Slowing down of vortex rings in Bose-Einstein condensates

Helm, John L.; Barenghi, Carlo F.; Youd, Anthony J.

doi:10.1103/physreva.83.045601

Cited by 22 publications

(23 citation statements)

References 23 publications

(21 reference statements)

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“…Its dynamics is well established. Recently attention was focused on dynamics of helical-vortex rings with largeamplitude Kelvin waves propagating around the ring [3][4][5]. This problem being interesting itself may have important implications for superfluid turbulence.…”

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confidence: 99%

Dynamics of helical vortices and helical-vortex rings

Sonin¹

2012

EPL

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-The Letter considers dynamics of helical vortices and helical-vortex rings either solving directly the equations of motions of a vortex line or using canonical relations following from the Hamiltonian equations of motion. An analytical solution in elliptical integrals was found for helical-vortex rings in the local-induction approximation. The analysis based on the canonical Hamilton relation provides a clear physical explanation for anomalous velocities of helical-vortex rings, i.e., for suppression of the velocity and even inversion of its direction at sufficiently large amplitude of the helical distortion. The extended local-induction approximation is suggested, which provides an exact solution for the equations of motion of helical vortices and helical-vortex rings in the limit when the small-pitch helical vortex reduces to a cylindric sheet of uniform vorticity.

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confidence: 99%

Dynamics of helical vortices and helical-vortex rings

Sonin¹

2012

EPL

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“…In Bose-Einstein condensates (BECs) of ultracold atomic gases, quantized vortex rings have been created through the decay of solitons and directly observed by imaging the density distribution [4][5][6][7]. The dynamics of quantized vortex rings in superfluids have been theoretically studied by many researchers [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-breaking instability of leapfrogging vortex rings in a Bose-Einstein condensate

2019

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Three coaxial quantized vortex rings in a Bose-Einstein condensate exhibit aperiodic leapfrogging dynamics. It is found that such circular vortex rings are dynamically unstable against deformation breaking axial rotational symmetry. The dynamics of the system are analyzed using the Gross-Pitaevskii and vortex-filament models. The dependence of the instability on the initial arrangement of the vortex rings is investigated. The system is found to be significantly unstable for a specific configuration of the three vortex rings.

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“…Although this was previously studied in Ref. [135], the results shown had very large error-bars and it is unclear how the velocity actually behaves depending on the mode amplitude. The large error-bars there were understandable since they used a vortex ring of radius d = 25 which is quite large, and thus its velocity is slow and hard to track (this can be seen in our velocity results of Fig.…”

Section: Quadrupole Oscillationsmentioning

confidence: 75%

“…A study of vortex rings perturbed by planar and helical Kelvin modes was performed in Ref. [135]. It was found that the Kelvin modes can slow down the vortex We also record the velocity of the ring versus the mode amplitude.…”

Section: Quadrupole Oscillationsmentioning

confidence: 99%

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Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

Carretero-González

Caplan

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We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles.Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.Due to the inherent lack of a closed form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size.The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. The codes are combined into a software package called NLSEmagic which is freely distributed on a dedicated website allowing reproducibility of the simulations presented in the study.vi

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Slowing down of vortex rings in Bose-Einstein condensates

Cited by 22 publications

References 23 publications

Dynamics of helical vortices and helical-vortex rings

Dynamics of helical vortices and helical-vortex rings

Symmetry-breaking instability of leapfrogging vortex rings in a Bose-Einstein condensate

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

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