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Abstract:
Several nonequilibrium systems display an ordered pattern whose typical
length scale either increases in the course of time through a coarsening
process, or it keeps constant with a possible diverging amplitude.
We analyze the dynamics of a one-dimensional growing front and
we argue that a coarsening process occurs if and only if the period L of
the steady state solution is an increasing function of its amplitude A.
This statement is rigorously proved for two important classes of conserved
and nonconserved equations by investigating the phase diffusion equation
of the steady pattern and by evaluating the relevant free-energy as a
function of L and A.
We provide further evidence of the relation between coarsening and the
behavior of L(A) through the numerical solution of more complicated
growth equations.
Finally, we discuss the time dependence of the length scale, L(t),
for some models displaying coarsening.
[PRESENTATION SLIDES - PDF]
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