Non-linear growth of interfaces
نویسندگان
چکیده
We develop a new technics to catch the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solubility condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be captured in simple ordinary differential equation. The density profile of the stationary regime which ends the non-linear growth is also well characterized. Numerical simulations are satisfyingly compared with the analytical results through three different fitting methods and asymptotic dynamics are well retrieved, even far from the region where the approximations hold. Pacs numbers : 05.45.Yv, 47.20.Ky, 47.54.+r
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