Fast soliton scattering by delta impurities

We study the Gross-Pitaevskii equation (nonlinear Schroedinger equation) with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L^2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.Comment: 32 pages, 3 figure

Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps

Forced Stratified Turbulence: Successive Transitions with Reynolds Number

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number, R, keeping fixed a strongly stable, volume-mean density stratification. At smaller values of R, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number, Ri, everywhere. At higher values of R there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales.Comment: 8 pages, 5 figures (submitted to Phys. Rev. E

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

Olympic legacy and cultural tourism: Exploring the facets of Athens' Olympic heritage

This study examines the effects of the Olympic Games on Athens’ cultural tourism and the city’s potential to leverage the Olympic legacy in synergy with its rich heritage in order to enhance its tourism product during the post-Games period. In doing so, a qualitative and interpretive approach was employed. This includes a literature review on Athens’ 2004 Olympics to identify the sport facilities and regeneration projects, which constitute the Olympic legacy and heritage. Based on that, an empirical analysis was undertaken, by collecting official documents about the 2004 Olympics, and conducting five semi-structured interviews with tourism/administrative officials. The findings indicate that the Olympiad contributed significantly to Athens’ built and human heritage, revealing the dimensions of new venues/facilities, infrastructure, transportation and aesthetic image of the city, and human capital enhancement. Hence, the Games affected to the multifaceted representation and reconstruction of the city’s identity and cultural heritage. However, the potential afforded from the post-Olympic Athens remains unrealised due to lack of strategic planning/management. The study concludes that there is a need to develop cross-leveraging synergies between the Olympic legacy and cultural tourism for the host city. Finally, a strategic planning framework for leveraging post-Games Olympic tourism is suggested in order to maximise the benefits of Olympic legacy and heritage in a host city’s tourism development

Travelling solitons in the parametrically driven nonlinear Schroedinger equation

We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths nonpropogating and moving solitons co-exist while strongly forced solitons can only be stably when moving sufficiently fast.Comment: The paper is available as the JINR preprint E17-2000-147(Dubna, Russia) and the preprint of the Max-Planck Institute for the Complex Systems mpipks/0009011, Dresden, Germany. It was submitted to Physical Review

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure