# gst: vortex-pair dance and oscillation

       Fig. 4

This AA study << focuses on fundamental dynamics of vortex-pair fields, specifically known as vortex-pair beams (VPBs) in optics. VPBs have gained increasing attention due to their unique properties, including vortex attraction and repulsion. Here, (AA)  explore the dynamics of pure-phase VPBs (PPVPBs) and observe intriguing helical and intertwined behaviors of vortices, resembling a vortex-pair dance. >>

They << uncover the oscillation property of the intervortex distance for PPVPBs in free space. The observed dancing and oscillation phenomena are intricately tied to the initial intervortex distance and can be explained well in the hydrodynamic picture. Notably, the vortex dancing and oscillation alter the process of vortex-pair annihilation, extending the survival range for opposite vortices. >>

<< This discovery enhances our understanding of vortex interactions and sheds light on the intricate dynamics of both vortex-vortex and vortex-antivortex interactions. >>

Dadong Liu, Lai Chen, Li-Gang Wang. Observation of vortex-pair dance and oscillation. arXiv: 2412.06634v1 [physics.optics]. Dec 9, 2024.

https://arxiv.org/abs/2412.06634

Also: vortex, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, dance 

# gst: order and chaos in systems of coaxial vortex pairs

Fig. B.12: Ex. with 4 interact. vortex pairs

AA << have analyzed interactions between two and three coaxial vortex pairs, classifying their dynamics as either ordered or chaotic based on strengths, initial sizes, and initial horizontal separations.  >>️

They << found that periodic cases are scattered among chaotic ones across different initial configurations. Quasi-periodic leapfrogging typically occurs when the initial distances between the vortex pairs are small and cannot coexist with vortex-pair overtake. When the initial configuration splits into two interacting vortex pairs and a single propagating vortex pair, the two interacting pairs consistently exhibit periodic leapfrogging. For the smallest initial horizontal separations, the system predominantly exhibits chaotic or quasi-periodic motions rather than periodic leapfrogging with a single frequency. This behavior is due to the strong coupling between all three vortex pairs. When the pairs are in close proximity, more complex and chaotic dynamics emerge instead of periodic motion. >>

Their << findings indicate that quasi-periodic leapfrogging and chaotic interactions generally occur when the three vortex pairs have similar strengths and initial sizes. Conversely, discrepancies in these parameters cause the system to disintegrate into two subsystems: a single propagating vortex pair and two periodically leapfrogging pairs. >>️

️

Christiana Mavroyiakoumou, Wenzheng Shi. Order and Chaos in Systems of Coaxial Vortex Pairs. arXiv: 2502.07002v1 [physics.flu-dyn]. Feb 10, 2025. ️

https://arxiv.org/abs/2502.07002

Also: chaos, vortex, order, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, vortex, order, disorder, disorder & fluctuations

# gst: apropos of collisions of a vortex dipoles, vortex unbinding, vortex pinning to the edge, and emission of rarefaction pulses.

<< Vortices and dark solitons are fundamental defects that appear in nonlinear physics at all scales, from nonlinear optics to cosmic fluids. In two or three dimensions, dark solitons are fundamentally connected to highly ordered vortex states through an intrinsic modulation instability in the surrounding matter. >>️

<< Here, [AA] report an experimental realization of ring dark soliton (RDS)  generation in a two-dimensional atomic superfluid trapped in a circular box. By quenching the confining box potential, [they] observe an RDS emitted from the edge and its peculiar signature in the radial motion. As an RDS evolves, [they] observe transverse modulations at discrete azimuthal angles, which clearly result in a patterned formation of a circular vortex dipole array. Through collisions of the vortex dipoles with the box trap, [they] observe vortex unbinding, vortex pinning to the edge, and emission of rarefaction pulses. >>

Hikaru Tamura, Cheng-An Chen, Chen-Lung Hung. Observation of Self-Patterned Defect Formation in Atomic Superfluids–from Ring Dark Solitons to Vortex Dipole Necklaces. Phys. Rev. X 13, 031029. Sep 14, 2023. 

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031029

Also: soliton, vortex, turbulence, waves, in: https://www.inkgmr.net/kwrds.html  

Keywords: gst, soliton, dark soliton, vortex, turbulence, waves. 

# gst: necklacelike pattern of vortex bound states

<< A vortex is a topological defect in the superconducting condensate when a magnetic field is applied to a type-II superconductor, (..). Because of the confinement of the quasiparticles by a vortex, it exhibits a circular-shaped pattern of bound states with discrete energy levels, (..) >>

 Here, AA << report a completely new type of vortex pattern which is necklacelike in an iron-based superconductor (..). (AA) theoretical analysis shows that this necklacelike vortex pattern arises primarily from selective off-shell interference between vortex bound states of opposite angular momenta in the presence of rotational symmetry breaking due to disorders. >>

<< This fascinating effect can be observed in a system with a small Fermi energy and wave vector, conditions fortuitously met in (Their) samples. (AA) results not only disclose a novel vortex structure, but also unravel a completely new quantum phenomenon in the superconducting condensate. >>️

Zhiyong Hou, Kailun Chen, et al. Necklacelike Pattern of Vortex Bound States. Phys. Rev. X 15, 011027. Feb 7, 2025.   https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011027   arXiv: 2407.08547v1 [cond-mat.supr-con]. Jul 11, 2024.    https://arxiv.org/abs/2407.08547

Also: vortex, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, vortex bound states, symmetry breaking, disorder, disorder & fluctuations, necklacelike patterns

# gst: multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials.

<< ️(AA) address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model may be realized in the spatial domain for bulk optical waveguides, the spatiotemporal domain for optical cavities, and for effectively two-dimensional Bose-Einstein condensates. The setup supports single- and multi-ring necklace vortex patterns, including monopoles, dipoles, tripoles, quadrupoles, pentapoles, sextupoles, octupoles, and 12-poles. >>

<< ️In contrast with the inherent instability of conventional vortex beams with high topological charges (winding numbers), vortex necklace-shaped solitons with large winding numbers are found to be stable in the present setup. In particular, octupoles exhibit stable breathing dynamics, and 12-pole necklaces with high winding numbers may be stable. >>

<< ️These (AA) findings provide a new way for generating stable vortex necklaces, offering a vast potential for manipulations of complex spatiotemporal light fields. >>

Ruolan Zhao, Jing Chen, Boris A. Malomed, et al. Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials. arXiv: 2602.18703v1 [physics.optics]. Feb 21, 2026.

https://arxiv.org/abs/2602.18703

Also: vortex, soliton, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, solitons, vortex necklace-shaped solitons, single-ring vorticity, multi-ring vorticity, stable vortex necklace, transitions.

# gst: complex flows by hairpin vortices behind hills with different scales

 << In the flow around protuberance, separation bubbles occur ahead and behind the protuberance, and a coherent vortex structure exists in the wake. In such a flow field, heat, substance, and momentum are actively transported by the vortex. (..) When multiple protuberances are set in the flow, the wakes of the protuberances interfere with each other, resulting in complicated flows. >> 

 << This study performed a numerical analysis of the hairpin vortex and heat transport generated by the interference of the wakes behind two hills in a laminar boundary layer. In the case of hills with the same scale, the interference between hairpin vortices in the wake is more intensive than in the different-scale hills. When the hills with different scales are installed, hairpin vortices with different scales are periodically shed. >> 

 

  << Regardless of the scale ratio of the hills, when the hill spacing in the spanwise direction is narrowed, the asymmetry of the hairpin vortex in the wake increases due to the interference between the wakes. At this time, the turbulence caused by the leg and the horn-shaped secondary vortex on the spanwise center side in the hairpin vortex increases, and heat transport around the hairpin vortex becomes active. >> 

 

Hideki Yanaoka, Tatsuya Hamada. Hairpin vortices and heat transfer in the wakes behind two hills with different scales. arXiv: 2306.17365v1 [physics.flu-dyn]. Jun 30, 2023. 

https://arxiv.org/abs/2306.17365

Also: vortex, turbulence in https://www.inkgmr.net/kwrds.html

Keywords: gst, vortex, hairpin vortex, turbulence

# gst: creating topological vortex rings (on demand)

<< Vortex rings are ubiquitous topological structures in nature. In solid magnetic systems, their formation leads to intriguing physical phenomena and potential device applications. >>

 Here, AA << theoretically show that topological vortex rings can be created by a current pulse in a chiral magnetic nanocylinder with a trench structure. The creation process involves the formation of a vortex ring street, i.e., a chain of magnetic vortex rings with an alternative linking manner. The created vortex rings can be bounded with monopole-antimonopole pairs and possess a rich and controllable linking topology (..) which is determined by the duration and amplitude of the current pulse. >>

Yizhou Liu, Naoto Nagaosa. Current-Induced Creation of Topological Vortex Rings in a Magnetic Nanocylinder. Phys. Rev. Lett. 132, 126701. Mar 19, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.126701

Ryan Wilkinson. Magnetic Vortex Rings on Demand. Physics 17, s29. Mar 19,  2024. 

https://physics.aps.org/articles/v17/s29

Also: vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: vortex, vortices, vortexes, vorticity, spin dynamics, spin texture, chiral magnets

# gst: when a turbulence can be confined

<< Turbulence is hard to control. Its ephemeral nature prevents us from treating it as an ordinary state of matter. Here (AA) create a stationary and isolated blob of turbulence using only elemental building blocks: vortex rings.  The turbulence is confined in a spherical region, surrounded by a quiescent environment, initiated and sustained by vortex rings. Crucially, vortex rings can be endowed with conserved quantities such as energy and helicity, which can be transferred to the turbulent state. Using 2D particle image velocimetry and 3D particle tracking velocimetry, (AA) demonstrate how confinement of turbulence occurs when vortex rings repeatedly collide, in contrast to coherent vortex reconnections. The pathlines depict the difference between these states of flow. >>️

Takumi Matsuzawa, Noah P. Mitchell, Stéphane Perrard, William T. M. Irvine. Turbulence through sustained vortex ring collisions. Phys. Rev. Fluids 8, 110507. Nov 16, 2023.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.110507

75TH ANNUAL MEETING OF THE APS DIVISION OF FLUID DYNAMICS (NOVEMBER 20, 2022 — NOV 22, 2022). V0008: Turbulence through sustained vortex ring collisions. 

https://doi.org/10.1103/APS.DFD.2022.GFM.V0008

Also: turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, vortex, vortex ring collisions

# gst: apropos of modulational instabilities, the case of vortex-ring quantum droplets in a radially-periodic potential.

FIG. 11: (Color online) Typical examples of stable nested patterns with soliton and vortex QDs (quantum droplets)  which were created in adjacent radial troughs. In panels (a1-b4) the pattern was created from the initial dynamical states with parameters (N,S,On) = (46,0,2) and (N,S,On) = (35,1,1) in the outer and inner troughs, respectively. In panels (c1-d4) the input was taken with parameter sets (N,S,On) = (120,1,3) and (N,S,On) = (46,0,2) in the outer and inner troughs.

AA << establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates. >>️

<< another noteworthy option is to construct a two-ring complex in which one vortex-ring component is subject to the MI  (modulational instability), hence it is replaced by an azimuthal soliton (or maybe several solitons), (..), while the vortex component trapped in another potential trough avoids the azimuthal MI and remains essentially axisymmetric. >>️

<< Examples of such heterogeneous robust states, produced by simulations of Eq. (3), are displayed in Fig. 11. Panels 11(a1-b4) show a complex in which the MI takes place in the outer circular trough, producing an azimuthal soliton which performs rotary motion, while the inner vortex ring is  modulationally stable. An opposite example is produced in Figs. 11(c1-d4), where the outer vortex ring remains stable against azimuthal perturbations, while the MI creates a soliton exhibiting the rotary motion in the embedded (inner) circular trough. The rotation direction of the soliton is driven by the vorticity sign of the underlying QD (quantum droplet). It is relevant to mention that the multi-ring potential considered here holds different vortex-ring or azimuthal-soliton states nearly isolating them from each other. (..) An additional problem, which is left for subsequent analysis, is interplay between adjacent radial modes in the case when the separation between the adjacent rings is essentially smaller. >>️

Bin Liu, Yi xi Chen, et al. Vortex-ring quantum droplets in a radially-periodic potential. arXiv: 2212.05838v1 [nlin.PS]. Dec 12, 2022.

https://arxiv.org/abs/2212.05838

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

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keyword 'goccia' in Notes 

(quasi-stochastic poetry): 

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keyword 'instability' | 'instabilities' in FonT

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keyword 'instabile' in Notes 

(quasi-stochastic poetry)

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Keywords: gst, drop, droplet, vortex, vortices, vortexes, vorticity, instability,  modulational instabilities

# gst: towards the characterization of lines, links, writhes and twists in a vortex.

<< Vorticity in turbulent flows is often organized into complex geometries that influence the dynamics. (AA) use a relatively novel approach to describe these geometries: that of obtaining segments of vortex lines embedded in the flow. This enables to quantify the geometric features of these objects. >>

<< Vortex lines differ widely in their behaviour but (AA) find some unifying features. The decay from high levels of vorticity is shown to happen over a short fraction of the vortex length. The local curvature is inversely related with the vorticity magnitude. Strong parts of vortex lines bundle together. >>

Saumav Kapoor, Rama Govindarajan, Siddhartha Mukherjee. Geometric characterization of vortex lines in turbulence. arXiv: 2301.06808v1 [physics.flu-dyn]. Jan 17, 2023.

https://arxiv.org/abs/2301.06808

Also

keyword 'vortex' in FonT

https://flashontrack.blogspot.com/search?q=vortex

keyword 'vortice' in Notes

 (quasi-stochastic poetry)

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Keywords: gst, vortex, vortices, vortexes, vorticity

# phys: stable vortex loops intersected by point singularities (in magnets)

<< Vortex rings are remarkably stable structures that occur in a large variety of systems (..) Although vortex rings have also been predicted to exist in ferromagnets, they have not yet been observed. >>

AA << imaged three-dimensional structures forming closed vortex loops in a bulk micromagnet. The cross-section of these loops consists of a vortex–antivortex pair and, on the basis of magnetic vorticity (they) identify these configurations as magnetic vortex rings. >>

<< In addition, (they) observe stable vortex loops intersected by point singularities at which the magnetization within the vortex and antivortex cores reverses. >>

Claire Donnelly, Konstantin L. Metlov, et al. Experimental observation of vortex rings in a bulk magnet. Nature Physics. doi: 10.1038/ s41567-020-01057-3. Nov 30,  2020.

https://www.nature.com/articles/s41567-020-01057-3

Magnetic vortices come full circle. 

Paul Scherrer Institute. Nov 30, 2020.

https://phys.org/news/2020-11-magnetic-vortices-full-circle.html

# gst: vortex solitons in twisted circular waveguide arrays.

AA << address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences of the fundamental properties of new vortex solitons with opposite topological charges that arise in the nonlinear regime. >>️

They << find that such system features the rare property that clockwise and counter-clockwise vortex states are nonequivalent. >>️

Liangwei Dong, Yaroslav V. Kartashov, et al. Vortex solitons in twisted circular waveguide arrays. arXiv:2208.05049v1 [physics.optics]. Aug 9, 2022.

https://arxiv.org/abs/2208.05049

Also

keyword 'solitons' in Font

https://flashontrack.blogspot.com/search?q=solitons

keyword 'vortex' in FonT

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keyword 'vortice' in Notes

 (quasi-stochastic poetry)

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Keywords: gst, solitons, vortex,  clockwise vortex, counter-clockwise vortex, waves

# gst: vortex structures under dimples and scars in turbulent free-surface flows

<< Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. >>️

AA << explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. >>️

<< The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale λT, this probability is independent of Reynolds and Weber number. >>️

<< Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately λT/4. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. >>️

AA << findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes. >>

Jørgen R. Aarnes, Omer Babiker, et al. Vortex structures under dimples and scars in turbulent free-surface flows. arXiv: 2409.05409v1 [physics.flu-dyn]. 

9 Sep 2024.

https://arxiv.org/abs/2409.05409

Also: vortex, turbulence, waves, bubble, drop, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, turbulence, waves, bubble, drop, transition

# astro: black holes (as Q-ball-type saturons) could admit multi-vortex dynamics

<< Theoretical physicists argue that black holes admit vortex structures >>

Img << Sketch of a black hole endowed with multiple vortices. Colors denote the orientation, with the associated trapped magnetic field lines in black. Credit: Dvali et al. >>️

<< Recently, a new quantum framework for black holes, namely in terms of Bose-Einstein condensates of gravitons (the quanta of gravity itself), has been introduced, (..) Up until our article was published, rotating black holes have not been thoroughly studied within this framework. However, they might not only exist, but also be the rule rather than the exception. >> Florian Kühnel. 

️

Ingrid Fadelli. Theoretical physicists argue that black holes admit vortex structures. Phys.org. Sep 09, 2022. 

https://phys.org/news/2022-09-theoretical-physicists-black-holes-vortex.html

AA << argue that black holes admit vortex structure. This is based both on a graviton-condensate description of a black hole as well as on a correspondence between black holes and generic objects with maximal entropy compatible with unitarity, so-called saturons. (They) show that due to vorticity, a Q-ball-type saturon of a calculable renormalizable theory obeys the same extremality bound on the spin as the black hole. Correspondingly, a black hole with extremal spin emerges as a graviton condensate with vorticity. (..) Next, (AA) show that in the presence of mobile charges, the global vortex traps a magnetic flux of the gauge field. This can have macroscopically observable consequences. >>

️

Gia Dvali, Florian Kuhnel, Michael Zantedeschi. Vortices in Black Holes. Phys. Rev. Lett. 129, 061302. Aug 3, 2022.  

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.061302

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keyword 'black hole' in FonT  

https://flashontrack.blogspot.com/search?q=black+hole

Keywords: astro, astrophysics, black hole, rotating black hole, vortex, vorticity

# gst: inertial particles within co-rotating dusty vortices

 << dispersed particles with moderate inertia cause the vortex pair to push apart to a separation nearly twice as large as the initial separation. >>

 

 << antisymmetric vorticity generated by particles flung out of the rotational cores causes the vortex pair repulsion. Eventually, the two dusty vortices merge into a single vortex with most particles accumulating outside the core similar to the dusty Lamb-Oseen vortex described in Shuai & Kasbaoui (2022) >>

 

 << For weakly inertial particles, (AA) find that the merger dynamics follow the same mechanics as those of a single-phase flow, albeit with a density that must be adjusted to match the mixture density. >>

 

<< Lastly, highly inertial particles tend to fragment the vortex cores leading to murky merger dynamics. >>

Shuai Shuai, Anubhab Roy, M. Houssem Kasbaoui. The merger of co-rotating vortices in dusty flows. arXiv: 2307.05413v1 [physics.flu-dyn]. Jul 11, 2023. 

https://arxiv.org/abs/2307.05413

Also: particle, vortex, in https://www.inkgmr.net/kwrds.html

Keywords: gst, particle, vortex 

# gst: dynamic expulsion of magnetic flux by vortices.

AA << study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. (They)  concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. >>

<< Within the context of a weak background field, (AA) are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. >>

<< Furthermore, in the case of a row of vortices, (AA) show that the orientation of the background field significantly influences the evolution, especially at higher field strengths. >>

Jonathan Tessier, Francis J. Poulin, David W. Hughes. Dynamic expulsion of magnetic flux by vortices. Phys. Rev. Fluids 10, 053702. May 19, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.053702

Also: vortex, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, transitions, flux expulsion, vortex disruption.

# gst: tandem droplets accelerated by continuous uniform airflow.

<< In a dense droplet environment, droplets influence each other's motion, deformation, and breakup behavior. The tandem droplet is a particularly relevant case for the study of its unsteady dynamic behavior. >>

<< A three-dimensional numerical simulation study was conducted to investigate the deformation process of tandem droplets under different conditions. >>

<< The results of the research show that under conditions of high density ratio and a significant Reynolds number, the edge morphological characteristics of droplets are predominantly influenced by the Rayleigh-Taylor instability. In the case of low density ratios, the pressure drag force on the leeward side exerts a dominant influence on the accelerated motion of the leading droplet. The shape of the droplet is significantly influenced by the vortex ring present in the recirculation region. The perturbation of the liquid edge induces the vortex ring to split into secondary vortex rings, which act back on the droplet, thereby affecting its morphological characteristics. The trailing droplet is subject to a reduction in cross-flow radius, drag coefficient, minimum length, and expansion speed of the liquid bag due to the influence of the wake of the leading droplet. The decrease in Reynolds number and relative distance leads to a stronger suppression effect, while the decrease in density ratio shortens the length of the recirculation region, thereby weakening the suppression of trailing droplets. >>

Shuting Peng, Fuzhen Chen, et al. Three-dimensional numerical simulation of tandem droplets accelerated by continuous uniform airflow. Phys. Rev. Fluids 10, 024304. Feb 25, 2025. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.024304  

Also: droplet, instability, vortex, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, droplet, instability, vortex, behavior

# gst: apropos of transitions, the vortex dynamics from a twisted baker map

<< A natural approach to understanding complicated systems is to analyze a col­lection of simple examples that retain some essential features of the complexity of the original systems. The baker map (..) is one of the simplest models of chaotic dynamical systems. It divides the unit square into p ≥ 2 equal vertical strips, and maps each strip to a horizontal one by squeezing it vertically by the factor p and stretching it horizontally by the same factor. The horizontal strips are laid out covering the square. Due to the squeezing/stretching, small initial errors get amplified under iteration, and results in an unpredictable long-term behavior. The name “baker” is used since the action of the map is reminiscent of the kneading dough (..). In this paper (AA) introduce a piecewise linear model of an interaction of stretching and twisting that produces vortex dynamics. >>

They << show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space >>

Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke. The twisted baker map. arXiv: 2202.04304v2 [math.DS]. Feb 9, 2022. 

https://arxiv.org/abs/2202.04304

Also

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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keyword 'vortex' in FonT

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keyword 'vortice' in Notes

 (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=vortice

keywords: gst, transition, vortex, baker map

# gst: a new type of vortex in the flight of a dandelion

<< Wind-dispersed plants have evolved ingenious ways to lift their seeds >>

AA << visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus. >>

<< The discovery of the separated vortex ring provides evidence of the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures. >>

Cathal Cummins, Madeleine Seale, et al. A separated vortex ring underlies the flight of the dandelion. Nature 2018; 562: 414–8. doi: 10.1038/s41586-018-0604-2.

https://www.nature.com/articles/s41586-018-0604-2

<< When dandelion seeds fly, a ring-shaped air bubble forms as air moves through the bristles, enhancing the drag that slows their descent. >>

Dandelion seeds reveal newly discovered form of natural flight. University of Edinburgh. Oct 17, 2018.

https://m.phys.org/news/2018-10-dandelion-seeds-reveal-newly-natural.html

# gst: superflows around corners.

<< ️(AA) investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, (They) focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, (They) show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. >>

<< ️For both wall and well configurations, (They) identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding an excellent agreement between the theory and (Their) numerical simulations. (Their) results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features and are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems. >>

Thomas Frisch, Christophe Josserand, Sergio Rica. Superflows around corners. arXiv: 2602.18876v1 [cond-mat.quant-gas]. Feb 21, 2026.

https://arxiv.org/abs/2602.18876

Also: vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vorticity, vortex nucleation, two-dimensional superflow, superflow stability, smooth obstacles, sharp corners.