Evelyn Sander

Unexpectedly linear behavior for the Cahn-Hilliard equation

This paper gives theoretical results on spinodal decomposition for the Cahn--Hillard equation. We prove a mechanism which explains why most solutions for the Cahn--Hilliard equation starting near a homogeneous equilibrium within the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius R. Namely, most solutions are driven into a region of phase space in which linear behavior dominates for much longer than expected.The Cahn--Hilliard equation depends on a small parameter

Monte Carlo Simulations for Spinodal Decomposition

\epsilon,

Period-doubling cascades galore

modeling the (atomic scale) interaction length; we quantify the behavior of solutions as

The geometry of chaos synchronization

\epsilon \rightarrow 0

A new proof of the stable manifold theorem

. Specifically, we show that most solutions starting close to the homogeneous equilibrium remain close to the corresponding solution of the linearized equation with relative distance

The Dynamics of Nucleation in Stochastic Cahn–Morral Systems

O(\epsilon^{2-n/2})

Pattern formation in a nonlinear model for animal coats

up to a ball of radius R in the

The Many Facets of Chaos

H^2(\Omega)

Homoclinic tangles for noninvertible maps

-norm, where R is proportional to

A period-doubling cascade precedes chaos for planar maps.

\epsilon^{-1+\rho+n/4}