Spinodal Decomposition and Coarsening Fronts in the Cahn–Hilliard Equation
نویسندگان
چکیده
منابع مشابه
Spinodal decomposition and coarsening fronts in the Cahn-Hilliard equation
We study spinodal decomposition and coarsening when initiated by localized disturbances in the Cahn-Hilliard equation. Spatio-temporal dynamics are governed by multi-stage invasion fronts. The first front invades a spinodal unstable equilibrium and creates a spatially periodic unstable pattern. Secondary fronts invade this unstable pattern and create a coarser pattern in the wake. We give linea...
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The initial stages of spinodal decomposition were studied by subjecting a critical blend of model polyolefins to a pressure quench and monitoring the evolution by time-resolved small angle neutron scattering. Contrary to the predictions of the widely accepted Cahn-Hilliard-Cook theory, we demonstrate that coarsening of the phase-separated structure begins immediately after the quench and occurs...
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The Cahn-Hilliard equation is a fourth-order parabolic partial differential equation that is one of the leading models for the study of phase separation in isothermal, isotropic, binary mixtures, such as molten alloys. When a spatially homogeneous alloy is rapidly quenched in a physical experiment, a fine-grained decomposition into two distinct phases is frequently observed; this phenomenon is ...
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We characterize the spatial spreading of the coarsening process in the Allen-Cahn equation in terms of the propagation of a nonlinear modulated front. Unstable periodic patterns of the Allen-Cahn equation are invaded by a front, propagating in an oscillatory fashion, and leaving behind the homogeneous, stable equilibrium. During one cycle of the oscillatory propagation, two layers of the period...
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We address spinodal decomposition for the stochastic Cahn-Hilliard equation. Solutions starting at the homogeneous equilibrium u(0) 0 will leave a neighborhood of 0 along a strongly unstable subspace X + " with high probability. This produces solutions of a characteristic wavelength, as discussed in 5]. All estimates are established for the linearized stochastic equation. We explain the charact...
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ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2015
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-015-9491-5