Some mathematical challenges in materials science

DOI10.1090/S0273-0979-02-00967-9zbMath1158.74438OpenAlexW2056608020MaRDI QIDQ4780391

Jean E. Taylor

Publication date: 19 November 2002

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-02-00967-9

Mathematics Subject Classification ID

Structured surfaces and interfaces, coexistent phases (74A50) Crystalline structure (74E15) Dynamics of phase boundaries in solids (74N20) Statistical mechanics of crystals (82D25) Variational problems in a geometric measure-theoretic setting (49Q20) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Sensitivity analysis for optimization problems on manifolds (49Q12)

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THE PONTRJAGIN–HOPF INVARIANTS FOR SOBOLEV MAPS ⋮ BV-ellipticity and lower semicontinuity of surface energy of Caccioppoli partitions of \(\mathbb{R}^n\) ⋮ Equilibria configurations for epitaxial crystal growth with adatoms ⋮ A Posteriori Error Estimates for the Laplace--Beltrami Operator on Parametric $C^2$ Surfaces ⋮ Crystals and polycrystals in \(\mathbb R^n\): lower semicontinuity and existence ⋮ Uniform local energy estimates and partial regularity for space partitions ⋮ A variational formulation of anisotropic geometric evolution equations in higher dimensions ⋮ B2-convexity and surface energy of space partitions ⋮ Motion of discrete interfaces on the triangular lattice ⋮ Numerical simulations of immiscible fluid clusters ⋮ Existence of surface energy minimizing partitions of ℝⁿ satisfying volume constraints

Uses Software

• Surface Evolver

Cites Work

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