Discrete double-porosity models for spin systems
Copyright policy )Discrete double-porosity models for spin systems
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases (or, possibly, between points of an additional "weak phase") are of lower order. Following a discrete-to-continuum approach we characterize the limit as a continuum energy defined on $N$-tuples of sets (corresponding to the $N$ strong phases) composed of a surface part, taking into account homogenization at the interface of each strong phase, and a bulk part which describes the combined effect of lower-order terms, weak interactions between phases, and possible oscillations in the weak phase.
arXiv admin note: text overlap with arXiv:1406.1752
Homogenization, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Γ-convergence, High contrast, Interfacial energie, Double porosity, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Γ-convergence; Civil and Structural Engineering; Computational Mathematics; Numerical Analysis, Discrete to continuum, Multiphase material, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Gamma convergence, 49M25, 39A12, 39A70, 35Q82, Settore MAT/05 - ANALISI MATEMATICA, Spin system, Mathematics - Analysis of PDEs, Γ-convergence, FOS: Mathematics, Lattice energie, Analysis of PDEs (math.AP)
Homogenization, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Γ-convergence, High contrast, Interfacial energie, Double porosity, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Γ-convergence; Civil and Structural Engineering; Computational Mathematics; Numerical Analysis, Discrete to continuum, Multiphase material, Discrete to continuum; Double porosity; High contrast; Homogenization; Interfacial energies; Lattice energies; Multiphase materials; Spin systems; Gamma convergence, 49M25, 39A12, 39A70, 35Q82, Settore MAT/05 - ANALISI MATEMATICA, Spin system, Mathematics - Analysis of PDEs, Γ-convergence, FOS: Mathematics, Lattice energie, Analysis of PDEs (math.AP)
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