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HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
2015/12/17
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
CONTINUUM RELAXATION OF INTERACTING STEPS ON CRYSTAL SURFACES IN 2+1 DIMENSIONS
crystal surface epitaxial growth morphological evolution Burton–Cabrera–Frank model Ehrlich–Schwoebel barrier entropic interactions elastic dipole interactions step chemical potential continuum limit surface mobility
2015/10/16
We study the relaxation of crystal surfaces in 2+1 dimensions via the motion ofinteracting atomic steps. The goal is the rigorous derivation of the continuum limit. The starting point is a discrete sc...
Anisotropic diffusion in continuum relaxation of stepped crystal surfaces
Anisotropic diffusion continuum relaxation stepped crystal surfaces
2015/10/16
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the sur...
ELECTROMIGRATION IN MACROSCOPIC RELAXATION OF STEPPED SURFACES
epitaxial relaxation crystal facet Burton–Cabrera–Frank model electromigration desorption surface diffusion step chemical potential macroscopic limit variational principle
2015/10/16
We study the effect of an external electric field E on macroscopic relaxation laws for crystal surfaces in 2 + 1 dimensions. We derive a nonlinear, fourth-order partial differential equation (PDE) for...
Homogenization of composite vicinal surfaces: Evolution laws in 1+1 dimensions
Crystal surface Burton–Cabrera–Frank (BCF) model Line defects Diffusion Macroscopic limit Multiscale expansion
2015/10/16
We apply classical homogenization to derive macroscopic relaxation laws for crystal surfaces with distinct inhomogeneities at the microscale. The proposed method relies on a formal multiscale expansio...
Exploring complex networks via topological embedding on surfaces
Complex Networks Maximal Embedded Graphs Triangulations Topological Froths Surface genus Hyperbolic networks
2011/10/8
Abstract: We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of t...
Exploring complex networks via topological embedding on surfaces
Exploring complex networks topological embedding surfaces
2011/8/17
Abstract: We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of t...
A construction of algebraic surfaces with many real nodes
singularities of surfaces real algebraic geometry Algebraic Geometry
2011/9/14
Abstract: A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction that has been used in previous works for the generation of substitutio...
No-Go theorem for energy surfaces
No-Go theorem energy surfaces Concavity property Nuclear Theory
2011/7/28
Abstract: Concavity properties prevent the existence of significant landscapes in energy surfaces obtained by energy minimizations under constraints. The contradiction holds at finite temperatures T a...
Surfaces immersed in Lie algebras associated with elliptic integrals
Generalized symmetries integrable models surfaces immersed in Lie algebras
2011/7/26
Surfaces immersed in Lie algebras associated with elliptic integrals.
Energy density in density functional theory: Application to crystalline defects and surfaces
Energy density density functional theory crystalline defects surfaces
2010/11/25
We propose a method to decompose the total energy of a supercell containing defects into
contributions of individual atoms, using the energy density formalism within density functional
theory. The s...
Unified Theory of Ghost and Quadratic-Flux-Minimizing Surfaces
Ghost Quadratic-Flux-Minimizing Surfaces
2010/4/1
A generalized Hamiltonian definition of ghost surfaces (surfaces defined by an action-gradient flow) is given and specialized to the usual Lagrangian definition. Numerical calculations show uncorrecte...