Dispersive shock waves
WebAug 29, 2006 · A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits … WebNov 7, 2024 · A dispersive shock wave is characterized by an expanding, coherent nonlinear waveform with a trailing large amplitude soliton edge, rank-ordered interior oscillations, and a leading small ...
Dispersive shock waves
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WebSep 8, 2015 · At variance with strongly dispersive wave systems that can be accurately described by the wave turbulence theory 1,2,3,4,5,6,7, a proper kinetic formulation of random nonlinear waves that exhibit ... WebOct 15, 2016 · Dispersive shock waves (DSWs) are non-stationary wave trains that form spontaneously in weakly dispersive media [1]. The underlying mechanism is the wave steepening driven by the nonlinearity which leads to a gradient catastrophe, regularized by dispersion that becomes important close to the point where strong gradients are formed. ...
WebThis occurs because the shock wave is a nonlinearly steepened dispersive fast/magnetosonic wave (which happens to be a compressive version of a whistler mode wave under the right conditions). The dispersive nature of the magnetosonic-whistler wave is such that smaller (larger) wavelengths (frequencies) propagate faster than the converse. WebDec 17, 2006 · Dispersive shock waves are difficult to study experimentally, and analytical solutions to the equations that govern them have only been found in one dimension (1D). …
WebOct 15, 2016 · Dispersive shock waves in the KdV and cKdV equations In this section we will investigate the DSW solutions associated with both the KdV and cKdV equations via Whitham modulation theory. We will compare Whitham theory at leading order and direct numerical simulations and show that they agree well. WebApr 12, 2024 · Under some constraints, we build exact and approximate first- and second-order rogue wave (RW) solutions with two control and one free parameters for a quasi-one-dimensional Gross–Pitaevskii (GP) equation with a time-varying interatomic interaction, an external trap and gain/loss term through the similarity transformation technique. …
WebAug 2, 2007 · In one case, two counter-propagating dispersive shock waves collide, interact, and eventually exit the interaction region with larger amplitudes and altered …
WebOct 15, 2016 · Mechanical balance laws for fully nonlinear and weakly dispersive water waves Physica D: Nonlinear Phenomena, Volume 333, 2016, pp. 243-253 Show abstract Research article Exact relations for the anti-plane effective magneto-electro-elastic coefficients of two-phase fibrous composites Mechanics Research Communications, … michelin star restaurants canadaWebOct 16, 2024 · 1. Introduction. Dispersive shock waves (DSWs) are rapidly oscillating solutions of hyperbolic partial differential equations that contrast the generation of multivalued regions through the formation of undular bores [1 – 12].This class of phenomena was investigated in several physical fields, initially in shallow water waves [] and ion … michelin star restaurants cebuWebUnlike dissipative shock waves in ordinary gases/fluids, which have a well-defined shock front due to viscosity, dispersive superfluid-like shock waves have an oscillatory front. These oscillations result from two basic, and related, properties of the superfluid state: nonlinearity and coherence. michelin star restaurants canterbury kentWebNov 15, 2007 · Dispersive shock waves (DSWs) are studied theoretically in the context of two-dimensional (2D) supersonic flow of a superfluid. Employing Whitham averaging theory for the repulsive Gross-Pitaevskii (GP) equation, suitable jump and entropy conditions are obtained for an oblique DSW, a fundamental building block for 2D flows with boundaries. michelin star restaurants chicago 2014Web3 Dispersion relations An extremely important concept in the study of waves and wave propagation is dispersion. Recall the dispersion relation is defined as the relationship between the frequency and the wavenumber: ω(k). For non-dispersive systems, like most of what we’ve covered so far, ω(k)=vk is a linear relation between ω and k. michelin star restaurants canberraWeb1. Introduction. Dispersive hydrodynamics encompass hyperbolic systems of equations regularized by dispersion rather than dissipation, modeling many physical media [14]. One of the most prominent features of these systems is a dispersive shock wave (DSW), in which gradient catastrophe at the purely hyperbolic level is michelin star restaurants chelseaDispersive shock waves (DSWs) are fascinating wave phenomena occurring in media when nonlinearity overwhelms dispersion (or diffraction). Creating DSWs with low generation power and realizing their active controls is desirable but remains a longstanding challenge. Here, we propose a scheme to generate weak-light DSWs and realize their manipulations in an atomic gas involving strongly ... michelin star restaurants cheshire