The discrete potential Boussinesq equation and its multisoliton solutions

An alternate form of discrete potential Boussinesq equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential Boussinesq equation is also obtained from the discrete potential Boussinesq equation using the ultradiscretization technique. The detail of the multisoliton solutions is discussed by using the reduction technique. The lattice potential Boussinesq equation derived by Nijhoff et al. is also investigated by using the singularity confinement test. The relation between the proposed alternate discrete potential Boussinesq equation and the lattice potential Boussinesq equation by Nijhoff et al. is clarified.Comment: 17 pages,To appear in Applicable Analysis, Special Issue of Continuous and Discrete Integrable System

Emergent quantum Euler equation and Bose-Einstein condensates

In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose-Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.Comment: 10 page

Long nonlinear internal waves

Author Posting. © Annual Reviews, 2006. This article is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Fluid Mechanics 38 (2006): 395-425, doi:10.1146/annurev.fluid.38.050304.092129.Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.KRH acknowledges support from NSF and ONR and an Independent Study Award from the Woods Hole Oceanographic Institution. WKM acknowledges support from NSF and ONR, which has made his work in this area possible, in close collaboration with former graduate students at Scripps Institution of Oceanography and MIT

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

Newly uncovered physics of MHD instabilities using 2-D electron cyclotron emission imaging system in toroidal plasmas

Validation of physics models using the newly uncovered physics with a 2-D electron cyclotron emission imaging (ECEi) system for magnetic fusion plasmas has either enhanced the confidence or substantially improved the modeling capability. The discarded "full reconnection model" in sawtooth instability is vindicated and established that symmetry and magnetic shear of the 1/1 kink mode are critical parameters in sawtooth instability. For the 2/1 instability, it is demonstrated that the 2-D data can determine critical physics parameters with a high confidence and the measured anisotropic distribution of the turbulence and its flow in presence of the 2/1 island is validated by the modelled potential and gyro-kinetic calculation. The validation process of the measured reversed-shear Alfveneigenmode (RSAE) structures has improved deficiencies of prior models. The 2-D images of internal structure of the ELMs and turbulence induced by the resonant magnetic perturbation (RMP) have provided an opportunity to establish firm physics basis of the ELM instability and role of RMPs. The importance of symmetry in determining the reconnection time scale and role of magnetic shear of the 1/1 kink mode in sawtooth instability may be relevant to the underlying physics of the violent kink instability of the filament ropes in a solar flare

From bore-soliton-splash to a new wave-to-wire wave-energy model

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound running into a contraction is disseminated experimentally in a wave tank. Maximum amplification in our bore–soliton–splash observed is circa tenfold. Subsequently, we summarise some nonlinear and numerical modelling approaches, validated for amplifying, contracting waves. These amplification phenomena observed have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is in a subtle way solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED loads, are added a posteriori. New is also the intricate and compatible finite-element space–time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging and involve a first study of the resonant behaviour and parameter dependence of the device

Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence

We present results of high-resolution numerical simulations of compressible 2D turbulence forced at intermediate spatial scales with a solenoidal white-in-time external acceleration. A case with an isothermal equation of state, low energy injection rate, and turbulent Mach number $M\approx0.34$ without energy condensate is studied in detail. Analysis of energy spectra and fluxes shows that the classical dual-cascade picture familiar from the incompressible case is substantially modified by compressibility effects. While the small-scale direct enstrophy cascade remains largely intact, a large-scale energy flux loop forms with the direct acoustic energy cascade compensating for the inverse transfer of solenoidal kinetic energy. At small scales, the direct enstrophy and acoustic energy cascades are fully decoupled at small Mach numbers and hence the corresponding spectral energy slopes comply with theoretical predictions, as expected. At large scales, dispersion of acoustic waves on vortices softens the dilatational velocity spectrum, while the pseudo-sound component of the potential energy associated with coherent vortices steepens the potential energy spectrum.Comment: 10 pages, 6 figures. To appear in: Turbulence in Complex Conditions, Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 201

Statistical mechanics of violent relaxation in stellar systems

We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small-scales and describe the ``coarse-grained'' dynamics. In a coarse-grained sense, the system is expected to reach an equilibrium state of a Fermi-Dirac type within a few dynamical times. We describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self-gravitating systems. Then, we introduce a small-scale parametrization of the Vlasov equation and propose a set of relaxation equations for the coarse-grained dynamics. These relaxation equations, of a generalized Fokker-Planck type, are derived from a Maximum Entropy Production Principle (MEPP). We make a link with the quasilinear theory of the Vlasov-Poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces. With the aid of this kinetic theory, we qualitatively discuss the concept of ``incomplete relaxation'' and the limitations of Lynden-Bell's theory