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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]

• 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]

To improve the low accuracy problem of existing point cloud registration algorithms attributed to deficient point cloud geometric features, we proposed a new point cloud registration network inspired by dynamic feature extraction and the graph attention mechanism. The model uses the dynamic graph edge convolution neural network to characterize the multi-level semantics of the point cloud at first, then uses a feature fusion module based on attention mechanism to fuse the representation information, and finally uses the singular value decomposition (SVD) method to generate the transformation matrix. The experimental verification was carried out on the ModelNet40, ShapeNet Part datasets, and the local industrial part dataset. Experiment results show that our model gets competitive registration performance compared with other advanced models on three datasets. When tested on the untrained data class and the noisy circumstances, our model gets lower average registration errors than compared models. It shows that our framework has not only the characteristics of high registration accuracy and generalization ability but also strong robustness. [ABSTRACT FROM AUTHOR]

In the field of biomedicine, efficiently and non-invasively isolating target cells has always been one of the core challenges. Optical fiber tweezers offer precise and non-invasive manipulation of cells within a medium and can be easily integrated with microfluidic systems. Therefore, this paper investigated the mechanism of cell manipulation using scattering force with optical fiber tweezers. We employed flat-ended single-mode fiber to drive and sort cells and derived the corresponding scattering force formula based on the T-matrix model. A single-mode optical tweezers system for cell sorting was developed, and an optofluidic experimental platform was constructed that effectively integrates the optical system with microfluidic chips. The chip, featuring an expanded cross-channel design, successfully achieved continuous separation of yeast cells (8~10 µm in diameter) and polystyrene microspheres (15~20 µm in diameter), with a sorting efficiency of up to 86% and maintaining viability in approximately 90% of the yeast cells. Compared to other sorting systems, this system does not require labeling and can achieve continuous sorting with cell viability at a lower cost of instrumentation. [ABSTRACT FROM AUTHOR]

Multiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the Tmatsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the Tmatsolver code. [ABSTRACT FROM AUTHOR]

When a wave, such as sound or light, scatters within a densely packed particulate, it can be rescattered many times between the particles, which is called multiple scattering. Multiple scattering can be unavoidable when trying to use sound waves to measure a dense particulate, such as a composite with reinforcing fibres. Here, we solve from first principles multiple scattering of scalar waves, including acoustic, for any frequency from a set of two-dimensional particles confined in a circular area. This case has not been solved yet, and its solution is important to perform numerical validation, as particles within a cylinder require only a finite number of particles to perform direct numerical simulations. The method we use involves ensemble averaging over particle configurations, which leads us to deduce an effective T-matrix for the whole cylinder, which can be used to easily describe the scattering from any incident wave. In the specific case when the particles are monopole scatterers, the expression of this effective T-matrix simplifies and reduces to the T-matrix of a homogeneous cylinder with an effective wavenumber k⋆. To validate our theoretical predictions, we develop an efficient Monte Carlo method and conclude that our theoretical predictions are highly accurate for a broad range of frequencies. [ABSTRACT FROM AUTHOR]

In this paper, the issue of exponential stabilization and sampled-data controller design for Takagi–Sugeno fuzzy large-scale networked control systems is studied by using the reduction-based ordinary differential equation prediction method. For the problem that matrices cannot be multiplied directly during the process of designing the sampled-data controller in this paper, a matrix dimensional transformation method is proposed. Firstly, a type of two-sided mode-dependent loop-based Lyapunov–Krasovskii functional is constructed, which compensates for the large delay and makes fuller use of the information in sampled-data interval. Secondly, the proposed method is used to give the design scheme of an aperiodic sampled-data controller, and furthermore, an iterative algorithm to verify the effectiveness of the requested control gains is provided. Finally, two coupled vehicle pendulum systems and two-area interconnected power systems are applied to demonstrate the efficiency of the presented approach. [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]

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]

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]

In this study, we created a multilayer SPR hydrogen sensor that is primarily based on an Ag-nd or Au-nd heterogeneous metal nanolayer. To characterize the response of the suggested structure, we used the Matlab program and the transfer matrix method (TMatrix) in this investigation. We developed a set of sensors (n1/Ag-nd/Pd Or n1/Aund/Pd) with varying densities of metal nanoparticles N = 400[1/μm³], 600[1/μm³], 800[1/μm³], and 1000 [1/μm³], respectively, to verify the sensor's performance. They are assessed using a number of conventional standards, including sensitivity and minimum reflectance (Rmin). The sensor with Ag-nd layer and N = 1000 [1/μm³] was found to attain the lowest Rmin of 0.04 and the highest sensitivity of S = 7.99[nm] with a maximum resonance wavelength shift of 2.4 [nm]. The suggested SPR hydrogen sensor may detect changes in palladium (Pd)'s optical characteristics and, consequently, leaks of hydrogen gas, according to simulation data. [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]

The 6-degrees-of-freedom (6-DOF) platform has gained popularity in industry owing to its advantages, especially in indoor simulation experiment requiring six-dimensional force environments. However, up to date, the measurement of such six-dimensional forces is challenging due to complex structures, difficult decoupling, and high costs. In this study, an electric 6-DOF loading device designed by ourselves is presented, with an ability to load high precision displacement and force. To measure the six-dimensional force of the device's moving platform, this paper proposes a scheme involving embedding tension-compression sensors in each leg of the device and describes the mechanical model of the device. Then a novel method with a variable transformation matrix is proposed, complemented by a decoupling study that optimizes the variable transformation matrix. Finally, we validate the proposed method through an external force loading experiment. The results indicate that the error in Fy experiment is less than 2.7%, and the error in Fz experiment is less than 1.6%. The novel method exhibits high accuracy, easy installation, fast response, and low cost. [ABSTRACT FROM AUTHOR]

Chirality plays a pivotal role in the interaction between light and matter, yet detecting chiral signals from natural materials remains a challenge, necessitating the enhancement of their intensity. In this study, we present an approach to investigate substrate chirality through exploiting light scattering from Mie particles. To comprehensively analyze the scattering phenomenon, we theoretically derive the T-matrix for a nonchiral Mie sphere positioned on a chiral substrate. Unlike the Mie sphere in free space, our derivation accounts for the intricate coupling between the scattered light by the sphere and the reflected light by the substrate. Employing the T-matrix framework, we calculate the scattering power and circular dichroism spectra. Our findings reveal a remarkable augmentation of chiral signals originating from the substrate, thanks to the Mie resonance within high-index spheres. This research underscores the feasibility of probing local chiral properties in the vicinity of a sample surface, promising new insights into chiral interactions at the nanoscale.

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]

This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. [J. Golak, K. Topolnicki, R. Skibiński, W. Glöckle, H. Kamada, A. Nogga, Few Body Syst. 54 , 2427 (2013)]. This innovative approach, referred to as t- matrix-free in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet–Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic t- matrix-free Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of the Faddeev equation, referred to as t- matrix-dependent in this paper, with boosted 2B t -matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B t -matrices and leading to significant computational time savings. [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]

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]

Efficient and accurate computation of the single‐scattering properties of black carbon (BC) aerosols is fundamental in various fields, including remote sensing and climate simulations. In this study, we developed a composite model of fractal aggregates of BC encapsulated with hygroscopic aerosols to represent the ambient BC. We used the invariant imbedding T‐matrix method to compute the optical properties of fully and partially encapsulated BC aerosols. In this new model, the traditional assumption of unoverlapped surfaces in the super‐position T‐matrix method is unnecessary. After extensive simulations, we established a database of single‐scattering properties, including the extinction efficiency, the single‐scattering albedo, the asymmetry factor and six phase matrix elements. Moreover, we obtained deep neural networks (DNNs) from this database using a deep learning method. These DNN models provide a universal interface for predicting the optical properties of ambient BC aerosols. Specifically, through a modified architecture of the DNN, we trained two models based on the database to predict three integrated optical properties (extinction efficiency, single‐scattering albedo, and asymmetry factor) and six phase matrix elements. We performed statistical assessments based on the true values in the database and the predicted values from the DNNs, demonstrating that the DNNs accurately predicted all single‐scattering properties. Therefore, the developed DNN models can be conveniently implemented in aerosol optical parameterization for remote sensing studies and atmospheric models. Plain Language Summary: Black carbon (BC) aerosol plays a significant role in the atmosphere, influencing climate through its interactions with radiation, such as scattering and absorbing. The accurate determination of the single‐scattering properties of BC, including the extinction efficiency, the single‐scattering albedo, the asymmetry factor and six phase matrix elements, is crucial for understanding its radiation effects. In this study, we developed a comprehensive model for BC particles that incorporates complex morphological characteristics and the mixing of BC with other hygroscopic aerosols. We established a database of single‐scattering properties for these models using the invariant imbedding T‐matrix method. However, the large storage space required by this database (over 20 GB) makes it impractical for widespread applications. Therefore, we employed a deep learning method to compress the storage consumption. Two deep neural networks (DNNs) were trained using the database, enabling the prediction of all single‐scattering properties. Remarkably, the performance of the DNNs was excellent, with a coefficient of determination greater than 0.99 for all single‐scattering properties, as determined through statistical assessment. These DNN models hold great potential for various atmospheric radiation and remote sensing studies in the future. Key Points: A flexible model of partially and fully encapsulated fractal black carbon particles was developedA database of single‐scattering properties of encapsulated fractal black carbon particles was constructedTwo deep neural networks were obtained, offering a flexible approach to calculating the optical properties of black carbon aerosols [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]

Purpose: The purpose of this paper is to conveniently and accurately design partial knitting knitted fabrics based on matrix transformation. Design/methodology/approach: Using mathematical modeling, the pattern diagram block matrix and process design matrix of partial knitting knitted fabrics are established, and the process knitting diagram with parameter information is generated. Based on the establishment of the mathematical model of the process knitting diagram, a loop deformation method based on three-dimensional (3D) coordinate point matrix transformation is proposed. Findings: The matrix transformation method can provide a suitable deformed loop mode for partial knitting knitted fabrics and helps to generate a 3D modeling diagram conveniently. Originality/value: This paper proposed a method of design and modeling of partial knitting knitted fabric based on matrix transformation. Taking the 3D modeling effect of conventional partial knitting as an example to test the modeling method, the results show that after matrix transformation, the loop model can realize the rapid transformation and calculation of the coordinates of the control point and generate a 3D modeling diagram. [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]

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]

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 field of biomedicine, efficiently and non-invasively isolating target cells has always been one of the core challenges. Optical fiber tweezers offer precise and non-invasive manipulation of cells within a medium and can be easily integrated with microfluidic systems. Therefore, this paper investigated the mechanism of cell manipulation using scattering force with optical fiber tweezers. We employed flat-ended single-mode fiber to drive and sort cells and derived the corresponding scattering force formula based on the T-matrix model. A single-mode optical tweezers system for cell sorting was developed, and an optofluidic experimental platform was constructed that effectively integrates the optical system with microfluidic chips. The chip, featuring an expanded cross-channel design, successfully achieved continuous separation of yeast cells (8~10 µm in diameter) and polystyrene microspheres (15~20 µm in diameter), with a sorting efficiency of up to 86% and maintaining viability in approximately 90% of the yeast cells. Compared to other sorting systems, this system does not require labeling and can achieve continuous sorting with cell viability at a lower cost of instrumentation.

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]

The Young's modulus is an essential factor for improving turbine blade design. The present study aims to obtain the flexural frequencies (f1) and corresponding dynamic Young's modulus (Ed) of Ni‐based single‐crystal DD6 across a temperature range of 25–1200 °C using a nondestructive dynamic testing method. The relationship between the elastic constants and various crystal orientations is derived by employing the transformation of the elastic matrix. In addition, finite element (FE) simulation is conducted to calculate the flexural frequency (f1) of the [001] crystal orientation. The findings indicate that the dynamic Young's modulus (Ed) decreases as the temperature increases within the range of 25–1200 °C. Furthermore, the Ed values for different crystal orientations follow the trend: Ed[1] < Ed[11] < Ed[111]. This suggests significant anisotropy in the material. The normalized model, matrix transformation calculation method, and finite element method demonstrate high accuracy in predicting the elastic modulus of DD6, as evidenced by the good correspondence between the fitting curves obtained using the normalization method and the test results. These results have practical applications in engineering, particularly in turbine blade design and other applications, and serve as valuable references for mechanical property testing and finite element simulations. [ABSTRACT FROM AUTHOR]

The detection of symmetries in a switching function is an NP-complete problem. In this paper a single line solution for detecting total symmetry been proposed. The proposed method exploits the linearity among Boolean terms to obtain the unique transformation matrix associated with every linear function. A theorem has been proved which relates the equality of coefficients in the transformation matrix, of the variables with symmetry detection. By using the proposed methodology, the simplicity for detecting total symmetries been improved in terms of cost in time-space domain. [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]

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]

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]

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 Denavit -- Hartenberg convention will be used to determine the kinematic parameters of the analysed structure. This convention uses homogeneous transformation matrices. The 4x4 homogeneous transformation matrices can contain rotation and translation matrices. The common elements formed by the first three rows and the first three columns of the 4x4 matrix define the orientation of the joint, while the common elements formed by the first three rows and the fourth column of the 4x4 matrix defines the position of the joint. The purpose of the Denavit -- Hartenberg method is to solve the direct kinematic problem, which is nothing more than determining the coordinates interpreted in the world coordinate system of the TCP point from the joint parameters. During the analysis of the structure, MAPLE and CREO software were used to perform the calculations and check. [ABSTRACT FROM AUTHOR]

Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are relevant for the understanding of the equilibrium properties of quantum systems with power-law interactions. [ABSTRACT FROM AUTHOR]

The rough hailstone scattering library is created to fill the need for results of non-spheroidal hailstone backscattering characteristics. The listed backscattering coefficients at the S-band (2.8 GHZ) are specifically tailored for computing the polarimetric variables. The National Weather Service's radar operates in this band; hence the library is pertinent to those studying hail in the USA. The library contains several axis ratios and a range of hail sizes from 5 mm to 100 mm. Moreover, hailstone surface roughness is expressed as a percentage of the equatorial diameter. Our computational electromagnetic approach to modeling hailstones is compared with typically employed simpler methods. The polarimetric variables calculated using our models can be compared to observations. Furthermore, we illustrate the potency of the CEM approach to hydrometeors with extreme axis ratios for which simpler methods (i.e., the T-matrix) fail. [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]

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]

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]

At present, the fastener installation in a wingbox facing a narrow space must be performed manually. Using a robot is an appropriate solution for automatic assembly. However, the existing robots cannot meet the internal fastening requirements. A new robot with a prismatic joint and four revolute joints (1P4R) was developed to perform the positioning and operation in the wingbox. A compact arm link was designed, and mechanical frame structures were set up. The control system was also set up for the robot's motion. Then, the forward kinematic model was carried out with the matrix transformation method, and in the analysis the workspace entirely covered the wingbox. The inverse kinematic model was established using the geometric method, and through calculation and simulation, the inverse kinematic equations were verified and refined. [ABSTRACT FROM AUTHOR]

We present the generalized optical theorem and its applications with special emphasis on the roles of bound states. First, we prove the theorem which gives a necessary and sufficient condition for a function |$\langle {\boldsymbol {k}}^{\prime } | T | {\boldsymbol {k}} \rangle$| of two variables |${\boldsymbol {k}}^{\prime }$| and |${\boldsymbol {k}}$| to be physically acceptable as a half-on-shell T-matrix, i.e., to have an underlying Hermitian potential V. Secondly, using the theorem, we construct a scattering theory starting from a physically acceptable half-on-shell T-matrix |$\langle {\boldsymbol {k}}^{\prime } | T | {\boldsymbol {k}} \rangle$|⁠ , which in turn introduces a very useful classification scheme of Hermitian potentials. In the end, as an application of our theory, we present the most general solution of the inverse scattering problem with numerical examples. [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 %.

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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]

Tightly focused vector fields, which can be generated by focusing a light beam through a high-numerical-aperture objective, play an important role in nano-optics research. How to fully characterize this kind of field in the subwavelength scale is a challenging but important task. The Mie scattering nanointerferometry technique has been proposed to reconstruct the tightly focused vector field accurately. In this work, we theoretically demonstrate that the technique can be realized by collecting the transmitted light with two orthogonal polarization states simultaneously. Therefore, when nanoparticles are employed to scan the fields to be measured, more information of the scattering field can be acquired in the far field. This is helpful for solving the linear inverse scattering problem by reducing the number of scanning points, thus making the measurement more efficient. [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]