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The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; t...
Regularity "in Large" for the 3D Salmon's Planetary Geostrophic Model of Ocean Dynamics
planetary geostrophic model global regularity ocean dynamics model global circulation
2011/2/28
It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model,
with vertical hydrostatic balance and horizontal Rayleigh friction, coupled to the heat diffusion and tra...
Effective evolution equations from many body quantum dynamics
Effective evolution equations many body quantum dynamics
2011/2/24
In these notes we review some recent results concerning the derivation of effective
equations from first principle quantum dynamics. In particular, we discuss the derivation
of the semi-relativistic...
Applications of Differential Chains to Complex Analysis and Dynamics
Differential Chains Complex Analysis Dynamics
2011/2/28
First and foremost, I would like to thank my advisor Sarah Koch for being so generous with her time and energy.
Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
Pattern Formation and Solitons (nlin.PS) Quantum Gases (cond-mat.quant-gas)
2010/11/10
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solito...
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption
Global dynamics above the ground state the nonlinear Klein-Gordon equation
2010/11/8
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy a...
The Gentlest Ascent Dynamics
Ascent Dynamics math
2010/11/8
Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are th...
Dynamics of a rational system of difference equations in the plane
Dynamics difference equations
2010/11/15
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the paramet...
Nearly linear dynamics of nonlinear dispersive waves
Nearly linear dynamics nonlinear dispersive waves
2010/12/14
Dispersive averaging e ects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly.
Maxwell-Lorentz Dynamics for Rigid Charges - Classical Absorber Electrodynamics Part I
Maxwell-Lorentz Equations Wheeler-Feynman Equations Absorber Electrodynamics
2010/12/7
This is the first part of our mathematical survey on the equations of motion of classical absorber electrodynamics, which shall be introduced and discussed briefly. Its basic equations of motion are t...
Ordered and disordered dynamics in monolayers of rolling particles
Ordereddisordered dynamics monolayers of rolling particles
2010/12/15
We consider the ordered and disordered dynamics for monolayers of rolling self-interacting par-
ticles with an o -set center of mass and a non-isotropic inertia tensor. The rolling constraint is cons...
Tangent bundles to regular basic sets in hyperbolic dynamics
Tangent bundles hyperbolic dynamics
2010/11/26
Given a locally maximal compact invariant hyperbolic set for a C1 flow or diffeomorphism on a Riemann manifold with C1 unstable laminations, we construct an invariant continuous bundle of tangent ve...
Dynamics of a compact operator
compact operator dynamic of linear operator average iterate
2011/1/17
Let T : X ! X be a compact linear (or more generally affine) operator from a Banach space into itself. For each x 2 X, the sequence of iterates T nx, n = 0, 1, · · · and its averages 1 k Pn k=0 T k...
Propagation of Molecular Chaos by Quantum Systems and the Dynamics of the Curie-Weiss Model
Molecular Chaos Quantum Systems Dynamics the Curie-Weiss Model
2010/11/1
The propagation of molecular chaos, a tool of classical kinetic theory, is generalized to apply to quantum systems of distinguishable particles. We prove that the Curie-Weiss model of ferromagnetism ...