Gradient theory of phase transitions in composite media

2003/04/01 by Nadia Ansini, Andrea Braides, Valeria Chiadò Piat · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Anisotropy #Condensed matter physics #Geometric Analysis and Curvature Flows #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Phase transition #Physics #Quantum mechanics #Regular polygon #Term (time)

paper · doi:10.1017/s0308210500002390

openalex publication_date 2003/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

We study the behaviour of non-convex functionals singularly perturbed by a possibly oscillating inhomogeneous gradient term, in the spirit of the gradient theory of phase transitions. We show that a limit problem giving a sharp interface, as the perturbation vanishes, always exists, but may be inhomogeneous or anisotropic. We specialize this study when the perturbation oscillates periodically, highlighting three types of regimes, depending on the frequency of the oscillations. In the two extreme cases, a separation of scales effect is described.

Citations

• Minimal Surfaces and Functions of Bounded Variation
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• THE SPACES BV AND QUASILINEAR EQUATIONS
• Su una teoria generale della misura (r − 1)-dimensionale in uno spazio adr dimensioni
• Weakly Differentiable Functions

Cited by

• Second-Order Gamma Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions
• Phase separation in multiply periodic materials with fine microstructures

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