Tunneling Effect in Proton Transfer: Transfer Matrix Approach

Using boundary conditions of electromagnetic waves , a new transfer matrix method that study electromagnetic waves in thin films and a dispersive formula of 1D photonic crystal are derived. Using the formula reflection and refraction of light is studied, the forbidden band of 1D photonic crystal is studied. The transfer matrix method and the classic characteristic matrix method are compared. The transfer matrix method can not only solve the problem that characteristic matrix method can solve, the transfer matrix method can also solve the problem that characteristic matrix method can not solve. Therefore the transfer matrix method is a more fundamental and wider range of application.

PyLlama: A stable and versatile Python toolkit for the electromagnetic modelling of multilayered anisotropic media

The transfer matrix method (TMM) is a powerful modeling approach with unique strengths for modeling flexible structures under feedback control. The TMM can model distributed parameter systems without spatial discretization, ensuring that the models are protected against model spillover. Feedback and actuator dynamics can be directly included in the structural model, leading to accurate models of ac-tuator/structure interaction. The TMM can produce closed-form symbolic expressions for the infinite-dimensional closed-loop transfer functions of distributed parameter systems under feedback control. These infinite-dimensional transfer functions can be used directly for compensator design via Bode plots. However, if modern state-space control design tools are to be applied to a flexible structure model with the TMM, the TMM model must first be discretized. The infinite-dimensional nature of TMM models and the fact that they involve transcendental expressions in the Laplace variable $s$ make it difficult to apply most of the model reduction procedures in the literature. This paper presents a technique for discretizing TMM models that is an improvement upon one discretization technique from the literature that is specific to the TMM.

Based on the similarity between the electric system and the mechanical system, this paper extends the transfer matrix method of multibody system, which has the advantages of low matrix order and fast computation speed in the mechanical system, to the field of circuit analysis to establish circuit equations. First, the transfer matrix of the basic circuit elements is derived; then, the transfer matrix of the element interconnection and the active branch is derived; then take the RLC circuit and the reverse amplification circuit as examples to verify the correctness of the transfer matrix derivation; finally, the transfer matrix method is compared with the current mainstream modified nodal approach, which proves that the transfer matrix method has the advantages of low matrix order and small calculation amount in constructing circuit equation.

In This search, the phenomena of resonance in series piping systems with oscillating valve have been studied. The one-dimensional flow, unsteady state flow, and partial differential equations have been solved by using transfer matrix method. The details of the transfer matrix method, the derivation of the field matrices and point matrices, and procedures for determining the natural frequencies and frequency response of piping system are then presented. A computer program (Resonance) was developed to calculate the pressure and discharge oscillations at the valve, the phase angle between the pressure head and relative gate opening of the valve, the phase angle between the discharge and the relative gate opening of the valve and also the pressure and discharge oscillations at certain sections of the pipes. To verify the transfer matrix method, the results have been compared with impedance method and agreement has been found.

The aim of this study is performing free vibration analysis of segmented Timoshenko beams on two parameter elastic foundation by using the transfer matrix method (TMM). The Pasternak foundation model which has an incompressible shear layer of vertical elements attached to the Winkler springs was considered. The transfer matrix formulations which are based on closed-form solutions of equations of motion of Timoshenko beams on Pasternak foundation were obtained. The natural frequencies were calculated by equating the determinant of global transfer matrix of structure to zero after the reduction according to boundary conditions. The mode shapes were plotted by normalising the state vectors at the ends. Firstly, the natural frequencies that obtained by using the proposed approach were validated by data in literature for a simply supported beam where a very good agreement was observed. Then, three-segmented beam models having various boundary conditions namely simple-simple (S-S), simple-fixed (S-F), fixed-simple (F-S) and fixed-fixed (F-F) were considered for numerical analysis. For the segmented beam models, the natural frequencies that calculated by using the TMM were compared to the results of finite element method (FEM) from SAP2000 by ignoring effects of shear layer of elastic foundation. The effects of shear layer as well as stiffness of Winkler springs on the natural frequencies of the segmented beam model were revealed for S-S, S-F, F-S and F-F boundary conditions, respectively. The mode shapes of the segmented beam model were presented. The results show that TMM can be used as an effective tool for free vibration analysis of multi-segmented Timoshenko beams on Pasternak foundation.

The sound absorptive performance of a proposed “meta-liner” are investigated in this paper. The structure is composed of closely placed plates connected by openings at alternating locations in a stacked format. This system presents multiple band gaps with high absorption and sub-wavelength behaviour (sample thickness equals 0.04 λ), achieved through tortuosity within the design. The acoustic response of the single layer is obtained numerically and with experimental verification under normal incidence. The repeating cellular design allows efficiencies in the viscothermal numerical analysis and using a transfer matrix approach, it is demonstrated that the response of the overall system may be efficiently predicted from a detailed model of a unit cell. Both the transfer matrix method and a full viscothermal model are validated against experimental data as a function of system depth. The analysis gives very satisfactory results which could form the basis for future designs.

We investigate ballistic spin transport in a two-dimensional electron-gas system containing magnetic barriers of various geometries by using the transfer matrix method. While most previous studies have focused on the effect of magnetic barriers perpendicular to the two-dimensional electron gas plane, we concentrate on the case of magnetic barriers parallel to the plane. We show that resonant oscillation occurs in the lower incident energy region in the transmission probability without any electrostatic potential compensation, which is an essential ingredient in the case of magnetic barriers perpendicular to the plane. The transmission probability in the magnetic barrier structure changes drastically according to the number of barriers and according to the additional electrostatic potential modulation applied in the magnetic barrier region. Using a hybrid model consisting of a superconductor, ferromagnets, and a two-dimensional electron gas plane, we show that the hybrid quantum structure can serve as a good spin filter, which can be operated totally by electrical modulation without any magnetic control.

Understanding dynamic behavior of a rotor system with a transverse crack is of great significance for operation reliability of rotating machinery. The transfer matrix method is widely used for rotor dynamic analysis, but it encounters difficulties modeling a crack. This study proposes a finite-width crack model that simulates the local stiffness reduction effect of a gaping crack in transfer matrix method. This model is obtained by comparing finite element analysis results of a shaft with a zero-width crack and its counterpart transfer matrix calculation results with a trial equivalent finite-width slot. Different shaft geometry and loading modes are considered to improve the generality of the model. An application example is given that uses the proposed model to calculate critical speeds of a multi-disk rotor system with a transverse crack at different positions.

The transfer matrix method together with a digital computer form the foundation of the dynamic analysis of rotor-bearing systems. The properties of each segment of the rotating shaft are expressed in simple matrix form and the overall dynamic behaviour is then obtained by successive multiplication of the element matrices. The main drawback associated with this method is the numerical instability in calculating natural frequencies for complex systems. The finite element method, on the other hand, uses the element stiffness and mass matrices to form the global equation of motion for the complete system. This avoids the numerical problems of the transfer matrix method at the expense of the computer memory requirements. The new method described in this paper combines the transfer matrix and finite element techniques to form a powerful algorithm for vibration analysis of rotor-bearing systems. It is shown that the accuracy improves significantly when the transfer matrix for each shaft segment is obtained from finite element techniques. The accuracy and efficiency of the hybrid method are compared with the transfer matrix method for a simply supported uniform rotating shaft where an analytical solution for the critical speeds and mode shapes is available. The method is then applied to a flexibly supported uniform shaft and a non-uniform shaft with a large disc to show the capability of the method for finding the critical speeds of complex rotor-bearing systems.

Recently, a new type of vibration isolator called a dynamic antiresonant vibration isolator (DAVI) has been studied for torsional systems as well as translational systems. In the DAVI for torsional systems, the inertia coupling for the anti-resonance effect is generated by a planetary gear that connects control inertia and inertias at the input and output terminals. In this research, an analytical modeling approach called the transfer matrix method is applied to design a planetary gear type DAVI for complex systems such as an automotive powertrain. Unlike a previous study, inertias of the pinion gears are newly included in the transfer matrix model to improve the model accuracy in this paper. In this part 1 of series papers, the internal configuration of a planetary gear type DAVI system is described and its dynamic model is derived using the transfer matrix method. The derived transfer matrix model is then validated by comparing its frequency response with those obtained by conventional and numerical methods. Finally, the effects of different gear ratios and pinion gear inertia are examined using the derived transfer matrix model.

The transfer matrix method (TMM) can be a powerful tool for modeling flexible structures under feedback control. It is particularly well suited to modeling structures composed of serially connected elements. The TMM is capable of modeling continuous elements such as beams or flexible robot links without discretization. The ability to incorporate controller transfer functions into the transfer matrix model of the system makes it a useful approach for control design. A limitation of the traditional formulation of the TMM is that it can only model feedback where the actuators and sensors are strictly collocated. The primary contribution of this paper is an algorithm for modeling noncollocated feedback with the TMM. Two cases of noncollocated sensors are considered (upstream and downstream). The approach is experimentally verified on a flexible robot that has one upstream and one downstream sensor in its feedback loops.

The presence of a leak within a single line system alters the dynamic behavior of the system when subjected to transient pressure fluctuations. This change in dynamic behavior is seen in the time-domain as an increased rate of energy loss (damping rate) of the pressure response and in the frequency-domain as an attenuation in the magnitudes of the eigenfrequencies (harmonics) of the system. Two recent developments in the literature on leak detection, based on exploiting the time- and frequency-domain behavior are the transient damping method, and the frequency response method respectively. These methods are both utilize linearized approximations of the original nonlinear water hammer equations. The frequency-domain methods are essentially based on the transfer matrix method (TMM) of modeling the transient pipeline system, whereas the transient damping method utilizes a modal damping method (MDM) of modeling the system. The methods adopt the same approach to linearizing the original nonlinear water hammer equations, however their main difference lies in the manner in which they incorporate the internal boundary condition associated with the leak. These different approaches give rise to different linear systems. The focus of this paper is the comparative analysis of these different systems and the nature of how their dynamics change for different leak parameter values. As is convenient for linear systems, the TMM and the MDM are analyzed in the Laplace-domain, where this analysis takes the form of deriving the Laplace-domain pressure response functions for each method and studying the dependency of the pole locations of these functions on the leak parameters. The Laplace-domain is a useful way to consider and compare the methods as it is shown that the location of the poles of the pressure response functions are directly related to the magnitude of the eigenfrequencies (as used by the frequency-domain methods to estimate the leak properties) and are also directly related to the modal damping rates (as used by the transient damping method to estimate the leak properties). Both methods behave similarly for small leaks, however, for large leaks vastly different behaviors are observed. The TMM yields a solution that is consistent with the underlying equations for the asymptotically large leak case, but the MDM does not, therefore a difference in the behaviors is attributed to limitations on the MDM. Additionally, from the study of the TMM, insight is given into a contention that has existed in the literature on the impact that a leak has on the frequency response of a system. Through studying the structure of the poles for the TMM, it is shown that a leak only effects the eigenfrequencies of a system and that no new eigenfrequencies are introduced as a result of the leak.

First Page

The axial strain sensitivity of long period fiber grating (LPFG) is analyzed by new transfer matrix method. The new transfer matrix method can be used to analyze the modes coupling between the core mode and multiple cladding modes. Compared with the previous method used, such as solving the coupled mode equation by the fourth order adaptive step size Runge-Kutta algorithm, the new transfer matrix method (TMM) has a faster calculation speed. Theoretical results are excellent agreement with the method of solving the coupled mode equation (SCME).