RUI: COLLABORATIVE RESEARCH: Balance Laws Modeling Heat Propagation in Solids at Low Temperatures

Loyola University New Orleans, New Orleans LA

Investigators

Abstract

Abstract DMS-0104508 Katarzyna Saxton This project concerns modeling of heat propagation in materials at low temperatures (including superconducting regions) which are characterized by fast processes whose properties cannot be explained simply through the use of Fourier's law. The models under study are applicable to a wide class of materials for which heat waves, or "second sound," can be detected, and they accommodate important hyperbolic/parabolic phase transitions between two temperature regions, which are not included in other general theories. Under study are qualitative properties of the long-time behavior of both smooth solutions and solutions having shocks. Free-boundary problems modeling phase transitions are also studied. Conventional models of heat conduction involve infinite speed of propagation. The approximations that lead to this counterintuitive situation work well in most practical settings. Experimental studies of heat propagation in systems at very low temperatures, however, show the need for a theory with finite speed of propagation. This research project concerns development of such a theory of heat propagation in crystalline materials at low temperatures and mathematical analysis of the resultant partial differential equations. The project, carried out with the participation of undergraduate students, will lead to an efficient, generally applicable theory of heat propagation in solids, with possible eventual application to high-temperature superconducting materials and fast process laser heating.