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Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type
Extended Supersymmetric Quantum Mechanics Fierz Schur Type
2011/1/18
We discuss two independent constructions to introduce an N-extended Super-symmetric Quantum Mechanics. The first one makes use of the Fierz identities while the second one (divided into two subcases) ...
Forced Nonlinear Resonance in a System of Coupled Oscillators
Forced Nonlinear Resonance System of Coupled Oscillators
2010/12/28
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t ∼ "−2 one component of ...
Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics
Rotating saddle Quadrupole trap Crystal optics Rotor dynamics
2010/12/28
In 1918 Brouwer considered stability of a heavy particle in a rotating vessel. This was the first demon-stration of a rotating saddle trap which is a mechanical analogue for quadrupole particle traps ...
Dynamic synchronization of a time-evolving optical network of chaotic oscillators
Dynamic synchronization chaotic oscillators
2010/12/28
Dynamic synchronization of a time-evolving optical network of chaotic oscillators.
Chiral Resonant Solitons in Broer-Kaup Type New Hydrodynamic Systems
Chiral Resonant Solitons Broer-Kaup Type New Hydrodynamic Systems
2010/12/28
New Broer-Kaup type systems of hydrodynamic equations are derived from the derivative reaction-diffusion systems arising in SL(2,R) Kaup-Newell hierarchy, represented in the non-Madelung hydrodynamic ...
Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
Oscillator populations Kuramoto transition hyperbolic chaos robust chaos
2010/12/28
We study chaotic behavior of order parameters in two coupled ensembles of selfsustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual intera...
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.
In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstand...
Transience in Dynamical Systems
Equilibrium states thermodynamic formalism transience interval maps
2010/12/6
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient ...
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...
Nielsen equivalence of generating sets for closed surface groups
Nielsen equivalence of generating sets closed surface groups
2010/11/29
Generating sets for closed surfaces are either reducible or Nielsen equivalent to a standard generating set.
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...
Fluid Dynamic Limit to the Riemann Solutions of Euler Equations: I. Superposition of rarefaction waves and contact discontinuity
Fluid Dynamic the Riemann Solutions of Euler Equations
2010/11/15
Fluid dynamic limit to compressible Euler equations from compressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider t...