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三亚国际数学论坛：Nonlinear PDEs in Continuum Mechanics and Related Topics
三亚国际数学论坛 Nonlinear PDEs Continuum Mechanics
2017/11/24
Mathematical theory of continuum mechanics gives rise to important classes of nonlinear partial differential equations, such as the celebrated Euler and Navier-Stokes equations for both compressible a...
Continuum description of profile scaling in nanostructure decay
Continuum description profile scaling nanostructure decay
2015/10/16
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g1 and step-step interaction energ...
Continuum approach to self-similarity and scaling in morphological relaxation of a crystal with a facet
Continuum approach self-similarity and scaling morphological relaxation crystal with a facet
2015/10/16
The morphological relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition temperature is studied analytically for diffusion-limited sDLd and attachment-detachme...
CONTINUUM DESCRIPTIONS OF CRYSTAL SURFACE EVOLUTION
CONTINUUM DESCRIPTIONS CRYSTAL SURFACE EVOLUTION
2015/10/16
It is well known that liquid surfaces evolve in shape due to the effect of surface tension, which drives configurations towards lower energy. The breakup of an initially cylindrical fluid thread into ...
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...
Continuum Theory of Nanostructure Decay Via a Microscale Condition
Continuum Theory Nanostructure Decay Microscale Condition
2015/10/16
The morphological relaxation of faceted crystal surfaces is studied via a continuum approach. Our formulation includes (i) an evolution equation for the surface slope that describes step line tension,...
Unified continuum approach to crystal surface morphological relaxation
Unified continuum approach crystal surface morphological relaxation
2015/10/16
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. Our goal is to unify previously disconnected experimental o...
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...
From crystal steps to continuum laws:Behavior near large facets in one dimension
Crystal surface Epitaxial relaxation Self-similar solution Burton–Cabrera–Frank (BCF) model Facet Macroscopic limit
2015/10/16
The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by exp...
DISCRETE AND CONTINUUM RELAXATION DYNAMICS OF FACETED CRYSTAL SURFACE IN EVAPORATION MODELS
crystal surface evaporation facet Burton–Cabrera–Frank model subgradient formalism free-boundary problem shock
2015/10/16
We study linkages of two scales in the relaxation of an axisymmetric crystal with a facet in evaporation-condensation kinetics. The macroscale evolution is driven by the motion of concentric circular,...
CONTINUOUS COLORINGS ASSOCIATED WITH CERTAIN CHARACTERISTICS OF THE CONTINUUM
CONTINUOUS COLORINGS ASSOCIATED CERTAIN CHARACTERISTICS
2015/8/17
A coloring c:[X]n → Z is said to be irreducible if for every Y; X of equal cardinality c00[Y ]n = Z. The focus of this note will be to show that there are continuous irreducible colorings on sets of r...
Open colorings,the continuum and the second uncountable cardinal
Open colorings the continuum second uncountable cardinal
2015/8/17
The purpose of this article is to analyze the cardinality of the continuum using Ramsey theoretic statements about open colorings or “open coloring axioms.” In particular I will show that the conjunct...
The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (pri...
FORCING AXIOMS AND THE CONTINUUM HYPOTHESIS,PART II:TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
FORCING AXIOMS CONTINUUM HYPOTHESIS TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
2015/8/17
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah.
One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natur...