Temporal and spatial chaos in a van der Waals fluid due to periodic thermal fluctuations
The \textit{V. K. Mel'nikov} method [Tr. Mosk. Mat. O.-va 12, 3-52 (1963; Zbl 0135.310)] to prove the existence of deterministic chaos in periodically forced evolution equations is used to analyze two problems arising in the van der Waal's theory of phase transitions. The first problem is concerned with the dynamics of spinoidal decompositions in a van der Waals type fluid. The effect of a small time- periodic fluctuation of temperature is considered. Once the fluid is initially quenched in the unstable spinoidal region, temporal chaos results as a consequence of the fluctuations about a subcritical temperature. This is proved by application of the relevant Holmes-Marsden Mel'nikov theory [e.g.: \textit{P. Holmes} and \textit{J. E. Marsden}, J. Math. Phys. 23, 669-675 (1982; Zbl 0497.70025)]. The second problem is concerned with the effect of a small thermal perturbation on the equilibrium configuration of an infinite tube of van der Waals type fluid under a given applied load. Once the ambient pressure is appropriately chosen, spatial chaotic solutions form as a result of small spatially periodic perturbations. The van der Waals fluid theory is also applied to the elastic bar model of \textit{J. L. Ericksen} [J. Elasticity 5, 191-201 (1975; Zbl 0324.73067)] with the aid of a non-monotone stress-strain constitutive relation.
van der Waal's theory of phase transitions
small time-periodic fluctuation of temperature
scientific article; zbMATH DE number 3978670
scientific article