# gst: a Reynolds-like criterion for the onset of universal active turbulence.

<< ️Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum E(k)∼k^(−3/2). (AA) show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. >>

<< ️Motivated by the competition between these processes, (AA) identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. >>

<< ️These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class. >>

Kunal Kumar, Sandip Sahoo, Kirti Kashyap, et al. A Reynolds-like Criterion for the Onset of Universal Active Turbulence. arXiv: 2609.39999v1 [physics.flu-dyn]. Sep 30, 2026.

https://arxiv.org/abs/2609.39999

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

Keywords: gst, turbulence, advection, saturation, instability, collapse, transition.

# 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: attraction-controlled torque organization and rotational states in frictional granular matter.

<< In this study, (AA) numerically investigate how interparticle attraction affects stress transmission, torque organization, and particle rotation in a two-dimensional frictional granular material. Although the attraction is a central force and exerts no direct torque on the particles, it strongly modifies the contact network and particle rotation. >>

<< Attraction produces a low-rate stress state and selects the high-stress state near the shear-thickening regime of the dry system, while leaving the high-rate thickened state almost unchanged. By decomposing the shear stress, (AA) find that the direct attractive contribution accounts for only a fraction of the total stress, while the repulsive contribution is strongly enhanced. >>

<< Attraction increases the coordination number and torque amplitude and can reverse the local torque-sign correlation. At low packing fractions and intermediate shear rates, a stress-collapse state emerges with strongly suppressed torque and rotation despite a finite contact network. >>

<< These (AA) results show that attraction controls macroscopic rheology through reorganization of the frictional contact network. >>

Kiwamu Yoshii. Attraction-controlled torque organization and rotational states in frictional granular matter. arXiv: 2609.35270v1 [cond-mat.dis-nn]. Sep 28, 2026.

https://arxiv.org/abs/2609.35270

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

Keywords: gst, particle, network, 2-D frictional granular particles, attraction, repulsion, shear stress, low- high- rate stress state, stress transmission, stress-collapse state, torque organization, torque amplitude, particle rotation, shear-thickening regime, frictional contact network.

# 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: avalanche assemblies in arbitrary connection topologies.

<< ️Complex systems are commonly modeled as networks of units that integrate external input and emit brief pulses of activity upon reaching a threshold. Such pulse-coupled interactions can give rise to cascades of activity propagating through the network in the form of avalanches. >>

<< While the statistics of these collective events are known to depend sensitively on network topology, rigorous analytical descriptions are usually restricted to homogeneous networks or mean-field approximations which are limited to particular aspects of generated avalanches like size and duration. >>

<< ️Here (AA) develop a mathematically rigorous theory of avalanche formation in recurrent networks of pulse-coupled units without assuming homogeneity. For arbitrary nonnegative coupling matrices, the framework provides a closed form for the avalanche assembly distribution, which quantifies the probability that a given subset of units is activated during an avalanche. >>

<< This (AA) approach represents a substantial conceptual advance over existing theories allowing analysis of the structure-function relation between network topology and detailed statistics of generated avalanches. This is particularly relevant for the irregular, highly structured, and asymmetric coupling topologies ubiquitous in natural systems, such as brain networks with pronounced columnar, modular, and hierarchical organization. >>

Maik Schünemann, Marc Kesseböhmer, Udo Ernst. Avalanche assemblies in arbitrary connection topologies. Phys. Rev. E 114, 034414. Sep 29, 2026.

https://journals.aps.org/pre/abstract/10.1103/nl7d-16n8

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

Keywords: gst, network, brain, complex systems, collective dynamics, pulse-coupled interactions, threshold cascades of activity, avalanches, avalanche assembly distribution, network topology, columnar- modular- hierarchical organization.

# life: emotions as intrinsic colored noise in biological systems.

<< ️The idea that emotions in biological systems are analogous to intrinsic colored noise (by AA) is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. >>

<< ️The agents of a biological network can be represented either by biological species, such as humans and animals, or by neurons of the brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. >>

<< ️At the initial step, the agents make decisions individually and then start exchanging information with each other and imitating the actions of other agents, thus forming a biological network of interacting agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of agents, one group possessing long-range memory, the other group, short-range memory, and the third group of super-rational agents acting strictly on the basis of utility, being deprived of emotions. >>

<< ️Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the evolution of decision choice. (by AA) it is shown  how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox. >>

V.I.Yukalov, E.P.Yukalova. Emotions as intrinsic colored noise in biological systems. arXiv: 2609.25970v1 [physics.soc-ph]. Sep 22, 2026.

https://arxiv.org/abs/2609.25970

Also: noise, brain, network, game, in https://www.inkgmr.net/kwrds.html 

Keywords: life, noise, brain, networks, biological noisy network, agents emotions, colored noise, affective operation, long-range memory, short-range memory, games.

# gst: topological phase transition driven by structural defects.

<< ️Structural defects, such as disclinations and dislocations, destroy the long-range crystalline order as they proliferate. In this work, (AA) continuously drive a system from a crystalline state on a decorated honeycomb lattice to a hyperuniform amorphous state, by consecutively introducing Stone-Wales (SW) defects, which can be viewed as dipoles of dislocations. >>

<< ️Using a topological Weaire-Thorpe Hamiltonian model to describe electrons in this system, (AA) demonstrate that SW defects can cause pseudo-band inversions and, correspondingly, a reversal of the Chern number. Using adiabatic arguments and a computationally efficient spillage indicator, (They) predict the topological phase diagram of the amorphous state from the crystalline one. (They) explain the nature of the pseudo-band inversion through the renormalization of the hopping in an effective Hamiltonian based on a single SW defect. >>

Andrii Syrota, Andrej Mesaros, Pascal Simon. Topological phase transition driven by structural defects. arXiv: 2609.26586v1 [cond-mat.dis-nn]. Sep 22, 2026. 

https://arxiv.org/abs/2609.26586

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

Keywords: gst, defect, order, disorder, transitions, structural defects, 

disclinations, dislocations, dipoles of dislocations, amorphous states, pseudo-band inversions.