# gst: stochastic adaptation, stochastic resonance.

<< Stochastic resonance is a phenomenon possessed by some nonlinear oscillators, in which a weak signal is boosted by noise. Both the monostable and bistable Duffing oscillators can exhibit this property. However, stochastic resonance has a strong frequency-dependence, as only a band of frequencies may be boosted by noise. >>️

<< Adaptive oscillators are a subset of nonlinear oscillators that can learn the features of an external force. (In this AA work), an adaptive state is added to a Duffing oscillator. This adaptive state enables the Duffing adaptive oscillator to outperform stochastic resonance over a wide range of frequencies by learning a resonance condition. >>️

Edmon Perkins. Comparison of stochastic adaptation and stochastic resonance. Phys. Rev. E 110, 064225. Dec 27, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.064225 

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

Keywords: gst, fluctuations, noise, transition, stochasticity, stochastic adaptation, stochastic resonance

# gst: nascent water waves induced by the impulsive motion of a solid wall; an unsteady hydraulic jump theory

Fig. 2: Representative cases of the different regimes of impulse waves observed: (a) dispersive wave; (b) solitary-like wave; (c) plunging breaking bore; (d) water jet 

AA << investigated the generation phase of laboratory-scale water waves induced by the impulsive motion of a rigid piston, whose maximum velocity U and total stroke L are independently varied, as well as the initial liquid depth h. By doing so, the influence of two dimensionless numbers is studied: the Froude number Frp (..), with g the gravitational acceleration, and the relative stroke Λp (..) of the piston. >>️

<< For large Froude numbers, an unsteady hydraulic jump theory is proposed, which accurately predicts the time evolution of the wave amplitude at the contact with the piston throughout the generation phase. At the end of the formation process, the dimensionless volume of the bump evolves linearly with Λp and the wave aspect ratio is found to be governed by the relative acceleration γ/g. As the piston begins its constant deceleration, the water bump evolves into a propagating wave and several regimes (such as dispersive, solitary-like and bore waves, as well as water jets) are then reported and mapped in a phase diagram in the (Frp, Λp) plane. While the transition from waves to water jets is observed if the typical acceleration of the piston is close enough to the gravitational acceleration g, the wave regimes are found to be mainly selected by the relative piston stroke Λp while the Froude number determines whether the generated wave breaks or not. >>️

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Wladimir Sarlin, Zhaodong Niu, et al. Nascent water waves induced by the impulsive motion of a solid wall. arXiv: 2412.08216v1 [physics.flu-dyn]. Dec 11, 2024. 

https://arxiv.org/abs/2412.08216

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

Keywords: gst, waves, soliton

# gst: bent and reverse bent solitons; obliquely interacting solitary waves and wave wakes in free-surface flows.

This AA paper << investigates the weakly nonlinear isotropic bi-directional Benney-Luke (BL) equation, which is used to describe oceanic surface and internal waves in shallow water, with a particular focus on soliton dynamics. Using the Whitham modulation theory, (AA) derive the modulation equations associated with the BL equation that describe the evolution of soliton amplitude and slope. By analyzing rarefaction waves and shock waves within these modulation equations, (AA) derive the Riemann invariants and modified Rankine-Hugoniot conditions. These expressions help characterize the Mach expansion and Mach reflection phenomena of bent and reverse bent solitons. >>

<< Furthermore, as a far-field approximation for the forced BL equation - which models wave and flow interactions with local topography - the modulation equations yield a slowly varying similarity solution. This solution indicates that the precursor wavefronts created by topography moving at subcritical or critical speeds take the shape of a circular arc, in contrast to the parabolic wavefronts observed in the forced KP equation. >>

Lei Hu, Xudan Luo, Zhan Wang. Obliquely interacting solitary waves and wave wakes in free-surface flows. arXiv: 2412.05034v1 [nlin.PS]. Dec 6, 2024. 

https://arxiv.org/abs/2412.05034

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

Keywords: gst, waves, solitons

# gst: chimera states in a system of stationary and flying-through deterministic particles with an internal degree of freedom.

<< This work greatly extends (AA)  understanding of the dynamics of flying-through oscillators in media with nonlocal interaction. >>

<< Let’s describe the results obtained. First, it was shown that, depending on the number of potential wells, particles can be stationary, flying-through, or split into two subensembles of stationary and flying-through particles.  Secondly, it has been demonstrated that in the case of stationary arrangement of particles, the fully synchronous regime can become unstable due to the inhomogeneity of particle distribution between potential wells. In a partially synchronous cluster, phase incoherent elements can be located within the same potential well. Third, when stationary and flying-through elements coexist, chimera regimes are realized at each subensemble and further coexist with each other. This means that, despite the nonlocal nature of the interaction between elements of the medium, what is important for structure formation is a relatively stable mutual arrangement of particles relative to each other, which leads to a chimera state in each of the subensemble. >>️

Maxim I. Bolotov, Lev A. Smirnov, et al. Chimera states in a system of stationary and flying-through deterministic particles with an internal degree of freedom. arXiv: 2412.05044v1 [nlin.CD]. Dec 6, 2024.

https://arxiv.org/abs/2412.05044

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

Keywords: gst, chimera, chaos

# gst: apropos of interweavings, linking dispersion and stirring in randomly braiding flows.

     Fig. 5 (a)

<< Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. (AA) show that these random flows belong to a pathline braiding 'universality class' that quantitatively links dispersion and chaotic stirring, meaning that the Lyapunov exponent can be estimated from the purely advective transverse dispersivity. (AA) verify this quantitative link for both unsteady 2D and steady 3D random flows. This result uncovers a deep connection between transport and mixing over a broad class of random flows. >>️

Daniel R. Lester, Michael G. Trefry, Guy Metcalfe. Linking Dispersion and Stirring in Randomly Braiding Flows. arXiv: 2412.05407v1 [physics.flu-dyn]. Dec 6, 2024.

https://arxiv.org/abs/2412.05407

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

Keywords: gst, random, random flows, randomly braiding flows, chaos

# life: apropos of impossible predictions, Lewis & Jackson (mjq) dipole, a bizarre form revisited

<< Qui un kernel di creativita' invece di autogenerarsi all'interno di un sistema cognitivo individuale emerge e si stabilizza grazie all' interazione cooperativa a lungo termine tra due personalita' ... >>

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<< Qui si potrebbe introdurre un ulteriore elemento di impredicibilita'  (..) quasi una meccanica a metano protonato, per dire ... >>

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2124 - attrattore cooperativo bipolare (nell'elastici spigoli). Notes. (quasi-stochastic poetry). Mar 05, 2007.

https://inkpi.blogspot.com/2007/03/2124-attrattore-cooperativo-bipolare.html   

Also: mjq, all the things you are (jazz night). 

https://youtu.be/6SLy0BhODLs?si=Pu43K2aYgBsbC3he

Also:  << Musk was indispensable to Trump’s campaign this year, endorsing the former president before pouring more than $100 million into the effort to elect him. Now he’s serving as one of Trump’s closest advisers, staying overnight at Mar-a-Lago and attending virtually every high-level meeting by his side. There are reports that he’s effectively living at the club. All of that was already inspiring headlines last month like, “Elon Musk may already be overstaying his welcome in Trump’s orbit.” >>

Eddie Scarry. Here’s How e Media Are Lying Right Now: Fake Trump-Musk. thefederalist.com. Dec 19, 2024.️

https://thefederalist.com/2024/12/19/heres-how-the-media-are-lying-right-now-fake-trump-musk-wedge-edition/

Also:  << In meno di tre giorni Elon Musk è riuscito a portare il governo degli Stati Uniti a un passo dalla chiusura e a interferire con le imminenti elezioni tedesche. Il tutto senza alzare gli occhi dal suo telefonino. È con un tweet sul social X ... >>️

Simona Siri. Il caso. lastampa.it  Dec 21, 2024.  https://www.lastampa.it/esteri/2024/12/21/news/elon_musk_germania_elezioni_ultradestra_afd-14899496/

Also: jazz, RAG-time, Mr. Donald, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, jazz, RAG-time, Mr. Donald, Mr. Elon

# gst: apropos of transitions, towards a theory for the formation of chimera patterns in complex networks

This AA work << formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks. >>

They << show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. (AA) findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. >>

Malbor Asllani, Alex Arenas. Towards a Theory for the Formation of Chimera Patterns in Complex Networks. arXiv: 2412.05504v1 [nlin.AO]. Dec 7, 2024.

https://arxiv.org/abs/2412.05504

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

Keywords: gst, chimera, network, transition