Bibliographic Details
| Title: |
Upper Bounds for Coarsening for the Deep Quench Obstacle Problem. |
| Authors: |
Novick-Cohen, Amy1 amync@techunix.technion.ac.il |
| Source: |
Journal of Statistical Physics. Oct2010, Vol. 141 Issue 1, p142-157. 16p. |
| Subjects: |
Ostwald ripening, Phase separation method (Engineering), Low temperatures, Quantum theory, Metal quenching |
| Abstract: |
The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, ), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t at early times as well as at times t for which $E(t)\le\frac{(1-\overline{u}^{2})}{4}$, where E( t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t or t at early times, depending on the value of E(0), as well as bounds of the form t whenever $E(t)\le\frac{(1-\overline{u}^{2})}{4}$. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
