2 00 4 Coalescence in the 1 D Cahn - Hilliard model
نویسنده
چکیده
We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless Cahn-Hilliard equation. Using properties of the soliton lattices, periodic solutions of the Ginzburg-Landau equation, we have construct a family of ansatz describing continuously the process of destabilization and period doubling predicted in Langer's self similar scenario [1].
منابع مشابه
m at h - ph / 0 50 50 36 v 1 1 1 M ay 2 00 5 Droplet minimizers for the Cahn – Hilliard free energy functional
We prove theorems characterizing the minimizers in a model for condensation based on the Cahn–Hilliard free energy functional. In particular we exactly determine the critical density for droplet formation.
متن کاملThe existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0
متن کاملThe Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility
In this paper, we apply the spectral method to approximate the solutions of Cahn-Hilliard equation, which is a typical class of nonlinear fourth-order diffusion equations. Diffusion phenomena is widespread in the nature. Therefore, the study of the diffusion equation caught wide concern. Cahn-Hilliard equation was proposed by Cahn and Hilliard in 1958 as a mathematical model describing the diff...
متن کاملShocks in Nonlinear Diffusion
Using two models that incorporate a nonlinear forward-backward heat equation, we demonstrate the existence of well-deened weak solutions containing shocks for diiusive problems. Occurrence of shocks is connected to multivalued inverse solutions and non-monotone potential functions. Unique viscous solutions are determined from perturbation theory by matching to a shock layer condition. Results o...
متن کامل1D Cahn-Hilliard equation: Ostwald Ripening and Modulated Phase Systems
Using an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition, we compute the characteristic time for one step of period doubling in Langer's self similar scenario for Ostwald ripening. As an application, we compute the thermodynamically stable period of a 1D modulated phase pattern.
متن کامل