# gst: wandering domains: a hypothetical scenario with bounded orbits.

<< A significant open question in transcendental dynamics asks if it is possible for a point, and thus all points, of a wandering domain to have a bounded orbit. >>

<< In other words, is there a transcendental entire function f with a wandering domain U such that its forward orbit, U_n≥0 f^n(U), is bounded? >>

AA << give a partial answer to this question by constructing an example of a such a wandering domain U which has a nearly bounded orbit; >>

<< In other words, the set of natural numbers n for which f^n(U) is contained in D has upper (and lower) natural density one. >>

<< This is in particularly strong contrast to all existing examples of wandering domains, for which the quantity (..) is equal to zero for any choice of bounded domain D. >>

Leticia Pardo-Simon, David J. Sixsmith. Wandering domains with nearly bounded orbits. arXiv: 2307.16682v1 [math.DS]. Jul 31, 2023. 

https://arxiv.org/abs/2307.16682

Also: Unbounded fast escaping wandering domains. https://arxiv.org/abs/2210.13350 ; Escaping sets of continuous functions. https://arxiv.org/abs/1601.04010 

Also: 'escape', in FonT: https://flashontrack.blogspot.com/search?q=escape

Also: 'fuga', in Notes (quasi-stochastic poetry): https://inkpi.blogspot.com/search?q=fuga 

Keywords: gst, wandering domain, escape 

# gst: reconfiguration and oscillations of sheets subject to vortex

<< The dynamics of a thin low-density polyethylene sheet subject to periodic forcing due to Bénard-Kàrmàn vortices in a long narrow water channel is investigated here. In particular, the time-averaged sheet deflection and its oscillation amplitude are considered. >>

<< The former is first illustrated to be well-approximated by the static equilibrium between the buoyancy force, the elastic restoring force, and the profile drag based on the depth-averaged water speed. >>

AA << observations also indicate that the presence of upstream vortices hinder the overall reconfiguration effect, well-known in an otherwise steady flow. For the sheet-tip oscillations, a simple model based on a torsional-spring-mounted flat plate correctly captures the measured tip amplitude δb over a wide range of sheet physical properties and flow conditions. >>

<< Furthermore, a rich phenomenology of structural dynamics including vortex-forced-vibration, lock-in with the sheet natural frequency, and flow-induced vibration due to the sheet wake, multiple-frequency, and modal response is reported. >>

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J. John Soundar Jerome, Yohann Bachelier, et al. Reconfiguration and oscillations of a vertical, cantilevered sheet subject to vortex shedding behind a cylinder. Phys. Rev. Fluids 8, 093801. Sep 15, 2023. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.093801

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

Keywords: gst, sheet, vortex, Benard-Karman vortices

# gst: apropos of transitions, three distinct new families of long-wave instabilities and potential new pathways to turbulence.

AA << reveal three previously unknown instabilities, distinct from the well-known Kelvin-Helmholtz Instability (KHI) and Holmboe Wave Instability (HWI), in that they have longer wavelengths (..) and often slower growth rates. >>

<< The circumstances under which turbulence can persist in strongly stratified flows remains a fascinating debate within the community. [AA] demonstrated that weakly unstable (very) long waves may trigger turbulence and mixing after long periods of time, even under initially very strongly stratified conditions. >>

Lu Zhu, Amir Atoufi, Adrien Lefauve, Rich R. Kerswell, P. F. Linden. Long-wave instabilities of sloping stratified exchange flows. arXiv:2309.10056v1 [physics.flu-dyn]. Sep 18, 2023.

https://doi.org/10.48550/arXiv.2309.10056

Also: waves, instability, transition, turbulence, chaos, in https://www.inkgmr.net/kwrds.html

Keywords: gst, waves, instability, long-wave instability, transition, turbulence, chaos

# 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: tuning of Janus particles under flows

<< Active colloidal systems with nonequilibrium self-organization constitute a long-standing, challenging area in material sciences and biology. To understand how hydrodynamic flow may be used to actively control self-assembly of Janus particles (JPs), (AA)  developed a model for the many-body hydrodynamics of amphiphilic JPs suspended in a viscous fluid with imposed far-field background flows. >>

They << alter the hydrophobic distribution on the JP-solvent interface to investigate the hydrodynamics that underlies the various morphologies and rheological properties of the JP assembly in the suspension. (They) find that JPs assemble into unilamellar, multilamellar, and striated structures. >>

AA << characterize the effective material properties of the JP structures and find that the unilamellar structure increases orientation order under shear flow, the multilamellar structure behaves as a shear thinning fluid, and the striated structure possesses a yield stress. >> ️

Szu-Pei Fu, Rolf Ryham, Bryan Quaife, and Y.-N. Young. Effects of tunable hydrophobicity on the collective hydrodynamics of Janus particles under flows. Phys. Rev. Fluids 8, 050501. May 11, 2023.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.050501

Also: Janus, in FonT:  https://flashontrack.blogspot.com/search?q=janus

Also: particle, self-assembly, in: https://www.inkgmr.net/kwrds.html

Keywords: particles, Janus, Janus particles, self-organization, self-assembly

# gst: chimera resonance, in analogy with the effects of stochastic and coherence resonance

AA << explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. >>

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<<  It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. >>

<< This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance. >>️

Elena Rybalova, Vasilii Nechaev, Eckehard Schöll, Galina Strelkova. Chimera resonance in networks of chaotic maps. arXiv:2307.00006v2 [cond-mat.dis-nn]. Jul 5, 2023.

https://arxiv.org/abs/2307.00006

Also: chimera, noise, chaos, network,  in: https://www.inkgmr.net/kwrds.html

Keywords: gst, chimera, noise, chaos, network, chimera resonance

# gst: sudden phase transitions among nonconservative system with nonreciprocal interactions

<< A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. >>️

Here AA reported << the emanation of a chimera in a network of Stuart-Landau oscillators. >>

<< The findings could have pragmatic implications in the areas of active matter, networks, and photonics. >>

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M. Paul Asir. Emergence of chimeras: An impetus by exceptional points. Phys. Rev. E 108, 024220. Aug 22, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024220

Also: Stuart–Landau equation. 

https://en.m.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation

Also: network, transition, chimera, chaos, in: https://www.inkgmr.net/kwrds.html

Keywords: network, transition, chimera, chaos, pattern formation