# gst: solitons as 'emergent elastic objects with spatially dependent stiffness'

<< Since the 1950s, topological solitons have been used to describe elementary particles and particle-like field configurations that appear in systems ranging from subatomic to cosmological scales. Particles are topologically protected, for which transitions to states with different topological charges are restricted. However, formation and annihilation of solitons are universal in almost all branches of physics, which implies that topological protection collapses at certain condition unrevealed. >>

<< Here, (AA) show that solitons can be regarded as emergent elastic objects with spatially dependent stiffness, and a second-order topological phase transition initiates at its softened points, i.e., points with a vanishing eigenvalue of the emergent stiffness matrix. >>

️

Yangfan Hu. Emergent elasticity and topological stability of solitons. arXiv: 2208.14916v1 [nlin.PS]. Aug 31, 2022. 

https://arxiv.org/abs/2208.14916

Also

'Second-order phase transitions' 

https://en.m.wikipedia.org/wiki/Phase_transition

keyword 'solitons' in FonT

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

Keywords: gst, solitons, transition, phase_transition

# gst: even repulsive interactions generate solitons

<< Solitons are nonspreading wave packets that exist in a wide range of real-world systems, including water waves, sound, DNA, optics, and so on. >>

<< Two or more solitons can bind together to form a soliton molecule with dynamics similar to matter molecules, such as vibration, synthesis, and dissociation. >>

<< Formation processes for three types of soliton molecules were studied: ground-, excited-state, and a new one termed an intermittent-vibration soliton molecule. While it is generally believed that attractive interactions of solitons are responsible for the formation of soliton molecules, the authors found that soliton interactions are not limited to attractive interactions. Counterintuitively, even repulsive interactions can lead to the formation of soliton molecules, >>

John Wallace. Investigation with a femtosecond fiber laser finds new type of soliton ‘molecule’. Aug 01, 2018.

https://www.laserfocusworld.com/articles/print/volume-54/issue-08/newsbreaks/investigation-with-a-femtosecond-fiber-laser-finds-new-type-of-soliton-molecule.html

<< For closely‐separated bound solitons, soliton interactions display wide diversities in repeated measurements, including soliton attraction, repelling, collision, vibration, and annihilation. For well‐separated bound solitons, repulsive interactions dominate the soliton interactions. >>

Junsong Peng, Heping Zeng. Build‐Up of Dissipative Optical Soliton Molecules via Diverse Soliton Interactions. Laser & Photonics Reviews 2018, 12, 1800009.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.201800009 

Also "soliton" in:

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

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

# 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

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

keyword 'vortice' in Notes

 (quasi-stochastic poetry)

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

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

# s-gst: when a destabilized soliton surprisingly generates a puff of sound waves ...

<< Solitons in the land of ultracold atoms are intriguing (..) because they are as close as you can get to observing the interface between quantum effects and the ordinary physics of everyday life >>

Joint  Quantum  Institute. Destabilized solitons perform a disappearing act. Feb. 27,  2017.

https://m.phys.org/news/2017-02-destabilized-solitons.html

Lauren M. Aycock, Hilary M. Hurst et al. Brownian motion of solitons in a Bose–Einstein condensate. Proceedings of the National Academy of Sciences. Mar. 4,  2017. DOI: 10.1073/pnas.1615004114

http://m.pnas.org/content/early/2017/02/13/1615004114

# 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: when a soliton juggles ('catches' and 'throws') droplets

<< Jugglers normally work with solid objects, but a research team has now demonstrated a system that juggles liquid drops. (AA)  have previously shown that liquid drops can bounce in place above the surface of the same liquid—or bounce while moving across the surface—if the container is continuously vibrated (..) In these past experiments, the surface was nearly flat, except for waves generated by the bouncing drop. In the new work by undergraduate student Camila Sandivari of the University of Chile and her colleagues, the vibrations cause the liquid surface to form a large standing wave that actively “catches” and “throws” the drop during each cycle of its oscillation. The trapping of the drop is similar in principle to other types of wave traps, such as laser-based optical tweezers, and the system could potentially lead to new types of traps for larger objects. >>

AA << placed water mixed with a dye and a surface-tension-reducing agent in a 20-cm-long, 2.6-cm-wide basin that supports an unusual type of surface wave when the basin is vibrated in a specific frequency range. In this wave, rather than a series of oscillating peaks and valleys, there is only a single standing wave peak, called a soliton. However, this peak doesn’t oscillate uniformly across the basin’s short dimension (the width). A peak appears at one of the long walls coincident with a valley at the opposite wall, and then the peak and the valley switch places moments later, keeping a relatively flat “node” line along the central long axis of the basin. >>

AA << used a pipette to place a few-millimeter-wide drop of the same fluid just above the oscillating soliton, close to one of the long walls, and found that drops could be juggled for up to 90 minutes. The team attributes this unusual stability in part to a property of the soliton: if the drop wanders off-center, the oscillating surface wave pulls it back toward its center, similar to the way the laser field in optical tweezers is able to stably hold a small particle at its center. >>

David Ehrenstein. Juggling Water Drops. Physics 16, 21. Feb 10, 2023. 

https://physics.aps.org/articles/v16/21

Also

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

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

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

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

keyword 'goccia' in Notes 

(quasi-stochastic poetry)

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

keyword 'solitons' in FonT

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

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

Keywords: gst, solitons, drop, droplet, droploids, goccia

# life: some scientists hypothesize the possibility of (A) traveling faster than light, (B) visiting the interior of a black hole, (C) being already under observation by alien entities.

(A) traveling faster than light

<< Lentz (Erik Lentz. https://iopscience.iop.org/article/10.1088/1361-6382/abe692 ) proposes one such way we might be able to do this, thanks to what he calls a new class of hyper-fast solitons – a kind of wave that maintains its shape and energy while moving at a constant velocity (and in this case, a velocity faster than light). According to Lentz's theoretical calculations, these hyper-fast soliton solutions can exist within general relativity, and are sourced purely from positive energy densities, meaning there's no need to consider exotic negative- energy- density sources that haven't yet been verified. (..) With sufficient energy, configurations of these solitons could function as 'warp bubbles', capable of superluminal motion, and theoretically enabling an object to pass through space-time while shielded from extreme tidal forces. >>

<< another recent analysis, published only this month ( David Nield.  https://www.sciencealert.com/engineers-have-proposed-the-first-model-for-a-physical-warp-drive  ;  Alexey Bobrick, Gianni Martire. https://iopscience.iop.org/article/10.1088/1361-6382/abdf6e ), which also proposes an alternative model for a physically possible warp drive that doesn't require negative energy to function. >>️️

Peter Dockrill. Faster-Than-Light Travel Is Possible Within Einstein's Physics, Astrophysicist Shows. Mar 11, 2021.

https://www.sciencealert.com/faster-than-light-travel-is-possible-within-einstein-s-physics-astrophysicist-shows

(B) visiting the interior of a black hole

<<  if a person found an isolated supermassive black hole suitable for scientific study and decided to venture in, everything observed or measured of the black hole interior would be confined within the black hole's event horizon.

Keeping in mind that nothing can escape the gravitational pull beyond the event horizon, the in-falling person would not be able to send any information about their findings back out beyond this horizon. Their journey and findings would be lost to the rest of the entire universe for all time. But they would enjoy the adventure, for as long as they survived … maybe …. >>️

Leo Rodriguez, Shanshan Rodriguez. Could a human enter a black hole to study it? A person could travel past (certain) black holes' event horizons without dying immediately — here's how. Feb 7, 2021. 

https://www.salon.com/2021/02/07/could-a-human-enter-a-black-hole-to-study-it_partner/  

(C) being already under observation by alien entities.

<< On June 25 the Pentagon and the Office of the Director of National Intelligence released their much hyped report on unidentified aerial phenomena, or UAP. (..) And while the report did not rule out an extraterrestrial origin for much of the documented UAP, it was short on details or bombshells. >> 

<<  we already know our world is easily detectable by extrasolar observers. A paper published on June 23 in Nature  

(Kaltenegger L., Faherty J.K.  https://www.nature.com/articles/s41586-021-03596-y ) shows that in the past 5,000 years, 1,715 stars have been in the right celestial position to view a populated Earth transiting the sun—with 319 more entering this sweet spot in the next 5,000 years. And seven of these far-off stars are known to have their own orbiting exoplanets that might support life. >>

<< Think of living in a room, and all the windows are open, and you do all your business, and you don’t know that all the windows are open, (..) Would you behave differently if you knew that you are being seen all your life? >>️  René Heller️

️

Tess Joosse. Aliens Might Already Be Watching Us. A new star map reveals more than 2,000 stars, some with their own planets, that have a direct view of our planetary presence. July 1, 2021

https://www.scientificamerican.com/article/aliens-might-already-be-watching-us

# s-gst: imaging a soliton, first in the centre (of the condensate) rather than at the edges

<< When a periodic waveform is subjected to small perturbations to its amplitude and phase, any nonlinearity in the system can lead to its fragmentation — a so-called modulation instability. The phenomenon often results in the formation of solitons — self-reinforcing solitary wave packets — aligned in a train >>

AA << found that [ in ultracold 7Li atoms ] solitons developed first in the centre of the condensate rather than at the edges, suggesting that the seed for the modulation instability is dominated by noise, which may be technical, thermal or quantum in origin >>

Yun Li. Ultracold gases. Search for the seed. doi:10.1038/nphys4172

http://www.nature.com/nphys/journal/v13/n6/full/nphys4172.html

Jason H. V. Nguyen, De Luo, Randall G. Hulet. Formation of matter-wave soliton trains by modulational instability. Science 2017, 356 (6336), 422–426. doi: 10.1126/science.aal3220. 28 Apr 2017.

http://science.sciencemag.org/content/356/6336/422

# s-gst: solitons (also) in angiogenesis

<< Here's what we humans have in common with oceans, lakes and rivers: We have solitons coursing through us >>

Sonia Fernandez. This Soliton is About You. Monday, October 3, 2016 10:30

http://www.news.ucsb.edu/2016/017218/soliton-about-you

L. L. Bonilla, M. Carretero et al. Soliton driven angiogenesis. Nature. Sci. Rep. 6, Article number: 31296 (2016)doi:10.1038/srep31296. Publ. 09 Aug 2016.

http://www.nature.com/articles/srep31296

# gst: a cylindrical solitonlike that collapses into a spherical shape, and, along the filaments, central cores of matter exhibit fuzzies

In AA simulation, << the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical solitonlike cores, which are unstable under gravity and collapse into kiloparsec-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter-a smoking gun signature of FDM ("fuzzy" dark matter). >>

Philip Mocz, Anastasia Fialkov, et al. First Star-Forming Structures in Fuzzy Cosmic Filaments. Phys. Rev. Lett. 123, 141301. Oct 2, 2019.     https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.141301  

Jennifer Chu. This is how a 'fuzzy' universe may have looked. Massachusetts Institute of Technology. Oct 3, 2019       https://m.phys.org/news/2019-10-fuzzy-dark-disrupts-conventional.html   

FonT

intrigante qui come una simulazione di evoluzione cosmologica - filamenti strutturati a cilindro mutanti (collassanti) in strutture sferoidali (ma non a generica fluttuante frittella) formanti, nei filamenti di gas,  serie (sciami?) di kernel a dinamiche fuzzy - possa far immaginare generici contesti altri ...

# gst: apropos of transitions, rich behaviors from chimeras or solitary states to traveling waves

AA << study numerically the spatiotemporal dynamics of a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. >>

<< It is shown that the discretized oscillator exhibits a richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Such regimes as the coexistence of multichimera state/traveling wave and solitary state are revealed for the first time and studied in detail. >>

<< It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient towards the purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, observation time, initial conditions, and influence of external noise. >>

Elena Rybalova, Sishu Muni, Galina Strelkova. Transition from chimera/solitary states to traveling waves. arXiv: 2212.07990v1 [nlin.AO]. Dec 15, 2022. 

https://arxiv.org/abs/2212.07990

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)

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

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

keyword 'waves' in FonT

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

keyword 'onda' in Notes (quasi-stochastic poetry)

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

Keywords: gst, behavior, van der Pol oscillator, transition, chimera state, solitons, solitary state, waves, noise

# s-phys: knotted solitary waves: the begin

<< a team of physicists (..) has found a way to create knotted solitary waves, or knot solitons, in a quantum-mechanical field >>

<< Knots are defined mathematically as closed curves in 3D space. A knot soliton consists of an infinite number of rings, each linked with all of the others to generate a toroidal structure >>

<< This is the beginning of the story of quantum knots >>

http://www.sci-news.com/physics/physicists-create-quantum-knots-03569.html

D. S. Hall, M. W. Ray, et al. Tying quantum knots. Nature Physics (2016) doi:10.1038/nphys3624

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3624.html

# gst: solitary wave billiards

<<  In the present work (AA) introduce the concept of solitary wave billiards. I.e., instead of a point particle, (they) consider a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. >>

J. Cuevas-Maraver, P.G. Kevrekidis, H. Zhang. Solitary wave billiards. arXiv: 2203.09489v1 [nlin.PS]. Mar 17, 2022. 

https://arxiv.org/abs/2203.09489

Also 

keyword 'chaos' | 'chaotic' in Font

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

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

keyword | 'soliton' in FonT

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

keywords: gst, waves, solitons, billiard, chaos 

# gst: the hypothesis of a new type of rogue waves.

<< Much attention of researchers has been paid in the recent decades to the study of rogue waves. Various mechanisms of formation of these waves were suggested. The occurrence of rogue waves is most often investigated on the basis of the mechanisms of modulation instability and superposition of waves. In both cases, an evolution of rogue waves takes place against the background of a wave field, which is reflected in the definitions of such waves. In this report, the localized waves developed in the absence of the background wave fields are considered. At the same time, their dynamics corresponds to the dynamics of rogue waves that ”appear from nowhere and disappear without a trace”. >>️

<< The waves of this type are distinguished by the fact that their dynamics occur on the zero background. This implies that rogue waves presented here are formed solely due to the nonlinear focusing. >>️

N.V. Ustinov. New type of rogue waves. arXiv:2310.17254v1 [nlin.SI]. Oct 26, 2023.  

https://arxiv.org/abs/2310.17254

Chaos, Solitons & Fractals V. 179, Feb 2024, 114467. https://www.sciencedirect.com/science/article/abs/pii/S0960077924000183

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

Keywords: gst, waves, rogue waves 

# gst: ️apropos of spontaneous active matter, the active droploids.

<< Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, (AA) take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. >>️

<< These structures hinge on mutually coupled structure formation processes of the colloids, which form an engine, and the surrounding solvent, which phase separates in regions of high colloidal density and encapsulates the engine within a droplet shell.  >>

️

Jens Grauer, Falko Schmidt, et al. Active droploids. arXiv:2109.10677v1 [cond-mat.soft]. Sep 22, 2021.

https://arxiv.org/abs/2109.10677

Also

keyword 'drop' | 'droplet' in FonT

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

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

keyword 'goccia' in Notes (quasi-stochastic poetry): 

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

keywords: gst, drops, droplets, colloids, active matter, active droploids, self-assembly, solitons.

# gst: the solitary route to chimera states.

AA << show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit (they) demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. (AA) demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators. >>

<<  While it is well known that self-organized wave patterns typically coexist within an interval of possible different wave numbers (..)(AA) show here the coexistence of coherence-incoherence patterns with different numbers of incoherent oscillators, which are in fact coexisting chaotic attractors with different Lyapunov dimensions. The incoherent oscillators in these coexisting attractors show extensive chaos of different dimensions. The total share of incoherent oscillators in a chimera state is a macroscopic quantity. Hence, within the range of such shares, where stable chimera states exist, (AA) find, for large systems, an increasing number of coexisting attractors with their numbers of incoherent oscillators increasing as well. (They) showed that, varying the coupling parameter, this extensive scenario is linked to the thermodynamic limit of the solitary regime, where the range of admissible numbers of incoherent oscillators shrinks down to one single oscillator in an infinitely large system. For this case, the emergence of the chaotic motion of the single incoherent oscillator could be shown in a period doubling cascade. >>

Leonhard Schulen, Alexander Gerdes, et al. The solitary route to chimera states. arXiv:2204.00385v1 [nlin.CD]. Apr 1, 2022.

https://arxiv.org/abs/2204.00385

Also

keyword 'FitzHugh-Nagumo oscillators' in APS | PubMed

https://journals.aps.org/search/

https://pubmed.ncbi.nlm.nih.gov/?term=FitzHugh-Nagumo+oscillators

keyword 'chaos' | 'chaotic' in Font

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

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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

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

keywords: gst, solitons, solitary states, period-doubling cascade, chaos, Lyapunov dimension, FitzHugh-Nagumo oscillator, chimera state, dynamical systems.

# s-gst: coupled solitons jiggle like molecules

<< The first direct observations of how "molecules of light" can vibrate have been made by >> AA << who have characterized the motions of soliton laser pulses that interact with each other in an optical fibre >>

Hamish Johnston. 'Molecules' of light wiggle and jiggle. Jun 19, 2017.

http://physicsworld.com/cws/article/news/2017/jun/19/molecules-of-light-wiggle-and-jiggle

AA << map the internal motion of a soliton pair molecule [..] revealing different categories of internal pulsations, including vibrationlike and phase drifting dynamics >>

AA results << agree well with numerical predictions and bring insights to the analogy between self-organized states of lights and states of the matter >>

Katarzyna Krupa, K. Nithyanandan, et al. Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules. Phys. Rev. Lett. 118, 243901 doi: 10.1103/PhysRevLett.118.243901 Publ. 13 June 2017.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.243901

# 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

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

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

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

keyword 'goccia' in Notes 

(quasi-stochastic poetry): 

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

keyword 'instability' | 'instabilities' in FonT

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

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

keyword 'instabile' in Notes 

(quasi-stochastic poetry)

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

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

# gst: dynamics and interactions of multiple bright droplets and bubbles, and interactions of kinks with droplets and with antikinks.

<< Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink-antikink interactions are repulsive, generating counter-propagating shock waves. >> 

 

G. C. Katsimiga, S. I. Mistakidis, et al. Interactions and dynamics of one-dimensional droplets, bubbles and kinks. arXiv: 2306.07055v2 [cond-mat.quant-gas]. Jul 26, 2023.

https://arxiv.org/abs/2306.07055

Also: drop, bubble, waves, soliton, in https://www.inkgmr.net/kwrds.html

Keywords: gst, drop, bubble, kink, wave, soliton, homoclinic orbits

# gst: the generation of solitary waves to move and direct a pulse-drive bot

<< The unique properties of nonlinear waves have been recently exploited to enable a wide range of applications, including impact mitigation, asymmetric transmission, switching, and focusing. (..) (AA) demonstrate that the propagation of nonlinear waves can be as well harnessed to make flexible structures crawl. By combining experimental and theoretical methods, (they) show that such pulse-driven locomotion reaches a maximum efficiency when the initiated pulses are solitons and that (their) simple machine can move on a wide range of surfaces and even steer. >>

<< nonlinear waves (..) demonstrates that they offer a new platform to make flexible machines to move. >>

Bolei Deng, Liyuan Chen, et al. Pulse-driven robot: Motion via solitary waves. Science Advances. Vol. 6, no. 18, eaaz1166. doi: 10.1126/ sciadv.aaz1166. May 1, 2020. 

https://advances.sciencemag.org/content/6/18/eaaz1166   

Pulse-driven robot: Motion via solitary waves. Thamarasee Jeewandara. May 8, 2020.

https://phys.org/news/2020-05-pulse-driven-robot-motion-solitary.html