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A simple necessary and sufficient condition ensuring that a real matrix of dimension 3 is similar to a Metzler matrix is exhibited. When this condition is satisfied, a construction of the transfer matrix is given. This construction is used to design an interval observer for a family of continuous-time systems. An example is provided with interval observer design for the so-called love dynamics in the case of limit cycles.

Layered materials are one of the most commonly used acoustical treatments in the automotive industry, and have gained increased attention, especially owing to the popularity of electric vehicles. Here, a method to model and couple layered systems with various layer types (i.e., poro-elastic layers, solid-elastic layers, stiff panels, and fluid layers) is derived that makes it possible to stably predict their acoustical properties. In contrast with most existing methods, in which an equation system is constructed for the whole structure, the present method involves only the topmost layer and its boundary conditions at two interfaces at a time, which are further simplified into an equivalent interface. As a result, for a multi-layered system, the proposed method splits a complicated system into several smaller systems and so becomes computationally less expensive. Moreover, traditional modeling methods can lose stability when there is a large disparity between the magnitudes of the waves within the layers (e.g., at higher frequencies, for a thick layer, or for extreme parameter values). In those situations, the contribution of the most attenuated wave can be masked by numerical errors, hence inducing instability when inverting the system. Here, the accuracy of the wave attenuation terms is ensured by decomposing each layer’s transfer matrix analytically and reformulating the equation system. Therefore, this method can produce a stable prediction of acoustical properties over a large frequency and parameter region. The fact that the proposed method can couple different layer types in a general, efficient, convenient, and stable way is beneficial, for example, when numerically optimizing the design of the acoustical treatments. The predicted acoustic properties of layered systems calculated using the proposed method have been validated by comparison with those predicted by previously existing methods. Further, an optimal design exercise is performed to find a lightweight layered dash panel treatment.

Here, it is shown that properly-designed limp porous materials such as fibrous layers can provide damping equivalent to conventional viscoelastic dampers while providing advantages such as light weight and effective sound absorption. This then allows porous layers to be used as multi-functional noise and vibration control solutions in automotive and aerospace applications. It has also been found that the addition of bulk elasticity to the solid phase of the porous medium is beneficial since it improves damping performance compared to equivalent limp treatments. In this study, porous media, such as fibers and foams, were designed to serve as treatments for various vibrating structures to examine their damping effectiveness. Both analytical modeling and numerical simulation based on finite element methods were involved depending on the complexity of the structure. Specifically, a Fourier transform-based computational method was introduced as the key step to realize the accurate prediction of a panel’s spatial response based on its wavenumber-frequency spectrum. Then, parametric studies were conducted on a porous layer to identify the optimal bulk properties that would allow the layer to provide the largest possible damping within the target frequency region. Finally, design concepts for achieving the maximum damping potential of porous layers are summarized.

This article addresses the almost surely exponential (ASE) stabilization problem of continuous-time jump systems realized by a stochastic scheduled controller. In this study, a stochastic scheduled controller based on the anytime algorithm is proposed. It is able to cope with the situation where no controller is added to subsystems during some time slices. Sufficient conditions for the existence of such a controller are established by applying novel techniques to its stochastic transfer matrix, and they are all presented with solvable forms. Particularly, both dwell times of the jump signal and distribution properties of stochastic scheduling are considered and proved to have played positive roles in obtaining better performance and applications. Two special situations about no jump systems with constant and varied dwell times are further studied, respectively. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.

A novel piezoelectric actuated rail-type mobile platform is proposed in this paper, which has potential application in the inspection and maintenance tasks of the Tokamak vacuum vessel as it holds good environmental adaptability to extreme environments such as strong magnetic fields, high vacuum, and high temperature. The rail-type piezoelectric actuated mobile platform consists of a rail and a framed piezoelectric actuator operating with two orthogonal bending vibrations. The framed piezoelectric actuator moves on the rail by friction. At first, a semi-analytical model is created for the framed piezoelectric actuator utilizing the transfer matrix method, in order to reveal its dynamic behaviour. Then the prototype of the proposed framed piezoelectric actuator is manufactured and assembled, and its vibration characteristics are measured to verify the feasibility of the developed transfer matrix model. Additionally, the mechanical output performances of the rail-type mobile platform prototype are investigated experimentally, and it is observed that 1) the maximum speed of the mobile platform prototype reached 384.68 mm/s when the amplitude of the driving voltage is 400 Vpp; 2) its maximum load-weight to self-weight ratio reached 7.6 when the excitation voltage is 300 Vpp; 3) its maximum output force is almost 1.8 N under the excitation voltage of 400 Vpp; and 4) the minimum displacement resolution is 4 m when operated in the stepping mode. Finally, the extreme environment (temperature: 0~120, vacuum: 310-3 Pa~105 Pa) tests are carried out to measure the output performances of the mobile platform prototype. The results show that the platform prototype is capable of carrying loads in a high-temperature and high-vacuum environment.

This paper addresses the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems (MJSs) with additional stochastic switches. Sufficient conditions for EAS stability are established by applying a method to its stochastic transfer matrix. Particularly, both sojourn time and distribution of such random switchings are considered in the design of a state feedback controller. Compared with some existing references, the proposed controller could bear unmatched or asynchronous signals. Moreover, it can be seen that our results are more general but less conservative, when the information on sojourn time and distribution is used. Some of them include previous work as special cases. Two examples are used to demonstrate the effectiveness and superiority of the methods proposed in our study.

In this paper, a generalized analytical approach is introduced to study the random crosstalk in multicore/multimode fibers. The proposed method is based on the stochastic differential equations (SDEs) for the coupled modal power as well as the coupled power covariance. While the existing analytical formulas for the inter-core/mode crosstalk are accurate in the weakly coupled regime, the proposed analytical tool is exact both in the weakly coupled regime and the strongly coupled regime. In addition to that, the proposed analytical method can compute the covariance of the modal power which is beyond the existing methods. Asymptotic behaviors of the power transfer matrix and the power covariance transfer matrix are discussed.

This paper deals with the harmonic resonance investigation of modern converter dominated power systems considering asymmetric operation conditions. Initially, the complex domain harmonic transfer matrix (HTM) models for the grid-following voltage source converters (VSCs) and the asymmetric network are derived to fully capture the frequency coupling effect. Then, the classical resonance mode analysis (RMA) is generalized by describing the system with a time-periodic impedance matrix obtained from the reformulation of the HTMs to identify the resonance frequencies. Based on the eigen-analysis of the time-periodic matrix, the definition of the participation factor is modified to determine the propagation areas and corresponding severities of a certain resonance. In addition, the impact of the VSC’s controller and the grid asymmetry on the resonance characteristics are evaluated using a sensitivity analysis method. Finally, the effectiveness of the proposed methodology is validated by case studies in an exemplary multiple-converter system.

This study proposed a transfer matrix with harmonic frequencies for a parametrically excited system. The proposed transfer matrix applied to noise and vibration of a helical gear system. Gears are part of the parametrically excited system because of mesh stiffness variation. The nonlinear equation of motion for gears was linearized to an equation with the excitation of harmonic frequencies. Transfer matrix with harmonic frequencies for gear vibration was derived. The helical gear system was modeled using a shaft-bearing-circular plate with helical gears. The assembled transfer matrix of the helical gear system was obtained. Moreover, the assembled transfer matrix with harmonic frequencies was used to investigate the effects of dynamic and noise characteristics of the helical gear system owing to axial excitation. Result showed that sound-pressure level was closely related to the first-harmonic plate displacement caused by the first-harmonic axial force. Significant peaks of sound pressure were closely related to the first-harmonic component and had some peaks in the second and third components. The proposed transfer matrix can easily show the contribution of the harmonic components.

The synthesis of information and energy schemes is posed as an extreme problem, the purpose of which is a weighted directed graph of the minimum length from the input value to the output value of the device. The nodes of the graph are the physical effects included in the given database, and the branches are the input and output values of the effects. Nodes and branches are mathematically defined by diagonal multidimensional matrices, whose elements are determined by the dimensions of the quantities in the selected system of physical coordinates with a given number of basic units of measurement. The weight or resource intensity of the graph elements is determined by the norm of the corresponding matrices. The resulting circuit is suitable for use in technical documentation to explain the operating principle of the device, as well as for patent protection.In the enhanced formulation of the extreme problem, restrictions are introduced on the numerical values of the input and output values of the effect and its dynamic properties in the form of the transfer function of the effect. In this case, the size of the transfer matrices of nodes and branches is expanded by one. As a result, the transfer matrix of the effect contains information not only about the dynamic properties of the effect, but also about the dimensions of the physical quantities at its input and output.In a detailed example, the case of searching for the operating principle of a measuring-converting device of a pressure sensor with an electric current output is considered. To simplify the geometric representation of graph vectors on a plane, the problem is considered for a two-dimensional system of physical quantities with basic units of length and time. The calculation of the resource capacity is carried out according to the scheme of dimensional simulation, in which the phase variables of the differential equation enter with their physical dimensions. According to the numerical value of the resource capacity, you can compare different versions of the implementation of the operating physical principle of the device.

Sprays generated by atomization processes have been used in a wide range of fields. The size and spatial distribution of volumetric droplets in a spray are critical parameters in industrial applications. Astigmatic interferometric particle imaging (AIPI), an extension of the traditional interferometric particle imaging (IPI), is developed to simultaneously measure the size and 3D position of volumetric droplets in a sparse spray. Based on the generalized Huygens–Fresnel integral and the transfer matrix, the size and depth position of droplet can be respectively extracted from the fringe spacing and orientation of interferogram in AIPI. An AIPI setup is established to characterize droplets in a sparse spray generated by a nozzle with the AIPI calibration procedure adopted. The measured parameters by AIPI are compared with those obtained synchronously by digital inline holography, which is regarded as a standard measurement technique. Results show that the average deviation values of droplet size and depth position are respectively 3.8% and 6.8%. AIPI has been demonstrated with high accuracy in simultaneous 3D positions and size measurements.

International audience; The optical properties of chiral plasmonic metasurfaces depend strongly on their architecture, in particular the orientation and spacing between the individual building blocks assembled into large arrays. However, methods to obtain chiral metamaterials with fully tunable chiroptical properties in the UV, visible and near infrared range are scarce. Here, we show that the chiroptical properties of silver nanowires assembled in helical nanostructures by Grazing Incidence Spraying and Layer-by-Layer assembly can be finely tuned over a broad wavelength range using simple design principles. The angle between the oriented nanowire layers controls the intensity of the circular dichroism, reaching ellipticity values higher than 13° and g-factor values up to 1.6, while the shape of the circular dichroism spectra depends strongly on the spacing between the layers which can be tuned at the nm-scale. The structure-dependent optical properties of the assembly are successfully modeled using a transfer matrix approach.

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.

In this article, the frequency coupling of weak grid-connected doubly fed induction generator (DFIG) based wind turbines (WT) during asymmetric faults have received little attention. To analyze the frequency coupling phenomenon of the system during asymmetric faults, this article established the complex transfer function model in αβ frame based on the transformation relationship between complex transfer function and transfer matrix. According to the complex transfer function, the frequency coupling mechanism of the DFIG system during asymmetric faults is revealed, and the transfer evolution law of coupling frequencies is described in detail. Finally, the correction of theoretical analysis and the validity of proposed complex transfer models are verified by the simulation and experiment.

Results on the generalization of the Ising model to an arbitrary number of translations of a linear chain in an external magnetic field, taking into account various interactions between spins, are presented. An exact analytical expression has been derived for the largest eigenvalue of the Kramers–Wannier transfer matrix with a translation per two chain periods in an external magnetic field when the nearest and second neighbors are taken into account. Exact expressions have been established for the zero-temperature entropies and magnetizations at various magnitudes and signs of the exchange interactions and the magnetic field. Many of the zero-temperature entropies and zero-temperature magnetizations found are represented via the so-called mathematical ratios long known in the wonderful world of number mathematics (the golden ratio φ, the silver ratio δ, the supergolden ratio ψ, the plastic number ρ, and new (nameless) ones). A result whereby the frustrating entropies and magnetizations can be expressed via the limit of the ratio of certain number sequences without invoking the formalism of the Kramers–Wannier transfer matrix has been obtained.

A new method for computation of positive realizations of given transfer matrices of linear discrete-time linear systems is proposed. Sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by an example.

This paper describes solutions to calibrate the photon beam from the gradient bending magnet and to minimize the cross-talk between blades in the photon-beam position monitors in beamlines at Pohang Light Source II. The cross-talk was reduced by 99% applying the sensitivity normalization for each electrodes. The precise calibration was also achieved by considering additional kicks in the gradient bending magnet. The focusing force by quadrupole component in the bending magnet gives rise to an effect that simultaneously changes the vertical displacement of the source point and the emission angle. Experimental results agreed well with the transfer matrix calculations.

We consider 1d random Hermitian $$N\times N$$ block band matrices consisting of $$W\times W$$ random Gaussian blocks (parametrized by $$j,k \in \Lambda =[1,n]\cap \mathbb {Z}$$ , $$N=nW$$ ) with a fixed entry’s variance $$J_{jk}=W^{-1}(\delta _{j,k}+\beta \Delta _{j,k})$$ in each block. Considering the limit $$W, n\rightarrow \infty $$ , we prove that the behaviour of the second correlation function of such matrices in the bulk of the spectrum, as $$W\gg \sqrt{N}$$ , is determined by the Wigner–Dyson statistics. The method of the proof is based on the rigorous application of supersymmetric transfer matrix approach developed in Shcherbina and Shcherbina (J Stat Phys 172:627–664, 2018).

A binary superconductor–dielectric photonic crystal (PC) is proposed. The PC has the structure (AB)N with layer A representing the superconducting layer and layer B the dielectric material. The transfer matrix technique is used to deduce the transmission coefficient through the PC. The properties of photonic bandgaps (PBGs) arising in the transmission spectra are studied with the angle of incidence and with all parameters of the superconductor such as thickness, London penetration length, and critical temperature. Many interesting findings were reached: The PBG width decreases with increasing the incidence angle until it disappears for high incidence angles. There is an optimum superconducting layer thickness at which the PBG shows a maximum. The critical temperature has the lowest effect on the PBG width among the superconductor parameters, whereas London penetration length has the topmost effect.

For complex and difficult-to-control blast furnace systems with hour-level delay, accurate prediction of molten iron quality plays a very important role in guaranteeing the stable and smooth operation. Recently, some data-driven multi-input multi-output (MIMO) modeling methods have been proposed to model multiple molten iron quality indicators including molten iron temperature, silicon content ([Si]), phosphorus content ([P]), and sulfur content ([S]). However, those data-driven MIMO models ignore the interindicator correlation, which leads to the suboptimal model for the estimation of multiple molten iron quality indicators. Moreover, the above methods do not pay attention to the molten iron quality indicators missing issue, which often occurs on blast furnace. To address the above two issues, this article proposed a novel MIMO Takagi–Sugeno (T–S) fuzzy model by utilizing an output transfer matrix. In the novel method, the interindicator correlation was explicitly modeled by a low-rank learning of the correlation matrix that overcame the great challenge of jointly determining the fuzzy rules of the MIMO T–S model and the interindicator correlation. Moreover, a new complete complementary matrix can be obtained by the output transfer from the original incomplete matrix resulting from molten iron quality indicators missing issues. For the corresponding optimization problem, an effective alternating optimization algorithm is presented, and the convergence of the optimization algorithm is also rigorously proved. The validity of the proposed method is verified by comparison with some related methods on real blast furnace data.

A $\\boldsymbol d$ - $\\boldsymbol q$ frame impedance model of modular multilevel converter (MMC), which is suitable for high-frequency resonance (HFR) analysis under the condition that the number of submodules in MMC reaches hundreds level, is presented in this work. A 10th-order dynamic phasor model for the MMC is linearized and combined with a control subsystem model. A modular modeling approach based on transfer matrix is applied to the overall linearized model to derive the impedance model. The validity and accuracy of the model are verified using a 501-level MMC aggregated model in SIMULINK. Results show that the impedance model has satisfactory accuracy in the frequency ranging from 1 to 3000 Hz. Then, the impedance model is used to analyze an HFR accident in a realistic MMC project. Therefore, a high time delay in controller is proved can provide negative resistance in high frequency and cause instability.

In this work, we investigate thermodynamic properties of the one-dimensional (1D) spin-crossover molecular chain being a subject of a constant external pressure. Effective compressible degenerate Ising model is used as a theoretical framework. Using transfer matrix formalism analytic results for the low spin -- high spin crossover were obtained. We derive the exact expressions for the fraction of molecules in the high spin state, correlation function and heat capacity. We provide analysis of parameters region where the spin crossover takes place and demonstrate how pressure changes location of the crossover., 9 pages, 5 figures, submitted to Low Temperature Physics

International audience; We have designed and experimentally studied several systems of standard coaxial cables with different impedances which mimic the operation of so-called photonic structures like coupled photonic crystal microcavities. Using elementary cells of half-meter long coaxial cables, we got resonances around 100 MHz, a range of frequencies that can be easily studied with standard teaching laboratory apparatus. Resonant mode frequency splitting has been obtained in the case of double and triple coupled cavities. Good agreement between experimental results and the transfer matrix model has been observed. The aim here is to demonstrate that a standard coaxial cable system is a very cheap and easy to implement structure to explain to undergraduate students complex phenomena that usually occur in the optical domain. © 2021 Author(s).

This paper proposes a novel displacement–strain transfer (DST) matrix method to estimate the local bending deformation of bridge deck using the measured strain. The DST matrix of the bi-dimensional plate with various boundary conditions is derived theoretically, and the local bending deformation of the plate can be further estimated. A plate with four simply supported edges, two simply supported edges, and one clamped edge under various load cases is simulated. The DST matrix is calculated, and the local bending deformation is finally estimated. The proposed method is also verified by the experimental test of a simply supported plate. Both the numerical and experimental results indicate that the proposed method can effectively estimate the local bending deformation of a bi-dimensional plate. Finally, a steel–concrete composite girder bridge is simulated, and the local bending deformation of the bridge deck is also effectively estimated based on the proposed method.

The analytical solutions are presented for the distributions of temperature, displacements, and stresses in simply-supported layered rectangular plates under thermo-mechanical loads. The material properties of every layer are temperature-dependent. A slice model is presented for discretization: dividing every layer into finite thin slices, the material properties within each slice are assumed to be uniform. The temperature varies along the thickness and follows the one-dimensional (1-D) heat conduction equations. An iterative algorithm is proposed for the prediction of the 1-D temperature field. Then, the exact three-dimensional (3-D) thermoelasticity theory and the transfer matrix technique are applied for the prediction of the displacement and stress fields in the plate. The influences of temperature can be divided into two parts: producing thermal deformations and thermal stresses and affecting the deformations and stresses induced by mechanical loads. Finally, the influences of the surface temperature and the layer thickness ratio on the thermo-mechanical responses of a sandwich plate are studied in detail.

This study presents a robust method towards the computation of dispersion curves of surface waves in an anisotropic semi-infinite periodically layered structure (PLS) coated by a stack of layers. Using the properties of the symplectic transfer matrix to analyze the relationship between the eigenequations of surface waves in a semi-infinite PLS and of its corresponding finite PLS, the eigenfrequencies within the stopbands for surface waves in a semi-infinite PLS are solved by a finite PLS consisting of a sufficient number of unit cells. The eigenvalues of a finite PLS are calculated by combining the precise integration method with the Wittrick–Williams (W-W) algorithm, which makes the present method accurate, efficient and numerically stable. On this basis, using the concept of the eigenvalue count in the W-W algorithm, the eigenfrequencies of surface waves in a semi-infinite PLS coated by a stack of layers are accurately computed for any given wavenumber. Unlike most existing approaches that determine dispersion curves by directly seeking roots from the transcendental eigenequation, the present method takes full advantages of the eigenvalue count to find all eigenfrequencies without the possibility of any being missed. The method can be applicable for surface wave problems in an arbitrarily anisotropic semi-infinite PLS and does not restrict layer number, layer thickness and material properties.

Industry is moving towards more data-oriented design and analyses to solve complex analytical problems. Solving complex and large finite element models is still challenging and requires high computational time and resources. Here, a modular method is presented to predict the transmission of vehicle body vibration to the occupants’ body by combining the numerical transfer matrices of the subsystems. The transfer matrices of the subsystems are presented in the form of data which is sourced from either physical tests or finite element models. The structural dynamics of the vehicle body is represented using a transfer matrix at each of the seat mounting points in three triaxial (X–Y–Z) orientations. The proposed method provides an accurate estimation of the transmission of the vehicle body vibration to the seat frame and the seated occupant. This method allows the combination of conventional finite element analytical model data and the experimental data of subsystems to accurately predict the dynamic performance of the complex structure. The numerical transfer matrices can also be the subject of machine learning for various applications such as for the prediction of the vibration discomfort of the occupant with different seat and foam designs and with different physical characteristics of the occupant body.

This study is concerned with an eigenvalue problem of a vibro-acoustic coupled system. In the conventional modal coupling method, the particle velocity normal to the surface of a panel is always calculated as zero, and the wave motion in the cavity cannot be directly treated. To overcome the problem, this study presents a novel formulation for a coupled system that expresses the correct boundary condition at the coupling plane and the wave motion in the cavity. First, a transfer matrix is introduced which can describe the characteristics of the sound field based on the wave dynamics. It is then clarified that if the panel vibration is regarded as the input to the cavity, the boundary condition of the sound field at the coupling plane should be a rigid wall. This is followed by the formulation of the eigenvalue problem of a vibro-acoustic coupled system. Finally, some numerical simulations are conducted, thereby clarifying the principles of the shift of natural frequencies and mode shapes, the accuracy of boundary condition at a coupling plane, and the orthogonality of coupled modes.

Electric field module for any isotropic multilayer thin film structure, is presented as analytical deduction. Analytic expressions for the electric field distribution are developed initially for a monolayer isotropic system based on Airy's formulae and boundary conditions, with an incident monochromatic source of light. The transfer matrix method 2×2, is used to deduce the distribution of the forward and backward electric field amplitudes on the inner layers in a general multilayer thin film structure. Analytical results are simulated in Transverse-Magnetic (TM) and Transverse-Electric (TE) modes making evident (when takes place) an electric field enhancement due to surface plasmons resonance. A graphical user interface is created to make steady simulations and create new structures as desired, minimizing time and optimizing resources.

Fluid wave code communication is used in layered water injection intelligent monitoring systems, but a model of fluid transient flow wave signal transmission is still unknown. Impedance and transfer coefficient in power transmission theory were used to describe transient flow waves in the transmission process of a tubular string in a water injection well and a transient flow wave model was built based on the transfer matrix method. The relationship between pressure and discharge was analyzed when the transient flow waves moved along the tubular string, and the influence of terminal impedance and dip angle of the tubular string on the wave transmission was studied. Simulations showed that the transient flow waves were with standing wave distribution when the transient flow wave signals transmitted in the tubular string. Moreover, the transmission volatility under different terminal impedances was analyzed. The communication frequency was selected according to the wave amplitude ratio between the two ends of the water injection tubular string. The relationship between the influence of tubular string parameters and fluid characteristics on the wave velocity and wave amplitude in the signal transmission process was obtained by simulation analysis. The wave velocity tended to decrease as the gas content increased. As the tube diameter–thickness ratio increased, the wave velocity decreased. Taking data from a water injection well in Daqing Oilfield as an example, a two-layer water injection test platform was built to study the fluctuation of discharge and pressure at monitoring points in the tubular string. The experiment condition was that the depth of the injection well was 1400 m. It was verified by the experiments that the pressure and flow changes in the downhole and wellhead had good consistency during the transmission of transient flow waves. Comparing the experimental results with the numerical results, the errors of the wave velocity and wave amplitude were 0.69% and 3.85%, respectively, indicating the verification of the simulation model. This study provides a theoretical support for the transmission of transient flow wave signals in a water injection tubular string.

In this work, a symmetric one dimensional quinary photonic crystal structure is proposed. The unit cell of the proposed structure is composed of materials chosen in such a way that the refractive i...

In this article, the coupling between the inner conductor and the shield of a coaxial cable is summarized with different coupling directions and shielding grounding conditions. An internal and external transmission line (IETL) transfer matrix is proposed to validate this coupling relationship. The induced voltage and current of the IETLs can be more intuitively represented by the IETL transfer matrix and the port voltage and current. By introducing the three-conductor system and the surface transfer impedance into the transmission line theory, the IETL transfer matrix representation of the transmission line equation with coupling components is obtained. Moreover, when analyzing the problems of coupling between field and transmission line, the coaxial cable can be equivalent to a bare wire by using IETL transfer matrix. According to this idea, an improved approximation method based on Hertzian dipole and a numerical method based on the finite element method algorithm are proposed to calculate the radiation of a coaxial cable and the crosstalk between a coaxial cable and a bare wire. Then, the results of the two methods are compared with the electromagnetic calculation software.

Most of the physical structures may be described in terms of mathematical models. The mathematical methods of system modelling also lead to a thorough explanation of the mechanism in the form of mathematical equations, which are often difficult to use for both analysis and controller synthesis. Consequently, it is useful and very important to determine the likelihood of different calculations of the same type, but in a lower-order representation, which can be assumed to correctly represent almost all the basic features of the system under examination. In this article, the proposed method is based on the modified balanced truncation method (BTM) by which the steady-state value from the problem of the BTM has been circumvented. This weakness has been eliminated by using a modified BTM to narrow the deviations by incorporating a gain factor into the response transfer matrix of the reduced-order model (ROM) to adjust the steady-state value of the ROM, without affecting the variations in dynamical behaviour as compared to the original system. To illustrate the proposed method, a real-time application model has been reduced where the ROM retains all the essential characteristics of the original system. In order to analyse the effectiveness, accuracy and validation with the other existing reduction methods, two standard numerical test systems have been taken from the literature and been tested also.

The dynamic behavior of bi-dimensional functionally graded beams is investigated by using the continuous elements method. The material properties are assumed to vary exponentially along the beam thickness and length. First, the transfer matrix is developed. Second, the characteristic frequency equation of simply supported beams is obtained. The proposed method is assessed and validated through comparison with available results. Then, parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

The principle of the ultrasonic technique consists of exciting the elastic plate immersed in water by an incident plane wave, the scattering acoustic phenomena are observed and then the backscattering waves are detected. In this study, we provide a theoretical model that is developed to study and understand the acoustic scattering. This model is based on the transfer matrix, taking into account the matrix components, we obtain the reflection and transmission coefficient by appropriate relationship. Furthermore, we will present a study an acoustic signal backscattering, under a normal incident wave, for different plates (Glass and Plexiglas). The time–frequency representations such as spectrogram (SP) are used. The images obtained by these representations are compared to the frequency spectral method. Consequently, the results obtained from the time–frequency analysis are interesting.

We present a new optimal power flow (OPF) design that not only optimizes fuel cost but also enhances dynamic performance of a power system. Performance is quantified by the $H_2$ -norm of the transfer matrix from any disturbance input to a set of performance outputs, which in this case are chosen as the frequencies of the generators. The $H_2$ -norm models the attenuation of the frequency amplitudes following the disturbance, and thereby quantifies the amount of damping torque induced on the tie-line flows. The method, referred to as $H_2$ -power flow modification ( $H_2$ -PFM) is carried out in two steps. First, the regular OPF is solved to obtain the optimal generator setpoints for active and reactive power dispatch. Second, the load setpoints are re-tuned to minimize the aforesaid $H_2$ -norm while keeping the generator setpoints fixed. In particular, manipulating the load reactive power in this way is found to reduce the norm remarkably, improving disturbance attenuation and damping. A gradient descent algorithm is proposed for this minimization. Results are validated using the 68-bus test system with a solar farm.

The aim of this paper is to present a theoretical study of the transmission coefficient for a periodic CdMnTe / C d T e system containing a geometric and material defect layer. The dynamic tuning of this defect layer is investigated using the transfer matrix for the theoretical calculations. It is shown that the thickness and the concentration of the defect layer have a strong impact on the electronic states (called also defect modes) localized in the band gaps. Moreover, the transmission coefficients of these defect states reach maximal values when the defect layer is placed in the middle of the structure; this is due to the constructive interferences caused by the symmetry of the system. Further, the defect states shift to lower energies with the increase of the concentration or the thickness of the defect layer as well as the decrease of the quality factor. These findings are useful to design a nano-energy filtering and sensoring devices.

A novel spectral transfer matrix for a cracked beam element is developed in this article and the same is used to identify the crack parameters on the beam structures. Spectral transfer matrix is developed from trigonometric functions based on the theory of fracture mechanics. This matrix determines the natural frequencies of a structure with crack with better accuracy than any other transfer matrices in the literature. The state vector at a node on the structure is formed which includes the displacement, rotation, internal and external forces, and moments at that node. When the state vector is multiplied with the transfer matrix, the state vector at the adjacent node is obtained. Each element is assumed to have a single open breathing crack with unknown depth and location. Initially, the developed spectral transfer matrix is used to determine the natural frequencies of a known cantilever, and after successful validation, the same is used for crack damage detection. By an inverse approach, crack parameters in each element are identified. The state vector at one node on the structure is obtained by measurement of input and out responses which is known as the initial state vector. Acceleration responses at selected nodes on the structure are measured and the state vectors at those nodes are predicted using spectral transfer matrices. The mean square error between measured and simulated responses is minimized using a heuristic optimization algorithm, with crack depth and location in each element as the optimization variables. Spectral transfer matrix method is applied to two numerical problems with single crack in each element; later, this method is successfully validated experimentally with structures having different boundary conditions. The accuracy in identified crack parameters and the applicability to sub-structures of a large structure are the important aspects of this method.

We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials, Jost solutions, spectral singularities and their time-reversal, and unidirectional reflectionlessness and invisibility. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of time-independent scattering theory in one dimension. This formulation relates the transfer matrix and therefore the solution of the scattering problem for a given potential to the solution of the time-dependent Schrodinger equation for an effective non-unitary two-level quantum system. We provide a self-contained treatment of this formulation and some of its most important applications. Specifically, we use it to devise a powerful alternative to the Born series and Born approximation, derive dynamical equations for the reflection and transmission amplitudes, discuss their application in constructing exact tunable unidirectionally invisible potentials, and use them to provide an exact solution for single-mode inverse scattering problems. The latter, which has important applications in designing optical devices with a variety of functionalities, amounts to providing an explicit construction for a finite-range complex potential whose reflection and transmission amplitudes take arbitrary prescribed values at any given wavenumber.

The Kramers–Wannier transfer matrix method is generalized to an arbitrary decoration number of the Ising chain. An exact analytical expression is obtained for the largest eigenvalue of the transfer matrix of a decorated Ising chain in the presence of an external magnetic field. Frustration points and the values of frustration magnetic fields are found that depend on the magnitudes and signs of exchange interactions. Exact expressions are obtained for zero-temperature entropies and zero-temperature magnetizations of the model under consideration. Magnetic phase diagrams of the ground state of the system are constructed for decoration values of d = 1 and d = 2, including those in the absence of a magnetic field. A comparison is made with a decorated square lattice not only in the absence but also in the presence of a magnetic field.

We compute resummed and matched predictions for jet angularities in hadronic dijet and Z+jet events with and without grooming the candidate jets using the SoftDrop technique. Our theoretical predictions also account for non-perturbative corrections from the underlying event and hadronisation through parton-to-hadron level transfer matrices extracted from dedicated Monte Carlo simulations with SHERPA. Thanks to this approach we can account for non-perturbative migration effects in both the angularities and the jet transverse momentum. We compare our predictions against recent measurements from the CMS experiment. This allows us to test the description of quark- and gluon-jet enriched phase-space regions separately. We supplement our study with SHERPA results based on the matching of NLO QCD matrix elements with the parton shower. Both theoretical predictions offer a good description of the data, within the experimental and theoretical uncertainties. The latter are however sizeable, motivating higher-accuracy calculations., Comment: 32 pages, 16 figures, extended discussion of uncertainties and included string model for hadronisation, added additional result as ancillary files, minor additional clarifications and text editing, version accepted for publication in JHEP

Purpose In this work a simulation study is performed to gain insights in the patterns of induced radiofrequency (RF) currents for various implant-like structures at 1.5 T. The previously introduced transfer matrix (TM) is used to determine why certain current patterns have a tendency to naturally occur. This can benefit current safety assessment techniques and may enable the identification of critical exposure conditions. Theory and methods The induced current on an elongated implant can be determined by multiplication of the incident electric field along the implant with its TM. The eigenmode spectrum of the TMs for various lengths and various types of implants are determined. The eigenvector with the highest eigenvalue describes the incident electric field pattern that induces the highest current which in turn will lead to highest heating. Subsequently, a statistical probability analysis is performed using a wide range of potential incident electric field distributions in a representative human subject model during a 1.5 T MR exam which are determined by means of electromagnetic FDTD simulations. These incident electric field distributions and the resulting induced current patterns are projected onto eigenvectors of the TM to determine which eigenmodes of the implant dominate the current patterns. Results The eigenvectors of the TM of bare and insulated wires resemble sinusoidal harmonics of a string fixed at both ends similar to the natural-current distribution on thin antennas(1). The currents on implants shorter than 20 cm are generally dominated by the first harmonic (similar to half a sine wave). This is firstly because for these implant lengths (relative to the RF wavelength), the first eigenvalue is more than three times bigger than the second showing the ability of an implant to accommodate one eigenmode better than another. Secondly, the incident electric fields have a high likelihood (≳95,7%) to project predominantly on this first eigenmode. Conclusion The eigenmode spectrum of the TM of an implant provides insight into the expected shape of induced current distributions and worst-case exposure conditions. For short implants, the first eigenvector is dominant. In addition, realistic incident electric field distributions project more heavily on this eigenvector. Both effects together cause significant currents to always resemble the dominant eigenmode of the TM for short implants at 1.5 T.

Mode-by-mode impulse responses, or spectral transfer matrix (STM) of birefringent fibers are measured by using linear optical sampling, with assist of polarization multiplexed probe pulse. By analyzing the STM, differential mode delays are estimated.

Purpose Crack damage detection for aluminum alloy materials using fiber Bragg Grating (FBG) sensor is a kind of structure health monitoring. In this paper, the damage index of full width at half maximum (FWHM) was extracted from the distorted reflection spectra caused by the crack-tip inhomogeneous strain field, so as to explain the crack propagation behaviors. Design/methodology/approach The FWHM variations were also investigated through combining the theoretical calculations with simulation and experimental analyses. The transfer matrix algorithm was developed to explore the mechanism by which FWHM changed with the linear and quadratic strain. Moreover, the crack-tip inhomogeneous strain field on the specimen surface was computed according to the digital image correlation measurement during the experiments. Findings The experimental results demonstrated that the saltation points in FWHM curve accorded with the moments of crack propagation to FBG sensors. Originality/value The interpretation of reflected spectrum deformation mechanism with crack propagation was analyzed based on both simulations and experiments, and then the performance of potential damage features – FWHM were proposed and evaluated. According to the correlation between the damage characteristic and the crack-tip location, the crack-tip of the specimen could be measured rapidly and accurately with this technique.

A frequency conversion mixer or single side band modulator using two cascaded MZM is proven experimentally. The operation of the circuit is modelled by a transfer matrix approach and verified by simulation in support of the experiment. A 10 GHz shift of the optical carrier in both left and right direction is demonstrated. The residual sideband suppression relative to the enhanced sideband is 22 dB for the best cases. Numerical analysis shows that the circuit has 3-dB optical and 3-dB electrical intrinsic advantage over the functionally equivalent DP-MZM.

Matrix displacement method, based on matrix operation without complex internal force analysis, gives accurate solutions and concise process for the kinetostatic analysis of the compliant mechanisms. However, there are some problems of tedious node numbering in the general matrix displacement method. In this paper, a multi-stage condensed modeling method is proposed to establish kinetostatic model for the compliant platform with complex configurations. Based on the matrix displacement method in structural mechanics and combining with the transfer matrix and coordinate transformation, the complex series–parallel configuration is subjected to multi-stage stiffness equivalent to obtain a concise input/output two-port mechanical network. Then, the proposed method is used to analyze the kinetostatic of the 6-degree-of-freedom (DOF) compliant platform. And a good prediction accuracy is shown by comparison with finite element analysis and experiment. Moreover, the results also show that the hinge thickness and the hinge spacing at the maximum amplification ratio of the bottom platform satisfies the linear condition, which provides implications for the design and optimization of the compliant mechanisms based on the bridge-type amplifiers.

This paper proposes an improved transfer-matrix method (TMM) for investigating the steady-state response of complex rotor-bearing systems. The internal damping of the shafts is considered to enhance the accuracy of the method. A transfer matrix of ball bearings with clearance and Hertzian contact is established. In addition, the incremental harmonic balance method is combined with the TMM to obtain the steady-state response of the rotor systems and simplify the investigation processes. The simulation results verify the superiority of this method in programming, reducing the order of system matrix, and determining stability. Thus, this method is efficient in investigating the nonlinear dynamic characteristics of large-scale rotor-bearing systems.