Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws

The stability of traveling wave solutions of scalar viscous conservation laws is investigated by decomposing perturbations into three components: two far-field components and one near-field component. The linear operators associated to the far-field components are the constant coefficient operators determined by the asymptotic spatial limits of the original operator. Scaling variables can be applied to study the evolution of these components, allowing for the construction of invariant manifolds and the determination of their temporal decay rate. The large time evolution of the near-field component is shown to be governed by that of the far-field components, thus giving it the same temporal decay rate. We also give a discussion of the relationship between this geometric approach and previous results, which demonstrate that the decay rate of perturbations can be increased by requiring that initial data lie in appropriate algebraically weighted spaces.     

Detonation in gases

We review recent progress in gaseous detonation experiment, modeling, and simulation. We focus on the propagating detonation wave as a fundamental combustion process. The picture that is emerging is that although all propagating detonations are unstable, there is a wide range of behavior with one extreme being nearly laminar but unsteady periodic flow and the other chaotic instability with highly turbulent flow. We discuss the implications of this for detonation propagation and dynamic behavior such as diffraction, initiation, and quenching or failure.     

Flows formed after the passage of a discontinuous wave over a bottom drop

The solvability of the problem of the flow formed after a discontinuous wave has passed over a bottom drop is studied within the framework of the first approximation of shallow water theory. Solutions in which the total energy of the flow is either conserved or lost at the drop are considered. Stable self-similar solutions of five qualitatively different types are derived and their domains of existence are determined in the dimensionless parameter plane.     

Analysis for Transmission Characteristics of Closed Trapezoidal-Groove Waveguide with Boundary Element Method

In this paper, the cut-off and dispersion characteristics of a new kind of closed trapezoidal-groove waveguide that has more advantages than open groove waveguides are analyzed with the help of the boundary element method, the relationship between cut-off wavelengths and variations of guide's relative sizes is discussed in detail. The calculated results are in good agreement with those in the relevant reference. So, the obtained conclusions are very important in theoretical studies and actual applications of closed trapezoidal-groove waveguides for millimeter and submillimeter waves.     

Absorption of shocked benzene

Abstract

We used absorption spectroscopy to observe decomposition of benzene (C₆H₆) subjected to the passage of strong shock waves generated by projectile impact. These measurements were made using a recently developed double-beam, double-pass, fiber-optic-coupled apparatus. Near 13 GPa, we observe absorption throughout most of the visible region, with strong absorption occurring for wavelengths below 400 nm. The absorption is most likely due to a combination of molecular absorption and Mie scattering from carbon particles formed as a result of shock decomposition.     

Wavespeed analysis: Approximating Arrhenius kinetics with step-function kinetics

The accuracy of using step-function approximations to the Arrhenius exponential in computing the wavespeed in combustion wave propagation is investigated. Gaseous and gasless combustion, and first- and second-order reactions are included in the study. The theoretical analysis is based on Melnikov theory from dynamical systems. The error is shown to be small in most instances. The analytical results are supported with numerical simulations.     

Mechanism of interaction of pressure waves at a discrete partial blockage

This paper analyses the mechanism of interaction between an incident pressure wave and blockages of different geometrical characteristics (i.e., a butterfly and a ball valves, two short stretches of pipe with a reduced diameter, and a device simulating a longitudinal body blockage) by means of laboratory and numerical tests. Experiments have shown that the mechanism of interaction with pressure waves is influenced by their path through the device: sinuous because of the device body for partially closed in-line valves (type I mechanism), and straight for the small bore pipe devices (type II mechanism). Type I mechanism is characterized by a rise followed by an almost constant value whereas in type II one a drop occurs after the rise. To complete the investigation the effect of the pre-transient condition is discussed.     

Some existence results for a simplified two fluid system in plasma theory

In this paper, we consider a simplified two fluid system in plasma theory. Some multiple existence results for this system are obtained by variational methods and topological degree methods.