-CB) code is extended to apply to dense discrete random media of optically soft spherical particles. This is achieved by utilizing the well-known static-structure-factor (SSF) correction derived from the Percus–Yevick approximation for sticky-hard-sphere (SHS) pair correlation function. The code is verified against the numerically exact electromagnetic method for small spherical media consisting of submicrometer-sized icy particles at optical wavelengths. The SSF-corrected RT-CB method significantly improves solution accuracy, and the solution agrees well with the numerically exact solution when the packing density is less than 20% and particles are optically soft, i.e., the refractive index of particles is close to that of the background medium. • RT-CB is extended to dense media using the static-structure-factor (SSF) correction. • The SSF correction is implemented using the Percus–Yevick approximation. • The SSF-corrected RT-CB code is compared with the superposition T-matrix code. • The SSF correction improves the accuracy of RT-CB solution for icy particles. [ABSTRACT FROM AUTHOR]

A convergence result is stated for the numerical solution of space-fractional diffusion problems. For the spatial discretization, an arbitrary family of finite elements can be used combined with the matrix transformation technique. The analysis covers the application of the implicit Euler method for time integration to ensure unconditional stability. The spatial convergence rate does not depend on the fractional power of the Laplacian operator. An efficient numerical implementation is developed avoiding the direct computation of matrix powers. • Fractional-order diffusion problems can be simulated efficiently using standard finite element discretization. • Higher-order spatial convergence can be proved, independently of the power of the Dirichlet Laplacian. • Implicit time stepping ensures unconditional stability. • Practically, only sparse matrix–vector products are computed resulting in an efficient computational algorithm. [ABSTRACT FROM AUTHOR]

The dual-channel phase-shifting interferometry (DC-PSI) has been focused widely in the dynamic measurement field because of its outstanding advantages. The interferograms matching between two channels is a key factor to the high precision phase retrieval. Suffered from the relative poses of different channel cameras in six-degree of freedom (S-DOF), the interferograms matching between two channels, including translation, rotation and scaling, is always a difficult problem in the DC-PSI. Aiming at the only translation mismatching is here considered and the iterations are needed to get the translation parameters in the translation method, a simplified matching method based on the transformation matrix is proposed, minding all kinds of interferograms mismatching. In the proposed method, only one shot to the calibration plate is needed to obtain the adjustment parameters and the interferograms is matched quickly and precisely. Both the simulation and experimental results demonstrate that the proposed method can improve the phase retrieval accuracy and interferograms matching efficiency. [ABSTRACT FROM AUTHOR]

• "Electrostatic T-matrix for a torus on bases of toroidal and spherical harmonics". • New analytic expressions for solving the extended boundary condition method for a dielectric torus in the static limit • Presentation of series relationships between toroidal and spherical harmonics in English (they have been presented before but in a Russian paper which is hard to access). New expressions for the series coefficients are also derived. • Analytic expressions for the long wavelength limit of the conventional electromagnetic T-matrix for a torus. • New method of calculating the plasmon resonance conditions. • New simple analytic approximations for the T-matrix and polarizability of a thin dielectric torus. Semi-analytic expressions for the static limit of the T -matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static excitation is solved using toroidal harmonics and the extended boundary condition method to obtain analytic expressions for auxiliary Q and P -matrices, from which the T -matrix is given by their division. By applying the basis transformations between toroidal and spherical harmonics, the quasi-static limit of the T -matrix block for electric multipole coupling is obtained. For the toroidal geometry there are two similar T -matrices on a spherical basis, for computing the scattered field both near the origin and in the far field. Static limits of the optical cross-sections are computed, and analytic expressions for the limit of a thin ring are derived. [ABSTRACT FROM AUTHOR]

• Objects can be places closely in T-matrix formalism. • Circumscribing spheres can intersect for non-spherical obstacles. • Transformation of spherical vector waves helps in superposition T-matrix method. • Accurate scattering results for two closely adjacent disks can be achieved. • Several scattering obstacles can be joined in a single T-matrix. This paper presents a novel method to calculate the T-matrix for two non-spherical obstacles positioned close to each other, where the individual circumscribed spheres intersect. This is achieved by translating the obstacles coordinate systems, using translation matrices for spherical vector waves. The new circumscribing spheres enables the obstacles to be positioned close to each other. A new total T-matrix of the two-obstacle system can then be calculated using methods for composite particles, i.e. , the superposition T-matrix method. This total T-matrix will generally be larger than the original ones, depending on the sizes of the circumscribing spheres used in the coordinate translation procedure. However, it is shown that the total T-matrix can be truncated after transformation to a common origin, without degrading the accuracy. The total truncated T-matrix is only slightly larger than the original individual ones. The method is demonstrated for electromagnetic scattering simulations of two metallic disks, closely adjacent to each other. [ABSTRACT FROM AUTHOR]

• A positional coding strategy is employed to incorporate timing information into the total power sequence. • A sequence matrix transformation method is proposed to create the time sequence matrix. • Feature expression ability of the time sequence matrix is enhanced through matrix dimension-rising. • A cross stage partial network is established by using a dimension-rising matrix for electrical load monitoring. Non-intrusive load monitoring can obtain the operation state of single device from the total power sequence. To achieve high-precision non-intrusive load monitoring, this study proposes a novel method by coupling sequence matrix reconstruction and cross stage partial network. The timing variation information hidden in the total power sequence is derived through sequence matrix transformation and matrix dimension rising, forming a three-dimensional matrix. Then, this matrix is sent into a cross stage partial network to estimate the device power consumption. Especially, the established cross stage partial network adopts a feature concatenation strategy, greatly reducing the network parameters. Unlike traditional neural network methods, the proposed method makes full utilization of the timing variation information of total power consumption. Experiments are carried out on the load monitoring platform to verify the method feasibility. Results show that the proposed method can non-intrusively decompose the device power consumption, with strong robustness and generalization ability. [ABSTRACT FROM AUTHOR]

Internal short circuit (ISC) is a serious safety hazard for lithium-ion battery packs. How to comprehensively detect and evaluate ISC in battery packs remains a challenging problem. Motivated by this, this paper proposes an ISC detection method based on the transformation matrix and an ISC resistance calculation method based on an improved state-space model. Specifically, benefiting from the descriptive ability of the transformation matrix for curve changes, the shear element in the transformation matrix is used to capture the skewed and downward voltage pattern of the ISC cell in the battery pack. An online detection flow is designed based on the opposite variation relationship between the shear elements calculated from adjacent cells. Moreover, an improved state-space model is developed to directly estimate the ISC current, which ensures that the weight of the ISC current in the model is unrestricted. A dual extended Kalman filter with separated time scales is deployed to obtain accurate state estimations. Experimental results validate the effectiveness and advantages of the ISC detection method, as well as the high accuracy of the ISC resistance calculation method. • Both ISC detection and ISC evaluation are implemented in this paper. • Transformation matrix and shear element are introduced to ISC detection. • An improved state-space model is developed to estimate ISC current and resistance. • Comparative studies demonstrate the superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

• T-matrix methods for structured beam illumination are reviewed for the fiducial period 2014–2018. • Main theoretical aspects concern GLMTs and EBCM. • Main experimental aspects concern mechanical effects of light and optical particle characterization. T-matrix methods for electromagnetic structured beams mainly encompass Generalized Lorenz-Mie Theories (GLMTs) which form a set of analytical approaches dealing with the interaction between electromagnetic structured beams and a class of particles possessing enough symmetries to allow one to use the method of separation of variables, and Extended Boundary Condition Method (EBCM) which is a semi-analytical method dealing in principle with arbitrary shaped particles. Both approaches, when dealing with structured beams (in principle in the case of GLMTs and occasionally in the case of EBCM) rely on the description of the illuminating beam in terms of Beam Shape Coefficients (BSCs). The present paper provides a commented reference database concerning GLMTs and EBCM for structured beams, and related topics for the period 2014–2018. [ABSTRACT FROM AUTHOR]

• Optical properties and radiative forcing of tar ball aggregates, individual tar balls, and volume equivalent spheres are calculated from 350 to 1150 nm using T-Matrix and Lorenz-Mie simulations. • A sensitivity analysis is performed for different refractive indices, and different monomer sizes and numbers. • Single scattering albedo and hemispherical upscatter fraction of tar ball aggregates differ from individual tar balls by up to 77% and more than 100%, respectively. • Over dark surfaces, the top of the atmosphere simple forcing efficiency of tar ball aggregates differs from individual tar balls by up to 53%. Image, graphical abstract Tar balls are frequently found in slightly aged biomass burning plumes. They are spherical in shape, have diameters between ∼100 and 300 nm, are amorphous and composed mostly of oxygen and carbon. Tar balls are light absorbing and considered to be a component of brown carbon. Tar balls have been typically reported and analyzed as individual spheres; however, in a recent study, we reported the presence of significant fractions of fractal-like aggregates made of several tar balls in fire plumes from different geographical locations. Aggregation affects the optical properties of particles; therefore, we use T-Matrix and Lorenz-Mie simulations to explore the effects of aggregation on the tar balls' optical properties in the 350 – 1150 nm wavelength range. We also evaluate the effects of different refractive indices available from the literature, different monomer numbers, and monomer sizes, as these are key factors determining the aggregates optical properties. Furthermore, we estimate the simple forcing efficiency for low and high surface albedos. Aggregates have a single scattering albedo (SSA) higher than that of individual tar balls (ΔSSA 550 nm up to 0.22). The hemispherical upscatter fraction of individual tar balls is more than 100% larger than for tar ball aggregates in many cases. The top of the atmosphere simple forcing efficiency over dark surfaces shows large variabilities with an increase up to ∼53% for tar ball aggregates compared to individual tar balls. These results demonstrate that aggregation of tar balls can have a significant impact on their optical properties and radiative forcing. [ABSTRACT FROM AUTHOR]

Abstract In the materials level, a review for damping capacity of cement-matrix composites modified by various additives is presented in order to summarize the knowledge development in this field. With the aid of stiffness mismatch between the phase interface and the viscoelasticity supplied by the appropriate polymer particle or latex in the cement-matrix composites, the damping capacity can be increased with slightly decrease of the stiffness and strength. Friction as the cracks in the matrix slides over the fiber at high shear stress is found to be the main damping mechanism in the fiber reinforced concrete. Filler effect should be taken care with the particle size and volume fraction of the inorganic powders modified cement matrix composites. The multiple phase boundaries and multiple interfaces between nanotubes and cement-matrix exhibit higher possibility of the interfacial slippage that can cause higher energy dissipation. Although not widely exploited yet, both network graphite and low stiffness aggregates show the potential to be tailored for damping enhancement purpose by interfacial engineering. Highlights • Damping problems needs to be always ameliorated in both theory and practice. • Damping mechanisms involving stiffness mismatch, interface friction, interlocking and interfacing engineering are reviewed. • Both micro-particle damping and interlocking damping microstructural engineering are very promising in the future. [ABSTRACT FROM AUTHOR]

Highlights • Beam shape coefficients of Laguerre–Gauss beams freely propagating cannot be speedily enough evaluated by using quadratures. • Evaluations by using a localized approximation must be used with care because they may e flawed. • We present a formulation to express rigorously and analytically the beam shape coefficients of Laguerre–Gauss beams by using finite series. Abstract When using some analytical and semi-analytical scattering theories such as Generalized Lorenz–Mie Theories (GLMTs) and Extended Boundary Condition Method (EBCM) for structured beams, electromagnetic fields, expanded over a set of vector wave functions, may be encoded in some coefficients known as Beam Shape Coefficients (BSCs). In the case of Laguerre–Gauss beams freely propagating, the evaluation of BSCs by using numerical quadratures is time-consuming while localized approximations have been shown to be of limited validity. The present paper therefore establishes finite series expressions to evaluate the BSCs of Laguerre–Gauss beams freely propagating in a rigorous framework, which has the known advantage of speeding up computations with respect to the use of a numerical quadrature technique. [ABSTRACT FROM AUTHOR]

Highlights • A model based on losses coupling is proposed for voice based disease detection. • Regression targets are relaxed to obtain more discriminant representation. • Low-rank constraints are imposed to make the representation more compact. • Key factors for the methods are separately analyzed by experiment. Abstract Voice analysis provides a non-invasive way for disease detection, in which most methods only consider a single audio, although different audios contain complementary information and a fusion of them is beneficial. In this paper, a novel model JOLL4R (JOint Learning based on Label Relaxed low-Rank Ridge Regression) is proposed to fuse audios for voice based disease detection. First, the model couples the regression losses from two audios together to jointly learn a transformation matrix for each audio. Secondly, the conventional zero-one regression targets are relaxed by the ϵ-dragging technique so that the margins between different classes are enlarged. Third, low-rank constraint is imposed to exploit the correlation structure among different classes. The proposed algorithm not only enables to consider multiple audios, but also adjusts the weight of each audio adaptively. Due to the design of losses coupling, ϵ-dragging technique, and low rank constraint, high performance is achieved. Experiments conducted on two disease detection tasks, each with six types of fusion, show that our fusion approach outperforms the case of using a single audio and another two fusion methods. Finally, key factors in JOLL4R are analyzed. [ABSTRACT FROM AUTHOR]

Abstract Previous JQSRT special issues devoted to the "Laser-light and Interactions with Particles (LIP)" conferences were accompanied by prefaces written for issues published in a single volume, followed by peer-reviewer papers based on the topics discussed during the conferences, see Gouesbet and Brunel (2013) [1] in [2] , Gouesbet and Onofri (2015) [3] in [4] , and Gouesbet and Onofri (2017) [5] in [6]. Papers associated to the last LIP-conference, however, have been published as a virtual topical issue, the word "virtual" meaning that the papers have been published once they have been accepted, rather than collected in a single issue of JQSRT. In other words, the authors of accepted manuscripts have seen their papers officially published without having to wait for the rest of the manuscripts to get accepted. The present text is therefore rather an afterword than a preface. [ABSTRACT FROM AUTHOR]

Abstract Transfer learning across heterogeneous feature spaces can, in general, be a very difficult problem in practice due to the heterogeneity of features and lack of correspondence between data points of different domains. In this paper, we present a novel supervised domain adaptation algorithm (SHDA-RF) that transfers knowledge from a data-rich source domain to a target domain with only few training instances. The proposed method makes use of random forests to identify pivot features that bridge the two domains. The key idea of the proposed feature transfer approach is that every path in a decision tree leading to a partition of the data is associated with a certain label distribution and the label distributions that appear both in the source and target random forest models can be used as pivots for bridging the two domains. This information is used to generate a sparse feature transformation matrix, which maps patterns from the source feature space to the target feature space. The target model is then retrained along with the projected source data. We conduct extensive experiments on diverse datasets of varying dimensions and sparsity to verify the superiority of the proposed approach over other baseline and state of the art transfer approaches. [ABSTRACT FROM AUTHOR]

Abstract Heterodyne lidar echoes in atmospheric detection are greatly affected by the shapes of aerosols. With the aid of T-matrix and vector Monte Carlo simulation, we investigated the properties of lidar echoes backscattered by randomly oriented polydisperse aerosols, including the soot, sea salt and mineral aerosols. The degree of polarization (DoP) and backscattered photon numbers in different range bins are calculated when the launched laser pulses are linearly polarized light and circularly polarized light at 1.55 μm. There are reductions of DoP along the 10 km detection path, which vary with aspect ratios (AR) and aerosol types. The ARs are chosen within 0.5–2.0 for cylinders and 0.3–1.0 for spheroids. The lidar echoes in soot aerosols have the largest DoP which is higher than 0.8. Moreover, the shape fading factor and polarization fading factor are defined and calculated based on the effective backscattered photon numbers, which shows that the mineral aerosols in nuc.mode (MINM) is less affected by aerosol shapes and laser polarization states, and that the LPL is suitable for the heterodyne detection of nonspherical atmospheric aerosols. The results provide echo characteristic deviations from the spherical particle scattering, which can be used in the practical modeling of atmospheric echoes and designs of heterodyne lidars. [ABSTRACT FROM AUTHOR]

Abstract A thermodynamic quantum many-body T -matrix approach is employed to study the spectral and transport properties of the quark-gluon plasma at moderate temperatures where nonperturbative effects are essential. For the partonic two-body interaction we utilize a QCD-inspired Hamiltonian whose color forces are motivated by the heavy-quark (HQ) limit including remnants of the confining force, and augmented by relativistic corrections. We solve the in-medium parton propagators and T -matrices selfconsistently and resum the skeleton diagrams for the equation of state (EoS) to all orders thereby accounting for the dynamical formation of two-body bound states. Two types solutions for the in-medium potential are found in when fitting to lattice-QCD data for the EoS, HQ free energy and quarkonium correlators: a weakly-coupled scenario (WCS) with a (real part of the) potential close to the free energy, resulting in moderately broadened spectral functions and weak bound states near T c , and a strongly-coupled scenario (SCS), with a much stronger potential which produces large imaginary parts ("melting" the parton spectral functions) and generates strong bound states near T c. We calculate pertinent transport coefficients (specific shear viscosity and HQ diffusion coefficient) and argue that their constraints from heavy-ion phenomenology unambiguously favor the strongly-coupled scenario. [ABSTRACT FROM AUTHOR]

Highlights • Speckle size from two-dimensional angular optical scattering (TAOS) is strongly negatively correlated with cluster size of aerosol. • Simulations show that analysis of two-dimensional angular optical scattering (TAOS) is able to distinguish between non-absorbing, weakly-absorbing, and strongly-absorbing single aerosol particles. Abstract Measuring the absorption of a single aerosol particle is a challenging endeavor. Of the few techniques available, none are suitable for measuring the single-particle absorption of coarse-mode nonspherical aerosols. Analysis of two-dimensional angular optical scattering (TAOS) patterns provide a possible pathway to perform this measurement. Using a Multiple-Sphere T-Matrix (MSTM) code, we simulate the captured TAOS patterns with geometries similar to a previously designed instrument. By analyzing the size of the speckle and the integrated irradiance of these simulated TAOS patterns, we are able to distinguish between high-absorbing, weak-absorbing, and non-absorbing particles over the size range of 2 µm to 10 µm. In particular, the speckle present in the scattering patterns provides a means to estimate the size of the particle. Once the size of the particle is known, the integrated irradiance provides insight into the absorption of the particle. [ABSTRACT FROM AUTHOR]

Highlights • The spheroidal beam shape coefficients are investigated by using an intrinsic method, for the case of general oblique illumination. • The analytic solution is constructed within the framework of the GLMT. • Numerical results concerning beam shape coefficients in spheroidal coordinates are presented. Abstract When dealing with T-matrix scattering, e.g. in the framework of Generalized Lorenz-Mie Theory (GLMT) or of Extended Boundary Condition Method (EBCM), the incident electromagnetic fields are expanded over a set of vectorial wave functions, with expansion coefficients expressed in terms of beam shape coefficients (BSCs). In the case of structured beams, the evaluation of these BSCs may constitute a challenging issue, particularly in the case of spheroidal coordinates. BSCs in spheroidal coordinates have been originally evaluated using an extrinsic method, i.e. they have been expressed in terms of more conventional BSCs in spherical coordinates. Later on, it has been possible to provide expressions to evaluate spheroidal BSCs using an intrinsic approach, i.e. by working only inside the spheroidal coordinate system used to deal with the scattering problem. Fairly recently, the intrinsic method for the evaluation of BSCs in spheroidal coordinates for on-axis standard configuration has been released in the archival literature. The present paper extends the intrinsic method to the case of oblique illumination. It also serves as a review devoted to GLMTs in spheroidal coordinates. [ABSTRACT FROM AUTHOR]

Highlights • We review the recurrence relations for T-matrix calculation. • It is proved that the recurrence relations of the invariant embedding T-matrix method and the superposition T-matrix method are analytically equivalent. • It is shown that the recurrence schemes of the superposition T-matrix method are morestable than that of the invariant embedding T-matrix method. Abstract In this paper, we present a consistent analysis of the methods dealing with the derivation of recurrence relations for calculation of the T -matrix. Central and forward recurrence relations are obtained in the framework of the invariant embedding T -matrix method, the matrix Riccati equation method, and the superposition T -matrix method. The accuracies and efficiencies of the central and forward recurrence schemes are analyzed, and some implementation issues related to the improvement of the numerical accuracy and to the problem of overcoming of overflow errors are discussed. [ABSTRACT FROM AUTHOR]

Highlights • The position relationship between the rotary and linear axis is characterized. • A method for identifying the position relationship by laser tracker is proposed. • Simulations and experiments verify the feasibility of the proposed method. Abstract In the multi-axis machining process, the relative position relationship between the linear and rotary axis also has certain influence on the machining accuracy in addition to 6 geometric errors of each axis. How to accurately detect and compensate for this error will have a positive effect on further improving the machining of multi-axis machine tool. The laser tracker is adopted multi-station and time-sharing measurement to identify the relative position relationship between the rotary and linear axis on the basis of global positioning system principle in this paper, which will provide data support for accuracy compensation for multi-axis machine tool. The relative position relationship between the rotary and linear axis is characterized by the homogeneous transformation matrix, and its influence on the motion accuracy of machine tool is also analyzed. Meanwhile, the mathematical model concerning on identifying the relative position relationship between the rotary and linear axis with laser tracker is established, and the corresponding measurement algorithm of machine tool motion and identification algorithm of the relative position relationship are derived respectively. The feasibility and accuracy of the derived algorithms are demonstrated in simulations. Meanwhile, the experiment further validates the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights • Scattering matrix of mineral dust is measured in laboratory from 176.0° to 180.0°. • A laboratory polarimeter has hence been built and validated on spherical particles. • The slopes of the scattering matrix elements tend towards zero at π-angle. • Our laboratory findings are in good agreement with T-matrix numerical code. Abstract In this paper, the scattering matrix elements of an ensemble of mineral dust particles are for the first time evaluated in laboratory for scattering angles ranging from 176.0° to the π-backscattering angle of 180.0° with a high angular resolution of 0.4° and compared with the outputs of T-matrix numerical code. Elastic light scattering is addressed at near and exact backscattering angles with a newly-built laboratory polarimeter, validated on spherical particles following the Lorenz–Mie theory. The ratios f ij (θ) = F ij (θ)/ F 11 (θ) of the scattering matrix elements of mineral dust particles are then precisely evaluated in laboratory from 176.0° up to 180.0° with a 0.4° angular resolution (even 0.2° between 179.2° and 180.0°), which is new. When approaching the π-backscattering angle, the slopes of the scattering matrix elements are almost zero, as theoretically predicted by Hovenier and Guirado [17]. Moreover, our laboratory findings are found in good agreement with the outputs of the T-matrix numerical code, showing the ability of the spheroidal model to describe light-scattering by mineral dust also from near to exact backscattering. Atmospheric implications for polarization lidar retrievals are then discussed in terms of linear and circular depolarization ratios for mineral dust. These results, which complement other existing light scattering experiments, may be used to extrapolate light scattering by mineral dust particles up the π-backscattering angle, which is useful in radiative transfer and climatology, in which backscattering is involved. [ABSTRACT FROM AUTHOR]

Abstract The introduction of the Parikh matrix mapping by Mateescu et al. in 2001 gave rise to the injectivity problem, that is, the characterization of words having the same Parikh matrix. Certain elementary rewriting rules have been successful in solving this problem for the binary alphabet, yet they do not suffice for the general case. This paper studies these elementary rewriting rules exclusively for the ternary alphabet. Certain labeled graphs, termed as core transformation graphs, are introduced and used to study the structural changes in ternary words upon applications of these elementary rewriting rules. For an arbitrary core transformation graph, all possibilities of the labels on its edges are exhausted and, for each label, the pairs of vertices forming the corresponding edges are characterized. Finally, we obtain results relating core transformation graphs to elementarily matrix equivalent words. [ABSTRACT FROM AUTHOR]

Abstract The paper examines the proposed approach of using T-matrix model to convert dynamic moduli (Young's modulus and Poisson's ratio) determined by sonic well logging to values equivalent to values of static moduli (called effective moduli). The chosen approach is particularly suitable for rock masses consisting of solid rocks with irregular local cracking. The proposed approach is based on the fact that for intact rock with Young's modulus values on the order of several tens of GPa and strength σ c on the order of several tens of MPa, the values of static and dynamic moduli are equivalent. Any fractures in the rock will cause the elastic behaviour to cease being linear and a difference will appear between the values of static and dynamic moduli. It is possible to approximate this difference using the T-matrix model. The starting point for creating a T-matrix model is a simplified layered geological model of a borehole profile. Added to this are values of static moduli determined by a uniaxial compression test on representative samples of the borehole core. Additional input data for calculating the T-matrix model include porosity determined from well logging measurements, and the presence of cracks as interpreted from an acoustic scan of the borehole wall. The given approach is demonstrated in the experimental measurement of a borehole in Silurian limestone. The procedure was verified by comparing the calculated effective moduli with values of static moduli, measured on control samples prepared from borehole core outside the collection intervals of samples used as input for calculation of the T-matrix model. This comparison showed that for majority of samples there was a decrease in the difference from nearly 40% (dynamic moduli) to under 10% (effective moduli). Highlights • Use of a T-matrix model made it possible to approximate static moduli from dynamic moduli. • The curves calculated by the model are significantly more detailed than the original well logging. • The calculated effective values can be used for calculations instead of the static values. [ABSTRACT FROM AUTHOR]

Highlights • l 2,1 -norm minimization based negative label relaxation linear regression for feature selection is presented. • The technique called negative label relaxation is integrated into LR model. • l 2,1 -norm regularization constraint is imposed on transformation matrix to achieve row sparsity. • We devised an efficient algorithm to solve the objective function. • Our feature selection method is more efficient due to joint relaxing class labels and l 2,1 -norm. Abstract Feature selection (FS) is an important issue in the field of pattern recognition and machine learning. Linear regression (LR) and its variants have been widely used for classification problems. In this paper, we propose a novel feature selection method, i.e., l 2,1 -norm minimization based negative label relaxation linear regression for feature selection (NLRL21-FS). The core idea of our method is that a technique called negative label relaxation is integrated into LR model for classification, and l 2,1 -norm regularization constraint is imposed on transformation matrix of the modified LR model to achieve row sparsity. Thus we incorporate feature selection into the training process of the classifier. An efficient algorithm is devised to solve the objective function and analysis of convergence of the proposed algorithm is presented. Our feature selection method is more efficient due to joint relaxing class labels and l 2,1 -norm regularization. Three groups of experiments on 6 benchmark data sets of different type demonstrate the effectiveness of the proposed feature selection method. [ABSTRACT FROM AUTHOR]

Highlights • The optical characteristics of a cluster consisting of zinc sulfide (ZnS) particles doped with a nonconcentric spherical copper (Cu) cores illuminated with an arbitrarily focused Gaussian beam are investigated. • The presented aggregations of nonconcentric doped particles (i.e. core with offset origin) form linear chains or densely packed clusters. • The laser beam is modeled using angular spectrum of plane waves method and then combined with the cluster T -matrix method which is modified to solve such difficult multiple scattering problem. • This combination provides a powerful mathematical technique to obtain the phase (scattering) matrix of a cluster illuminated with any incident electromagnetic fields. • The scattering matrix provides complete descriptions of the scattering characteristics in the far field zone. • The computed results are shown for different beam waists with respect to the cluster. • The scattering processes and its results help understanding many cluster characteristics and nonlinear processes. • The presented numerical results show that the elements of the scattering matrix are sensitive to the focusing of the incident beam and characteristics of the cluster constituents. • The illustrated results are important for researches aim to improve polymer properties and to study several branches of practical sciences and industries such as nanotechnology, pharmaceuticals, chemistry, and biology. • This paper represents the first attempt to study the multiple scattering from a cluster of nonspherical particles with nonconcentric spherical cores illuminated by an arbitrarily focused laser beam. Abstract The optical characteristics of a cluster consisting of zinc sulfide (ZnS) particles doped with a nonconcentric spherical copper (Cu) cores illuminated with an arbitrarily focused Gaussian beam are investigated. The presented aggregations of nonconcentric doped particles (i.e. core with offset origin) form linear chains or densely packed clusters. The laser beam is modeled using angular spectrum of plane waves method and then combined with the cluster T -matrix method which is modified to solve such difficult multiple scattering problem. This combination provides a powerful mathematical technique to obtain the phase (scattering) matrix of a cluster illuminated with any incident electromagnetic fields. The scattering matrix provides complete descriptions of the scattering characteristics in the far field zone. The computed results are shown for different beam waists with respect to the cluster. The scattering processes and its results help understanding many cluster characteristics and nonlinear processes. The presented numerical results show that the elements of the scattering matrix are sensitive to the focusing of the incident beam and characteristics of the cluster constituents. The illustrated results are important for researches aim to improve polymer properties and to study several branches of practical sciences and industries such as nanotechnology, pharmaceuticals, chemistry, and biology. This paper represents the first attempt to study the multiple scattering from a cluster of nonspherical particles with nonconcentric spherical cores illuminated by an arbitrarily focused laser beam. [ABSTRACT FROM AUTHOR]

The single-shot random speckle pattern method can be used for dynamic scene 3D reconstruction. However, the homonymous points search process based on spatial correlation is sensitive to changes in factors such as illumination, perspective, and curvature, which results in low reconstruction accuracy. This paper proposes an improved random speckle 3D reconstruction method with enhanced reconstruction accuracy. To accurately search homonymous points, the proposed method employs a novel spatiotemporal correlation model simultaneously with a subpixel interpolation strategy. Analysis conducted of the reconstruction accuracy associated with correlation region size and the number of patterns to be projected based on the model indicate that using a few (e.g., three) speckle patterns with an appropriate correlation size produces highly accurate results. Experimental results further verify that the proposed method is suitable for high-accuracy dynamic 3D shape measurement. [ABSTRACT FROM AUTHOR]