Prof. Tapio Ala-Nissila
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Phase Field Modeling of Dynamic Interface Phenomena
I will discuss recent developments and applications of phase-field models to describe interface phenomena far from equilibrium. The basic idea of phase-field models is to coarse-grain over microscopic degrees of freedom and replace the corresponding variables with continuum fields, describing different physical phases or states of the system. In principle and in some cases even in practice, the coefficients in this effective description can be related to the microscopic physical variables. Phase field models are usually constructed for the (non-critical) bulk states of the system, and interfaces arise naturally from the boundary conditions for the bulk states. Nonequilibrium conditions can also be easily implemented through boundary and initial conditions. The main advantages of the phase field models are (i) systematic development of the continuum limit which allows to reach mesoscopic and macroscopic time and length scales; (ii) natural emergence of interfaces and nonequilibrium conditions; (iii) relative ease of numerical implementation; (iv) possibility for analytic work through projection techniques. I will discuss some recent applications of phase-fiels models which include the dynamics of slow combustion fronts [1] and interface dynamics of liquids [2].1. N. Provatas, T. Ala-Nissila, M. Grant, K. Elder, and L. Piche, Phys. Rev. E vol. 51, 4232 (1995); J. Stat. Phys. vol. 81, no. 3/4, 737 (1995); M. Karttunen, N. Provatas, T. Ala-Nissila, and M. Grant, J. Stat. Phys. vol. 90 (5/6), 1401 (1998).
2. M. Dubé, M. Rost, K. R. Elder, M. Alava, S. Majaniemi and T. Ala-Nissila, Phys. Rev. Lett. vol. 83, 1628 (1999); European Phys. J. B vol. 15, 701 (2000).