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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...
On the stabilization of ion sputtered surfaces
Ion beam sputtering the classical theory ion incidence Angle the surface dynamics dynamic response function
2014/12/20
The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the avera...
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.
Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
Gross-Neveu Models Nonlinear Dirac Equations
2010/12/23
Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. ...
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...
Phase space barriers and dividing surfaces in the absence of critical points of the potential energy
Phase space dividing surfaces critical points the potential energy
2010/11/12
We consider the existence of invariant manifolds in phase space governing reaction dynamics in situations where there are no saddle points on the potential energy surface in the relevant regions of co...
Fluctuation-induced forces between atoms and surfaces: the Casimir-Polder interaction
Fluctuation-induced forces atoms surfaces Casimir-Polder interaction
2010/11/5
Electromagnetic fluctuation-induced forces between atoms and surfaces are generally known as Casimir-Polder interactions. The exact knowledge of these forces is rapidly becoming important in modern ex...