Nonlinear waves and "negative heat capacity" in a medium with competitive sources

For a wave equation with sources, new running-wave type solutions are built. The results are expressed in terms of the heat transfer theory. We study two types of alternating volume energy sources q_υ with a nonlinear temperature dependence T. Let q_υ (T = Т¹) = 0 where Т¹ is the temperature of the source sign change. The source is positive at Т>Т¹ (heat input) and negative at Т<Т¹ (heat output) when is has technical origin. A source of biological origin differs from technical ones. It serves as a compensator: at Т>Т¹ it takes the heat in; at Т<Т¹, it gives the heat out. Three types of analytical solutions are obtained: the sole wave, the kink structure, and the wave chain. Subsonic and supersonic wave processes are studied with respect to the rate of heat perturbations. The examples for a non-classical phenomenon of "negative heat capacity" are given when heat input/output leads to a temperature decrease/increase. We have considered a nonlinear medium liable to an exact analytical description of a wave problem with a having a resonance type of the temperature dependence: its oscillations have a crescent amplitude. As an example of physical interpretation for one solution, the rate of crystal growth is calculated as a function of the melt undercooling.

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