J. Jena

Self-similar shocks in a dusty gas

Abstract A group theoretic method is used to establish the entire class of self-similar solutions to the problem of shock wave propagation through a dusty gas. Necessary conditions for the existence of similarity solutions for shocks of arbitrary strength as well as for strong shocks are obtained. It is found that the problem admits a self-similar solution only when the ambient medium ahead of the shock is of uniform density. Collapse of imploding cylindrical and spherical shocks is worked out in detail to investigate as to how the shock involution is influenced by the mass concentration of solid particles in the medium, the ratio of the density of solid particles to that of initial density of the medium, the relative specific heat and the amplification mechanism of the flow convergence.

Interaction of an acceleration wave with a strong shock in reacting polytropic gases

In this paper, we have studied the evolution of an acceleration wave for the system of partial equations describing one dimensional, unsteady, flow of reacting polytropic gases with same @c-law. The system consists of two species, burnt gas and unburnt gas. The amplitude of the acceleration wave propagating along the characteristic associated with the largest eigenvalue has been evaluated. The interaction of the strong shock with the acceleration wave has been investigated. The amplitudes of the reflected and transmitted waves after interaction are evaluated by using the results of general theory of wave interaction.

Evolution and interaction of a characteristic shock with an acceleration wave in a reacting gas

In this paper, we consider the evolution and propagation of a characteristic shock through a reacting gas and studied its interaction with an acceleration wave. A particular solution to the governing system, which exhibits space-time dependence, has been considered to study the evolutionary behavior of the characteristic shock. The amplitudes of the reflected and transmitted waves and the jump in shock acceleration, influenced by the incident wave amplitude after interaction are evaluated.

Lie group of transformations to study anisotropic diffusion of scalar images

Lie group of transformations associated with anisotropic diffusion equation is derived using the invariance properties. The equation is of great importance in the study of geometrical diffusion of scalar images. Infinitesimals of Lie group of transformations with respect to independent and dependent variables along with invariant surface conditions are used to obtain a general form of edge stopping function. The edge stopping functions used by Perona & Malik and their successors are obtained in particular cases. The equation in three independent variables reduced in terms of fewer independent variables.

Propagation and interaction of waves in a non-ideal gas

The propagation of disturbances through a non-ideal medium, where the solid behaves like a fluid with an equation of state of Mie-Gruneisen type is considered. The method of relatively undistorted waves is used to study the situations when the disturbance amplitude is finite, arbitrarily small, and not so small. The effects of the solid particles and that of the non-planar wave front configuration on the distortion attenuation, and shock formation of propagating pulses are described in detail. The resonant multiwave theory of weakly nonlinear geometrical optics, which takes into consideration systems where many waves coexist and interact with one another resonantly, is applied to derive transport equations for signals having all possible wave modes which are mutually coupled and interact resonantly among themselves.

Far-field behavior of waves in a relaxing gas

Abstract An asymptotic equation is derived which describes the far-field behavior of the governing system of partial differential equations for a one dimensional unsteady plane and radially symmetric flow of an inviscid relaxing gas; this evolution equation, is a generalized Burgers equation, which enables us to study in detail the various effects that appear in the propagation of plane, cylindrical and spherical waves in a dissipative medium with a quadratic nonlinearity. An approximate solution of this equation is obtained by using the method of matched asymptotic expansions; the method enables us to determine how the shock amplitude and the shift in the shock center are influenced by the relaxation effects.

On evolution of non-linear waves in polytropic reacting gases

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in polytropic reacting gases with same

Lie group transformations for self‐similar shocks in a gas with dust particles

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