# gst: turbulence spreading and anomalous diffusion on combs.

<< This (AA) paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process is shown to result universally in a subdiffusive spreading of the wave field. The dispersion of this spreading process is found to depend exclusively on the type of the interaction process (three- or four-wave), but not on a particular underlying instability. The asymptotic transport equations for field spreading are derived with the aid of a specific geometric construction in the form of a comb. >>

<< The results can be summarized by stating that the asymptotic spreading proceeds as a continuous-time random walk (CTRW) and corresponds to a kinetic description in terms of fractional-derivative equations. The fractional indexes pertaining to these equations are obtained exactly using the comb model. >>

<< A special case of the above theory is a situation in which two waves with oppositely directed wave vectors couple together to form a bound state with zero momentum. This situation is considered separately and associated with the self-organization of wave-like turbulence into banded flows or staircases. >>

<< Overall, (AA) find that turbulence spreading and staircasing could be described based on the same mathematical formalism, using the Hamiltonian of inelastic wave-wave interactions and a mapping procedure into the comb space. Theoretically, the comb approach is regarded as a substitute for a more common description based on quasilinear theory. Some implications of the present theory for the fusion plasma studies are discussed and a comparison with the available observational and numerical evidence is given. >>

Alexander V. Milovanov, Alexander Iomin, Jens Juul Rasmussen. Turbulence spreading and anomalous diffusion on combs. Phys. Rev. E 111, 064217 – Published 24 June, 2025

https://journals.aps.org/pre/abstract/10.1103/cmf5-sf8x#d93038b1-6671-419d-be1e-219e5bf78523

Also: waves, turbulence, walk, self-assembly, instability, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, walk, self-assembly, instability, chaos, comb model, inelastic resonant interactions, inelastic wave-wave interactions, continuous-time random walk, self-organization of wave-like turbulence, Lévy flights, Lévy walks

# gst: interactive anisotropic walks in 2D generated from a 3-state opinion dynamics model.

<< A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. >>

In this article AA has performed the mapping << in such a way that the walk is directed along the 𝑌 axis while it can move either way along the 𝑋 axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. >>

<< For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power-law behavior, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents. >>

Surajit Saha, Parongama Sen. Interactive anisotropic walks in two dimensions generated from a three-state opinion dynamics model. Phys. Rev. E 111, 064123. Jun 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/5c2y-yj1z

arXiv: 2409.10413v3 [cond-mat.stat-mech]. Apr 28, 2025. 

https://arxiv.org/abs/2409.10413

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

Keywords: gst, walk, walking, random walk, randomness, noise, transitions, noise-induced transitions, criticality.

# gst: apropos of absorbing targets, persistence exponents of self-interacting random walks

<< The persistence exponent, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. >> 

In their Letter, AA << consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time 𝑡 with the territory already visited at earlier times 𝑡′ <𝑡. (AA)  compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, (They) also determine the splitting probability of these processes. >>

<< Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and nonreversible Monte Carlo methods. >>

J. Brémont, L. Régnier, et al. Persistence Exponents of Self-Interacting Random Walks. Phys. Rev. Lett. 134, 197103. May 16, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.197103

arXiv:2410.18699v1 [cond-mat.stat-mech]. 

https://arxiv.org/abs/2410.18699

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

Keywords: gst, walk, walking, self-interacting random walk, walker self-repulsion, walker self-attraction, stochasticity, absorbing targets.

# gst: accelerated first detection in discrete-time quantum walks using sharp restarts.

<< Restart is a common strategy observed in nature that accelerates first-passage processes, and has been extensively studied using classical random walks. In the quantum regime, restart in continuous-time quantum walks (CTQWs) has been shown to expedite the quantum hitting times [Phys. Rev. Lett. 130, 050802 (2023)]. >>

 Here, AA << study how restarting monitored discrete-time quantum walks (DTQWs) affects the quantum hitting times. (They) show that the restarted DTQWs outperform classical random walks in target searches, benefiting from quantum ballistic propagation, a feature shared with their continuous-time counterparts. >>

Kunal Shukla, Riddhi Chatterjee, C. M. Chandrashekar. Accelerated first detection in discrete-time quantum walks using sharp restarts. Phys. Rev. Research 7, 023069. Apr 21, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023069

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

Keywords: gst, networks, randomness, walk, random walk, quantum walk, stochasticity, sharp restart.

# gst: apropos of random walks, intermittent random walks under stochastic resetting

AA << analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. >>

AA << demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. (They) calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, (..) the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. >>

<< the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition. >>️

Rosa Flaquer-Galmes, Daniel Campos,  Vicenc Mendez. Intermittent random walks under stochastic resetting. Phys. Rev. E 109, 034103. March 4, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034103  

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

Keywords: gst, walk, intermittent random walk, stochasticity, stochastic resetting

gst: actually and counterintuitively a coherent jump could generate disorder.

AA << consider a quantized version of a model for “random walk in random environment.” (..) For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. >>

Ben Avnit, Doron Cohen. Quantum walk in stochastic environment. Phys. Rev. E 108, 054111. Nov 7, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054111

Also:  Voli a casaccio. Notes (quasi-stochastic poetry). Oct 01, 2006.

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

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

Keywords: gst, walk, random walk, quantum walk, qu-walk, jump, transition, disorder, chaos

# game: noise-induced Parrondo's paradox in discrete-time qu-walks

<< Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. >>

AA << show that noise can induce Parrondo's paradox in one-dimensional discrete-time quantum walks with deterministic periodic as well as aperiodic sequences of two-state quantum coins where this paradox does not occur in the absence of noise. >>️

Zbigniew Walczak, Jarosław H. Bauer. Noise-induced Parrondo's paradox in discrete-time quantum walks. Phys. Rev. E 108, 044212. Oct 11, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.044212

Also: parrondo, walk, noise, in: https://www.inkgmr.net/kwrds.html

Keywords: games, parrondo, walk, noise

# gst: influence of disorder on the spreading and entanglement properties of coined quantum walks.

AA << investigate the influence of disorder on the spreading and entanglement properties of coined quantum walks. Specifically, (AA) consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. (They) find that coin disorder alters the usual ballistic transport properties of coined quantum walks considerably and yields an extremely slow dynamics with strong evidence for localization behavior. (They) investigate this slow dynamics by comparing different properties of the walker occupation probability with the standard Hadamard walk. (They) find that the walker distribution, and a number of properties associated with it, are significantly altered by the coin disorder. Special focus is given to the influence of coin disorder on entanglement properties. (AA) observe that generically, coin disorder decreases the coin-walker entanglement. The behavior of the entanglement properties further supports the premise that coin disorder induces localization in coined quantum walks. >>

Louie Hong Yao, Sascha Wald. Coined Quantum Walks on the Line: Disorder, Entanglement and Localization. arXiv: 2303.15978v1 [quant-ph]. doi: 10.48550/ arXiv.2303.15978. 28 Mar 28, 2023.

https://arxiv.org/abs/2303.15978

Also

Voli a casaccio. Notes. Oct 01, 2006. 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

keyword 'disorder' in FonT

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

keyword 'disordine' in Notes 

(quasi-stochastic poetry)

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

keyword 'walk' | 'walking' in FonT

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

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

keyword 'passo lieve' | 'walk' | 'walking' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=passo+lieve

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

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

Keywords: gst, disorder, quantum physics, walk, walking, coined quantum walks

# behav: learning walks related to home burrow navigation (among desert grassland scorpions Paruroctonus utahensis)

<< The Navigation by Chemotextural Familiarity Hypothesis (NCFH) suggests that scorpions use their midventral pectines to gather chemical and textural information near their burrows and use this information as they subsequently return home. For NCFH to be viable, animals must somehow acquire home-directed “tastes” of the substrate, such as through path integration (PI) and/or learning walks. >>️

AA << found that once animals established their home burrows, they immediately made one to several short, looping excursions away from and back to their burrows before walking greater distances. We also observed similar excursions when animals made burrows in level sand in the middle of the arena (i.e., no mound provided). These putative learning walks, together with recently reported PI in scorpions, may provide the crucial home-directed information requisite for NCFH. >>️

Douglas D. Gaffin, Maria G. Munoz, Marielle Hoefnagels. Evidence of learning walks related to scorpion home burrow navigation. bioRxiv 2021.12.28.474378; Dec 30, 2021. 

https://www.biorxiv.org/content/10.1101/2021.12.28.474378v1

Also

keyword 'walk' | 'walking' in FonT

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

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

keyword 'passo lieve' | 'walk' | 'walking' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=passo+lieve

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

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

Keywords: behav, walk, walking, learning walk, NCFH

# gst: near a critical point, switching between exploitation and exploration, to approach life with Lévy's (chaotic) walk

<< Lévy walks are common biological movements. However, the functional advantages of Lévy walks emerging near a critical point are poorly understood. >>

AA << showed that there could be functional advantages associated with Lévy walks emerging near a critical point, including a large dynamic range to stimuli and highly flexible switching between exploitation and exploration. >>

Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point. PNAS.  doi: 10.1073/ pnas.2001548117.  Sep 14, 2020.

https://www.pnas.org/content/early/2020/09/11/2001548117

Chaotic 'Lévy walks' are a good strategy for animals. Riken. Sep 17, 2020.

https://phys.org/news/2020-09-chaotic-lvy-good-strategy-animals.html   

Also

Lévy flight hypothesis, not only for predation ...  Nov 22, 2015.

https://flashontrack.blogspot.com/2015/11/s-gst-levy-flight-hypothesis-not-only.html

keyword 'Lévy' in FonT

https://flashontrack.blogspot.com/search?q=L%C3%A9vy&m=1

# behav: backward walking, navigational uncertainties (among Cataglyphis velox)

<< Current opinion in insect navigation assumes that animals need to align with the goal direction to recognise familiar views and approach it. Yet, ants sometimes drag heavy food items backward to the nest and it is still unclear to what extent they rely on visual memories while doing so. >>

<< ants do indeed recognise and use the learnt visual scenery to guide their path while walking backward. In addition, the results show that backward homing ants estimate their directional certainty by combining visual familiarity with other cues such as their path integrator and the time spent backward. >>

Sebastian Schwarz, Leo Clement, et al.  How do backward walking ants (Cataglyphis velox) cope with navigational uncertainty? doi: 10.1101/2019.12.16.877704. Dec 17, 2019.

https://www.biorxiv.org/content/10.1101/2019.12.16.877704v1