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This study introduces a novel approach to achieving nonreciprocal transmission by implementing time modulation to the bianisotropic metasurface. For the first time, we present the analytical solution of the excitation of anti-symmetric surface waves on penetrable metasurfaces depending on the excitation direction. Exploiting this finding, we numerically demonstrate asymmetric control of the transmission coefficient under a fast-time scale by employing solely time modulation. This approach lowers the complexity of the modulation scheme and implementation encountered in the space-time modulation technique. We develop and simulate a 3D unit cell model in the microwave domain, which forms a surface cavity that incorporates time-varying capacitors. The impedance transfer matrix method and harmonic balance numerical solutions are applied to the retrieved equivalent circuit for the numerical simulations. The results reveal optimized phase-coherent and incoherent nonreciprocal transmission at the significant isolation level (≥ 40 dB) for forward and backward transmissions. We discuss the consistency and discrepancies between numerical methods and consider the impact of the losses and nonlinearity on the metastructure performance. [ABSTRACT FROM AUTHOR]

A new class of acoustic black hole (ABH) waveguides is presented, which relies in its operation on an array of optimally designed functionally graded perforated rings (FGPRs). In this manner, the developed ABH is provided with built-in energy dissipation characteristics generated by virtue of the flow through perforations, which enhances its acoustic absorption behavior and makes the speed of the propagating waves vanish faster when reaching the end of the waveguide. Furthermore, the particular design of the rings enables sandwiching of additional porous absorbing layers between the rings to further boost the absorption characteristics of the proposed ABH. Accordingly, the operating principle of the new class of ABH is radically different from that of the conventional ABH that employs sequential solid-flat rings of decreasing inner radii to create a virtual power law taper necessary for generating the black hole effect, but through reactive means rather than the effective dissipative means of the proposed ABH. Therefore, this paper develops a transfer matrix modeling (TMM) approach to model the absorption and reflection characteristics of the new class of ABH, in an attempt to predict its behavior, optimize the selection of its design parameters, and more importantly, demonstrate its merits as effective means for controlling sound propagation. Numerical examples are presented to highlight the merits and behavior of the proposed ABH. Predictions of the TMM are validated against experimental results that are available in the literature for one and two micro-perforated plates. Comparisons are also established between the ABH with FGPR and the conventional ABH in order to distinguish the behavior and underlying principles of their operations. [ABSTRACT FROM AUTHOR]

A bipartite system is defined as two microscopic entities being able to exchange energy. When excited by light, the complete optical response functions at first (polarizabilities) and second orders (first hyperpolarizabilities) of such a system are determined using the diagrammatic theory of optics. The generality of the method is ensured by the free choice of light–matter and matter–matter interaction Hamiltonians and by the arbitrary number of quanta involved in the energy exchange. In the dipolar approximation, the optical response functions of the system (i.e., of the interacting entities) are linked to the responses of the interaction-free entities by transfer matrices. These universal matrices identically modify the optical response functions at all orders in the electromagnetic field, allowing the implementation of matter–matter interactions in higher-order processes, such as stimulated or spontaneous Raman scattering and four-wave mixing. This formalism is then applied to various composite systems: dimers, multimers and lattices of nanoparticles and molecules, dense molecular layers, and substrate-induced image dipoles. [ABSTRACT FROM AUTHOR]

This study illustrates the successful achievement of tunable defect bands in one-dimensional defective phononic crystals (PnCs) through the incorporation of piezoelectric defects with synthetic negative capacitances (SNCs) for the first time. The efficacy of SNCs in creating tunable bandpass filters across a broad frequency range is thoroughly examined using the proposed analytical and numerical models. A newly developed electroelastically coupled transfer matrix that incorporates SNCs is presented, considering either series or parallel connection between bimorph piezoelectric elements. Defect band and transmittance analyses are conducted using the transfer matrix and S-parameter methods. Two key findings emerge from this investigation. First, when the total equivalent capacitance of the bimorph piezoelectric elements and SNC becomes zero, the defect band representing the point-symmetric defect-mode shape can be customized throughout the entire phononic bandgap. Second, the constant transmittance value, resembling short-circuit conditions, highlights the remarkable ability of SNCs to tune defect bands without energy dissipation, paving the way for fully tunable bandpass filters. To propel this research forward, future investigations could explore expanding the design space with double defects, adopting enhanced modeling techniques to account for lateral and shear effects, developing a control algorithm for the automatic optimization of SNC values in actively tunable bandpass filters, and incorporating artificial intelligence into design methods for piezoelectric defects with electrical connections. [ABSTRACT FROM AUTHOR]

Layered franckeite is a natural superlattice composed of two alternating layers of different compositions, SnS 2 - and PbS-like. This creates incommensurability between the two species along the planes of the layers, resulting in spontaneous symmetry-break periodic ripples in the a-axis orientation. Nevertheless, natural franckeite heterostructure has shown potential for optoelectronic applications mostly because it is a semiconductor with 0.7 eV bandgap, air-stable, and can be easily exfoliated down to ultrathin thicknesses. Here, we demonstrate that few-layer franckeite shows a highly anisotropic nonlinear optical response due to its lattice structure, which allows for the identification of the ripple axis. Moreover, we find that the highly anisotropic third-harmonic emission strongly varies with material thickness. These features are further corroborated by a theoretical nonlinear susceptibility model and the nonlinear transfer matrix method. Overall, our findings help to understand this material and propose a characterization method that could be used in other layered materials and heterostructures to assign their characteristic axes. [ABSTRACT FROM AUTHOR]

Strong coupling of a confined optical field to the excitonic or vibronic transitions of a molecular material results in the formation of new hybrid states called polaritons. Such effects have been extensively studied in Fabry–Pèrot microcavity structures where an organic material is placed between two highly reflective mirrors. Recently, theoretical and experimental evidence has suggested that strong coupling can be used to modify chemical reactivity as well as molecular photophysical functionalities. However, the geometry of conventional microcavity structures limits the ability of molecules "encapsulated" in a cavity to interact with their local environment. Here, we fabricate mirrorless organic membranes that utilize the refractive index contrast between the organic active material and its surrounding medium to confine an optical field with Q-factor values up to 33. Using angle-resolved white light reflectivity measurements, we confirm that our structures operate in the strong coupling regime, with Rabi-splitting energies between 60 and 80 meV in the different structures studied. The experimental results are matched by transfer matrix and coupled oscillator models that simulate the various polariton states of the free standing membranes. Our work demonstrates that mechanically flexible and easy-to-fabricate free standing membranes can support strong light–matter coupling, making such simple and versatile structures highly promising for a range of polariton applications. [ABSTRACT FROM AUTHOR]

Oxygen vacancies in indium tin oxide (ITO) thin films provide a direct route to effectively tune the free electron density and thereby, controlling the epsilon-near-zero (ENZ) cut-off wavelength, the wavelength at which the real part of permittivity crosses zero of the permittivity axis. In this report, oxygen vacancies in pulsed laser deposited ITO thin films are systematically tuned using different background gases (O 2 , N 2 , Ar, and He). ENZ cut-offs are observed for the films deposited under He and Ar gases. In contrast, no such cut-offs are observed in the case of other two gases. An ITO thin film deposited under He gas exhibits deeper resonance signal than the one deposited under Ar gas. As expected, no such dip in the resonance spectra is observed for the films deposited under O 2 and N 2 gases. This observation is directly correlated to the change in the number of oxygen vacancies under different ambient gases. A modified transfer matrix method which incorporates surface roughness as an effective medium layer is developed to describe the experimentally observed resonance spectra numerically. Angular invariancy of ENZ plasmon resonance and the difference in absorption values for ITO films deposited under different gases is understood in terms of local field intensity enhancement factor. The study presented here will certainly be very useful in understanding the ENZ plasmon resonance phenomena as a whole. Additionally, ITO films deposited under an inert gas environment could be excellent material platforms for realizing several exotic ENZ applications. [ABSTRACT FROM AUTHOR]

In the present study, we have explored the absorption properties of a monolayer graphene-based photonic heterostructure, which consists of topological photonic configurations, graphene, and a Bragg mirror. The optical attributes were computed by using the 4 × 4 transfer matrix method. The results indicate that the creation of topological interface states and strong coupling between these resonant modes result in mode splitting, leading to the formation of hybrid modes known as coupled topological interface states with unity transmittance. The number of absorption modes can be modulated with an appropriate selection of cascaded photonic structures. Our proposed design with 1, 3, 5, and 7 cascaded topological photonic structures provides 1, 5, 9, and 13 absorption modes with greater than 90 % absorption. The findings also reveal that absorption peak strength is greatly influenced by Fermi-level and magnetic fields; switching of the modes from absorption to reflection and vice versa is achieved by suitable electrical and magnetic biasing. Our proposed design offers various applications, such as switchable filters, absorbers, and modulators. [ABSTRACT FROM AUTHOR]

Hyperbolic metamaterials (HMMs) are artificial subwavelength-structured media that exhibit excellent hyperbolic properties. The Casimir force for HMMs can be predicted by effective medium theory (EMT), which simplifies the calculations considerably. However, the conditions of EMT in the Casimir force between HMMs have not been investigated. In this work, we compare the exact results of the Casimir force calculated by the transfer matrix method (TMM) with those from EMT. The numerical results suggest that EMT can accurately calculate the Casimir force only when the gap distance is 100 times larger than the period of a unit cell. When the gap distance and period of unit cell values are comparable, EMT is not suitable for TMM, and the main error occurs in the hyperbolic band. Furthermore, the effect of the filling ratio on the applicable conditions of EMT is also studied. This work demonstrates the conditions of EMT in calculating the Casimir force between HMMs and provides help for the development of micro- and nanoelectromechanical systems. [ABSTRACT FROM AUTHOR]

Aperiodic order is ubiquitous in nature and quite relevant in science and technology. There are extensive works in aperiodic structures studying fundamental characteristics in physical properties, such as fractality, self-similarity, and fragmentation. However, there are fewer reports in which aperiodicity signifies an improvement in physical quantities with practical applications. Here, we show that the aperiodicity of fractal or self-similar type optimizes the tunneling magnetoresistance and spin-valley polarization of magnetic silicene structures, raising the prospects of spin-valleytronics. We reach this conclusion by studying the spin-valley-dependent transport properties of complex (Cantor-like) magnetic silicene structures within the lines of the transfer matrix method and the Landauer–Büttiker formalism. We find that the self-similar arrangement of magnetic barriers in conjunction with structural asymmetry reduces the conductance oscillations typical of periodic magnetic silicene superlattices and more importantly makes the K ′ -spin-down conductance component dominant, resulting in nearly perfect positive and negative spin-valley polarization states accessible by simply reversing the magnetization direction. The tunneling magnetoresistance is not as prominent as in periodic magnetic silicene superlattices; however, it is better than in single magnetic junctions. Furthermore, the optimization of the spin-valley-dependent transport properties caused by the complex structure is superior than the corresponding one reported in typical aperiodic structures, such as Fibonacci and Thue–Morse magnetic silicene superlattices. [ABSTRACT FROM AUTHOR]

The well-known formalism for Sum-Frequency Generation (SFG) reflected or transmitted by a three-layer system involves three equations defining the emitted SFG intensity, the effective nonlinear susceptibility, and a set of Fresnel factors specific to the three-layer system. We generalize the equations to an N-layer system, where all media have non-vanishing thicknesses, by leaving the first two equations unchanged and modifying only the Fresnel factors. These universal Fresnel factors bear all the complexity of light propagation and interference in the system, in amplitude and phase. They are analytically known anywhere in the N-layer system, either at any interface or in any of the bulks, and share common expressions for the three beams, incoming or emitted, of the SFG process in reflection. Enclosing an ultrathin layer (e.g., a molecular monolayer) in the system does not modify the Fresnel factors except for boundary conditions at this layer, as in the three-layer case. Specific rules are elaborated to simplify systems containing macroscopic layers. Equations for the four- and five-layer systems are explicitly provided. Simulations in the four-layer system allow for the recovery of the results of the transfer matrix formalism at a lower complexity cost for SFG users. Finally, when several interfaces in the system produce SFG signals, we show that it is possible to probe only the most buried one by canceling all the SFG responses except at this last interface, generalizing the results of the three-layer system. [ABSTRACT FROM AUTHOR]

This paper presents a study of wave propagation through an infinite periodic structure that consists of elastic Timoshenko beams interconnected with rigid bodies. This is a generalized approach in which the beams are not coaxial and the centre of mass of each rigid body is placed away from the intersection of their neutral axes. An analytical approach is used by applying the transfer matrix method (TMM), along with the Floquet–Bloch theorem for elastic wave propagation. Subsequent parametric analysis is performed with visualization of resulting band diagrams of a representative structure. These results are verified through comparison with solutions obtained using the finite-element method (FEM). In this manner, a comprehensive dynamical analysis of tailored metastructures is provided. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

The Acoustic Black Hole (ABH) is an effective structure for harvesting and dissipating energy from flexural waves. It works by reducing the thickness of the ABH wedge in a power law relationship with m ≥ 2, which rapidly decreases the local phase velocity of flexural waves and leads to an energy convergence effect. However, the vibration performance may differ if the tapered wedge does not meet the requirements of a typical ABH. This article introduces and discusses two types of "pseudo-ABH" wedges: linear-degenerate ABH and step-degenerate ABH. These wedges do not follow the power-law and continuity conditions of typical ABH, respectively. To establish the dynamic models of pseudo-ABH wedges, the lumped-mass transfer matrix method (LTMM) and traveling wave analysis are introduced and validated using analytic solutions of the non-uniform one-dimensional Euler-Bernoulli beam and finite element method. Meanwhile, a good match between the results of the Timoshenko and Euler-Bernoulli beam theory also indicates the correctness of our model. The energy ratio and reflection coefficient are defined to characterize the energy accumulation effect and vibration absorption performance of the pseudo-ABH wedges. The vibration performance of the linear-degenerate ABH is closer to the typical ABH than the step-degenerate ABH. The step-degenerate ABH has more effective energy accumulation and reduction performance for individual frequencies. However, as the number of segments in the step-degenerate ABH increases, its dynamic performance becomes closer to that of the typical ABH. The novelty of this article is to study vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedges using LTMM model, disclose the differences of linear and step degenerate ABH for their performance, and recommend the step degenerate ABH in place of the typical ABH of a power law thickness relationship. [ABSTRACT FROM AUTHOR]

This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet–Bloch theory to validate the proposed scheme. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1).' [ABSTRACT FROM AUTHOR]

This paper uses the Transfer Matrix Method (TMM) to investigate the transmission rate and the photonic band structure of one-dimensional photonic comb-like waveguides (CWGs) system. This study is crucial as it provides valuable insights into the properties of photonic waveguides, which can be leveraged to design high-performance guiding, filtering and multiplexing devices. The primary objective of our study is to comprehend the impact of defects on the transmission and band structure of CWGs. Specifically, how changes the geometrical and material properties of defective resonators affect defect modes in photonic band gaps. By modifying the relative permittivity and length of these defective resonators, we observed a shift of defect modes to lower frequencies. This work shows, for the first time, the influence of these defects on defect modes and their potential applications in the development of high-performance guidance and electromagnetic filtering devices. [ABSTRACT FROM AUTHOR]

This paper presents a novel locally resonant metamaterial structure and proposes a method to analyze its elastic wave dispersion properties. The structure is conceived as a multiple beam system with parallel beams transversely interconnected by periodic arrays of small resonators, each consisting of a spring-mass-spring subsystem in parallel with a couple of springs. Inserting the resonators between the beams, instead of attaching them as external appendages like in some alternative examples of locally resonant beams in the literature, makes the structure appealing for practical realization and use; furthermore, hosting several arrays of resonators gives the possibility to open multiple band gaps. The proposed method is a homogenization approach for flexural wave dispersion analysis, which removes the equations for the resonators from the set governing the dynamics of the system and reverts the original structure to an equivalent one featuring a tri-diagonal effective mass matrix with frequency dependent terms. The advantage of the homogenization approach is twofold: (1) it demonstrates that the band gaps arise in the frequency ranges where the effective mass matrix is negative definite, generalizing the well-established concept of band gaps attributable to negative mass effects in single locally resonant beams; (2) it provides dispersion curves and band gaps very efficiently, and the band gaps are identified upon calculating the eigenvalues of the tri-diagonal effective mass matrix. Analytical expressions of the band gap edges are obtained for the baseline case of a double beam system, to be readily used for design. Additionally, the exact transfer matrix method in conjunction with the Bloch theorem is formulated as alternative to the homogenization approach for wave dispersion analysis. Finally, the proposed concept of locally resonant structure and pertinent homogenization approach are validated by calculating the transmittance properties of the corresponding finite structure, via the standard finite element method. [ABSTRACT FROM AUTHOR]

Rapid launching is a crucial technology for the digitalization and regularization of space transportation systems. This paper focuses on the fast trajectory prediction of the launch-vehicle boost phase. A high-precision and high-efficiency analytical solution of the whole boost phase dynamics model of the rocket is obtained by adopting one of the regular perturbation methods called the state-space perturbation method in the launch rotated coordinate system. An analytical framework known as the perturbation expansion framework is proposed by first figuring out the correlation with the state variables/independent variables and then performing the approximate expansion. This framework can successfully address the issue of analytically solving the transfer matrix and integral term caused by the coupling and time-varying properties among state variables of the affine equations of the boost phase. The analytical solution developed in this paper has great fidelity and takes into account the combined effects of various factors, including thrust, aerodynamic force, Earth's gravity, oblateness, and rotation. It can serve as a theoretical guide for the rapid launch requirements and iterative design processes for early rocket demonstrations in engineering. [ABSTRACT FROM AUTHOR]

This paper introduces a linear version of the reduced multibody system transfer matrix method for studying the eigenvalue problems and steady-state responses of tree multibody systems. The core idea is to recursively transfer mechanical information between elements, utilizing a directed rooted tree to depict the system topology. Reduced transfer equations are provided for both spatial rigid and flexible bodies. For flexible bodies, the derivation is based on the dynamical equations from the finite element method and component mode synthesis. The effectiveness and numerical stability of this method is validated through three numerical examples. • A novel recursive method is introduced for eigenvalue problems and steady-state responses of tree multibody systems. • A directed rooted tree depicts information transfer in systems and presents a recursive algorithm. • Derivation for flexible bodies utilizes dynamical equations from the finite element method or component mode synthesis. • This recursive method is concise, highly structured, and highly programmable. [ABSTRACT FROM AUTHOR]

• A rigid-flexible coupling dynamics model of the CFRP in-situ machining system was proposed. • The dynamics characteristics of the CFRP in-situ machining system under different layout was studied by applying the FEMSTMM. • The optimization model of overall layout of the multi-support reconfigurable compliant tooling was established. • The modal test, excitation test and milling test are designed to verify the effectiveness of the proposed method. The multi-support reconfigurable compliant tooling and robotic in-situ processing method provide a new technical direction for CFRP milling edge processing. Aiming at the layout optimization of CFRP in-situ machining system (CFRPIMS), the dynamics characteristics of the whole system were studied. A rigid-flexible coupling dynamics model of the CFRPIMS was proposed by applying transfer matrix method for multibody systems (MSTMM), treating CFRP as a thin-walled flexible plate and supporting fixtures as rigid bodies. And then the natural frequency and dynamics responses under the different support layout are simulated, which are verified by modal tests and excitation tests. To improve the support rigidity of CFRP workpieces, the optimization model of overall layout of the compliant tooling was established combined with genetic algorithm. Based on the milling test results, compared with the original scheme, the optimization method can effectively reduce the vibration response of the workpiece in the y -direction (along the milling edge direction) and the z -direction (perpendicular to milling edge direction) by more than 60 %. [ABSTRACT FROM AUTHOR]

Drawing upon the fundamental principles of mixture continuum and thermodynamics, planar S-wave incident model for layered unsaturated soil is formulated. Employing the Helmholtz vector decomposition principle, the wave field within the layered unsaturated soil is analyzed using the transfer matrix method, accounting for the influence of thermal effects. An analytical solution is obtained for the seismic response in layered unsaturated soil under the action of thermal effect. The results of the numerical analyses show that the thermo-physical parameters such as relative heat of solid, temperature, and thermal expansion coefficient have a notable effect on the seismic response of the site. [ABSTRACT FROM AUTHOR]

Split-step quantum walk operators can be expressed as a generalized version of CMV operators with complex transmission coefficients, which we call rotated CMV operators. Following the idea of Cantero, Moral and Velazquez's original construction of the original CMV operators from the theory of orthogonal polynomials on the unit circle (OPUC), we show that rotated CMV operators can be constructed similarly via a rotated version of OPUCs with respect to the same measure, and admit an analogous $ \mathcal {LM} $ LM -factorization as the original CMV operators. We also develop the rotated second kind polynomials corresponding to the rotated OPUCs. We then use the $ \mathcal {LM} $ LM -factorization of rotated alternate CMV operators to compute the Gesztesy–Zinchenko transfer matrices for rotated CMV operators. [ABSTRACT FROM AUTHOR]

This paper demonstrates design and simulation of an acoustic wave resonator-based ammonia gas sensor which is resonating at ∼ 3.95 GHz resonant frequency. The bulk acoustic wave-based solidly mounted resonators (SMRs) are robust, simple to manufacture, miniaturized and most suitable for high sensitivity gas sensors. The designed sensor consists of multilayer stack of (Si/SiO2/BR/Mo/ZnO/Mo/rGO) thin films. Here, reduced graphene oxide (rGO) is utilized as an ammonia gas-sensing layer and zinc oxide (ZnO) as piezoelectric layer. Bragg reflector (BR) is applied to confine the acoustic wave. The simulated sensor is based on the resonant frequency shift due to mass loading effect by adsorbed ammonia gas molecules. The amount of frequency shift depends on the concentration of ammonia gas. The ammonia gas sensor results in sensitivity (S) of 7.113 MHz pg−1 with outstanding selectivity over other exposed gases to the sensor. The SMR-based ammonia gas sensor is designed using air tight gas chamber and gases are exposed to the sensor in controlled ambient. In addition, the number of BR pairs (Mo/SiO2) is also optimized for optimal performance of sensor, using transfer matrix model. The simulated ammonia gas sensor is small in size, highly sensitive and can find applications in safety and environmental monitoring in various industries, including chemical plants, refrigeration systems and agricultural applications. [ABSTRACT FROM AUTHOR]

Under unsteady operating conditions in turbomachinery, the performance is unable to respond rapidly enough to follow characteristic curves for the steady condition. To design a reliable turbomachinery under unexpected unsteady conditions, we evaluated the dynamic transfer matrix of a three-dimensional centrifugal impeller. The working fluid is incompressible air. To make the current results more applicable in a broader sense such as pumps, all parameters and results were normalized. The experimental results showed a more significant negative slope in the unsteady performance curve compared to that in the steady performance curve. This was mainly caused by the phase delay of the pressure rise to the pulsating flowrate. We clarified the changes in gain and phase delay under unsteady conditions by conducting numerical simulations. The numerical results showed that the unsteady pressure rise was primarily generated by inertia and power terms in the unsteady energy conservation equation. The power term was predominantly influenced by the angular momentum flowrate difference and the change rate of angular momentum. Each term was quantitatively evaluated, and its contribution to the unsteady pressure rise was discussed. Within the range of frequencies tested in this study, the transfer matrix for the three-dimensional centrifugal impeller could be effectively approximated through a first-order lag approximation considering a series-connected derivative system. We believe that our findings can be extended to centrifugal pumps when disregarding the compressibility effects such as cavitation. [ABSTRACT FROM AUTHOR]

Aiming at the attitude cooperative control problem of multi-spacecraft system, the attitude estimation of the spacecraft is estimated by invariant extended Kalman filter (InEKF), and the attitude estimation of the spacecraft is made independent of the transfer matrix. Then, the multi-spacecraft special orthogonal group (SO(3)) attitude model is constructed by combining the undirected communication topology, and the attitude coordination error on SO (3) is deduced. Among them, an attitude coordination control algorithm based on the consistency theory is proposed based on the special orthogonal group SO(3). The radial basis function neural network is used to tit and compensate virtual disturbances. The proposed algorithm considers spatial disturbances to ensure that the collaborative controller is applicable to the entire attitude space. Multi-satellite attitude collaboration, tracking desired attitude, and collaboration under the constraints of actuator capabilities are realized. The system is analyzed based on LaSalle invariant set theory, proving that the system has global asymptotic stability. Finally, the effectiveness of the proposed attitude collaborative control algorithm is verified by using a six-satellite spacecraft system. [ABSTRACT FROM AUTHOR]

This study analyses the decrease in soil organic carbon (SOC) stocks due to changes in land use following the earthquake in Düzce, Turkey, 1999. The primary objective of the study is to determine the changes in land use within Düzce and to provide a multi-dimensional approach to the spatial and quantitative distributions of SOC losses. Corine Land Use- Land Cover (LULC) within the study is used to determine the change in land use. The loss of LULC and carbon stocks were identified by means of LULC with transfer matrix method and GIS-based analysis. The study of land-use change caused by urbanisation and agricultural activity shows that the limited green spaces around the urban core created by degrading natural areas do not compensate for the loss of SOC. SOC stocks decline after the land use changes from agricultural regions to artificial areas (− 5%), Natural- Semi-natural (N-SN) regions to artificial areas (− 15%), N-SN areas to agricultural areas (− 20.9%) and agricultural areas to water bodies (− 9%), and SOC stocks increase after land use changes from artificial areas to N-SN areas (+ 29.6%), artificial areas to agricultural areas (+ 8%), agricultural areas to N-SN areas (+ 25%). However, in some agricultural areas, SOC stocks are similar to semi-natural and natural areas. For instance, in sparsely vegetated areas, SOC stocks from fruit and berry plantations may be poor. Although it is generally assumed that SOC loss can occur on land transformed from natural areas, this rule of thumb may be revised in some particular circumstances. Therefore, local ecological restoration decisions should not be based on land cover generalisations. [ABSTRACT FROM AUTHOR]

Background: The incongruity between the regional supply and demand of healthcare services is a persistent challenge both globally and in China. Patient mobility plays a pivotal role in addressing this issue. This study aims to delineate the cross-provincial inpatient mobility network (CIMN) in China and identify the underlying factors influencing this CIMN. Methods: We established China's CIMN by applying a spatial transfer matrix, utilizing the flow information from 5,994,624 cross-provincial inpatients in 2019, and identified the primary demand and supply provinces for healthcare services. Subsequently, we employed GeoDetector to analyze the impact of 10 influencing factors—including medical resources, medical quality, and medical expenses—on the spatial patterns of CIMN. Findings: Beijing, Shanghai, Zhejiang, and Jiangsu provinces are the preferred medical destinations for cross-provincial inpatients, while Anhui, Henan, Hebei, and Jiangsu provinces are the main sources for cross-provincial inpatients. Patient flow between provinces decreases with distance. The spatial distribution of medical resources, medical quality, and medical expenses account for 87%, 73%, and 56% of the formation of CIMN, respectively. Additionally, interactions between these factors enhance explanatory power, suggesting that considering their interactions can more effectively optimize medical resources and services. Conclusions: The analysis of CIMN reveals the supply and demand patterns of healthcare services, providing insights into the inequality characteristics of healthcare access. Furthermore, understanding the driving factors and their interactions offers essential evidence for optimizing healthcare services. [ABSTRACT FROM AUTHOR]

This paper seeks to progress the field of topological photonic crystals (TPC) as a promising tool in face of construction flaws. In particular, the structure can be used as a novel temperature sensor. In this regard, the considered TPC structure comprising two different PC designs named PC1 and PC2. PC1 is designed from a stack of multilayers containing Silicon (Si) and Silicon dioxide (SiO2), while layers of SiO2 and composite layer named hyperbolic metamaterial (HMM) are considered in designing PC2. The HMM layer is engineered using subwavelength layers of Si and Bismuth Germinate, or BGO ( Bi 4 Ge 3 O 12 ). The mainstay of our suggested temperature sensor is mainly based on the emergence of some resonant modes inside the transmittance spectrum that provide the stability in the presence of the geometrical changes. Meanwhile, our theoretical framework has been introduced in the vicinity of transfer matrix method (TMM), effective medium theory (EMT) and the thermo-optic characteristics of the considered materials. The numerical findings have extensively introduced the role of some topological parameters such as layers' thicknesses, filling ratio through HMM layers and the periodicity of HMM on the stability or the topological features of the introduced sensor. Meanwhile, the numerical results reveal that the considered design provides some topological edge states (TESs) of a promising robustness and stability against certain disturbances or geometrical changes in the constituent materials. In addition, our sensing tool offers a relatively high sensitivity of 0.27 nm/°C. [ABSTRACT FROM AUTHOR]

The coupling coordination of digitalization and green development has become an inevitable requirement for building a new development pattern and achieving high-quality development of China's economy. Based on the panel data of 284 Chinese cities from 2011 to 2021, this study uses the coupling coordination degree model, Dagum Gini coefficient, spatial convergence, Markov transfer probability matrix, and panel Tobit model to quantitatively analyze the spatial–temporal evolution characteristics and influencing factors of the coupling coordination degree of digitization and green development. The study results show that the coupling coordination degree (CCD) of digitalization and green development has an overall increasing trend during the study period, and the eastern region is higher than other regions which showing spatial non-equilibrium characteristics. The spatial difference of the CCD continues to downward, and inter-regional differences are the main source of the CCD. In the long run, there is a "catch-up effect" between cities with low CCD and those with high CCD, and the CCD of digitalization and green development will tend to a steady state. The transfer type of the CCD has the characteristics of "club convergence", the probability of maintaining the original state is high, and the overall CCD shows a good development trend in the future. Factors such as environmental regulation, green innovation, industrial structure upgrading and financial efficiency can significantly contribute to the CCD of digitalization and green development. The above findings provide empirical evidence of the CCD of digitalization and green development to achieve high-quality economic development. [ABSTRACT FROM AUTHOR]

Modern optical systems are important components of contemporary electronics and communication technologies, and the design of new systems has led to many innovative breakthroughs. This paper introduces a novel application based on deep reinforcement learning, D3QN, which is a combination of the Dueling Architecture and Double Q-Network methods, to design distributed Bragg reflectors (DBRs). Traditional design methods are based on time-consuming iterative simulations, whereas D3QN is designed to optimize the multilayer structure of DBRs. This approach enabled the reflectance performance and compactness of the DBRs to be improved. The reflectance of the DBRs designed using D3QN is 20.5% higher compared to designs derived from the transfer matrix method (TMM), and these DBRs are 61.2% smaller in terms of their size. These advancements suggest that deep reinforcement learning, specifically the D3QN methodology, is a promising new method for optical design and is more efficient than traditional techniques. Future research possibilities include expansion to 2D and 3D design structures, where increased design complexities could likely be addressed using D3QN or similar innovative solutions. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to investigate a one-dimensional photonic crystal containing N-doped germanium semiconductor as a nonlinear defect layer with an intensity-dependent refractive index, silica (SiO2) and zinc selenide (ZnSe) as crystal cells. Bistability of the TE polarization of the transmission spectrum due to the nonlinear property of the defect layer is investigated by the transfer matrix method (TMM). The refractive index of the germanium nonlinear semiconductor layer is simultaneously depending on the doping density and the intensity of the irradiated light. The changes in both factors are investigated. The impact on the transmission spectrum of the bistability threshold due to the change in the thickness of the defect layer, the thickness of other layers of crystal cells, and the angle of incident light are investigated. The nonlinear effect caused by light intensity as well as doped density effect on the germanium nonlinear semiconductor medium is used simultaneously. As a result, the nonlinear effect caused by the light intensity to create bistability is more than the doping density. [ABSTRACT FROM AUTHOR]

The dispute over the authenticity of video has become a hot topic in judicial practice in recent years. Despite detection methods being updated rapidly, methods for determining authenticity have limitations, especially against high-level forgery. Deleting the integral group of pictures (GOP) length in static scenes could remove key information in the video, leading to unjust sentencing. Anyone can conduct such an operation using publicly available software, thus escaping state-of-the-art detection methods. In this paper, we propose a detection method based on noise transfer matrix analysis. A pyramid structure and a weight learning module are adopted to improve the detection rate and reduce the false positive rate. In total, 80 videos were examined through delicate anti-forensic forgery operations to verify the detection performance of the proposed method and three previously reported methods against anti-forensic forgery operations. In addition, two of the latest learning-based methods were included in our experiments to evaluate the proposed method. The experimental results show that the proposed method significantly improves the detection of frame deletion points compared with traditional and learning-based methods, especially in low false positive rate (FPR) intervals, which is meaningful in forensic science. [ABSTRACT FROM AUTHOR]

To effectively reduce vibration, a metamaterial beam with carbon fiber-reinforced polymer (CFRP) is proposed. The dispersion curves are calculated by the transfer matrix method (TM). The frequency response is investigated by the spectral element method (SEM). Displacement fields at different representative frequencies are displayed by the finite element method (FEM). The effects of the geometry, material parameters, and cross-ply angle of CFRP on the band gap are considered numerically, three types of beams are discussed and compared. From the results, it was found that the cross-ply angle and length of CFRP have significant influence on the band gaps. The frequency and width of the band gaps are different when the CFRP layers are imparity. Finally, a CFRP beam with ten periods was fabricated and the experiment was carried out to test transmission characteristics. Although the number of periods is only ten, it was found that the experimental results agree well with the numerical results in the low-frequency range. The results obtained in the paper can provide some useful reference for understanding and optimization of the design for metamaterial beam with wide band gaps, lightweight and high strength. [ABSTRACT FROM AUTHOR]

Cervical cancer is a disease that affects a lot of people all over the world. The success of treatment is significantly increased by early detection. The new surface plasmon resonance sensor (SPRS) described in this article is constructed from layers of silver, BaTiO3, and graphene, as well as a coupling prism. The transfer matrix (TM) approach is used to evaluate the SPRS structure. To obtain the highest sensitivity of the suggested SPRS, the thicknesses of the Ag and BaTiO3 and the number of Gr sheets are evaluated. Investigations are done on all factors of performance of the proposed device. Exemplary efficiency is achieved using 4 nm (BaTiO3) and 60 nm (Ag) materials. Three layers are chosen as the optimal amount of graphene after investigation. When the optimal thicknesses are employed, the suggested SPRS's greatest sensitivity of 300° RIU−1 has been attained. The suggested SPRS displays better sensitivity when compared to SPRS structures that have already been published in the literature. This SPRS is promising to be used in different biosensing applications due to its high performance. [ABSTRACT FROM AUTHOR]

Based on Biot's dynamic wave theory and Novak's plane strain model (PSM), an analytical model for the horizontal vibration of a partially embedded pipe pile group (PEPPG) in layered saturated soil (LSS) that considers the soil‐plugging effect was established: First, the frequency‐domain analytical expressions of the saturated surrounding soil (SSS) and soil plug were obtained by introducing operator decomposition theory and the variable separation method. Second, the analytical solution of the horizontal impedance of a partially embedded pipe pile in the LSS is derived using the coupled condition of the pile–soil interface and transfer matrix method. Finally, an analytical solution for the horizontal impedance of PEPPG in LSS was derived by introducing the horizontal dynamic interaction factor of piles and the superposition method. The derived solution is then reduced and compared with existing theoretical solutions to verify its rationality. In addition, further parametric analysis was conducted to investigate the influences of pile spacing, embedment ratio, properties of layered SSS, and soil‐plugging on the horizontal vibration characteristics (HVCs) of PEPPG. [ABSTRACT FROM AUTHOR]

In order to strengthen the overall planning and coordination of urban construction and ecological space in Baishan City, we should formulate a scientific land type planning of Production-Living-Ecological Space (PLES). In this paper, land use dynamic attitude model, land use transfer matrix, land use function center of gravity transfer model, eco-environmental quality index(EEQI) and geographic detector model are used to discuss the spatio-temporal evolution of PLES in Baishan City from 2000 to 2020. Spatio-temporal evolution of EEQI and its influencing factors. The results show that: (1) During the study period, Baishan City showed the characteristics that the production space first increased and then decreased, the ecological space decreased, and the living space continued to increase. Among them, the ecological space is the dominant space of Baishan City, covering an area of more than 80%. From the perspective of the transformation of PLES, from 2000 to 2020, Baishan City is mainly characterized by the transformation of ecological space into production space and living space. In the second type of space, green ecological space, forestry ecological space and other ecological space have decreased, while other types of space have increased in varying degrees. (2) During the study period, the overall EEQI of Baishan City remained in good condition, and the ecological environment quality(EEQ) of the three periods were 0.6571, 0.6412 and 0.6562 respectively. The higher EEQI is distributed in Changbai County and Linjiang City, while the areas with lower EEQI are concentrated in the north-central part of Hunjiang City, the middle part of Jiangyuan District and the northwest of Fusong County. (3) According to the analysis of the influencing factors of EEQ, the influence of the factors of spatial differentiation of EEQI in Baishan City changed significantly from 2000 to 2020, and the average annual rainfall was the core factor affecting the spatial differentiation of EEQ in Baishan City, the second is the urbanization rate and the distance from the county government, and the interaction between the average annual rainfall and the distance from the county government has a strong influence on the spatial differentiation of EEQ in Baishan City. This study reveals the evolution of spatial types and EEQ of PLES in Baishan City, and provides a scientific reference for the effective management and utilization of land resources in Baishan City. [ABSTRACT FROM AUTHOR]

Preparing young people who have been removed from their parents for leaving alternative care is vital to their success as young adults. Most research on this preparation centres on care-leavers’ views of their support requirements. However, there is little evidence on how to develop practice guidelines for leaving care that may work in real-world settings. This paper aims to achieve two things. First, it presents a first-hand narrative account of a qualitative, collaborative and emic methodology for developing practice guidelines. The methodology emerged over four years through a collaborative bottom-up process between researchers and practitioners in South Africa. The author argues that this methodology may be helpful in other countries and practice contexts. Second, it presents examples of the resultant care-leaving practice guidelines, structured according to set headings and designed to be practicable in resource-constrained settings. While the practice guidelines, being emic, may not transfer across contexts, the author argues that the development process, the structure of the guidelines and the larger practice matrix may transfer well. [ABSTRACT FROM AUTHOR]

Sound source identification technology based on a microphone array has many application scenarios. The compressive beamforming method has attracted much attention due to its high accuracy and high-resolution performance. However, for the far-field measurement problem of large microphone arrays, existing methods based on fixed grids have the defect of basis mismatch. Due to the large number of grid points representing potential sound source locations, the identification accuracy of traditional grid adjustment methods also needs to be improved. To solve this problem, this paper proposes a sound source identification method based on adaptive grid splitting and refinement. First, the initial source locations are obtained through a sparse Bayesian learning framework. Then, higher-weight candidate grids are retained, and local regions near them are split and updated. During the iteration process, Green's function and the source strength obtained in the previous iteration are multiplied to get the sound pressure matrix. The robust principal component analysis model of the Gaussian mixture separates and replaces the sound pressure matrix with a low-rank matrix. The actual sound source locations are gradually approximated through the dynamically adjusted sound pressure low-rank matrix and optimized grid transfer matrix. The performance of the method is verified through numerical simulations. In addition, experiments on a standard aircraft model are conducted in a wind tunnel and speakers are installed on the model, proving that the proposed method can achieve fast, high-precision imaging of low-frequency sound sources in an extensive dynamic range at long distances. [ABSTRACT FROM AUTHOR]

To address the challenges in establishing the state transfer matrix and the complexity of eigenvalue calculation in determining the multi-parameter stability boundaries of high-order nonlinear Vienna rectifiers, a novel numerical computation method is proposed in this paper. This method leverages a numerical stability criterion and a grid variable step search to efficiently calculate these stability boundaries. The small-signal model of the Vienna rectifier is derived by constructing the time-varying state transfer matrix using the periodic solution of the harmonic balance method. Eigenvalues are rapidly calculated via the periodic numerical solution of the state transfer matrix. The proposed parameter sensitivity-based grid variable step search method ensures a fast and accurate determination of stability boundaries. A hardware experimental setup is established to validate the stability boundaries of the Vienna rectifier under various parameter variations, including load, component, and control changes. The experimental results closely match the simulations, confirming the correctness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Summary In this paper, we design a transfer sparse identification algorithm under the Bayesian framework through introducing other system knowledge into the system to be identified. This method provides a new identification solution for a nonlinear autoregressive model with exogenous inputs (NARX). The estimates of the transferred parameters are calculated by adding the transfer correction term to the un‐transferred estimates. To achieve this, a joint prior distribution is devised for the parameters, ultimately enhancing the efficient utilization of existing data, reducing the reliance on new data, and achieving more accurate identification. The maximized marginal likelihood method is used to find the transfer gain and the transfer information matrix in the transfer correction term. Meanwhile, in order to make the algorithm automatically adapt to different data, we design an automatic structure detection method based on the transfer framework. The method automatically determines the sparsity threshold based on the maximum inter‐class variance. Two examples are provided to demonstrate the advantages of our algorithm. [ABSTRACT FROM AUTHOR]

This work presents an innovative platform of a multi-channel one-dimensional photonic crystal (1-DPC) based on blood refractive index data of different patients in the aspect of the main protein components like hemoglobin. This photonic crystal (PC) contains a defect center infiltrated with plasma using a microorder size syringe. When binary silica and III–V semiconductor (InSb) materials are combined, they increase the refractive index difference between the alternate layers of the composite material, resulting in a wide photonic band gap (PBG). We use the well-known transfer matrix method (TMM) to observe the reflectance of various blood samples that were previously published. We assess and contrast the influence of different refractive index data on the dynamic shift in PBG calculation for novel superior and resourceful sensor in the prevention of microscopic organisms such as SARS-CoV-2, the virus linked with COVID-19. Yet, the performance of this PC has more moral content and unlimited casting efficacy in the face of an incurable virus. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve the parameter estimation accuracy of the system to be identified by using measurements from a known system. By introducing the transfer gain matrix and setting the effective identification criterion, a novel transfer sparse identification method is raised, which deals with the sparse issues more precise. Besides, the unbiased form is given in the parameter analysis and the recursion form can prevent the dimension catastrophe related problems. Moreover, in order to test the effects of the transfer and avoid bad performance, a negative transfer analysis condition is carried out. Finally, the simulation verifies the enhancements and benefits of the proposed transfer sparse identification method, confirming that the transfer performance outperforms better than that of no transfer, especially on the zero parameters identification. [ABSTRACT FROM AUTHOR]

Sophisticated infrared detection technology, operating through atmospheric transmission windows (usually between 3 and 5 μm and 8–13 μm), can detect an object by capturing its emitted thermal radiation, posing a threat to the survival of targeted objects. As per Wien's displacement law, the shift of peak wavelength towards shorter wavelengths as blackbody temperature rises, underscores the significance of the 3–5 μm range for ultra-high temperature objects (e.g., at 400 °C), emphasizing the crucial need to control this radiation for the objects' viability. Additionally, effective heat management is essential for ensuring the consistent operation of these ultrahot entities. In this study, based on a database with high-temperature resist materials, we introduced a material-informatics-based framework aimed at achieving the inverse design of simultaneous thermal camouflage (low emittance in the 3–5 μm range) and radiative cooling (high emittance in the non-atmospheric window 5–8 μm range) tailored for ultrahigh-temperature objects. Utilizing the transfer matrix method to calculate spectral properties and employing the particle swarm optimization algorithm, two optimized multilayer structures with desired spectral characteristics are obtained. The resulted structures demonstrate effective infrared camouflage at temperatures up to 250 °C and 500 °C, achieving reductions of 86.7 % and 63.7 % in the infrared signal, respectively. At equivalent heating power densities applied to the structure and aluminum, structure 1 demonstrates a temperature reduction of 29.4 °C at 0.75 W/cm2, while structure 2 attains a temperature reduction of 57.5 °C at 1.50 W/cm2 compared to aluminum, showcasing enhanced radiative cooling effects. This approach paves the way for attenuating infrared signals from ultrahigh-temperature objects and effectively managing their thermal conditions. [ABSTRACT FROM AUTHOR]

Graphene-based surface plasmon resonance (SPR) biosensors have emerged as a promising technology for the highly sensitive and accurate detection of biomolecules. This study presents a comprehensive theoretical analysis of graphene-based SPR biosensors, focusing on configurations with single and bimetallic metallic layers. In this study, we investigated the impact of various metallic substrates, including gold and silver, and the number of graphene layers on key performance metrics: sensitivity of detection, detection accuracy, and quality factor. Our findings reveal that configurations with graphene first supported on gold exhibit superior performance, with sensitivity of detection enhancements up to 30% for ten graphene layers. In contrast, silver-supported configurations, while demonstrating high sensitivity, face challenges in maintaining detection accuracy. Additionally, reducing the thickness of metallic layers by 30% optimizes light coupling and enhances sensor performance. These insights highlight the significant potential of graphene-based SPR biosensors in achieving high sensitivity of detection and reliability, paving the way for their application in diverse biosensing technologies. Our findings pretend to motivate future research focusing on optimizing metallic layer thickness, improving the stability of silver-supported configurations, and experimentally validating the theoretical findings to further advance the development of high-performance SPR biosensors. [ABSTRACT FROM AUTHOR]

There has been a considerable number of studies on the reflection and transmission of plane waves in anisotropic elastic half-spaces. However, the obtained formulas of the reflection and transmission coefficients are implicit, and the numbers of reflected and transmitted waves are undetermined. In this paper, the reflection of qP waves from an orthotropic elastic layer overlying an orthotropic elastic half-space is considered. It has been proved that an incident qP wave always creates two reflected waves, one qP wave and one qSV wave, and the reflection angle of the reflected qP wave is equal to the incident angle. Based on this fact, formulas for the reflection coefficients have been derived by using the transfer matrix method along with the effective boundary condition technique. It should be noted that, different from the previously obtained implicit formulas, these formulas are totally explicit functions of the incident angle, the (dimensionless) layer thickness and the material parameters of the half-space and the layer. Since the obtained formulas are totally explicit, they will be useful in various practical applications, especially in nondestructively evaluating the mechanical properties of deposited layers. [ABSTRACT FROM AUTHOR]

Objective The aims of this study are to explore the spatiotemporal dynamic evolution characteristics of land use in the Two Screens and Three Belts ecological barrier area, to reveal its differentiation rules, and to provide a basis for the integration of land resources in the study area and the construction of a national ecological security barrier. [Methods] Based on 8 periods of land use data from 1985 to 2020 in the Two Screens and Three Belts' ecological barrier area, methods such as single land use dynamic degree, comprehensive land use dynamic degree and transfer matrix, three models were used to comprehensively analyze the spatiotemporal dynamic evolution characteristics and differentiation rules of land use change from the aspects of land use structure, dynamic degree and spatial transfer. [Results] (1) In the *Two Screens and Three Belts ecological barrier area from 1985 to 2020, except for the northern sand control belt whose grassland area increased by 20 618.03 km², the other four major barrier areas had decreased. Among them, the northeastern forest belt's grassland area had decreased the most, reaching up to 18 031.03 km. The area of construction land in the five major ecological barrier areas all increased with the northern sand control belt increasing the most reaching up to 7 280.79 km². The ecological land in the northeastern forest belt significantly decreased, and the non-ecological land increased significantly, which was consistent with the ecological barrier area contrary to the development requirements. (2) From 1985 to 2020, the land use type change rate in the south-central hilly and mountainous areas of the Two Screens and Three Belts' ecological barrier area was the highest (the average comprehensive dynamic degree was 24.27%), and the difference in change rates among each stage was the largest (the comprehensive dynamic degree range was 31.23%). Except for the decrease in the dynamic degree of comprehensive land use in the northeastern forest belt, other barrier areas were on the rise, (3) The degree of land use conversion in the *two screens and three belts' ecological barrier areas had increased from 1985 to 2020. Among them, the Sichuan-Yunnan-Loess Plateau barrier and the northern sand control belt had increased significantly, with increases of 3.89% and 3.82%, respectively. The main types of land converted in each barrier area were cultivated land and grassland, and unused land accounted for a large proportion of the ecological barrier conversion in the northern sand control belt and Qinghai-Tibet Plateau. [Conclusion] From 1985 to 2020, the land use in the two screens and three belts' ecological barrier area showed uneven evolution characteristics, land use planning and management should be carried out according to local conditions to further build the national ecological security barrier. [ABSTRACT FROM AUTHOR]

The optical properties of a graphene-based cylindrical photonic crystal are theoretically investigated based on the generalized cylindrical transfer matrix method to include the out-of-plane propagation of the cylindrical waves. It is found that Maxwell's equations have solutions for both E- and H-polarized waves only at the azimuthal mode number $ m = 1 $ m = 1. We study the reflectance spectrum of the structure to obtain its photonic bandgaps. We show that the reflection spectrum, in addition to the usual Bragg gaps, contains an omnidirectional bandgap at low terahertz frequencies for both E and H-polarized cylindrical waves. The robustness of this bandgap under random variations of geometrical parameters is investigated. This few-period structure is an ideal candidate for guiding waves at the low terahertz region because of its weak absorption and transmission losses. In contrast to the usual Bragg gap, the results show that in both polarizations, the width of graphene-produces bandgap reaches its maximum value when the refractive indices of the two cylindrical shells have their lowest possible values. The width of this unusual omnidirectional bandgap increases by decreasing the thicknesses of the cylindrical shells and increasing the chemical potential of the graphene monolayers. [ABSTRACT FROM AUTHOR]

The Hosoya index is an important topological index in graph theory, which is defined as the total number of s-matchings, denoted as m (G , s) , in a graph G. Therefore, computing the number of s-matchings for various molecular structures holds significant importance. By applying the concept of symmetry, defining the s-matching vector of the graph with a specified edge, using the transfer matrix, and iteratively applying two recursive formulas to derive the reduction formula, we compute the number of s-matchings of cyclooctatetraene chains. [ABSTRACT FROM AUTHOR]

Recently, Bazhanov and Sergeev have described an Ising-type integrable model which can be identified as a sinh-Gordon-type model with an infinite number of states but with a real parameter q. This model is the subject of Sklyanin's Functional Bethe Ansatz. We develop in this paper the whole technique of the FBA which includes: (1) Construction of eigenstates of an off-diagonal element of a monodromy matrix. The most important ingredients of these eigenstates are the Clebsh-Gordan coefficients of the corresponding representation. (2) Separately, we discuss the Clebsh-Gordan coefficients, as well as the Wigner's 6j symbols, in details. The later are rather well known in the theory of 3 D indices. Thus, the Sklyanin basis of the quantum separation of variables is constructed. The matrix elements of an eigenstate of the auxiliary transfer matrix in this basis are products of functions satisfying the Baxter equation. Such functions are called usually the Q-operators. We investigate the Baxter equation and Q-operators from two points of view. (3) In the model considered the most convenient Bethe-type variables are the zeros of a Wronskian of two well defined particular solutions of the Baxter equation. This approach works perfectly in the thermodynamic limit. We calculate the distribution of these roots in the thermodynamic limit, and so we reproduce in this way the partition function of the model. (4) The real parameter q, which is the standard quantum group parameter, plays the role of the absolute temperature in the model considered. Expansion with respect to q (tropical expansion) gives an alternative way to establish the structure of the eigenstates. In this way we classify the elementary excitations over the ground state. [ABSTRACT FROM AUTHOR]