Cnoidal, Dnoidal and Snoidal Spatial Waves in a Nonlinear Reflection Grating

Alatas, Husin; Saputra, Andrial

doi:10.1063/1.3537893

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…Instead of transforming Eq. (6) into the related elliptic integral, in a recent report [20] a direct method by substituting a specific ansatz into Eq. (6) has been used to find the solutions.…”

Section: Jacobi's Elliptic Spatial Wavesmentioning

confidence: 99%

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Dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating

Alatas

2011

Phys. Rev. A

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This paper presents the results of our study on the dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating based on a generalized coupled-mode model. We discuss the characteristics of their amplitudes, widths, and spatial periods as well as their bifurcation in the associated phase plane. Our study on the dynamical propagation of perturbed profiles reveal that these waves can suffer breathing and broadening due to the diffraction effect. A remarkable split-off phenomenon of a spatial wave with wide stripes into several narrow and shallow oblique stripes is observed, as well as their passing and bouncing collisions.

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Section: Jacobi's Elliptic Spatial Wavesmentioning

confidence: 99%

“…[8][9][10][11] was briefly reported in Ref. [20]. However, to our knowledge, a detailed study regarding the dynamics of these nonlinear spatial waves in the corresponding planar waveguide gratings has never been reported.…”

Section: Introductionmentioning

confidence: 95%

Dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating

Alatas

2011

Phys. Rev. A

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Mixing driven by transient buoyancy flows.II. Flow dynamics

2021

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The chaotic advection of the interface between two miscible liquids inside a closed cavity, generated by a damped oscillatory buoyancy-driven (BD) regular flow field, is investigated experimentally for BD mixing. The Lagrangian history of interface motion, determined using the planar laser-induced fluorescence and the photographic full-field view method, is contrasted against the Eulerian flow field measured from particle image velocimetry. Chaotic advection stretches and folds the interface at an early stage to produce an asymmetric pairwise Rayleigh–Taylor (RT) morphology (RTM) structure from long wavelength RT instability and short-time Richtmyer–Meshkov instability and its fractal interface structure at a high impulsive-Reynolds number. The mechanism of folding, from global bifurcation of the flow field, caused by a hyperbolic point, served as an organizing center for multiple vortex interactions. The intermediate-stage kinematics of the RTM structure exhibits RT mixing and shows unfolding of the lamellar structure from the net effect of stretching, folding, and molecular diffusion prior to its breakdown; and it has a probabilistic outcome of exhibiting topological transitions through a breakup of the RTM structure in phase space from necking singularity and pinch-off, indicating sensitivity to the initial conditions. The effectiveness of mixing determined from mixing efficiency is contrasted against mechanical and lamellar models of mixing. The determination of topological entropy, from an approximate Gaussian distribution of the interface length stretch, yields time scale for information decay comparable to time scale for which a low-order horseshoe map emerges from flow, indicating local chaos of the interface. The late-stage breakdown of the RTM structure from internal and wall collision drives the interaction between advection and diffusion, which indicates that critical mixing time scales as the logarithmic of Peclet number, comparable to time-periodic sine flow and blinking vortex flow chaotic mapping models.

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Cnoidal, Dnoidal and Snoidal Spatial Waves in a Nonlinear Reflection Grating

Cited by 2 publications

References 9 publications

Dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating

Dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating

Mixing driven by transient buoyancy flows.II. Flow dynamics

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