CHIRAL POTTS MODEL: CORNER TRANSFER MATRICES AND PARAMETRIZATIONS

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3489-3500 ◽  
Author(s):  
R.J. BAXTER
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Functions ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Difference Property ◽  
The Difference

We consider the star-triangle relation and the form of its solutions. We present some simple parametrizations of the weight functions of the three-state chiral Potts model. This model does not have the “difference property”: we discuss the resulting difficulties in attempting to use the corner transfer matrix method for this model.

Flexural Vibration Response of Beams With General Boundary Conditions: A Transfer Matrix Approach

1991 ◽  
Author(s):  
T. Önsay
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Response ◽  
General Boundary ◽  
Phase Variable ◽  
General Boundary Conditions ◽  
Transfer Matrices ◽  
Analytical Results

Abstract The wave-mode representation is utilized to obtain a more efficient form to the conventional transfer matrix method for bending vibrations of beams. The proposed improvement is based on a phase-variable canonical state representation of the equation governing the time-harmonic flexural vibrations of a beam. Transfer matrices are obtained for external forces, step-change of beam properties, intermediate supports and for boundaries. The transfer matrices are utilized to obtain the vibration response of a point-excited single-span beam with general boundary conditions. The general characteristic equation and the transfer mobility of a single-span beam are determined. The application of the analytical results are demonstrated on physical structures with different boundary conditions. A hybrid model is developed to incorporate measured impedance of nonideal boundaries into the transfer matrix method. The analytical results are found to be in excellent agreement with experimental measurements.

Riccati Transfer Equations for Linear Multibody Systems with Indeterminate In-Span Conditions

2019 ◽  
Vol 86 (6) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Junjie Gu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody Systems ◽  
Internal Force ◽  
State Variables ◽  
Transfer Matrices ◽  
Transfer Equations ◽  
Mechanical Elements

The transfer matrix method for linear multibody systems is capable of providing precise solutions for the dynamics of various mechanical systems, but it may also suffer from numerical instability in some cases, where serial chains with a large number of mechanical elements are involved or high-frequency harmonic responses are computed. Combining such a transfer strategy with the Riccati transformation yields the Riccati transfer matrix method (RTMM), which can help improve the numerical stability. According to the existing method, the conventional transfer matrices of all the mechanical elements should be obtained first; in other words, the existence of conventional transfer matrices is a prerequisite for the application of the RTMM. Thus, it seems that the RTMM is incapable of performing the dynamics analysis of linear multibody systems with indeterminate in-span conditions due to the nonexistence of the corresponding conventional transfer matrices. Observe that, for any state variables with indeterminate input–output relationships, the complementary state variables (the complementary state variable of a displacement is the corresponding internal force and vice versa) are identically equal to zero, and that the dimension of the Riccati transfer equation is only half of that of the conventional transfer equation. It reveals that the Riccati transfer equations for the connection points associated with indeterminate in-span conditions can be formulated directly, and that there is no need to rely on the conventional transfer equation. Two numerical examples are simulated and the computational results are compared with those obtained by the finite element method, which verifies the proposed method.

scholarly journals MODELLING CHARGE TRANSPORT IN DNA USING TRANSFER MATRICES WITH DIAGONAL TERMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4138-4149 ◽  
Author(s):  
STEPHEN A. WELLS ◽  
CHI-TIN SHIH ◽  
RUDOLF A. RÖMER
Keyword(s):  
Damage Detection ◽  
Charge Transport ◽  
Transport Properties ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Tight Binding ◽  
Transfer Matrices ◽  
Dna Charge Transport ◽  
Binding Models

There is increasing evidence that DNA can support a considerable degree of charge transport along the strand by hopping of holes from one base to another, and that this charge transport may be relevant to DNA regulation, damage detection and repair. A surprisingly useful amount of insight can be gained from the construction of simple tight-binding models of charge transport, which can be investigated using the transfer-matrix method. The data thus obtained indicate a correlation between DNA charge-transport properties and the locations of cancerous mutation. We review models for DNA charge transport and their extension to include more physically realistic diagonal-hopping terms.

scholarly journals Modeling of Sonotrode System of Ultrasonic Consolidation With Transfer Matrix Method

2021 ◽  
Vol 8 ◽  
Author(s):  
Yin Wang ◽  
Ziyan Chen ◽  
Qing Yu ◽  
Fang Cheng
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Matrix Model ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Experimental Result ◽  
Ultrasonic Consolidation ◽  
Modeling Methods ◽  
Resonance Frequencies ◽  
The Difference

To establish an efficient model for sonotrode system, a key part that continuously applies ultrasonic oscillation on metal foils to form solid state bond in ultrasonic consolidation equipment, this research presents modeling methods for sonotrode system. After an introduction to the construction of sonotrode system along with its operating principle, the transfer matrix method was adopted to build the model for the system consisting two ultrasonic transducers and one sonotrode. Simulation results of transfer matrix model were compared to that of finite element method. A prototype was fabricated and tested. A comparison of the resonance frequencies calculated by two modeling methods to the experimental result showed that the difference between transfer matrix model and prototype is 6.96% while the difference between finite element model and prototype is 9.26%. The proposed transfer matrix method is an efficient way to simulate dynamic performances for sonotrode system, which provide a better foundation for further optimization.

scholarly journals Transfer Matrix Method for Natural Vibration Analysis of Tree System

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bin He ◽  
Xiaoting Rui ◽  
Huiling Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Damage Identification ◽  
Continuous System ◽  
Dynamical Response ◽  
Transfer Matrices ◽  
Chain System ◽  
Mechanics Model

The application of Transfer matrix method (TMM) ranges from linear/nonlinear vibration, composite structure, and multibody system to calculating static deformation, natural vibration, dynamical response, and damage identification. Generally TMM has two characteristics: (1) the TMM formulae share similarity to the chain mechanics model in terms of topology structure; then TMM often is selected as a powerful tool to analyze the chain system. (2) TMM is adopted to deal with the problems of the discrete system, continuous system, and especial discrete/continuous coupling system with the uniform matrix form. In this investigation, a novel TMM is proposed to analyze the natural vibration of the tree system. In order to make the TMM of the tree system have the two above advantages of the TMM of the chain system, the suitable state vectors and transfer matrices of the typical components of the tree system are constructed. Then the topology comparability between the mechanics model and its corresponding formulae of TMM can be adopted to assembling the transfer matrices and transfer equations of the global tree system. Two examples of natural vibration problems validating the method are given. The formulation of the proposed TMM is mathematically intuitive and can be held and applied by the engineers easily.

scholarly journals Modelling of Critical Velocities of the Cardan Mechanism using Transfer Matrix Method

2021 ◽  
Vol 23 (1) ◽  
pp. B33-B38
Author(s):  
Petr Hrubý ◽  
Tomáš Náhlík
Keyword(s):  
Mechanical Properties ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Physical And Mechanical Properties ◽  
Transfer Matrices ◽  
Concentrated Mass ◽  
Method Transfer ◽  
Eigen Frequencies ◽  
Critical Velocities

The presented paper focuses to rotating components of mechanical constructions. The problem of the spatial combined bending-gyratory vibration and calculation of the Eigen frequencies is studied. The model of Cardan Mechanism is solved by the transfer matrix method. Transfer matrices were derived for shaft, concentrated mass and elastic bearing. The physical and mechanical properties of each part of the mechanism are hidden in these matrices. A procedure for calculating Eigen frequencies was proposed.

The Analysis of Line Structures by Transfer Matrices Derived from Finite Elements

1975 ◽  
Vol 19 (01) ◽  
pp. 57-61
Author(s):  
W. D. Pilkey ◽  
J. K. Haviland ◽  
P. Y. Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Large Scale ◽  
The Finite Element Method ◽  
Transfer Matrices ◽  
Finite Element Systems

It is shown that the finite-element method can be efficiently employed in the analysis of line structures, in particular, ship structures, if it is combined with the transfer matrix method. Advantage is taken of the finite element method's structural modeling capability in representing complicated substructures. The substructures are pieced together along the length of the structure using transfer matrices. It is demonstrated that this approach can be superimposed on available large scale finite-element systems to improve their efficiency and increase their capabilities.

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