# 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: breakthrough in unstable growth processes, shorter branches can revive when a striking transition of the leading branch reaches the boundary of the system.

<< Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They often emerge as a result of unstable growth processes, in which growing branches compete for the available flux. This leads to effective repulsion between the branches and screening of the shorter ones. (AA) show that a striking transition in growth dynamics takes place as the leading branch reaches the boundary of the system. The shorter branches revive then and grow toward the leading one forming loops. These effects are observed both in living and inanimate systems. >>

Stanisław Zukowski, Annemiek Johanna Maria Cornelissen, et al. Finger revival and reconnections near breakthrough in unstable growth processes. arXiv: 2212.08878v1 [physics.flu-dyn]. Dec 17, 2022.

https://arxiv.org/abs/2212.08878

Also

keyword 'transition' in FonT: 

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

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

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

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

Keywords: gst, transition, growth, growth dynamics, transport networks, spatial networks

# 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

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

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

# gst: slow dynamics of a interacting mobile impurity (in a bath of localized particles)

AA << investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, (AA) show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. (AA) observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential. >>

Piotr Sierant, Titas Chanda, Maciej Lewenstein, Jakub Zakrzewski. Slow dynamics of a mobile impurity interacting with an Anderson insulator. arXiv: 2212.07107v1 [cond-mat.dis-nn]. Dec 14, 2022. 

https://arxiv.org/abs/2212.07107

Also

keyword 'particle' | 'quasiparticle' in FonT

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

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

keyword 'particelle' in Notes

(quasi-stochastic poetry)

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

Keywords: gst, particles, impurity, disorder, sub-diffusive growth, transition, entanglement entropy

# gst: behavior of microswimmers in a vortex with translational and rotational noise

AA << propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices, namely active particles in two- and three-dimensional rotlets. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. (AA) further discover a conserved quantity of motion that allows (..) to map the phase space according to the type of the orbit (bounded vs unbounded). (They) next introduce translational and rotational noise into the system. Using a Fokker--Planck formalism, (AA) quantify the quality of trapping near the centre of the vortex by examining the probability of escape and the mean time of escape from the region of deterministically bounded orbits. (AA) finally show how to use these findings to formulate a prediction for the radius of the depletion zone, which compares favourably with the experiments of Sokolov and Aranson (2016). >>

Ivan Tanasijevic, Eric Lauga. Microswimmers in vortices: Dynamics and trapping. arXiv: 2211.05866v1 [physics.bio-ph].  Nov 10, 2022. 

https://arxiv.org/abs/2211.05866

Also

'microswimmers' in FonT 

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

Keywords: gst, behav, translation,  rotation, trapping, noise, swimmer, swimming,  microswimmers, fluid dynamics, vortex, vortices, vortexes, vorticity

# gst: transitions, how two saddles can increase the transient times.

FIG. 8. Attractor and chaotic saddles (..) amplified around three bands of the chaotic attractor.  The global chaotic saddle is colored blue, and the local chaotic saddle is colored red. The attractors are colored black. 

AA << consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems, they are responsible for chaotic transients, fractal basin boundaries, chaotic scattering and they mediate interior crises. >>

<< In this work (AA) discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. (They) show how the presence of two saddles increase the transient times and analyze the phenomenon of crisis induced intermittency. >>️

Rodrigo Simile Baroni, Ricardo Egydio de Carvalho, et al. Chaotic saddles and interior crises in a dissipative nontwist system. arXiv: 2211.06921v1 [nlin.CD]. Nov 13, 2022. 

https://arxiv.org/abs/2211.06921

Also

keyword 'intermittency' in FonT

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

keyword 'dissipation' in FonT

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

keyword 'saddle' in FonT

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

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)

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

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

Keywords: gst, transitions, dissipation, 

dissipative systems, chaos, saddle, chaotic saddle, crisis, interior crisis, intermittency

# life: a proposito di Sadico Predatore Ambiguo Mutaforma (SPAM), di Selvatico 'Gris-Gris Simile' (SGGS), di 'Mariuolo' Dialogico- Estetico (MDE) e di Risonante Tamagotchi (RT) ...

Una senz'altro ipotetica, immaginifica  (purtuttavia funzionale, non morale) complessificazione, ampliando il  bizzarro scenario derivabile anche da componenti 'gris-gris' simile (GSSG)/ 'tamagotchi risonante' (TR): 

https://flashontrack.blogspot.com/2022/11/life-qui-una-ipotesi-sulla-rete-deventi.html

qui si configurerebbero - intriganti senz'altro - ulteriori intrecciati (in simil topo-maglina 3D coi 'respiri' a fisarmonica quasi-stocastica, jazzy,  permododidire ed anzicheforse) scenari dove l'ipotetico post 'mariuolo' (MDE), 'animato' dall'ipotetico mimetico negriero abile Sadico Predatore Ambiguo Mutaforma (SPAM), non solo 'inclinerebbe' verso la sottrazione reiterata (oppure in casi senz'altro più rari in modalità stocastica) delle classiche caramelle allo sprovveduto classico 'Neuro- Moscardino in Quasi- Mezza- Semicroma' (NMQMS), ma, a imitazione (probabile pessima imitazione) del suo padrino standard di riferimento SPAM, configurerebbe -  ampliando anche in modalità motu sua propria perfino -  l'adatti (prestidigitation inside) mimetici scenari atti a orientare, indirizzare, ancorare (celando coll'adatti svirgolamenti a copertura teoretico- ideologica) lo sfortunato, il circoscritto, il confinato, l'indifeso, l'inerme, lo sprovveduto, l'accucciato, il ricattabile, il neuro- impotente, l'incatenabile/ incatenato, le moltitudini entità neuro- devastabili/ devastate, verso l'irreversibile disdicevole perpetua condizione di CTZ- battitore estremo costretto 

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

all'intorno dell'adatto suo lampione. 

Qui l'immagini, campate in aria senz'altro, di 'adatti svirgolamenti a copertura ideologica' e 'perpetuo battitore all'intorno dell'adatto suo lampione' meriterebbero una serie  di note poetiche, quasistocastiche perfino  https://inkpi.blogspot.com  

ma mi astengo.

Anche

(+) << Tornando all'analogia con la fisica, il potere, come l'energia, muta continuamente di forma >>. In: Onda anti rumore. Notes (quasi-stochastic poetry). April 21, 2005.

https://inkpi.blogspot.com/2005/04/1644b-onda-anti-rumore.html

(+) Il sé sadico, *mutaforma, *compassionevole, *mistico predatore, *schizofrenico predatore. (quasi-stochastic poetry). (cit.) FonT. Oct 21, 2022.  

https://flashontrack.blogspot.com/2022/10/life-il-se-sadico-mutaforma.html

(+) keyword 'deposition' in FonT

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

Keywords: life, gris-gris, tamagotchi, Bertrand Russell, forme del potere, forms of power, AI, CTZ, MDE, NMQMS,  SGGS, SPAM, RT