Нелинейные бегущие волны и «отрицательная теплоемкость» в среде с конкурирующими источниками

Abstract

Получены новые точные решения волнового уравнения с нелинейными источниками. Построены уединенные бегущие волны и кинк-решения, формирующиеся при конкуренции двух источников. Определены условия возникновения аномального температурного отклика среды на тепловое воздействие («отрицательная теплоемкость»). Дан пример физической интерпретации одного из решений: вычислена скорость роста кристалла как функция переохлаждения расплава.

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 qυ with a nonlinear temperature dependence T. Let qυ (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.