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Jonathan Tennyson - One of the best experts on this subject based on the ideXlab platform.
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electron molecule collision calculations using the r Matrix Method
Physics Reports, 2010Co-Authors: Jonathan TennysonAbstract:Abstract The R -Matrix Method is an embedding procedure which is based on the division of space into an inner region where the physics is complicated and an outer region for which greatly simplified equations can be solved. The Method developed out of nuclear physics, where the effects of the inner region were simply parametrized, into atomic and molecular physics, where the full problem can be formulated and hopefully solved ab initio. In atomic physics R -Matrix based procedures are the Method of choice for the ab initio calculation of electron collision parameters. There has been a number of R -Matrix procedures developed to treat the low-energy electron–molecule collision problem or particular aspects of this problem. These Methods have been extended to both positron physics and the R -Matrix treatment of vibrational motion. The physical basis of the R -Matrix Method as well as its theoretical formulation are presented. Various electron scattering models within an R -Matrix formulation including static exchange, static exchange plus polarization and close coupling are described with reference to various computational implementations of the Method; these are compared to similar models used within other scattering Methods. The need for a balanced treatment of the target and continuum wave functions is emphasised. Extensions of close-coupling based models into the intermediate energy regime using pseudo-states is discussed, as is the adaptation of R -Matrix Methods to problems involving photons. The numerical realisation of the R -Matrix Method is based on the adaptation of quantum chemistry codes in the inner region and asymptotic electron–atom scattering programs in the outer region. Use of bound state codes in scattering calculations raises issues involving continuum basis sets, appropriate orbitals, integral evaluation, orthogonalization, Hamiltonian construction and diagonalization which need to be addressed. The algorithms developed to resolve these issues are described as are ones associated with the outer region where Methods to characterize resonances have received particular attention. Results from a few illustrative calculations are discussed: (i) electron collisions with polar systems with water as an example; (ii) electron collisions with molecular ions focusing on H3+; (iii) electron collisions with organic species such as methane and uracil and (iv) positron–molecule collisions. Finally some outstanding issues that need to be addressed are mentioned.
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Electron-molecule collisions at low and intermediate energies using the R-Matrix Method
European Physical Journal D: Atoms, Molecules and Clusters and Optical Physics, 2005Co-Authors: Jonathan TennysonAbstract:We present the latest developments of the R-Matrix Method as applied to electron-molecule collisions. A variety of calculations for H2O are presented including the study of rotational excitation and preliminary data for dissociative electron attachment. Results for the application of the recently developed molecular R-Matrix with pseudostates (MRMPS) Method to neutral and cationic targets are also included. This Method is currently being applied to the study of collisions with anionic targets.
Stanislav I Rokhlin - One of the best experts on this subject based on the ideXlab platform.
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stable recursive algorithm for elastic wave propagation in layered anisotropic media stiffness Matrix Method
Journal of the Acoustical Society of America, 2002Co-Authors: Stanislav I Rokhlin, L WangAbstract:An efficient recursive algorithm, the stiffness Matrix Method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer Matrix Method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) Matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) Matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the Method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this Method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.
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stable reformulation of transfer Matrix Method for wave propagation in layered anisotropic media
Ultrasonics, 2001Co-Authors: L Wang, Stanislav I RokhlinAbstract:The numerical instability problem in the standard transfer Matrix Method has been resolved by introducing the layer stiffness Matrix and using an efficient recursive algorithm to calculate the global stiffness Matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in Matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness Matrix is represented analytically. It is shown that the elements of the stiffness Matrix are as simple as those of the transfer Matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness Matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer Matrix Method. The stiffness Matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this Method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness Matrix Method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.
Pochi Yeh - One of the best experts on this subject based on the ideXlab platform.
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Extended Jones Matrix Method. II
Journal of the Optical Society of America A, 1993Co-Authors: Pochi YehAbstract:We derive an extended Jones Matrix Method to treat the transmission of light through birefringent networks, where the incident angle of light and the optical axis of the birefringent media are arbitrary. As an example, we employ the Method to analyze the leakage problem of a twisted nematic liquid-crystal display and to suggest its possible solutions. A generalization of the Method covers all dielectric media, including uniaxial and biaxial crystals and also gyrotropic materials that exhibit optical rotation and Faraday rotation.
L Wang - One of the best experts on this subject based on the ideXlab platform.
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stable recursive algorithm for elastic wave propagation in layered anisotropic media stiffness Matrix Method
Journal of the Acoustical Society of America, 2002Co-Authors: Stanislav I Rokhlin, L WangAbstract:An efficient recursive algorithm, the stiffness Matrix Method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer Matrix Method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) Matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) Matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the Method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this Method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.
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stable reformulation of transfer Matrix Method for wave propagation in layered anisotropic media
Ultrasonics, 2001Co-Authors: L Wang, Stanislav I RokhlinAbstract:The numerical instability problem in the standard transfer Matrix Method has been resolved by introducing the layer stiffness Matrix and using an efficient recursive algorithm to calculate the global stiffness Matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in Matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness Matrix is represented analytically. It is shown that the elements of the stiffness Matrix are as simple as those of the transfer Matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness Matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer Matrix Method. The stiffness Matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this Method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness Matrix Method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.
Guoping Wang - One of the best experts on this subject based on the ideXlab platform.
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discrete time transfer Matrix Method for dynamics analysis of complex weapon systems
Science China-technological Sciences, 2011Co-Authors: Bao Rong, Guoping Wang, Bin HeAbstract:Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new Method developed in recent years, the discrete time transfer Matrix Method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer Matrix Method of multibody system is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This Method does not need the global dynamic equations of system and has the low order of system Matrix, high computational efficiency. The proposed Method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.
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modified finite element transfer Matrix Method for eigenvalue problem of flexible structures
Journal of Applied Mechanics, 2011Co-Authors: Bao Rong, Xiaoting Rui, Guoping WangAbstract:The speedy computation of eigenvalue problems is the key point in structure dynamics. In this paper, by combining transfer Matrix Method and finite element Method, the modified finite element-transfer Matrix Method and its algorithm for eigenvalue problems are presented. By using this Method, the speedy computation of eigenvalue problem of flexible structures can be realized, and the repeated eignvalue problem can be solved simply and conveniently. This Method has the low order of system Matrix, high computational efficiency, and stability. Formulations of this Method, as well as some numerical examples, are given to validate the Method.
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transfer Matrix Method for linear multibody system
Multibody System Dynamics, 2008Co-Authors: Guoping Wang, Yuqi LuAbstract:A new Method for linear hybrid multibody system dynamics is proposed in this paper. This Method, named as transfer Matrix Method of linear multibody system (MSTMM), expands the advantages of the traditional transfer Matrix Method (TMM). The concepts of augmented eigenvector and equation of motion of linear hybrid multibody system are presented at first to find the orthogonality and to analyze the responses of the hybrid multibody system using modal Method. If using this Method, the global dynamics equation is not needed in the study of linear hybrid multibody system dynamics. The MSTMM has a small size of Matrix and higher computational speed, and can be applied to linear multi-rigid-body system dynamics, linear multi-flexible-body system dynamics and linear hybrid multibody system dynamics. This Method is simple, straightforward, practical, and provides a powerful tool for the study on linear hybrid multibody system dynamics. This Method can be used in the following: (1) Solve the eigenvalue problem of linear hybrid multibody systems. (2) Obtain the orthogonality of eigenvectors of linear hybrid multibody systems. (3) Realize the accurate analysis of the dynamics response of linear hybrid multibody systems. (4) Find the connected parameters between bodies used in the computation of linear hybrid multibody systems. A practical engineering system is taken as an example of linear multi-rigid-flexible-body system, the dynamics model, the transfer equations and transfer matrices of various bodies and hinges; the overall transfer equation and overall transfer Matrix of the system are developed. Numerical example shows that the results of the vibration characteristics and the response of the hybrid multibody system received by MSTMM and by experiment have good agreements. These validate the proposed Method.
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riccati discrete time transfer Matrix Method for elastic beam undergoing large overall motion
Multibody System Dynamics, 2007Co-Authors: Xiaoting Rui, Guoping WangAbstract:An efficient Method for dynamics simulation for elastic beam with large overall spatial motion and nonlinear deformation, namely, the Riccati discrete time transfer Matrix Method (Riccati-DT-TMM), is proposed in this investigation. With finite segments, continuous deformation field of a beam can be decomposed into many rigid bodies connected by rotational springs. Discrete time transfer matrices of rigid bodies and rotational springs are used to analyze the dynamic characteristic of the beam, and the Riccati transform is used to improve the numerical stability of discrete time transfer Matrix Method of multibody system dynamics. A predictor-corrector Method is used to improve the numerical accuracy of the Riccati-DT-TMM. Using the Riccati-DT-TMM in dynamics analysis, the global dynamics equations of the system are not needed and the computation time required increases linearly with the system’s number of degrees of freedom. Three numerical examples are given to validate the Method for the dynamic simulation of a geometric nonlinear beam undergoing large overall motion.
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discrete time transfer Matrix Method for multibody system dynamics
Multibody System Dynamics, 2005Co-Authors: Bin He, Wenguang Lu, Yuqi Lu, Guoping WangAbstract:A new Method for multibody system dynamics is proposed in this paper. This Method, named as discrete time transfer Matrix Method of multibody system (MS-DT-TMM), combines and expands the advantages of the transfer Matrix Method (TMM), transfer Matrix Method of vibration of multibody system (MS-TMM), discrete time transfer Matrix Method (DT-TMM) and the numerical integration procedure. It does not need the global dynamics equations for the study of multibody system dynamics. It has the modeling flexibility and a small size of matrices, and can be applied to a wide range of problems including multi-rigid-body system dynamics and multi-flexible-body system dynamics. This Method is simple, straightforward, practical, and provides a powerful tool for the study of multibody system dynamics. Formulations of the Method as well as some numerical examples of multi-rigid-body system dynamics and multi-flexible-body system dynamics to validate the Method are given.
