# gst: avalanche assemblies in arbitrary connection topologies.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

https://arxiv.org/abs/2609.25970

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

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

# gst: topological phase transition driven by structural defects.

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

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

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

https://arxiv.org/abs/2609.26586

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

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

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

# gst: disorder-promoted stability.

<< Previous studies of network dynamics have suggested that heterogeneity among nodes inhibits stability, at odds with the ubiquity of inherently heterogeneous natural and engineered systems. >>

<< ️Here, (AA) show that this conclusion arises from model reductions introduced for mathematical tractability and breaks down when nodal dynamics are higher-dimensional, yielding non-Hermitian Jacobians. In such systems, including neural, power-grid, and material networks, nodal heterogeneity can instead enhance stability, even when parameters are randomly disordered. >>

<< ️Non-Hermiticity also underlies the stabilizing effects of network heterogeneity, which can arise even in one-dimensional nodal dynamics through nonreciprocal interactions, as shown for ecological networks. >>

<< ️(AA) framework reveals disorder not as a liability but as a general resource for stabilizing complex systems. >>

Arthur N.Montanari, Pietro Zanin, Adilson E.Motter. Disorder-promoted stability. arXiv: 2609.25226v1 [cond-mat.dis-nn]. Sep 21, 2026.

https://arxiv.org/abs/2609.25226

Science. 393: 6817, 1241-1249. Sep 17, 2026. DOI: 10.1126/science.aeg3946.

https://www.science.org/doi/10.1126/science.aeg3946

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

Keywords: gst, noise, disorder, networks.

# 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: odd slip at chiral active surfaces.

<< ️Odd slip at solid-liquid interfaces, characterized by a velocity component perpendicular to the applied shear stress, introduces a novel class of odd transport phenomena with transverse momentum transfer at boundaries, distinct from odd viscosity, odd elasticity, or odd diffusivity. This effect arises on chiral active surfaces with persistent energy input and defined handedness, such as carpets of rotating biological or synthetic cilia with flexible anchoring. Although odd slip itself is dissipationless, its maintenance comes at an energetic cost, which we estimate from the microscopic model. With respect to its orientation dependence, odd slip can be classified as pseudo-scalar or pseudo-vectorial. >>

<< ️(AA) use a perturbative expansion to determine the resistance tensors of problems with different levels of broken symmetries. They reveal how the surface chirality and body asymmetry together violate the Onsager symmetry, but uphold the Onsager-Casimir reciprocity. Strikingly, suspensions of particles with odd slip embedded in a conventional Newtonian bulk fluid exhibit odd viscosity, providing a new minimal mechanism for its emergence beyond current microscopic models. >>

Yuto Hosaka, Andrej Vilfan. Odd slip at chiral active surfaces. arXiv: 2609.17005v2 [cond-mat.soft]. Sep 16, 2026. 

https://arxiv.org/abs/2609.17005

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

Keywords: gst, particles, solid-liquid interfaces, chiral active surfaces, surface chirality, parity-violating phenomena, shear stress, odd viscosity, odd diffusivity, odd elasticity, odd slip, broken symmetries. 

# gst: how turbulent flows grow vorticity at a point.

<< ️(AA) describe how strong vorticity fluctuations appear in three-dimensional incompressible turbulence driven by a large-scale random force. By combining analytical and numerical methods, (They) construct a vorticity instanton: the most probable force history driving the flow to a prescribed large vorticity at a given point and time. >>

<< ️(AA) show how the smooth, large-scale force produces a long vortex filament with a thin, viscous-scale core. (Their) main finding is that the standard mechanism of amplifying a vortex tube through radial compression and axial stretching is only effective up to a threshold value. Producing vorticity above the threshold requires an additional ingredient: vorticity waves propagating along the tube. >>

<< ️The final vorticity is the result of two colliding waves. This mechanism has striking similarities to the one recently suggested by OpenAI for creating infinite vorticity in finite-time Navier--Stokes blow-up. >>

Timo Schorlepp, Vladimir Rosenhaus, Gregory Falkovich. How turbulent flows grow vorticity at a point. arXiv: 2609.13056v1 [physics.flu-dyn]. Sep 11, 2026.

https://arxiv.org/abs/2609.13056

Also: vortex, turbulence, random, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, turbulence, randomness, waves, vorticity instanton, vortex filaments, colliding waves.

# gst: extreme events in an active fluid medium.

<< ️(AA) observe the emergence of extreme events in an active fluid involving two distinct chemical species that regulate active stress. One species is slow diffusing and the other is fast diffusing, and the growth of the fast-diffusing species is modelled using a nonlinear logistic term. >>

<< ️(AA) demonstrate the presence of extreme events in the temporal evolution of the concentrations, as well as in the spatial profile of the system,in regimes of merging-emerging soliton-like dynamics and spatio-temporal chaos, through analysis of the time-series, bifurcation diagrams, probability distribution functions of the concentration of the two species, return maps and distributions of inter-event intervals. >>

<< ️Interestingly, (They) also find evidence of pronounced bunching of extreme events and super-extreme events in the slow chemical species in the soliton-like regime. (They) go on to systematically explore the dependence of the extreme event occurrences on the Péclet number and the strength of the nonlinear growth term, and find that the probability of extreme events increases after a critical Péclet number, while increasing the nonlinearity suppresses extreme events. >>

<< ️Lastly, in order to gain further insight, (AA) investigate a modified mode-truncated reduced order model comprising of coupled differential equations mimicking this active fluid system. (They) find that this reduced order model also exhibits extreme events whose emergence is correlated with a sudden expansion in attractor size due to a crisis arising from attractor collision. >>

<< ️So these results demonstrate the existence of extreme events in an active fluid system, and are of potential relevance to biological phenomena where active transport plays an important role. >>

Joydeep Das, Abhishek Chaudhuri, Sudeshna Sinha. Extreme Events in an Active Fluid Medium. arXiv: 2609.14334v1 [nlin.PS]. Sep 13, 2026.

https://arxiv.org/abs/2609.14334

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

Keywords: gst, chaos, solitons, attractors, extreme events, merging-emerging soliton-like dynamics, soliton-like regimes, criticality, active transport.

# gst: permeability of deforming soft particle packs.

<< ️The permeability of the fluid between packs of particles is an important parameter for a range of natural and industrial applications. Here, (AA) start from experiments in which soft spherical particles—“soft balls”—are compressed uniaxially, resulting in particle-particle flattening and an overall decrease in interstitial volume fraction 𝜙 down to very low values. >>

<< ️During deformation, the soft particle packs were scanned in three dimensions using x-ray tomography; (AA) segment these data to isolate the fraction between the particles. (They) then run lattice Boltzmann fluid flow simulations through the domains to determine the permeability. >>

<< ️Additionally, (AA) determine the specific surface area 𝑠 and 𝜙. Together, (They) use these parameters to test and validate a semiempirical extension to a theoretical percolation model, to propose a framework for predicting permeability in deforming soft particle systems. >>

<< ️Once validated, (AA) compare this model to the permeability of the fluid in packs of hard particles and during particle sintering; (They) conclude that this model is applicable to a wide range of initially particulate systems with all the geometric information encoded in 𝑠. >>

Jérémie Vasseur, Fabian B. Wadsworth, Jingwei Zhang, et al. Permeability of deforming soft particle packs. Phys. Rev. E 114, 035424. Sep 18, 2026.

https://journals.aps.org/pre/abstract/10.1103/zpm1-lp4n

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

Keywords: gst, particles, percolation, permeability, flows in porous media, granular compaction, laminar flows, mechanical deformation, granular materials.

# 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.

# gst: collective hysteresis and multistability in threshold networks.

<< ️In a mechanistic model of the dawn chorus, Kaye showed that heterogeneous activation thresholds and a shared feedback signal determined by the population's active fraction can produce abrupt collective activation and hysteresis. >>

<< ️(AA) extend this mechanism to a network of interacting agents. Each node has a continuous activation level, and a nonnegative row-stochastic matrix determines how node activities contribute to individual feedback. (They) prove that sufficiently weak feedback yields a unique globally attracting equilibrium. For all feedback strengths, the homogeneous dynamics exactly reproduce Kaye's scalar equation; consequently, network topology does not alter the folds or cusp of the homogeneous branch, and no heterogeneous mode becomes unstable before the homogeneous mode. >>

<< ️For equitable partitions, the network admits an exact quotient system in which nodes within a block receive the same aggregate input from every block. When blocks are uncoupled, the quotient reduces to independent copies of Kaye's scalar equation. (AA) show that every assignment of stable scalar equilibria to blocks persists under sufficiently weak interblock coupling, producing a combinatorial family of stable quotient equilibria that lift to stable full-network equilibria and remain under small perturbations that break exact equitability. >>

<< ️For two symmetrically coupled blocks, branches with unequal block activities terminate at a pair of symmetry-related cusp bifurcations. Near the onset of bistability, (AA) derive scaling laws for the interblock coupling at which these bifurcations occur, the activity difference between the blocks at bifurcation, and the corresponding shift of the external stimulus from the scalar cusp. Numerical continuation confirms the scaling laws for gamma, logistic, and normal threshold distributions. >>

Moses Boudourides. Collective Hysteresis and Multistability in Threshold Networks. arXiv: 2609.10580v1 [cs.SI]. Sep 5, 2026.

https://arxiv.org/abs/2609.10580

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

Keywords: gst, hysteresis, collective hysteresis, networks, threshold networks, stability, bistability, multistability, randomness, small perturbations, bifurcations, cusp bifurcations, Kaye's dawn chorus, stochasticity, heterogeneous activation thresholds, weak feedbacks, shared feedback signals, attracting equilibrium.

# gst: reconstructing the information processing capacity of physical systems from noisy observations.

<< ️Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. >>

<< ️In this work, (AA) clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, (They) show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. (They) explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. (They) then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. >>

<< ️At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. (AA) find the same advantage in a quantum reservoir subject to unavoidable measurement noise. (Their) results provide a general route to recovering the computational structure of noisy physical systems from finite observations. >>

Shun Kotoku, Rodrigo Martínez-Peña, Takatomo Mihana, et al. Reconstructing the information processing capacity of physical systems from noisy observations. arXiv: 2609.11268v1 [nlin.AO]. Sep 10, 2026.

https://arxiv.org/abs/2609.11268

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

Keywords: gst, noise, information processing capacity (IPC), covariance reconstruction by orthogonal projection (CROP), stochasticity.

# gst: thermodynamics of bouncing grains.

<< When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. >>

<< Using a heterogeneous, nonresonating plate, (AA) investigate experimentally this type of diffusion. (They) find that, for the most part, it is comparable to classical molecular diffusion. (They) can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. (They) also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. >>

<< However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, (Their) experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. >>

<< Finally, (AA) propose an expression for the heat flux associated to the nonequilibrium steady state predicted by this new relation and test it against observations. >>

O. Devauchelle, P. Popović, P. Szymczak, et al. Thermodynamics of bouncing grains. Phys. Rev. E 114, 025420. Aug 24, 2026.

https://journals.aps.org/pre/abstract/10.1103/zlsc-w7m4

arXiv: 2606.05930v1 [cond-mat.stat-mech]. Jun 4, 2026.

https://arxiv.org/abs/2606.05930

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

Keywords: gst, particles, active brownian particles, brownian ratchet, granular materials, bouncing grains, vibrating plate, molecular diffusion, fluctuation-dissipation.

# gst: hierarchy in Gilbert's tessellation; multifractal behavior.

<< ️(AA) have introduced two types of hierarchies in a classical Gilbert tessellation. The cascading process that follows gives rise, in both cases, to a tile area distribution function that fits surprisingly well with a generalized gamma function. The latter is a truncated power function which, in turn, in the spirit of Brown’s sequential fragmentation theory, is derived from a stretched exponential hazard function that is also truncated. >>

<< ️This theoretical finding finds a natural counterpart in the experimental observations of Kooij and coworkers [S. Kooij et al., Nat. Commun. 12, 2521 (2021)], according to which the fragmentation of a brittle sample follows two distinct regimes: a random breakup that gives rise to a simple exponential distribution of mass fragments (canonical Gilbert), whereas a hierarchical crushing leads to a power-law distribution (hierarchical Gilbert, in fact g3(x) ∼ x^(c−1) for x → 0). >>

<< ️(AA) study demonstrates that the DG and HG cascade processes (i.e. Dichotomous Gilbert (DG), Hierarchical Gilbert (HG)) display a multifractal nature. Both models produce a heterogeneous distribution with different characteristics, quantitatively described by two different multifractal spectra. A direct, quantitative comparison between (Their) geometric models and specific experimental datasets remains, at present, an open challenge and would require fragmentation experiments capable of resolving a sufficiently wide range of fragment sizes to reliably probe the hierarchy-induced effect. >>

E.Consolini, B.Bonanni, M.Fanfoni. Hierarchy in Gilbert's tessellation: Multifractal behavior. Phys. Rev. E 114, 034120. Sep 11, 2026.

https://journals.aps.org/pre/abstract/10.1103/p5xq-nj2g

Also: fracture, crack, random, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fracture, crack, randomness, fragmentation process, fragment-size distribution, scale-free behavior, 2-D random tessellation, fractals, multifractal systems, multifractal scaling. 

# behav: collective turns in spinless flocks.

<< ️Using a minimal aggregation-based model, (AA) address the efficient information transfer observed in natural flocks during collective turns. In (Their) system, the turning signal emitted by a single individual propagates throughout the collective primarily at a constant speed. >>

<< ️To characterize the source of this capability, (AA) analyze the system in the continuum limit. Thus, (They) demonstrate that wave-propagating features arise solely from the nonreciprocal nature of interactions. (They) explore spectral anomalies that emerge due to this mechanism and provide an explanation through a perturbative analysis. >>

<< ️Remarkably, within this scenario, the description of velocity fluctuations is found to follow a structure analogous to a Born approximation. (Their) model can be extended to study other physical contexts exhibiting polar order, and (Their) arguments can be tested in natural systems. >>

Joao Lizárraga, Marcus A. M. de Aguiar. Collective turns in spinless flocks. Phys. Rev. E 114, 035401. Sep 1, 2026.

https://journals.aps.org/pre/abstract/10.1103/6976-lcw7

arXiv: 2511.17804v2 [nlin.AO]. Nov 21, 2025.

https://arxiv.org/abs/2511.17804

Also: behav, flock, flocking, fluctuations, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, flock, flocking, fluctuations, waves, collective turns, turning signals.

# 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.

gst: nonreciprocal dynamics with weak noise: aperiodic “Escher cycles” and their quasipotential landscape.

<< ️(AA) present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic “Escher cycles,” similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. >>

<< (AA) calculate the quasipotential analytically to first order in nonreciprocality. (They) characterize it along a one-dimensional reaction coordinate that connects the attractors, and (They) also obtain the full two-dimensional landscape, at leading order in perturbation theory. >>

<< ️The resulting landscapes feature flat regions and extended plateaus, together with nondifferentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features. >>

Janik Schüttler, Robert L. Jack, Michael E. Cates. Nonreciprocal dynamics with weak noise: Aperiodic “Escher cycles” and their quasipotential landscape. Phys. Rev. E 114, 024104. Aug 3, 2026.

https://journals.aps.org/pre/abstract/10.1103/slp9-rd27

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

Keywords: gst, noise, randomness, stochasticity, transitions, singularity, nonreciprocal interactions, noise-induced transitions, metastable attractors, Escher cycles, perturbation theory, escape problems, large deviation & rare event statistics. 

# gst: apropos of persistence or extinction, lag-induced critical transitions to extinction in replicating systems; the 𝜏-tipping mechanism.

<< Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. >>

<< Motivated by experimental evidence that polymerase-targeting antivirals limit replication, (AA) analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. (Their) approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. (They)  identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. >>

<< At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In (Their) delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. >>

<< These (AA) results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, (They) propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which (They) denote as 𝜏-tipping. >>

Edward A. Turner, Francisco Crespo, Joan Gimeno, et al. Lag-induced critical transitions to extinction in replicating systems: the 𝜏-tipping mechanism. Phys. Rev. E 114, 024401. Aug 5, 2026.

https://journals.aps.org/pre/abstract/10.1103/gyd9-ctnc

arXiv: 2603.02036v1 [q-bio.PE]. Mar 2, 2026. 

https://arxiv.org/abs/2603.02036

Also: transition, pause, silence, virus, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, pause, silence, virus, error, collapse, genomes, RNA virus, replication, replicating systems, enzymatic amplification, criticality, persistence, extinction, mutation rates, fitness landscape topographies, error threshold, time-delay systems, lag-time-induced tipping, lag-induced critical transition, loss of temporal coordination.