# gst: vortex clusters and vortex-filled bubbles in a modified Abelian-Higgs model.

<< (AA) investigate a single-component Abelian-Higgs model with an eighth-order scalar potential whose vacuum manifold consists of two disconnected circles. The model supports two species of vortices and domain walls interpolating between the two vacuum components. (They) find type-1.5-like behavior characterized by nonmonotonic intervortex interactions and bound states of spatially separated vortices. >>

<< Inner-vacuum vortices form clusters through short-range repulsion and long-range attraction, whereas outer-vacuum vortices form vortex-filled bubbles in which a closed domain wall confines multiple inner-vacuum-vortex cores. >>

<< (AA) construct the domain wall analytically, derive the asymptotic vortex-wall interactions, and analyze the fluctuation spectra of coincident multivortices to identify their splitting instabilities. >>

D. Miguélez-Caballero, S. Navarro-Obregón, Muneto Nitta, et al. Vortex clusters and vortex-filled bubbles in a modified Abelian-Higgs model. arXiv: 2610.21930v1 [hep-th]. Oct 15, 2026.

https://arxiv.org/abs/2610.21930

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

Keywords: gst, vortex, bubbles, instability, transitions, short-range repulsion, long-range attraction.

# 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.

# 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: 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: 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.

# gst: mixing, anisotropy, and Lagrangian dispersion in Rayleigh-Taylor turbulence under variable acceleration.

<< ️This (AA) study investigates miscible Rayleigh-Taylor (RT) turbulence subjected to gravity removal or reversal at different stages of its development, using high-resolution numerical simulations and Lagrangian passive-particle tracking. The state of the mixing layer at the switching time, particularly its thickness and turbulent intensity, is shown to control the subsequent evolution. >>

<< ️Gravity reversal transforms the unstable RT layer into a weakly turbulent, stably stratified flow with a thick mixed region. The vertical mass flux and kinetic-energy anisotropy exhibit decaying oscillations whose characteristic period increases with the mixing-layer thickness at reversal and is described by the Brunt-Väisälä frequency. >>

<< ️In contrast, gravity removal eliminates further buoyancy production without imposing a restoring force, allowing the mixing layer to continue broadening through inertial coasting while retaining the large-scale structure inherited from the preceding RT stage. The Lagrangian analysis distinguishes absolute material transport from relative turbulent stirring. >>

<< ️After gravity removal, the vertical velocity correlation remains positive over a comparatively long interval, sustaining both single-particle displacement and particle-pair separation. Gravity reversal instead drives the correlation through zero and induces particle oscillations consistent with the Brunt-Väisälä timescale, thereby suppressing both absolute transport and the relative stretching of initially neighboring particles. >>

<< ️These (AA) results show that the postswitch dynamics are governed jointly by the flow state at the switching time and by whether the modified forcing preserves or actively destroys vertical velocity memory. >>

Dongxiao Zhao, Gaojin Li. Mixing, anisotropy, and Lagrangian dispersion in Rayleigh-Taylor turbulence under variable acceleration. Phys. Rev. Fluids 11, 093903. Sep 18, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/r4vw-jkyc

Also: Dongxiao Zhao, Gaojin Li. Evolution of Rayleigh-Taylor turbulence under vorticity and strain-rate control. arXiv: 2506.07012v1 [physics.flu-dyn]. Jun 8, 2025.

https://arxiv.org/abs/2506.07012

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

Keywords: gst, particles, turbulence, Lagrangian dispersion, Rayleigh-Taylor turbulence, anisotropy, reversal, buoyancy, inertial coasting, particle-pair separation, particle oscillations, vertical velocity memory, Rayleigh-Taylor instability, turbulent mixing.

# gst: rupture dynamics of dense granular films; from liquidlike bursting to solidlike fracturing.

<< ️(AA) investigate the bursting dynamics of dense granular films punctured at imposed controlled liquid pressure. Using high-speed imaging, (They) reveal a two-stage opening process.️ At early times, the hole expands in a liquidlike manner with a nearly circular shape and a constant velocity, though significantly lower than the Taylor-Culick speed. This velocity is modeled by a balance between surface tension and effective surface viscosity, which depends on particle size and liquid depression. >>

<< ️(AA) show that as liquid pressure decreases, the initial opening slows down progressively until it ultimately reaches a jamming state. As the opening progresses, the film undergoes a transition to a solidlike regime, where faceting occurs due to fracture propagation within the granular skeleton. >>

<< ️(AA) show that the characteristic fracture size follows a 𝑡3/4 scaling, consistent with a balance between surface energy release and viscous dissipation induced by liquid redistribution within the 2D granular network. ️These findings advance (Their) understanding of the mechanics of granular films and their transition between fluidlike and solidlike behaviors. >>

Paul Gauthier, Nabil Retailleau, Yacine Khidas, et al. Rupture dynamics of dense granular films: From liquidlike bursting to solidlike fracturing. Phys. Rev. Fluids 11, 094301. Sep 8, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/c9bz-d2yg

Also: particle, fracture, crack, drop, droplet, droploid, bubble, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, fracture, crack, drops, droplets, droploids, bubbles, transitions, fluid-particle interactions, granular fluids, granular films, granular network, bursting dynamics, surface tension, surface viscosity, viscous dissipations, jamming states, surface energy.

# gst: shear v. stretching as drivers for mixing in 3-D porous media flows.

<< ️Solute mixing in porous media results from the interplay between molecular diffusion and the deformation of fluid parcels, which elongates solute elements and steepens concentration gradients in the pore space. >> 

<< ️In three-dimensional porous media, fluid deformation is asymptotically governed by exponential stretching, arising from the chaotic stretching and folding of fluid elements. However, early-time deformation may be dominated by shear, induced by no-slip boundary conditions at grain surfaces, leading to linear elongation. Yet, the persistence and relative contributions of linear shear and exponential stretching to fluid deformation and solute mixing remain poorly understood. >>

<< ️Here, (AA) address this question using numerical simulations of fluid deformation and mixing in body-centered cubic bead packs, where the rate of chaotic stretching can be varied with the direction of flow, while maintaining the same average shear rate. (They) quantify the mean deformation dynamics of elementary surfaces as a function of their initial orientation with respect to streamlines, and their consequences on mixing through Lagrangian methods. >>

<< ️(AA) show that surface elements with certain initial orientations relative to the streamline direction experience a transient phase of shear-dominated deformation at early times, leading to persistently larger deformation compared to those with initial orientations that yield purely exponential growth. By expressing the deformation components in streamline coordinates, (They) derive approximate analytical expressions linking the different components of fluid deformation to shear, helicity, and chaotic stretching. (They) discuss consequences for the mixing of solute sheets and blobs, highlighting generic behaviors as well as differences between these two representations. >>

Manuel Maeritz, Tanguy Le Borgne, Daniel R. Lester, et al. Shear versus stretching as drivers for mixing in three-dimensional porous media flows. Phys. Rev. Fluids 11, 094501. Sep 17, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/4wyw-nkrb

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

Keywords: gst, chaotic advection, fluid deformation, flows in porous media, laminar flows, mixing enhancement, shear flows, chaotic stretching, porous media.

# life: early warning signals can vanish or amplify; dimensionality in complex systems.

<< Early warning signals (EWS), such as increasing variance and autocorrelation, are widely used to anticipate critical transitions associated with saddle-node bifurcations. However, real-world systems are often high-dimensional and multiscale, potentially altering the classical behavior of EWS. >>

<< Here, (AA) investigate how dimensionality, inertia, and red noise influence the detectability of EWS prior to tipping points. (They) show that when observations are not aligned with the critical direction, stable dynamics in orthogonal directions can mask EWS until very near the bifurcation. >>

<< (AA) further demonstrate that second-order dynamics with damping modify the autocorrelation structure and may either enhance or reduce signatures of critical slowing down. >> 

<< Finally, (AA) study how colored noise influences EWS. (Their) results show that the presence and strength of EWS are not universal properties of tipping systems but depend critically on system geometry and stochastic forcing, implying that the absence of detectable EWS does not necessarily rule out an approaching critical transition. >>

Susanne Ditlevsen, Peter Ditlevsen. Early Warning Signals Can Vanish or Amplify: Dimensionality in Complex Systems. arXiv: 2609.01164v1 [math.DS]. Sep 1, 2026.

https://arxiv.org/abs/2609.01164

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

Keywords: gst, noise, transitions, early warning signals (EWS), criticality, saddle-node bifurcations, dimensionality, inertia, red noise, colored noise, tipping points, critical slowing down, stochastic forcing.

# gst: still apropos of particle rafts, Marangoni swimmer pushing particle raft under 1D confinement.

<< Active matter systems, due to their spontaneous self-propulsion ability, hold potential for future applications in healthcare and environmental sustainability. Marangoni swimmers, a type of synthetic active matter, are a common model system for understanding the underlying physics. >>

<< Existing studies of the interactions of active matter with passive particles have mostly focused on the modification of the behavior of the passive particles. In contrast, (AA) analyse here experimentally the impact on the self-propulsion of camphor-infused agarose disks (active) of their interactions with floating hollow glass microspheres (passive) within an annular channel. >>

<< Two distinct regimes are observed: a steady regime with uni-directional motion of the swimmer at low packing fractions (ϕ_ini ≲ 0.45) and an oscillatory regime with to-and-fro motion at higher packing fractions (ϕ_ini ≳ 0.45). In the former, the swimmer pushes nearly the entire particle raft together with it, like a towing cargo, causing a decrease in swimmer speed with increasing packing fraction due to the additional drag from the particle raft. A simplified force-balance model is finally proposed that captures the experimental trend in swimmer speed reasonably well. >>

Abhradeep Maitra, Anupam Pandey, Sebastien Michelin, et al. Marangoni swimmer pushing particle raft under 1D confinement. arXiv: 2508.15205v1 [cond-mat.soft]. Aug 21, 2025.

https://arxiv.org/abs/2508.15205

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

Keywords: gst, particles, waves, instability, transitions, active matter systems, spontaneous self-propulsion, Marangoni swimmers, particle rafts.

# gst: densely packed particle raft at vertically vibrated air-water interface.

<< ️(AA) investigate the dynamics of a dense raft of millimeter-sized granular particles at a vertically vibrated air-water interface, which displays a rich set of patterns and particle dynamics as we vary the vibration amplitude, frequency, and particle packing fraction. >>

<< ️While the classical parametric instability with standing waves still occurs over a certain range of parameters, the measured wave dispersion relations indicate an increasing role of the raft's emergent elasticity at higher packing fractions, where the effective surface tension decreases and the out-of-plane bending modulus increases. >>

<< ️At higher vibration frequencies and lower amplitudes, (They) identify a regime without standing waves. Instead, individual particles exhibit thermal-like motion, with transport crossing over from diffusive to sub-diffusive as the packing fraction increases. >>

<< ️The particle dynamics also display spatial and temporal heterogeneity, as in supercooled liquids. Starting from this regime, when the vibration amplitude is further increased, a large cavity eventually forms inside the raft, whose size and shape depend on the vibration frequency and the injected vibration energy. The cavitation results in the coexistence of free-surface water waves inside the cavity and thermal-like particle motion in the surrounding raft. >>

Xiuhe Yan, Tabitha C. Watson, Hongyi Xiao. Densely packed particle raft at vertically vibrated air-water interface. Phys. Rev. E 114, 025427. Aug 31, 2026.

https://journals.aps.org/pre/abstract/10.1103/95rf-w6fd

arXiv: 2602.17539v2 [cond-mat.soft]. 

https://arxiv.org/abs/2602.17539

Also: particle, waves, instability, transition, elastic, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, waves, instability,  transitions, elasticity, chaos, granular particles, air-water interface, raft elasticity, emergence of patterns, surface & interfacial phenomena, granular materials.

# life: mudskippers use tail thrusting to help crutching to move on mud of various wetness.

<< ️At the water-land interface, amphibious fishes encounter wet flowable substrates made of granular solid-water mixtures, which can stay solid or flow like a fluid. As these substrates become wetter or drier, their yield strength (at which solid-fluid transition occurs) and cohesion (how sticky they are) both change, challenging locomotion. Despite substantial understanding of tetrapod locomotion on flowable substrates (mostly dry sand), we know little about how amphibious fishes cope with wet flowable substrates of various wetness. >>

<< ️Here, (AA) studied mudskippers on clay mud of controlled, variable wetness over the range where solid-fluid transition occurs. As mud became wetter, its strength decreased by 100-fold, leading the animal to sink deeper, with larger areas of body and fins contacting mud. By contrast, mud stuck most easily at intermediate wetness. The increased sinkage and contact and stickiness change caused more mud to stick to and pull against the animal on wetter mud. >>

<< ️(AA) also tested dry mud, which stuck to animal fins as its mucus dried. Despite these challenges, the mudskipper predominately used a conserved crutching gait on all except the wettest mud tested, with a modest performance reduction. When normal crutching became less effective, the animal assisted it with tail thrusting, by bending and straightening it to push downward and backward to generate additional thrust and lift, or even thrusting the tail to jump. >>

<< ️These observations suggest that mudskipper's crutching motor program is well adapted to its native muddy substrates but inflexible, with most novelty in tail use. >>

Divya Ramesh, Gargi Sadalgekar, Jiangqi Tan, et al. Mudskippers use tail thrusting to help crutching to move on mud of various wetness. arXiv: 2609.00564v1 [physics.bio-ph]. Sep 1, 2026.

https://arxiv.org/abs/2609.00564

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

Keywords: life, locomotion, walk, walking, dance, transitions, wet flowable substrates, granular solid-water mixtures, solid-fluid transitions, mudskippers. 

# gst: braids of three strands and geodesics shooting in SL_2(R).

<< ️(AA) describe in detail and provide computer code for constructing optimal geometric braids of three strands from algebraic data encoding the braiding pattern. >>

<< ️The exposition is complete and multi-pronged, aimed at a broad spectrum of readers. (Numerous figures are the backbone of the narrative and should be viewed in color.) >>

Jaroslaw (Jarek) Kwapisz. Braids of Three Strands and Geodesics Shooting in SL_2(R). arXiv: 2608.21484v1 [math.DG]. Aug 21, 2026.

https://arxiv.org/abs/2608.21484

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

Keywords: gst, perception, metamorphosis, transitions. 

# gst: self-organizing chimera states in adaptive networks.

<< ️(AA) propose a minimal adaptive network model with product-form coupling that reduces dimensionality while capturing key features of synaptic plasticity. The system spontaneously self-organizes into adaptive chimera states, where identical oscillators separate into synchronized and desynchronized groups through adaptive weight dynamics. >>

<< These adaptive chimeras organize into branches with fixed coherent cluster fraction and exhibit transitions between stationary, breathing, and chaotic collective dynamics, revealing a collective bifurcation structure. Crucially, the resulting attractor landscape is highly multistable: repeated cluster reorganizations generate distinct dynamical pathways that coexist within the same parameter regime and depend sensitively on initial conditions. >>

Felix Augustsson, Rok Cestnik, Matthias Wolfrum, et al. Self-organizing Chimera States in Adaptive Networks. arXiv: 2608.20517v1 [nlin.AO]. Aug 20, 2026.

https://arxiv.org/abs/2608.20517

Also: chimera, self-assembly, network, chaos, transition, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, self-assembly, networks, transitions, brain, oscillators, adaptive chimera, synaptic plasticity, synchronized- desynchronized stationary states, breathing, chaotic collective dynamics, collective bifurcations, multistable attractors.

# gst: non-normal route to chaos

<< Deterministic chaos is usually associated with local spectral expansion: Jacobian eigenvalues are expected to exceed unity somewhere on the attractor. (AA) show that this view is incomplete in dimensions 𝑑>1. For non-normal Jacobians, pointwise spectral stability can suggest everywhere local contraction, while nonorthogonal eigenvectors still allow transient singular-vector amplification. >>

<< (AA) construct four low-dimensional deterministic maps realizing this mechanism: partition-reinjected, phase-prescribed, feedback-driven, and affine-reinjected non-normal routes to chaos. In all cases, the sampled one-step Jacobian remains spectrally stable at every point on the attractor away from switching boundaries, with the eigenvalues of the common planar core fixed inside the unit disk. Nevertheless, increasing non-normality raises the maximal Lyapunov exponent from negative to positive values, corresponding to sustained asymptotic chaos, not transient chaos. Across the four classes, the common signature is spectral radius 𝜌max traj<1, singular value 𝜎max traj>1, maximal Lyapunov exponent 𝜆1>0, and an increase of attractor dimension. >>

<< These examples identify non-normality and recurrent reinjection of transiently amplified directions as a deterministic route to chaos distinct from eigenvalue instability. >>

D. Sornette, V.R. Saiprasad, V. Troude. Non-normal route to chaos. Phys. Rev. E 114, 024222. Aug 27, 2026.

https://journals.aps.org/pre/abstract/10.1103/z9qv-51yj

arXiv: 2603.08191v2 [nlin.CD]. 

https://arxiv.org/abs/2603.08191

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

Keywords: gst, attractor, chaos, transitions

# gst: skimming transition in flexible granular sweeping.

<< ️A flexible body placed in a steady flow bends to reduce drag. This self-streamlining is a hallmark of fluid-structure interaction (FSI). Granular-structure interaction is equally ubiquitous in nature. However, it remains poorly understood. >>

<< ️Thus, (AA) investigate inertial granular-structure interaction (IGSI). Specifically, ejection induced by a flexible plate sweeping a granular bed is experimentally examined. (They) find that a faster sweep results in less ejection, particularly for a flexible plate. >> 

<< ️To understand the underlying physics of this behavior, a dimensionless number Sk is introduced as the ratio of the plate elastic timescale to the sweep timescale. At Sk≲1, the plate deflection follows the self-streamlining law of FSI and induces substantial ejection. At Sk≳1, on the other hand, the plate skims the bed and the mass of ejected grains decreases sharply. Sk organizes IGSI as the granular counterpart of FSI. >>

Y. Ochi, H. Katsuragi. Skimming transition in flexible granular sweeping. arXiv: 2608.15069v1 [cond-mat.soft]. Aug 15, 2026.

https://arxiv.org/abs/2608.15069

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

Keywords: gst, grain, transitions, fluid-structure interaction (FSI), inertial granular-structure interaction (IGSI)

# behav: amoeboid swimming of active vesicles.

<< ️(AA) investigate the shape dynamics and migration of weakly deflated active vesicles driven by processes acting either directly in the membrane or transmitted by the cytoskeleton. For a force-free vesicle, local membrane incompressibility suppresses rigid-body translation, so that migration arises from time-dependent shape deformations. Assuming small excess area enables a systematic analysis of the coupled deformation and migration dynamics in free space, i.e. in the absence of substrate adhesion or confinement. >>

<< ️Depending on the strength and frequency of the activity, the vesicle exhibits several dynamical regimes, including synchronized oscillations, quasiperiodic shape changes, transitions between non-propelling and propelling states, and intermittent motion. >>

Reiner Kree, Annette Zippelius. Amoeboid swimming of active vesicles. arXiv: 2607.14714v1 [cond-mat.soft]. Jul 16, 2026.

https://arxiv.org/abs/2607.14714

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

Keywords: behavior, transitions, 

swim, vesicles, weakly deflated active vesicles, migration, time-dependent shape deformations, synchronized oscillations, quasiperiodic shape changes, transitions between non-propelling, propelling states, intermittent motion. 

# gst: apropos of stretching during transitions, singularities in soft matter systems.

<< ️When a liquid thread pinches off, its neck thins as it separates into two unconnected regions. Using continuum mechanics, we can predict that the neck reaches zero radius in finite time while its curvature grows without bound. Together, the vanishing neck and diverging curvature form a finite-time singularity. >>

<< ️However, a real fluid does not realise these mathematical limits as molecular or material physics takes over once the neck becomes sufficiently small. Similar singularities arise throughout soft matter whenever a smooth continuum description is used at vanishing length scales. >>

<< ️This (AA) review asks what the shrinking region forgets, what it retains, and which material length, time, or stress cuts off the apparent divergence. The dynamics near a singularity often become self-similar, with profiles at different times collapsing onto one shape when rescaled by the shrinking local length. Sometimes that collapse is universal enough that the surrounding geometry and forcing no longer determine the local dynamics. Nonetheless, the measured output could still depend on how the shrinking region is fed by the surrounding flow and on the small-scale physics that finally replaces the ideal divergence. >>

<< ️Complex fluids and active matter change the same local balance by bringing their own timescales into the shrinking region. Beyond interfaces, the same logic applies when the localised object is a stress concentration or a defect in geometry or order rather than a moving surface. Singularities matter because they show where continuum theory stops being the relevant description and how the small-scale cutoff sets the outputs that count in printing, coating, aerosols, and stretchable solids. >>

Vatsal Sanjay. Singularities in Soft Matter Systems. arXiv: 2608.11060v1 [cond-mat.soft]. Aug 11, 2026.

https://arxiv.org/abs/2608.11060

Also: elastic, singularity, transition, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elasticity, singularity, transitions, collapse, soft matter