Absrtract. Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers [1], [2] is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are des...

In this paper, the equations of structural motion are expressed in time-invariant state-space equations by expressing the frequency dependent self-excited forces in terms of rational functions. Accordingly, the multimode coupled flutter analysis is reduced to evaluate the eigenvalues of a constant matrix at each prescribed wind velocity. This formulation is computationally efficient in comparis...

The two coupled linear equations C*X-Z%B = A^ C^Y+Z^A^B^ in polynomial matrices are studied in detail. These equations are crucial in the theory and design of linear optimal dynamic regulators via frequency-domain methods. The solvability of these equations is established under natural conditions. All solutions are characterized and then a specific solution is studied. Relation to other matrix ...

The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions between viscoelastic deformations of a plant cell wall and chemical processes in the cell wall matrix. We consider elastic deformations of the cell wall microfibrils and viscoelastic Kelvin–Voigt type deformations of the...

An efficient black-box algorithm for self-consistent analysis of three-dimensional (3-D) microelectromechanical systems (MEMS) is described. The algorithm is matrix-free based and employs a multilevel Newton technique to solve the coupled electromechanical equations. The new approach is shown to converge very rapidly and is much faster than relaxation algorithm for tightly coupled cases. While ...

We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

A self-contained coupled-mode theory for the coupled two asymmetric photonic crystal waveguides (PCWs) is presented. The first-order coupled-mode equations are derived under a weak coupling assumption. The coupling coefficients are obtained systematically by a matrix calculus using the modal solutions of each PCW in isolation. The coupled-mode equations are solved for contra-directional couplin...