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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,...
EXISTENCE OF WEAK SOLUTIONS TO KINETIC FLOCKING MODELS
flocking kinetic equations existence velocity averaging CuckerSmale self-organized dynamics
2015/10/15
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric...
Divergent directions in some periodic wind-tree models
Divergent directions periodic wind-tree models Dynamical Systems
2011/9/5
Abstract: The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by P. Hubert...
A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with th...
Self-similarity and power-like tails in nonconservative kinetic models
Granular gases overpopulated tails Boltzmann equation
2010/12/6
In this paper, we discuss the large–time behavior of solution of a simple kinetic model of Boltzmann–Maxwell type, such that the temperature is time decreasing and/or time increasing.
ANALYTIC STUDY OF SHELL MODELS OF TURBULENCE
Turbulence Dynamic models Shell models Navier–Stokes equations.
2014/4/4
In this paper we study analytically the viscous sabra shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic de...