# gst: directed extended-range percolation.

<< ️For standard percolation, directionality is known to increase the complexity of percolation, requiring the distinct statistical treatment of in messages and out messages for determining the percolation order parameters. >>

<< ️Here (AA) show that when connectivity is ensured by paths of length 𝑅≥2, network directionality, impeding backtracking, can significantly reduce the complexity of percolation. To illustrate this finding, (AA) introduce directed extended-range percolation (DERP), defined on directed networks with nonreciprocal edges and motivated by applications in quantum communication. >>

<< ️In this framework, message transmission is enabled between trusted nodes separated by a directed path of length at most 𝑅. Using a message-passing approach, (AA) show that, on locally treelike structures, directionality enables an exact determination of the percolation threshold and the anomalous critical indices with a number of distinct statistical messages smaller than the naive expectation, which would require twice as many messages as in the undirected version. This reduction arises because directionality suppresses backtracking paths, thereby considerably simplifying the resulting equations. >>

<< ️On random directed networks (AA) find that the critical behavior of DERP depends sensitively on degree correlations. These analytical predictions are corroborated by extensive Monte Carlo simulations, highlighting the profound impact of directionality and correlations on long-range connectivity in complex networks. >>

Wenbo Liu, Yiwen Zeng, Xueming Liu, et al. Directed extended-range percolation. Phys. Rev. E 114, L042301. Oct 26, 2026.

https://journals.aps.org/pre/abstract/10.1103/hs2n-6rsn

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

Keywords: gst, networks, transitions, percolation, directed extended-range percolation, percolation threshold, percolation phase transition, random directed networks, network phase transitions, long-range connectivity, critical phenomena.

# gst: enhanced turbulent clustering of time-varying particles in random flow fields.

<< ️Particles suspended in turbulent flows tend to cluster within specific regions of the flow field. Previous research consistently reported that clustering is reduced at both very small and very large Stokes numbers for moderate Reynolds numbers. However, understanding how clustering evolves with varying Stokes numbers remains elusive. >> 

<< ️This (AA) work utilizes kinematic simulations to explore clustering of particles with varying inertia at high Reynolds numbers. (Their) results show that when the Stokes number varies over time, noticeable clusters form, even for low-Stokes-number particles that typically exhibit negligible clustering. This suggests that transient effects associated with evolving particle inertia can significantly enhance clustering behavior beyond what would be predicted based on a constant Stokes number alone. >>

<< ️(AA) findings may suggest a different outlook on the enhanced clustering observed in many applications, including natural and atmospheric science, and cloud microphysics. >>

Boaz Ofarim, Yuval Dagan. Enhanced turbulent clustering of time-varying particles in random flow fields. Phys. Rev. E 114, 045104. Oct 21, 2026.

https://journals.aps.org/pre/abstract/10.1103/kdm3-spck

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

Keywords: gst, particles, turbulence, fluid-particle interactions, homogeneous turbulence, isotropic turbulence, multiphase flows, particle-laden flows, turbulent multiphase flows.

# gst: apropos of decorrelation in turbulence, space-time correlations of passive scalars in colored-noise flows.

<< ️The space-time correlation of a passive scalar advected by a Gaussian colored-noise velocity with wavenumber-dependent correlation times and power-law spatial spectra (by AA) is investigated. Within the inertial-convective subrange, (They) derive an analytical solution for the space-time correlation. >>

<< ️(AA) results clarify the underlying decorrelation mechanism of passive scalars: mean-flow advection and large-scale sweeping dominate temporal decorrelation, and small-scale distortion dominates spatial decorrelation. >>

Long Wang, Guowei He. Space-time correlations of passive scalars in colored-noise flows. arXiv: 2604.07052v2 [physics.flu-dyn]. Oct 2, 2026.

https://arxiv.org/abs/2604.07052

Phys. Rev. E 114, 045106. Oct 22, 2026.

https://journals.aps.org/pre/abstract/10.1103/z1s1-kspl

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

Keywords: gst, turbulence, transitions, noise, space-time correlation, inertial-convective subrange, random-sweeping mechanism, mean-flow advection, large-scale sweeping, small-scale distortion. 

# brain: dynamics of random recurrent neural networks; colored noise and sublinear activations.

<< ️(AA) study the dynamics of recurrent neural networks with random couplings, sublinear odd activation functions, and temporally correlated noise. Using large N methods, (They) determine stationary correlations and distinguish the loss of local linear stability from the onset of chaos, characterized by a positive largest Lyapunov exponent. >>

<< These thresholds delimit an intermediate regime in which local instability coexists with asymptotic stability under a common noise history. Their separation depends on both the noise correlation time and the asymptotic growth of the activation function. (AA) show that internal noise with any finite correlation time cuts off the divergence of the network’s intrinsic correlation time τ_(corr) at the edge of chaos; it exhibits a critical scaling τ_(corr,max) ∼ 1/√D_0, where D_0 is the integrated noise strength. >>

<< Static random input instead produces coincident thresholds and a divergent correlation time. (AA) also calculate the frequency-dependent participation dimension from a four-point correlation function. Its zero-frequency value is inversely proportional to the fourth power of the network correlation time, predicting a smooth minimum at the weak-noise chaos threshold. Numerical simulations support the large-network predictions and reveal appreciable finite-size effects. >>

German Mato, Facundo Rigatuso, Gonzalo Torroba. Dynamics of random recurrent neural networks: colored noise and sublinear activations.  arXiv: 2610.31575v1 [q-bio.NC]. Oct 22, 2026.

https://arxiv.org/abs/2610.31575

Also: brain, network, chaos, soliton, disorder, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, network, chaos, solitons, disorder, noise, weak-disorder expansion, white and colored noise, quenched noise.

# gst: emergence and coexistence of periodic and unstructured motion in future-avoiding random walks.

<< ️Self-avoiding random walks on graphs can be seen as walkers interacting with their own past history. Here, (AA) consider a complementary class of dynamics, mutual future-avoiding random walks (MFARWs), where stochastically driven walkers are avoiding each other's planned future trajectories. ️Such systems arise naturally in conceptual models of shared mobility. >>

<< ️(AA) show that periodic behavior emerges spontaneously in two different MFARWs, and that periodic and unstructured behavior coexist, providing an example of chimera like behavior of nonoscillatory paths on networks. >>

<< Further, (AA) analytically describe and predict the onset of structure. (They) find that the transition from unstructured to periodic behavior is driven by a mechanism of self-amplifying coupling to the periodic components of the stochastic drivers of the system. In the context of shared mobility applications, these states imply a regime of naturally stable coexistence between flexible and line-based public transport. >>

A. Schmaus, K. Stiller, N. Molkenthin. Emergence and coexistence of periodic and unstructured motion in future-avoiding random walks. Phys. Rev. E 114, 044219. Oct 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/9q1j-dlw8

arXiv: 2602.03308v1 [nlin.AO]. Feb 3, 2026.

https://arxiv.org/abs/2602.03308

Also: walk, walking, random, behav, chimera, network, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, walk, walking, randomness, behavior, chimera, networks, transitions, mutual future-avoiding random walks (MFARWs), stochastically driven walkers, periodic behavior, self-amplifying coupling, discontinuous phase transition. 

# gst: how mobile oscillators reshape dynamical robustness in complex networks.

<< ️While the robustness of collective dynamics in static networks is well established, how agent mobility and network topology jointly shape dynamical robustness remains largely unexplored. >>

<< ️In this letter, (AA) investigate the robustness of mobile Stuart-Landau oscillators performing random walks on networks and interacting diffusively when co-located. In the rapid-mobility regime, (They) reduce the dynamics to a mean-field framework linking network degree statistics to an effective global coupling strength. >> 

<< ️(AA) show analytically that increased degree heterogeneity in the network enhances the effective coupling strength, and strictly lowers the critical threshold of functional degradation for amplitude death. Numerical simulations confirm the predicted heterogeneity-dependent ordering of the transition thresholds, showing an earlier collective collapse in scale-free networks than in random or regular networks. >> 

<< ️(Their) results establish mobility and network heterogeneity as key determinants of robustness in mobile oscillator populations, with implications for resilient biological and engineered collectives. >>

Sayantan Nag Chowdhury, Srilena Kundu. How Mobile Oscillators Reshape Dynamical Robustness in Complex Networks. arXiv: 2610.16608v1 [nlin.AO]. Oct 12, 2026.

https://arxiv.org/abs/2610.16608

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

Keywords: gst, networks, randomness, walks, collapse, mobile oscillators, mobility, transition thresholds.

# gst: recovery random walks and extreme events on complex networks.

<< ️Extreme events are widely studied within simple random walk frameworks, where their probability is determined by the network structure and stationary walker distribution. >> 

<< ️Here, (AA) propose a recovery random walk (RRW) model in which extreme events temporally `freeze' the nodes where they occur for a fixed duration Δ (Δ=0 recovers the original model), trapping walkers and reducing the effective mobile population, thereby making the model more practical. >>

<< ️(AA) derive a first-principles description of this feedback and a delayed differential equation for the frozen-node fraction. This finite freezing produces an initial overshoot, followed by damped oscillatory relaxation to a steady state for the fraction of the frozen nodes. (They) find that freezing suppresses extreme event probability while preserving its degree dependence dynamics, and suppresses the EE frequency. >>

<< Further, the analytical prediction for the fraction of the frozen nodes agrees closely with simulations. This model closely reflects real-world scenarios, yielding more practical EE statistics. >>

Karan Singh, R.V.Narendran, V.K.Chandrasekar, et al. Recovery Random Walks and Extreme Events on Complex Networks. arXiv: 2609.39377v1 [nlin.AO]. Sep 30, 2026.

https://arxiv.org/abs/2609.39377

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

Keywords: gst, walk, walking, randomness, networks, transitions, random walk, extreme events (EE), stationary walker distribution, recovery random walk (RRW), frozen-node fractions, damped oscillatory relaxation. 

# gst: locking transition in coupled disordered systems.

<< ️When a system of many interacting constituents is extended across space, every region carries the same disordered landscape, and it is unclear whether distant regions settle into the same state. >> 

<< ️(AA) study copies of the Random Energy Model (REM), sharing one disorder realization, coupled along a chain. A first-order transition separates a phase with short-range correlations, from a locked phase in which the entire chain occupies the lowest-energy state with probability one, even at positive temperature. No intermediate ordering lengths occur. >>

<< In the Generalized REM the chain locks either to the lowest-energy state or to the lowest free-energy valley. >>

Guy Bunin. Locking transition in coupled disordered systems.  arXiv: 2609.36846v1 [cond-mat.dis-nn]. Sep 29, 2026.

https://arxiv.org/abs/2609.36846

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

Keywords: gst, disorder, randomness, transitions, random energy model (REM), short-range correlations, locked phase, lowest free-energy valley.

# gst: how turbulent flows grow vorticity at a point.

<< ️(AA) describe how strong vorticity fluctuations appear in three-dimensional incompressible turbulence driven by a large-scale random force. By combining analytical and numerical methods, (They) construct a vorticity instanton: the most probable force history driving the flow to a prescribed large vorticity at a given point and time. >>

<< ️(AA) show how the smooth, large-scale force produces a long vortex filament with a thin, viscous-scale core. (Their) main finding is that the standard mechanism of amplifying a vortex tube through radial compression and axial stretching is only effective up to a threshold value. Producing vorticity above the threshold requires an additional ingredient: vorticity waves propagating along the tube. >>

<< ️The final vorticity is the result of two colliding waves. This mechanism has striking similarities to the one recently suggested by OpenAI for creating infinite vorticity in finite-time Navier--Stokes blow-up. >>

Timo Schorlepp, Vladimir Rosenhaus, Gregory Falkovich. How turbulent flows grow vorticity at a point. arXiv: 2609.13056v1 [physics.flu-dyn]. Sep 11, 2026.

https://arxiv.org/abs/2609.13056

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

Keywords: gst, vortex, turbulence, randomness, waves, vorticity instanton, vortex filaments, colliding waves.

# gst: collective hysteresis and multistability in threshold networks.

<< ️In a mechanistic model of the dawn chorus, Kaye showed that heterogeneous activation thresholds and a shared feedback signal determined by the population's active fraction can produce abrupt collective activation and hysteresis. >>

<< ️(AA) extend this mechanism to a network of interacting agents. Each node has a continuous activation level, and a nonnegative row-stochastic matrix determines how node activities contribute to individual feedback. (They) prove that sufficiently weak feedback yields a unique globally attracting equilibrium. For all feedback strengths, the homogeneous dynamics exactly reproduce Kaye's scalar equation; consequently, network topology does not alter the folds or cusp of the homogeneous branch, and no heterogeneous mode becomes unstable before the homogeneous mode. >>

<< ️For equitable partitions, the network admits an exact quotient system in which nodes within a block receive the same aggregate input from every block. When blocks are uncoupled, the quotient reduces to independent copies of Kaye's scalar equation. (AA) show that every assignment of stable scalar equilibria to blocks persists under sufficiently weak interblock coupling, producing a combinatorial family of stable quotient equilibria that lift to stable full-network equilibria and remain under small perturbations that break exact equitability. >>

<< ️For two symmetrically coupled blocks, branches with unequal block activities terminate at a pair of symmetry-related cusp bifurcations. Near the onset of bistability, (AA) derive scaling laws for the interblock coupling at which these bifurcations occur, the activity difference between the blocks at bifurcation, and the corresponding shift of the external stimulus from the scalar cusp. Numerical continuation confirms the scaling laws for gamma, logistic, and normal threshold distributions. >>

Moses Boudourides. Collective Hysteresis and Multistability in Threshold Networks. arXiv: 2609.10580v1 [cs.SI]. Sep 5, 2026.

https://arxiv.org/abs/2609.10580

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

Keywords: gst, hysteresis, collective hysteresis, networks, threshold networks, stability, bistability, multistability, randomness, small perturbations, bifurcations, cusp bifurcations, Kaye's dawn chorus, stochasticity, heterogeneous activation thresholds, weak feedbacks, shared feedback signals, attracting equilibrium.

# gst: hierarchy in Gilbert's tessellation; multifractal behavior.

<< ️(AA) have introduced two types of hierarchies in a classical Gilbert tessellation. The cascading process that follows gives rise, in both cases, to a tile area distribution function that fits surprisingly well with a generalized gamma function. The latter is a truncated power function which, in turn, in the spirit of Brown’s sequential fragmentation theory, is derived from a stretched exponential hazard function that is also truncated. >>

<< ️This theoretical finding finds a natural counterpart in the experimental observations of Kooij and coworkers [S. Kooij et al., Nat. Commun. 12, 2521 (2021)], according to which the fragmentation of a brittle sample follows two distinct regimes: a random breakup that gives rise to a simple exponential distribution of mass fragments (canonical Gilbert), whereas a hierarchical crushing leads to a power-law distribution (hierarchical Gilbert, in fact g3(x) ∼ x^(c−1) for x → 0). >>

<< ️(AA) study demonstrates that the DG and HG cascade processes (i.e. Dichotomous Gilbert (DG), Hierarchical Gilbert (HG)) display a multifractal nature. Both models produce a heterogeneous distribution with different characteristics, quantitatively described by two different multifractal spectra. A direct, quantitative comparison between (Their) geometric models and specific experimental datasets remains, at present, an open challenge and would require fragmentation experiments capable of resolving a sufficiently wide range of fragment sizes to reliably probe the hierarchy-induced effect. >>

E.Consolini, B.Bonanni, M.Fanfoni. Hierarchy in Gilbert's tessellation: Multifractal behavior. Phys. Rev. E 114, 034120. Sep 11, 2026.

https://journals.aps.org/pre/abstract/10.1103/p5xq-nj2g

Also: fracture, crack, random, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fracture, crack, randomness, fragmentation process, fragment-size distribution, scale-free behavior, 2-D random tessellation, fractals, multifractal systems, multifractal scaling. 

# gst: noise-shaped synchrony in neuronal oscillator networks.

<< ️Stochastic fluctuations often act as promoters of activity in excitable and oscillatory systems, giving rise to phenomena such as coherence resonance. Here, (AA) show that in the low-intensity regime, noise plays a dual role in weakly coupled neuronal units: It can both inhibit collective spiking and, with increasing intensity, restore coordinated activity. For a ring of diffusively coupled, oscillatory FitzHugh-Nagumo neurons, (They) demonstrate how the interplay of noise and coupling strength organizes a rich set of collective dynamical states. >> 

<< ️(AA) systematically classify emergent dynamical scenarios by an in-depth time-series analysis that integrates multiple complementary measures. (They) are able to automatically identify five distinct dynamical clusters in parameter space: pure noise, quiescent state, noisy synchronization, complete synchronization, and intermittent switching. (Their) workflow provides a general, automated framework for characterizing collective dynamics in coupled oscillator networks. >>

Max Contreras, Philipp Hövel. Noise-shaped synchrony in neuronal oscillator networks. Phys. Rev. E 114, L022302. Aug 26, 2026. 

https://journals.aps.org/pre/abstract/10.1103/sxl4-6mdm

Also: noise, brain, neuro, disorder & fluctuations, random, intermittency, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, brain, disorder, fluctuations, randomness, networks, coupled oscillator networks, stochasticity, stochastic fluctuations, coherence resonance, collective spiking inhibition, restored coordinated activity, pure noise, quiescent state, noisy synchronization, complete synchronization, intermittent switching.

# life: apropos of birth-and-death processes, framework for fluctuating times and counting observables in stochastic excursions.

<< ️Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to quantum thermal machines. >>

<< ️In an accompanying Letter, (AA) introduced the notion of stochastic excursions−a framework to analyze out of equilibrium processes via sub-trajectories. Through counting observables, this framework captures finite-time fluctuations and trajectory-level behavior, which provides insights into thermodynamical trade-offs between thermodynamic quantities of interest, such as entropy production and dynamical activity. >>

<< ️In this work, (AA) enhance this formalism by providing a suite of technical results on how to efficiently compute excursion-related quantities. (Their) analytical results provide explicit formulas for general moments of counting variables and excursion duration, as well as their covariance and conditional moments. (They) show that excursion statistics recover full counting statistics results, and uncover a relation between fluctuations of counting observables at single-excursion level and the steady state diffusion coefficient (noise). >> 

<< ️(AA) also discuss a fluctuation theorem for individual excursions and show that it implies a modified thermodynamic uncertainty relation at the excursion level. In addition, (They) explore how analyzing excursions and using the results developed here can yield insights into three problems of interest: the three-qubit absorption refrigerator, cellular sensing, and birth-and-death processes. >>

Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Framework for fluctuating times and counting observables in stochastic excursions.

Phys. Rev. E 114, 024129. Aug 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/jydr-1853

arXiv: 2506.05160v3 [cond-mat.stat-mech]. Aug 19, 2026.

https://arxiv.org/abs/2506.05160

Also: Guilherme Fiusa, Pedro E. Harunari, Abhaya S. Hegde, et al. Counting observables in stochastic excursions. Phys. Rev. E 114, L022102 (2026). 

https://journals.aps.org/pre/abstract/10.1103/1blp-2b27

Also: walk, walking, uncertainty, fluctuations, random, noise, behav, Nomads, in https://www.inkgmr.net/kwrds.html 

Keywords: walk, walking, noise, uncertainty, behavior, fluctuations, randomness, stochasticity, stochastic excursions, Nomads. 

# gst: escape over a saddle by colored noise.

<< ️Stochastic dynamical systems allow modeling of transitions induced by random disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. While the small-noise limit is well-described by the large deviation principle, existing computational methods often struggle with stochastic forcings any more complicated than nondegenerate Gaussian white noise, and with unbounded time intervals. >>

<< ️The primary innovations of this (AA) work are extending the framework to cater for colored and degenerate forcing and unbounded time horizons—scenarios that are physically realistic but numerically challenging. (They) cater for degenerate noise by using the Hamiltonian optimal control method. (They) cater for a class of colored noises by using linear filters on white noise. (They) cater for infinite time horizon by introducing the method of division (MOD), a computational approach for approximating rare transition events, including their most likely paths and the exponential scaling laws of their transition rates. >>

<< ️The effectiveness of MOD and the above approaches to colored noise, is demonstrated by illustration on two examples: an inverted double-well potential and a simplified roll-heave model for ship capsize. >>

Jiayao Shao (邵家瑶), Tobias Grafke, Robert S. MacKay. Escape over a saddle by colored noise: Theory and numerics. Phys. Rev. E 114, 024210. Aug 12, 2026.

https://journals.aps.org/pre/abstract/10.1103/w8dd-9cqg

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

Keywords: gst, escape, noise, randomness, stochasticity, transitions, noise-induced transitions, method of division (MOD), inverted double-well potential, simplified roll-heave model, large deviation & rare event statistics.

gst: nonreciprocal dynamics with weak noise: aperiodic “Escher cycles” and their quasipotential landscape.

<< ️(AA) present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic “Escher cycles,” similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. >>

<< (AA) calculate the quasipotential analytically to first order in nonreciprocality. (They) characterize it along a one-dimensional reaction coordinate that connects the attractors, and (They) also obtain the full two-dimensional landscape, at leading order in perturbation theory. >>

<< ️The resulting landscapes feature flat regions and extended plateaus, together with nondifferentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features. >>

Janik Schüttler, Robert L. Jack, Michael E. Cates. Nonreciprocal dynamics with weak noise: Aperiodic “Escher cycles” and their quasipotential landscape. Phys. Rev. E 114, 024104. Aug 3, 2026.

https://journals.aps.org/pre/abstract/10.1103/slp9-rd27

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

Keywords: gst, noise, randomness, stochasticity, transitions, singularity, nonreciprocal interactions, noise-induced transitions, metastable attractors, Escher cycles, perturbation theory, escape problems, large deviation & rare event statistics. 

# gst: vortex formation around islands in random waves.

<< ️Wave vortices are fundamental topological features of interference fields, occurring at nodal points where the wave amplitude vanishes. A distinct class of vortices can instead form around it islands or `holes' in two-dimensional wavefields, where the wave intensity remains finite and may even peak at the boundary. >> 

<< ️Here (AA) develop a statistical theory of vortices around islands in random two-dimensional wavefields, with and without the Coriolis effect, and test it experimentally. (They) determine the probabilities of vortices with different topological charges as functions of island size and Coriolis parameter.  ️(They) find that island-bound vortices emerge with unexpectedly high probability, approaching 50% in non-rotating systems and nearly 100% in rotating systems. Moreover, for a broad range of parameters, the presence of a subwavelength island dramatically enhances vortex formation compared with homogeneous random wavefields. >>

<< ️(AA) results explain the formation of tidal vortices around ocean islands of particular sizes (~0.1 of the characteristic wavelength) and establish a general mechanism for generating localized high-intensity vortices around defects in diverse wave systems, from water waves to nanophotonic structures. >>

Alex J. Vernon, Junyi Ye, Wenzhe Liu, et al. Vortex formation around islands in random waves. arXiv: 2607.15938v1 [physics.flu-dyn]. Jul 17, 2026.

https://arxiv.org/abs/2607.15938

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

Keywords: gst, waves, vortex, randomness, defects, wave vortices, tidal vortices, interference fields, homogeneous random wavefields, random two-dimensional wavefields, rotating non-rotating systems.

# gst: interwoven long-range order induced by random fields.

<< (AA) propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by random-field disorder that couples to a composite vestigial order parameter. >>

<< The proposed ``implectic'' phase is characterized by spontaneous symmetry breaking on the background of the spatially interwoven domain structure created by the random fields. (They) explicitly demonstrate the existence of this phase in a layered J1−J2 Ising magnet by means of large-scale Monte Carlo simulations. (AA) then discuss numerous potential applications in systems featuring charge and spin density wave order including frustrated magnets, cuprate and iron-based superconductors, and ultracold atoms. >>

Jeremiah Bender, Thomas Vojta. Interwoven long-range order induced by random fields. arXiv: 2607.10337v1 [cond-mat.dis-nn]. Jul 11, 2026.

https://arxiv.org/abs/2607.10337

Also: particle, waves, order, disorder, fracture, crack, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, waves, order, disorder, fracture, crack, transitions, impurities, defects, locally break, spontaneous symmetry breaking, random-field disorder, implectic long-range ordered phases.

# gst: twisted state stability under local order parameter adaptation.

<< ️Twisted states commonly arise in nonlocally coupled ring networks. (AA) study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. >>

<< ️The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. >>

<< Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics. >>

Xueqin Wang, Hong He, Wende Tang, et al. Twisted state stability under local order parameter adaptation. Phys. Rev. E 114, 014209. Jul 13, 2026. 

https://journals.aps.org/pre/abstract/10.1103/p2wd-nfbr

Also: network, stability, chimera, order, disorder, fluctuations, random, twist, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, stability, chimera, order, disorder, fluctuations, randomness, synchronization, coupled oscillators, adaptive feedbacks, twisted states, basin stability. 

# life: apropos of trick-shot artists, one shot, twenty-one balls; existence and rarity of a total clearance in a single stroke of snooker.

<< ️Snooker folklore holds that no single stroke can pocket all twenty-one object balls. (AA) examine the claim in an idealized but fully specified model of billiard dynamics. Within the model (They) exhibit an admissible configuration of the twenty-two balls and a stroke of the cue ball that pockets all twenty-one object balls, and (They) show that the set of such strokes has positive Lebesgue measure in the natural shot space: total clearances are not flukes of measure zero but open events. >>

<< ️For the regulation opening configuration (AA) conjecture the same and explain both why a simulation cannot settle the conjecture by brute force and what kind of computation could settle it in principle. Monte Carlo experiments in the same model estimate the probability P(k) that a uniformly random stroke pockets exactly k balls; the observed decay of P(k), extrapolated conditionally on the conjecture, places the probability of a total clearance from the break far beyond anything observable. The folk claim is thus right in practice and wrong in principle, and the gap between the two is exactly the distance between measure zero and unobservably small. >>

Avner Kantor. One Shot, Twenty-One Balls: Existence and Rarity of a Total Clearance in a Single Stroke of Snooker.  arXiv: 2607.12995v1 [cs.CG]. Jul 14. 2026.

https://arxiv.org/abs/2607.12995

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

Keywords: life, billiard, snooker, single stroke, games. 

# gst: stability of vortex lattices in rotating flows.

<< Vortex lattices—highly ordered arrays of vortices—are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. >>

<< (AA) explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end (They) construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. (They) then characterize their evolution across different Rossby numbers and domain geometries. >>

<< By introducing an Ekman drag (AA)  are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of “melting,” occurs. (They) examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. >>

<< (AA) results reveal that the stability of the lattices is a memory-less random process whose mean lifetime depends sensitively on the system parameters that if finely tuned can lead to very long-lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres. >>

Julián Amette Estrada, Alexandros Alexakis, Marc E. Brachet, et al. Stability of vortex lattices in rotating flows. Phys. Rev. Fluids 11, 074401. Jul 10, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/k8zw-s6kj

arXiv: 2510.06374v1 [physics.flu-dyn]. Oct 7, 2025.

https://arxiv.org/abs/2510.06374

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

Keywords: gst, vortex, turbulence, randomness, vortex lattices, rotating flows, mean lifetime, spontaneous breakups, memory-less random process, metastable states, criticality.