Get A Cauchy Problem for the System of Elasticity Equations PDF

Get A Cauchy Problem for the System of Elasticity Equations PDF

By Makhmudov O. I.

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Sample text

For the modeling of such a layer in the experimental tank an abrupt drop in the air temperature in the laboratory is set up over the medium with the negative temperature, in combination with the blowing of air over the water surface by means of fans. This technique can be used to generate a surface isothermal layer from 2 to 10 cm thick. Beneath this layer there remains a negative temperature gradient that differs only slightly from the original one. Diffus ion Method. The diffusion method for the simulation of media characterized by a velocity of sound smoothly varying by depth is based on the dependence of the latter on the concentration of aqueous solutions of certain substances.

In order to prevent motion of the liquids and any disturbance of the stratification of the medium the liquids must be poured very slowly (the preparation of the medium is a several-hour process). Gradually between the solution and pure water diffusion causes the formation of a transition layer (a layer of sudden change in the density of the liquid), in which the salinity gradient can be computed by means of the diffusion equation if the medium can be regarded as layeredinhomogeneous and as having a salinity gradient in the direction of the z axis.

O~,-~~----~~----~~----~~----~~ 2 4 8 z, ern Fig. 22. Vertical profile of the velocity of sound in a surface sound channel with an absorbing layer. tance from the transmitter for pulses long enough to be equivalent to continuous radiation. 5°, and the depth of immersion of the transmitter and receiver is 3 cm. The distance from the transmitter is plotted on the horizontal axis on log scale. The sound intensity maxima in Fig. 21 correspond to caustics, the loci of which are found from the ray pattern (in the figure they are marked by vertical dashed lines).

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A Cauchy Problem for the System of Elasticity Equations by Makhmudov O. I.


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