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A multiphase field concept: Numerical simulations of moving phase boundaries and multiple junctions. (English) Zbl 0942.35095
In this work the authors present simulations which support the formal asymptotic analysis relating a multiorder parameter Allen-Cahn system to a multiphase interface problem with curvature-dependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen-Cahn system, the normal to an interface between phases \(i\) and \(j\) is modeled by the irreducible representations \((u_i\nabla u_j -u_j\nabla u_i)/|u_i\nabla u_j -u_j\nabla u_i |\), where \( u_i\) and \( u_j \) are the \(i\)th and \(j\)th components of the vectorial order parameter \( u \in \mathbb{R}^n \).

MSC:
35K55 Nonlinear parabolic equations
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
65-05 Experimental papers (numerical analysis) (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35B25 Singular perturbations in context of PDEs
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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