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A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
Dispersive estimates interaction Morawetz type (correlation) estimates many-body Hamiltonian many-body Schrodinger equation quantum hydrodynamics BBGKY hierarchy
2015/10/16
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
Facet evolution on supported nanostructures:Effect of finite height
Facet evolution nanostructures finite height
2015/10/16
The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have fo...
Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons.I.
Second-Order Corrections Mean Field Evolution Weakly Interacting Bosons
2015/10/16
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
Second-order corrections to mean field evolution of weakly interacting Bosons.II
Second-order corrections Mean field evolution Weakly interacting bosons
2015/10/16
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
Evolution of particle separation in slowly decorrelating velocity fields
particle separation slowly decorrelating velocity fields
2015/7/14
We consider the evolution of the separation distance between two particles advected by a random velocity field with slowly decaying temporal and spatial correlations in the weak coupling regime. It ha...
Evolution systems of measures for stochastic flows
Evolution systems measures stochastic flows
2010/11/12
A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existen...
Over the evolution of fundamental ideas of fracture mechanics
history of mathematics fracture mechanics history of mechanics
2009/2/19
This paper presents three major directions of the evolution of fundamental ideas
of fracture mechanics: experimental methods, numerical methods and analytical
methods, starting with the observation ...
Over the evolution of fundamental ideas of fracture mechanics
history of mathematics fracture mechanics history of mechanics
2009/1/8
This paper presents three major directions of the evolution of fundamental ideas
of fracture mechanics: experimental methods, numerical methods and analytical
methods, starting with the observation ...
Blow-up of the solution for a kind of six order hyperbolic and parabolic evolution systems
Nonlinear hyperbolic equation Blow-up
2010/9/15
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time .By introducing the ``blow-up f...
Unified approach to evolution equations for non-isothermal phase transitions
Evolution equation Phase field Non-isothermal transitions
2010/9/15
The purpose of the paper is to set up a scheme which embodies and generalizes a wide class of phase-transition models and, moreover, provides a direct approach which avoids ad-hoc assumptions. The sta...