# 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. 

# gst: the ultimate state of elastic turbulence.

<< The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. >>

<< In this work, using direct numerical simulations of turbulence in a triperiodic box, (AA) show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). >>

<< In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model. >>

Piyush Garg, Marco Edoardo Rosti. The ultimate state of elastic turbulence. arXiv: 2608.26479v1 [physics.flu-dyn]. Aug 27, 2026.

https://arxiv.org/abs/2608.26479

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

Keywords: gst, elasticity, turbulence, chaos, vanishing viscosity, inertial turbulence, elastic turbulence, elastic stress, viscoelastic fluids, polymer relaxation.

# 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: hypothesis of stable rotating vortex clusters in three-dimensional quantum droplets

<< ️(AA) predict a new type of stable three-dimensional (3D) vortex quantum droplets in binary Bose-Einstein condensate arranged into ring clusters that per-sistently rotate in the external potential. In contrast to clusters composed from localized quantum droplets, the states introduced here represent interacting vortex lines with identical topological charges nested in common 3D envelope and existing in much broader parameter range in comparison with local-ized quantum droplets. >>

<< ️The intricate interplay between mean-field nonlinearity of Bose-Einstein condensate, quantum fluctuations described by Lee-Huang-Yang correction, Coriolis force arising due to rotation, and external potential leads to substantial variations of cluster shape upon increase of its rotation frequency. >>

<< ️Rotating vortex clusters bifurcate from single-vortex quantum droplets and exist only above critical value of the rotation frequency that decreases with increase of chemical potential and depends on the number of vortex lines in the cluster. The radius of the cluster decreases with increase of rotation frequency and weakly varies with chemical potential, which determines mostly localization of the individual vortices in cluster and overall width of its envelope. >>

<< ️Vortex droplet clusters are very robust objects existing in stable form in wide intervals of the number of particles for any number (odd or even) of vortex lines forming them. (AA) results may open the route to observation of stable arrays of vortex lines of different configurations per-forming regular collective motion in condensate. >>

Liangwei Dong, Yaroslav V. Kartashov. Stable rotating vortex clusters in three-dimensional quantum droplets. arXiv: 2608.24036v1 [nlin.PS]. Aug 25, 2026.

https://arxiv.org/abs/2608.24036

Also: Vortex solitons in twisted circular waveguide arrays. Ago 22, 2022. https://flashontrack.blogspot.com/2022/08/gst-vortex-solitons-in-twisted-circular.html

Also: vortex, drop, droplet, droploid, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, drops, droplets.

# 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: foliated by invariant quadrics, outer contact billiards.

<< ️(AA) introduce outer contact billiards as an odd dimensional counterpart to outer symplectic billiards. Until now, outer billiards have only been considered in even dimensional symplectic vector spaces. By projectivizing outer symplectic billiards, (They) obtain outer contact billiards, where the affine midpoint condition descends to its projective analog, namely harmonic conjugation. (They) prove that outer contact billiards generate contactomorphisms. >>

<< ️For quadratic surfaces in RP^3, (AA) show that the correspondence is completely integrable: its domain is foliated by invariant quadrics and, on each leaf, the dynamics is determined by the iteration of an explicit linear transformation. (They) also establish two rigidity results for periodic trajectories: outer contact billiards admit no 3-periodic orbits and, among quadratic tables, only one admits 4-periodic orbits. >>

Ana Chavez Caliz, Connor Jackman. Outer Contact Billiards. arXiv: 2608.19393v1 [math.DS]. Aug 19, 2026.

https://arxiv.org/abs/2608.19393

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

Keywords: gst, billiard, outer contact billiards, symplectic billiards, harmonic conjugation, contactomorphisms, foliated domain. 

# gst: dissipative self-assembly of colloidal suspensions.

<< Suspensions of paramagnetic colloids exhibit kinetic arrest in strong magnetic fields. Through a dissipative process of toggling the field on and off, suspensions self-assemble into dense and dynamic steady-state phases. >>

<< (AA) construct a phase diagram using 𝑘-means clustering analysis based on domain elongation, α-shapes, contour metrics, and the degree of phase separation. (They) identify six characteristic structural regimes: a structureless phase, an arrested structure, sheets, ribbons, a spiky phase, and a transient fluid-fluid regime. >>

<< (AA) further report the distribution and alignment of domains and the generality of the results. (They) model self-assembled domain shapes using an equilibrium mean-field magnetostatic energy calculation, which predicts the surprising emergence of highly anisotropic structures driven by the sample's confinement. >>

Jason Conradt, Eric M. Furst. Dissipative self-assembly of colloidal suspensions. Phys. Rev. E 114, 025416. Aug 21, 2026.

https://journals.aps.org/pre/abstract/10.1103/8h2w-vhcn

arXiv: 2603.14637v1 [cond-mat.soft]. 

https://arxiv.org/abs/2603.14637

Also: dissipation, self-assembly, colloids, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, dissipation, self-assembly, colloids, anisotropic structures, steady-state phases. 

# 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: flip rate prediction in the double pendulum.

<< ️The intermediate-energy double pendulum is a prototypical chaotic system. Despite its irregular motion, it exhibits recurrent flips - events in which one of the arms passes over the top. >>

<< ️(AA) develop a statistical prediction for the mean flip rate in terms of phase space flux. Applying this flux-based approach to the equal-mass, equal arm ("egalitarian") double pendulum, (They) find excellent agreement between the statistical prediction and numerical simulations: ensemble-averaged flip rates agree at about the 1% level, while even the statistics of individual chaotic trajectories agree at the few-percent level, quantifying the validity of the ergodic approximation. This agreement holds for flips of either arm and over a broad range of energies. This flux-based approach is closely related to that used for the egalitarian three-body system. >>

<< ️A central role is played by the saddle orbits: periodic orbits that tend to the stable saddle eigenmode as the energy approaches the saddle energy from above and approximately follow the ridge of the potential at higher energies. These orbits provide a natural dividing surface for defining flips while avoiding recrossings. Indeed, the resulting distribution of crossing times exhibits a distinct gap. >>

<< ️(AA) also present two alternative simplified dividing surfaces, one of which is based on an accurate analytic approximation to the saddle orbits. >>

Peleg Haham, Barak Kol. Flip rate prediction in the double pendulum. arXiv: 2608.20276v1 [nlin.CD]. Aug 20, 2026.

https://arxiv.org/abs/2608.20276

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

Keywords: gst, pendulum, double pendulum, chaos, recurrent flips, egalitarian three-body system, saddle orbits, crossing times.

# 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: 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

# gst: stabilities in the attachment of a particle to a pendant droplet.

<< ️Attachment of a particle to a pendant drop was experimentally investigated by Feng et al. (2022)]. The attachment force on the particle, consisting of the surface tension force and the pressure force, can overcome the gravity force. The attachment in equilibrium is possibly hard to maintain in practice due to instabilities. >>

<< This (AA) paper aims to discover the condition for the particle to be successfully attached under the liquid drop (bridge) through analyzing the stabilities of the capillary system. With disturbances potentially existing for both the liquid bridge and the particle, the two corresponding types of stabilities are studied. >>

<< Considering the cases with liquid surfaces checked to be stable, (AA) find four regimes for the attachment of the particle: the regimes of stable attachment, possibly stable attachment, overloaded attachment, and nonphysical attachment. Only the first two regimes mean feasible attachments in practice. (Their) prediction of feasible attachments agrees well with Feng et al., indicating the validity of (Their) stability theory. Whether for fixed-density particles of different sizes or fixed-size particles of different densities, the attachment capability for the liquid bridge first decreases, then increases, and decreases again as the volume of the liquid bridge increases. This can guide practice for lifting particles of higher weight with the pendant drop. >>

Wanqiu Zhang, Fei Zhang, Xinping Zhou. Stabilities in the attachment of a particle to a pendant droplet. Phys. Rev. Fluids 11, 084001. Aug 7, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/b63k-qk8s

Also: drop, droplet, droploid, particle, stability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, particles, stability, fluid-particle interactions, interfacial flows, liquid bridges, surface & interfacial phenomena.

# 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.