| We consider the gasless solid fuel combustion model of the Self-Propagating High-Temperature Synthesis process in which combustion waves are employed to synthesize desired materials. Specifically, we consider the combustion of a solid sample in which combustion occurs on the surface of a cylinder. We describe solution behavior as parameters of the problem are varied. The study of different wave types is important since the mode of propagation determines the structure of the product. We describe (i) planar uniformly propagating waves having a planar interface with a uniform spatial temperature distribution separating the burned from the unburned region, (ii) planar pulsating waves, whose propagation velocity oscillates in time. As parameters are varied transitions to more complex, nonplanar waves occur. These include waves exhibiting dissipative soliton behavior, such as (iii) spin waves, in which a localized hot spot (temperature maximum) develops on the interface, and rotates around the surface as it propagates axially, thus executing a helical path, (iv) counterpropagating (CP) waves of various types, which collide and interact in a variety of ways, including passing through each other essentially unchanged except for a phase shift, much the same as actual solitons, and spots which "apparently" annihilate each other only to be reborn again further along the sample in a variety of ways, (v) alternating spin CP waves (ASCP), in which actual creation and annihilation of spots occurs, e.g., periodically, (vi) modulated spin waves, (vii) multiheaded spin waves, in which a number (n) of identical spots, separated from one another by angle 2 pi/n, rotate together as a traveling wave around the cylinder, (viii) bound states of asymmetric spin waves, in which nonidentical spots, not separated by 2 pi/n, rotate together as a traveling wave, and others. |
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