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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...
SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I
SECOND ORDER equation
2015/10/15
Inspired by the works of Rodnianski and Schlein [31]
and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation
that describes a second-order correction to the usual tensor product (mean-ʂ...
SECOND-ORDER CORRECTIONS TO MEAN FIELD EVOLUTION OF WEAKLY INTERACTING BOSONS. II
SECOND-ORDER WEAKLY INTERACTING BOSONS
2015/10/15
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction
to a mean-field e...
BEYOND MEAN FIELD: ON THE ROLE OF PAIR EXCITATIONS IN THE EVOLUTION OF CONDENSATES
BEYOND MEAN FIELD PAIR EXCITATIONS
2015/10/15
This paper is in part a summary of our earlier work
[17, 18, 19], and in part an announcement introducing a renement
of the equations for the pair excitation function used in our previous work with...
EVOLUTION OF ADIABATIC INVARIANTS IN STOCHASTIC AVERAGING
STOCHASTIC AVERAGING ADIABATIC INVARIANTS
2015/9/29
An averaging problem with Markov fast motion is
considered. The diusive limit is obtained for the evolution of adabatic invariants under the assumption that the averaged motion
is ergodic on almost...
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...
Finite Volume Local Evolution Galerkin Method for Two-dimensional Relativistic Hydrodynamics
Finite volume local evolution Galerkin method evolution operator genuinely multi-dimensional method relativistic hydrodynamics
2014/9/26
The paper proposes a second-order accurate nite volume local evolution Galerkin
(FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) e-quations. Instead of using the dimensio...
Applying the Wiener-Hermite Random Technique to Study the Evolution of Excess Weight Population in the Region of Valencia (Spain)
Random SIS Type—Epidemiological Model Wiener—Hermite Expansion Perturbation Method
2013/1/30
This paper proposes a stochastic model to study the evolution of normal and excess weight population between 24 - 65 years old in the region of Valencia (Spain). An approximate solution process of the...
A New Graded Algebra Structure on Differential Polynomials: Level Grading and its Application to the Classification of Scalar Evolution Equations in 1+1 Dimension
New Graded Algebra Structure Differential Polynomials Level Grading Classification of Scalar Evolution Equations 1+1 Dimension
2012/4/26
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
Free evolution on algebras with two states II
Free evolution algebras two states II Operator Algebras
2012/4/17
Denote by $J$ the operator of coefficient stripping. We show that for any free convolution semigroup of measures $\nu_t$ with finite variance, applying a single stripping produces semicircular evoluti...
Evolution of curvature along the hyperbolic Ricci flow
Evolution of curvature hyperbolic Ricci
2018/4/19
We consider the hyperbolic geometric flow $\frac{\partial^2 g(t)}{\partial t ^2} = −2Ric_g(t)$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Usi...
Sub-Supersolution Method for a Class of Higher Order Evolution Hemivariational
Evolution hemivariational inequality sub-solution super-solution extremal solution sub-supersolution method
2011/11/17
In this paper, we extend extremality results for the variational inequality to a higher order evolution hemivariational inequality. More precisely, we give an existence theorem of solution for the hig...