A Theory for steady and self-sustained premixed combustion waves

Based on the compressible Navier – Stokes equations for reactive flow problems, an eigenvalue problem for the steady and self-sustained premixed combustion wave propagation is developed. The eigenvalue problem is analytically solved and a set of analytic formulae for description of the wave propagation is found out. The analytic formulae are actually the exact solution of the eigenvalue problem in the form of integration, based on which author develops an iterative and numerical algorithm for calculation of the steady and self-sustained premixed combustion wave propagation and its speed. In order to explore the mathematical model and test the computational method developed in this paper, three groups of combustion wave propagation modes are calculated. The computational results show that the non-trivial modes of the combustion wave propagation exist and their distribution is not continuous but discrete

Transition Fronts in Time Heterogeneous and Random Media of Ignition Type

The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous media admit transition fronts or generalized traveling wave solutions with time dependent profiles and that such equations in time random media admit generalized traveling wave solutions with random profiles. Important properties of generalized traveling wave solutions, including the boundedness of propagation speeds and the uniform decaying estimates of the propagation fronts, are also obtained

A renormalisation approach to excitable reaction-diffusion waves in fractal media

Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice

Measurements and Simulations of Wave Propagation in Agitated Granular Beds

Wave propagation in a granular bed is a complicated, highly nonlinear phenomenon. Yet studies of wave propagation provide important information on the characteristics of these materials. Fundamental nonlinearities of the bed include those in the particle contact model and the fact that there exists zero applied force when grains are out of contact. The experimental work of Liu and Nagal showed the strong dependence of wave propagation on the forming and breaking of particle chains. As a result of the nonlinearities, anomalous behavior such as solitary waves and sonic vacuum have been predicted by Nesterenko. In the present work we examine wave propagation in a granular bed subjected to vertical agitation. The agitation produces continual adjustment of force chains in the bed. Wave propagation speed and attenuation measurements were made for such a system for a range of frequencies considerably higher than that used for the agitation. Both laboratory experiments and simulations (using a two-dimensional, discrete soft-particle model) have been used. The present paper is a progress report on the simulations

Trapping of Vibrational Energy in Crumpled Sheets

We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behaviour of the dispersion curves near the ridges and on the flat facets. This analysis suggests that ridges act as barriers to wave propagation and that modes in a certain frequency regime could be trapped in the facets. A simulation study of the wave propagation qualitatively supported our analysis and showed interesting effects of the ridges on wave propagation.Comment: RevTex 12 pages, 7 figures, Submitted to PR