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Dynamic projection operator method in the theory of hyperbolic systems of partial differential equations with variable coefficients

Leble S., Vereshchagina I.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2017

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Vol. 21, No 2

109--120

EN

We consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients. It is supposed that the dependence of coefficients on the only variable χ is weak, that is described by the introduction of a small parameter. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics in waveguides with a variable cross-section. Projection operators are constructed for the Cauchy problem to fix unidirectional modes. The method of successive approximations (perturbation theory) is developed and based on the pseudodifferential operators theory. The application of projection operators adapted for the case under consideration allows deriving approximate evolution equations corresponding to the separated directed waves.

2

Surface waves in non-homogeneous, general magnetothermo, viscoelastic media of higher order

Sethi M., Gupta K. C., Rani M.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

1221--1236

EN

The aim of the present paper is to investigate surface waves in a non-homogeneous, isotropic, visco-elastic solid medium of n-th order including the time rate of strain. The theory of generalised surface waves has firstly been developed and then it has been employed to investigate particular cases of waves, viz., Stoneley, Rayleigh and Love type. The wave velocity equations have been obtained for different cases and are in well agreement with the corresponding classical result, when the effects of viscosity, temperature, magnetism as well as nonhomogeneity of the material medium are ignored.

3

Numerical-experimental studies on penetration of multilayered targets containing ceramics

Jach K., Lis J., Mroczkowski M., Świerczyński R., Wiśniewski A.

Journal of Technical Physics

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2002

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Vol. 43, no 1

35-41

EN

In the paper we present the results of numerical and experimental studies of the impact of penetrators onto ceramic-composite and ceramic-metal targets. The main purpose of this paper is to show the possibilities of computer-aided interpretation of experimental results using "free particles" hydrocodes modelling of multilayered targets containing ceramics. Model for ceramics is based on the modified Steinberg's constitutive relations for non-damaged, ideal ceramic material. The model of the composite is based on the isotropic multilayered model of composite panels with different material characteristics in each layer. The numerical simulations and experiments were carried out for several combinations of ceramic/metal and ceramic/composite layers: Al2O3/aluminium, SiC/AlN/steel, AIN/SiC/steel, SiC/Al2O3/steel, AIN/Al2O3/steel and Al2O3/Dyneema. The exemplary results of our studies are shown. The results of theoretical and experimental investigations are in good agreement with one another.

4

The technique of numerical solution of 2-D direst current modelling problem in inhomogeneous media

Sapuzhak Y., Zhuravchak L.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 2

149-163

EN

Effective numerical technique for solving the direct problem ofd electrical prospecting for homogenous media with inclusions of arbitrary shape and constant or changenable electrical characteristics is suggested. It is based on a simultaneous application of fundamental solution of Laplace's equation for halfplane and principal ideas of the boundary integral equation method and the methods of simple layer potential and collocation, as well as finite-difference correlations inlocal inhomogenous regions with changeable characteristics. Numerical solutions for some mathematical models illustrating the high accurancy and potential abilities of the technique suggested have been considered.