# gst: triadic percolation on multilayer networks.

<< ️Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In presence of triadic interactions, a percolation process occurring on a single-layer network becomes a fully-fledged dynamical system, characterized by period-doubling and a route to chaos. >>

<< ️Here, (AA) generalize the model to multilayer networks and name it as the multilayer triadic percolation (MTP) model. (They) find a much richer dynamical behavior of the MTP model than its single-layer counterpart. MTP displays a Neimark-Sacker bifurcation, leading to oscillations of arbitrarily large period or pseudo-periodic oscillations. >>

<< Moreover, MTP admits period-two oscillations without negative regulatory interactions, whereas single-layer systems only display discontinuous hybrid transitions.  >> 

Hanlin Sun, Filippo Radicchi, Ginestra Bianconi. Triadic percolation on multilayer networks. arXiv: 2510.09341v1 [nlin.AO]. Oct 10, 2025.

https://arxiv.org/abs/2510.09341

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

Keywords: gst, network, chaos, 

percolation, multilayer triadic 

percolation, higher-order 

interactions, triadic interactions.

# gst: apropos of waves that escape trapping; on internal wave whispering gallery modes in channels and critical-slope wave attractors.

<< ️Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and super-attractors in 2D & 3D and the exceptional class of standing global internal wave modes. >>

<< ️However, most of these works did not deal with waves that escape trapping. By using continuous symmetries (AA) analytically prove the existence of internal wave Whispering Gallery Modes (WGMs), internal waves that propagate continuously without getting trapped by attractors. WGMs neutral stability with respect to different perturbations enable whispering gallery beams, a continuum of rays propagating together coherently. The systems' continuous symmetries also enable projection onto 2D planes that yield effective 2D billiards preserving the original dynamics. >>

<< ️By examining rays deviating from these WGMs in parabolic channels (They) discover a new type of wave attractor which is located along the channel instead of across it as in previous works. This new wave attractor leads to a re-understanding of WGMs as sitting at the border between the two basins of attraction. >>

<< ️Finally, both critical-slope wave attractors and whispering gallery beams are used to propose explanations for along-channel energy fluxes in submarine canyons and tidal energy intensification near critical slopes. >>

Nimrod Bratspiess, Eyal Heifetz, Leo R. M. Maas. On internal wave whispering gallery modes in channels and critical-slope wave attractors. arXiv: 2510.07218v1 [physics.flu-dyn]. Oct 8, 2025.

https://arxiv.org/abs/2510.07218

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

Keywords: gst, waves, internal waves, internal wave whispering gallery modes (WGMs), wave attractors, basins of attraction, billiards.

# gst: apropos of stochastic resetting, abrupt transitions in the optimization of diffusion with distributed resetting.

<< ️Brownian diffusion subject to stochastic resetting to a fixed position has been widely studied for applications to random search processes. In an unbounded domain, the mean first-passage time at a target site can be minimized for a convenient choice of the resetting rate. >>

<< ️Here (AA) study this optimization problem in one dimension when resetting occurs to random positions, chosen from a probability density function with compact support that does not include the target. Depending on the shape of this distribution, the optimal resetting rate either varies smoothly with the mean distance to the target, as in single-site resetting, or exhibits a discontinuity caused by the presence of a second local minimum in the mean first-passage time. These two regimes are separated by a critical line containing a singular point that (They) characterize through a Ginzburg-Landau theory. >>

<< ️To quantify how useful is a given resetting point for the search, (AA) calculate the probability density function of the last resetting position before absorption. The discontinuous transition separates two markedly different optimal strategies: one with a small resetting rate where the last path before absorption starts from a rather distant but likely position, while the other strategy has a large resetting rate, favoring last paths starting from not-so-likely points but which are closer to the target. >>

Pedro Julián-Salgado, Leonardo Dagdug, Denis Boyer. Abrupt transitions in the optimization of diffusion with distributed resetting. Phys. Rev. E 112, 044110. Oct 6, 2025.

https://journals.aps.org/pre/abstract/10.1103/b15f-47qw

arXiv: 2507.14483v2 [cond-mat.stat-mech]. Oct 7, 2025.

https://arxiv.org/abs/2507.14483

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

Keywords: gst, randomness, transitions, stochastic resetting, small-- large resetting rate.

# gst: effects of inertia on the asynchronous state of a disordered Kuramoto model.

<< ️(AA) investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. (They) extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation statistics, specifically, the power spectra of network noise and single oscillators. >>

<< ️Comparison with network simulations demonstrates that this works well whenever the system is in an asynchronous state. >>

 

 << ️(AA) also find an unexpected effect when varying the degree of inertia: the correlation time of the oscillators becomes minimal at an intermediate mass of the oscillators; correspondingly, the power spectra appear flatter and thus more similar to white noise around the same value of mass. (They) also find a similar effect for the Lyapunov spectra of the oscillators when the mass is varied. >>

Yagmur Kati, Ralf Toenjes, Benjamin Lindner. Effects of inertia on the asynchronous state of a disordered Kuramoto model. Phys. Rev. E 112, 044301. Oct 6, 2025.

https://journals.aps.org/pre/abstract/10.1103/xt4m-bkp8

Also: network, noise, order, disorder, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, noise, order, disorder, fluctuations, inertia, asynchronous states, transitions, Kuramoto model.

# gst: predicting the response of structurally altered and asymmetrical networks.

<< ️(AA) investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. >>

<< ️The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, (They) consider the challenging problem of multiplicative structural alterations and asymmetrical interaction coupling. >>

<< ️(AA) introduce a framework to approximate the averaged response at each network node for general structural alterations, including non-normal and asymmetrical ones. (Their) findings indicate that both the asymmetry and non-normality of the structural alterations impact the global and local responses at different orders in time. (They) propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration. >>

Melvyn Tyloo. Predicting the response of structurally altered and asymmetrical networks. Phys. Rev. E 112, L042301. Oct 10, 2025. 

https://journals.aps.org/pre/abstract/10.1103/3s3d-qr4l

Also: network, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, disorder & fluctuations, transitions.

# gst: why and when merging surface nanobubbles jump.

<< Gas bubble accumulation on substrates reduces the efficiency of many physicochemical processes, such as water electrolysis. For microbubbles, where buoyancy is negligible, coalescence-induced jumping driven by the release of surface energy provides an efficient pathway for their early detachment. >>

<< At the nanoscale, however, gas compressibility breaks volume conservation during coalescence, suppressing surface energy release and seemingly disabling this detachment route. >>

<< Using molecular dynamics simulations, continuum numerical simulations, and theoretical analysis, (AA) show that surface nanobubbles with sufficiently large contact angles can nevertheless detach after coalescence. In this regime, detachment is powered by the release of pressure energy associated with nanobubble volume expansion. This (AA) finding thus establishes a unified driving mechanism for coalescence-induced bubble detachment across all length scales. >>

Yixin Zhang, Xiangyu Zhang, Detlef Lohse. Why and when merging surface nanobubbles jump. arXiv: 2509.22934v1 [cond-mat.soft]. Sep 26, 2025.

https://arxiv.org/abs/2509.22934

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

Keywords: gst, bubbles, surface nanobubbles, surface energy release, coalescence, coalescence-induced jumping, coalescence-induced bubble detachment.

# gst: random trajectories in bounded domains

<< ️Can we deduce the total length of a random trajectory by observing only its local path segments within a confined domain? Surprisingly, the answer is yes—for curves randomly placed and oriented in space, whether stochastic or deterministic; generated by ballistic or diffusive dynamics; possibly interrupted by stopping or branching; and in two or more dimensions. More precisely, the mean total length ⟨𝐿⟩ relates to the mean in-domain path length ⟨ℓ⟩ and the mean chord length of the domain ⟨𝜎⟩ via the following simple and universal relation:

              1/⟨ℓ⟩ = 1/⟨𝐿⟩ + 1/⟨𝜎⟩

Here, ⟨𝜎⟩ is a purely geometric quantity, dependent only on the volume-to-surface ratio of the domain. Derived solely from the kinematic formula of integral geometry, the result is independent of step-length statistics, memory, absorption, and branching, making it equally relevant to photons in turbid tissue, active bacteria in microchannels, cosmic rays in molecular clouds, or neutron chains in nuclear reactors. Monte Carlo simulations spanning straight needles, Y shapes, and isotropic random walks in two and and three dimensions confirm the universality and demonstrate how a local measurement of ⟨ℓ⟩ yields ⟨𝐿⟩ without ever tracking the full trajectory. >>

T. Binzoni, E. Dumonteil, A. Mazzolo. Universal property of random trajectories in bounded domains. Phys. Rev. E 112, 044105. Oct 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/dng6-9519

arXiv: 2011.06343v3 [math-ph]. May 16, 2025. 

https://arxiv.org/abs/2011.06343

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

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

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

Keywords: gst, randomness, random trajectories,  walk, random walk, bounded domains.