APPROACH TO A LARGE CLASS OF INSTABILITIES OF DISSIPATIVE CONTINUA

Abstract

As a contribution toward unification and interdisciplinary perspective it seems appropriate here to call attention to an extensive body of results established by another school regarding the thermodynamic aspects of instability leading to dissipative structures. The theory deals with the linear irreversible thermodynamics of deviations from a state of equilibrium which is unstable, as distinguished from unstable perturbations in the vicinity of a nonequilibrium steady state. However, as pointed out below, special cases of instability of steady-state flows may also be analyzed by similar methods. This general approach provides a systematic thermodynamic analysis of continua which are initially stressed in a state of unstable equilibrium. Typical classical examples are elastic buckling in compression, and a viscous fluid in equilibrium in a gravity field with an unstable density gradient. In general perturbations of the unstable equilibrium obey the Lagrangian equation

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oai:CiteSeerX.psu:10.1.1.210.3943Last time updated on 10/22/2014

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