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KINETIC HIERARCHIES AND MACROSCOPIC LIMITS FOR CRYSTALLINE STEPS IN 1+1 DIMENSIONS
kinetic theory epitaxial growth crystal surface Burton–Cabrera–Frank model particle system Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy closure evaporation-condensation surface diffusion correlation function step chemical potential macroscopic limit propagation of chaos
2015/10/16
We apply methods of kinetic theory to study the passage from particle systems to nonlinear partial differential equations (PDEs) in the context of deterministic crystal surface relaxation. Starting wi...
Density of crystalline points on unitary Shimura varieties
Density of crystalline points unitary Shimura varieties Number Theory
2012/6/25
We prove that crystalline points are dense in the spectrum of the completed Hecke algebra on unitary Shimura varieties.
Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra
Disordered Quasicrystalline Crystalline Phases Densely Packed Tetrahedra
2011/3/3
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts.Firstly as field theories on noncommutat...
Cauchy-Born Rule and the Stability of Crystalline Solids: Static Problems
Atomistic models of solids nonlinear elasticity Cauchy-Born rule stability of crystals
2012/8/1
We study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature. We prove, under certain sharp stability conditions, that the corre...