# gst: using analogues to investigate error growth and predictability in turbulence.

<< ️In this study, (AA) revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, (They) successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. >>

<< (AA) analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. (They) interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. >>

<< ️These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events. >>

Carlos Granero-Belinchon, Mickaël Bourgoin, Bérengère Dubrulle. Using analogues to investigate error growth and predictability in turbulence. arXiv: 2610.11796v1 [physics.flu-dyn]. Oct 8, 2026.

https://arxiv.org/abs/2610.11796

Also: chaos, turbulence, error, analogy, intermittency, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, turbulence, error, analogy, intermittency, rare events, Lorenz's error growth regimes, chaotic exponential regime, algebraic regime of spontaneous stochasticity, saturation regime, transitions.

# life: scaling laws for the spread of defection in evolutionary games on networks.

<< ️(AA) study the spread of defection in evolutionary games on networks using deterministic replicator dynamics posed on graphs. Each node hosts a mixed population of cooperators and defectors interacting through a Prisoner's Dilemma payoff matrix, with nearest-neighbor coupling determined by the network adjacency matrix. >>

<< ️(AA) develop two complementary analytical approximations that quantify how network architecture influences the timescale over which cooperation collapses. In a weak-coupling regime, internode interactions act as a small perturbation, yielding explicit approximate solutions on general graphs. For networks with strongly heterogeneous degree distributions, (They) derive a quasisteady approximation based on the natural separation of timescales between high- and low-degree nodes. >>

<< ️Using these approximations, (AA) introduce a defection spreading-time metric and show that the collapse of cooperation exhibits robust power-law scaling with system size across a broad range of network topologies. Analytical predictions are validated numerically on lattices, star graphs, incrementally connected graphs, small-world networks, and scale-free networks. >>

<< ️The (AA) analysis shows that, to leading order, defection dynamics are controlled by local nodal degree, while network coupling and degree heterogeneity provide secondary corrections that influence the global collapse dynamics. (They) further show that increasing degree heterogeneity increases the average defection time, providing a complementary spectral interpretation through the principal eigenvalue of the adjacency matrix and related measures of graph irregularity. >>

<< ️These results quantify how network architecture controls the transient dynamics of evolutionary collapse and establish new connections between evolutionary game dynamics and spreading processes on networks. >>

M. Giles, P.K. Newton. Scaling laws for the spread of defection in evolutionary games on networks. Phys. Rev. E 114, 044301. Oct 1, 2026.

https://journals.aps.org/pre/abstract/10.1103/25qf-sfsw

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

Keywords: games, networks, collapse, transitions, Prisoner's Dilemma, defection, defection spreading-time, internode interactions, transient dynamics.

# life: 3-D microprinting anisotropic and deformable active matter.

<< ️Active colloidal particles are a versatile model system for exploring nonequilibrium physics in motile matter. To date, most experimental realizations have focused on spherical particles, largely due to fabrication constraints. However, theoretical and computational studies have long predicted that particle anisotropy and flexibility can dramatically enrich single-particle dynamics, interparticle interactions, and emergent collective behavior. >>

<< ️Here, (AA) highlight recent advances in the fabrication of anisotropic active particles and architectures enabled by the unprecedented design freedom of three-dimensional microprinting. (They) discuss how additive manufacturing is expanding the accessible parameter space of active soft matter, allowing precise control over shape, location of active forces, and functionality at the microscale. These advances enable the development of new model platforms for uncovering fundamental principles of active and soft matter, and simultaneously pave the way toward microrobotic systems with programmable dynamics and emergent functionalities. >>

Mengshi Wei, Daniela J. Kraft. Three-dimensional microprinting anisotropic and deformable active matter. Phys. Rev. E 114, 041001. Oct 2, 2026.

https://journals.aps.org/pre/abstract/10.1103/vvnp-l1sb

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

Keywords: gst, particles, motile matter, soft matter, active colloidal particles, three-dimensional microprinting, colloids, additive manufacturing.

# brain: stability of phase-locked states of weakly coupled Izhikevich neurons.

<< ️The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical system, which means the methods for applying weakly coupled oscillator theory developed for continuous dynamical systems cannot be applied. Therefore, the collective behaviour of coupled Izhikevich model has not been fully studied. >>

<< ️To (Their) knowledge, (AA) carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model (They) study the existence and stability of phase-locking states and how these vary with parameters. >>

<< ️Moreover, (AA) find an interesting connection between the stability of anti-phase states of the phase model and the bifurcation behaviour of the uncoupled Izhikevich model itself. The accuracy of the prediction of the phase model is supported by simulations of two weakly coupled Izhikevich neurons. >>

XinYe Cheng, Sue Ann Campbell. Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons. arXiv: 2610.04025v1 [q-bio.NC]. Oct 2, 2026.

https://arxiv.org/abs/2610.04025

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

Keywords: gst, brain, behavior, collective behavior, weakly coupled oscillator theory, phase models, phase-locking states, synchronization, bifurcations, discontinuous bifurcations.

# gst: apropos of survival, diffusion with stochastic resetting in the presence of a delta killing trap; drift-controlled survival regimes.

<< ️(AA) study a one-dimensional diffusive particle subject to stochastic resetting to its initial position, in the presence of an imperfect, localized target that can absorb (kill) the particle, modeled by a delta-function killing rate. >>

<< ️The central question is how stochastic resetting competes with drift-induced transience and the target's finite reactivity. >>

 

<< ️The long-time behavior separates into distinct regimes. Without resetting, unbiased diffusion exhibits the recurrent algebraic survival law 𝑆⁡(𝑡)∼𝑡−1/2, whereas any nonzero drift renders the motion transient with respect to the target and leaves a nonzero ultimate survival probability. >>

<< ️By contrast, any 𝑟>0 and 𝑘>0 repeatedly renew encounters with the target and restore eventual absorption, yielding an exponential survival law 𝑆⁡(𝑡)∼𝐴⁢𝑒−𝜃⁢𝑡. The decay rate 𝜃 is given by the dominant (rightmost) pole of the Laplace transform, and the surviving density converges after normalization to an explicit quasistationary profile. The driftless and perfectly absorbing limits recover standard resetting results. >>

<< ️These (AA) formulas provide a unified description of the crossover between recurrence-controlled, transience-controlled, and renewal-controlled survival. >>

A. Mazzolo. Diffusion with stochastic resetting in the presence of a delta killing trap: Drift-controlled survival regimes. Phys. Rev. E 114, 044105. Oct 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/3s1c-k5vg

arXiv: 2609.22527v1 [cond-mat.stat-mech]. Sep 18, 2026.

https://arxiv.org/abs/2609.22527

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

Keywords: gst, particles, behavior, transitions, stochasticity, stochastic processes, stochastic resetting, drift-induced transience, target finite reactivity, survival probability, long-time behavior, unbiased diffusion, absorption, decay rate, recurrence-controlled survival, transience-controlled survival, renewal-controlled survival, brownian motion, diffusion.

# 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.