Subharmonic Sequences in the Faraday Experiment: Departures from Period Doubling

Keolian, Robert M.; Turkevich, Leonid A.; Putterman, Seth; Rudnick, I.; Rudnick, Joseph

doi:10.1103/physrevlett.47.1133

Cited by 86 publications

(28 citation statements)

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“…The mechanism is basically the same already described in [11,12] for elongated condensates in a modulated 1D optical lattice and it is analogous to the spontaneous pattern formation discussed in [13] in different geometries. It has also interesting similarities with the phenomenon of Faraday's instability [10,14] for classical fluids in annular resonators [15].…”

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confidence: 97%

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

2006

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We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. A periodic modulation of the transverse confinement is shown to produce a density pattern due to parametric amplification of phonon pairs. By imaging the density distribution after free expansion one obtains i) a precise determination of the Bogoliubov spectrum and ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations. [2]. The aim is to create a system in which fundamental properties, like quantized circulation and persistent currents, matter-wave interference, propagation of sound waves and solitons, can be observed in a clean and controllable way. An important issue concerns the feasibility of high-sensitivity rotation sensors.In this work we show that key properties of condensates in toroidal traps can be measured by means of parametric amplification. This corresponds to an exponential growth of some excited modes of the system induced by a periodic modulation of an external parameter [3]. We consider the modulation of the transverse confinement, which is shown to drive a spatially periodic pattern in both density and velocity distributions as a consequence of the amplification of pairs of counter-rotating Bogoliubov phonons. If the trap is switched off, this pattern produces a peculiar flower-like density distribution of the freely expanding gas. The number of "petals" and their shape provide a sensitive measure of the excitation spectrum and the superfluid rotation of the condensate.We perform numerical simulations by integrating the Gross-Pitaevskii equation [4] for N bosonic atoms of mass M , confined in an external potential V ext :The mean-field coupling constant is given by g = 4πh 2 a/M , where the s-wave scattering length a is assumed to be positive. The order parameter of the condensate, ψ(r, t), is normalized to dr|ψ| 2 = N and may by written as ψ = n 1/2 exp(iS), where n is the condensate density and the phase S is related to the superfluid velocity by v = (h/M )∇S. We consider a condensate of N = 2 × 10 5 atoms of 87 Rb confined in a torus of length L = 2πR = 100 µm by an axially symmetric potential which has a minimum, V ext = 0, at z = 0 and r ⊥ = R. The trap is harmonic and isotropic in the (z, r ⊥ )-plane around this minimum, with frequency ω ⊥ = 2π × 1 kHz. With this choice the transverse width of the condensate, r 0 , is significantly smaller than the radius of the torus. This implies that curvature effects are almost negligible in the ground state and in the in-trap dynamics and one can replace the torus of radius R with a cylinder of length L with periodic boundary conditions [5]. Curvature effects are instead important during the free expansion of the condensate, and therefore the full toroidal geometry is used for simulating the dynamics after the release from the trap. The choice made for the geometry and the parameters is intended to simulate feasible experiments, but the effects we are goi...

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confidence: 97%

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

2006

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“…From Alvarez et al, 2009. yet it has been known for some time that the mechanism is not that simple. Indeed, Keolian et al (1981) showed the appearance of capillary waves in shallow water at subharmonic frequencies with other ratios of f=i, where i ¼ 2, 4, 12, 14, 16, 18, 20, 22, 24, 28, and 35. This, and more complex wave patterns [see, e.g., Binks and van de Water (1997)], is made possible, as shown by Chen and Viñals (1997), by the interaction of triad (three-wave) resonant interactions of the waves on the free surface that does not rely on the quadratic nonlinearity presumed by the weakly nonlinear form that results in the Mathieu equation form.…”

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confidence: 99%

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

2011

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This article reviews acoustic microfluidics: the use of acoustic fields, principally ultrasonics, for application in microfluidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

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“…The main conclusion is that such a phenomenon is due to parametric resonance of Mathieu's equation. Further experiments by Keolian et al [5], Gollub and Meyer [6], and Cilberto and Gollub [7] observed chaotic instabilities. Weakly nonlinear analysis has been conducted on Faraday resonance, in particular, by John Miles [8,9].…”

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confidence: 94%

Chaos in Miles' equations

Li¹

2004

Chaos, Solitons & Fractals

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Subharmonic Sequences in the Faraday Experiment: Departures from Period Doubling

Cited by 86 publications

References 23 publications

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

Chaos in Miles' equations

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