# 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: buckling prediction for nonlinear elastic beams with soft inclusions.

<< (AA) develop an efficient and accurate multiscale computational framework for predicting the buckling and post-buckling behaviour of elastic beams containing periodically distributed soft inclusions. The framework extends (Their) previous multiscale, patch, computational homogenisation for linear elasticity by incorporating nonlinearity, and thus enables accurate prediction of both the buckling onset and the subsequent post-buckling response. >>

<< The (AA) results show that reducing the inclusion stiffness lowers both the critical buckling strain and the critical buckling stress, indicating an increased susceptibility to instability, while producing a milder post-buckling response with smaller transverse deflections and stress drops. Eigenvalue analysis of the Jacobian matrix accurately predicts the onset of instability and the corresponding critical strain and stress. Bifurcation diagrams of the nonlinear buckled configurations under compressive loading, and a quantitative analysis of the effect of the interpolation order on the predicted buckling and post-buckling responses, are also presented. >>

<< Comparisons with full-domain simulations demonstrate that the proposed framework accurately predicts both the buckling threshold and the post-buckling behaviour while substantially reducing the computational cost. The methodology is readily extendable to heterogeneous beams, plates, shells, and other engineering structures. >>

Thien Tran-Duc, J.E. Bunder, A.J. Roberts. Buckling Prediction for Nonlinear Elastic Beams with Soft Inclusions. arXiv: 2609.02956v1 [math.NA]. Sep 2, 2026.

https://arxiv.org/abs/2609.02956

Also: elastic, instability, transition, fracture, crack, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elasticity, instability, transitions, buckling, post-buckling, buckling threshold, elastic beams, linear- nonlinear elasticity, criticality, critical buckling strain, critical buckling stress. 

# 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: 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.

# 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.