Evolution of Heterogeneous Systems

  • Alexander Umantsev
Part of the Lecture Notes in Physics book series (LNP, volume 840)


In this chapter, we apply the ideas of the previous chapters to the dynamics of heterogeneous systems and obtain the celebrated time-dependent Ginzburg-Landau equation (TDGLE) of the order parameter evolution. This equation was applied to various heterogeneous states of the system. Application of TDGLE to an equilibrium state shows that the criteria of the dynamic and local thermodynamic stability coincide. In case of a plane interface, TDGLE yields a traveling wave solution with a finite thickness and specific speed proportional to the deviation of the system from equilibrium. The drumhead approximation of this equation reveals different driving forces exerted on a moving interface and allows us to study evolution of droplets of a new phase. We extend the definition of the interfacial energy into the nonequilibrium domain of the thermodynamic parameters (phase diagram). We analyze growth dynamics of the anti-phase domains using results of FTM and the Allen-Cahn self-similarity hypothesis. The analysis reveals the coarsening regime of evolution, which was observed experimentally.


Travel Wave Solution Free Energy Density Capillary Wave Goldstone Mode Relevant Length Scale 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Alexander Umantsev
    • 1
  1. 1.Department of Chemistry and PhysicsFayetteville State UniversityFayettevilleUSA

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