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Internal wave diffraction by a strip of an elastic plate on the surface of a stratified fluid

Dolai P., Dolai D. P.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

5--26

EN

The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.

2

Wiener-Hopf analysis of diffraction of acoustic waves by a soft/hard half-plane

Ayub M., Mann A. B., Ahmad M., Tiwana M. H.

Archives of Mechanics

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2010

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Vol. 62, nr 2

157-174

EN

In this paper, firstly, the far field due to a line source scattering of acoustic waves by a soft/hard half-plane is investigated. It is observed that if the line source is shifted to a large distance, the results differ from those of [16] by a multiplicative factor. Subsequently, the scattering due to a point source is also examined using the results of line source excitation. Both the problems are solved using the Wiener–Hopf technique and the steepest descent method. Some graphs showing the effects of various parameters on the diffracted field produced by the line source incidence are also plotted.

3

An Implementation of the Steepest Descent Method to Evaluation of Equilibrium Composition of Reactive Mixtures Containing Components in Condensed Phases

Papliński A.

Central European Journal of Energetic Materials

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2007

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Vol. 4, nr 1-2

135-150

EN

Thermodynamic evaluation of equilibrium state of the reacting mixture is considered. The principle of minimization of the Gibbs free energy is adopted for determining of the final chemical composition and thermodynamic state of the mixture. The steepest descent method is employed to evaluate the distribution of individual species concentrations of considered chemical system. A particular attention is paid to the cases in which substances in solid or liquid phase are present in the reactive medium. A method of reduction of the number of equations in the primary set of equations is described. Accuracy of calculations performed with the presented method is discussed.

4

Optimizing properties of an inertial dynamical system with geometric damping : link with proximal methods

Attouch H., Bolte J., Redont P.

Control and Cybernetics

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2002

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Vol. 31, no 3

643-657

EN

The second-order dynamical system x + [alpha]x + Beta[...] = 0, alpha > 0, Beta > 0, where the Hessian [...]Phi(x) acts as a geometric damping, is introduced, mainly in view of the minimization of [Phi]. Minimizing [Phi] is a problem equivalent to the minimization of the functional [Psi]a,b(x, y) = 1/b^2Phi(x) + 1/2|ax + by|^2, a > 0, b > 0. The latter naturallv appears in the proximal regularization of Phi ; it may also be viewed as an energy. The continuous steepest descent method applied to [Psi]a,b yields a first-order system, which proves to he equivalent to the above-mentioned second-order system, when [Phi] is of class [C^2].