Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index

We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $\Lambda$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagating radiation waves, and hot spots of medium excitation.Comment: 9 pages, 6 figure

Frequency Locking for Combustion Synthesis in Periodic Medium

Solutions of a 1-D free-interface problem modeling solid combustion front propagating in combustible mixture with periodically varying concentration of reactant exhibit classical phenomenon of mode locking. Numerical simulation shows a variety of locked periodic, quasi-periodic and chaotic solutions.Comment: 11 pages, 6 figure

CSUMS Project: Flame propagation in random media

Combustion is a very difficult process to study because it couples chemistry and fluid dynamics. Fortunately there is a meaningful physical system (gasless condensed phase combustion) where the solid fuel mixture is transformed directly into a solid product, thus eliminating the fluids part. In addition to its theoretical interest, gasless solid phase combustion currently finds technological applications as a method of synthesizing certain ceramics and metallic alloys, see The most primitive model of gasless combustion in a one-D medium involves a freeboundary problem for the temperature T (x, t). The free-boundary problem (for a PDE) and its qualitative approximation by a 3×3 system of ODEs are explained in If the flame propagates in a nonuniform medium, say with some irregularities or inclusions, so that the fuel concentration Z is changing around some average then the equations take the formḋ The independent variable s is the position of the flame (w − 1 is its velocity); the other variables are related to the temperature of the burning medium, see the last section of here the function g describes the chemical kinetics; this makes the system even more nonlinear. In our work [2]we used a power kinetics (defined through its inverse

Compact attractors for a Stefan problem with kinetics

We prove existence of a unique bounded classical solution for a one-phase free-boundary problem with kinetics for continuous initial conditions. The main result of this paper establishes existence of a compact attractor for classical solutions of the problem