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

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

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

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

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

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

https://arxiv.org/abs/2609.01164

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

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

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

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

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

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

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

https://arxiv.org/abs/2508.15205

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

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

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

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

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

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

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

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

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

arXiv: 2602.17539v2 [cond-mat.soft]. 

https://arxiv.org/abs/2602.17539

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

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

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

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

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

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

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

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

https://arxiv.org/abs/2609.00564

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

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

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

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

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

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

https://arxiv.org/abs/2608.21484

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

Keywords: gst, perception, metamorphosis, transitions. 

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

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

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

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

https://arxiv.org/abs/2608.20517

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

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

# gst: non-normal route to chaos

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

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

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

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

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

arXiv: 2603.08191v2 [nlin.CD]. 

https://arxiv.org/abs/2603.08191

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

Keywords: gst, attractor, chaos, transitions

# gst: skimming transition in flexible granular sweeping.

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

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

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

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

https://arxiv.org/abs/2608.15069

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

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

# behav: amoeboid swimming of active vesicles.

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

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

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

https://arxiv.org/abs/2607.14714

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

Keywords: behavior, transitions, 

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

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

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

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

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

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

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

https://arxiv.org/abs/2608.11060

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

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

# 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.

# behav: noise-induced stability of insect swarms.

<< ️Flying insect swarms exhibit cohesion without the local velocity alignment observed in flocks of birds or schools of fish. The interaction rules and channels of communication between insects that lead to collective behavior have not yet been determined. >>

<< ️(AA) propose a theoretical model based on acoustic communication between swarm members, where each individual is attracted to a weighted mean field of its neighbors. (They) demonstrate that this simple framework can describe a wide range of swarming dynamics, including a phenomenon where pairs of insects break free from the swarm in a helical orbit around each other. >>

<< ️Counterintuitively, (Their) numerical model suggests that stochastic noise enhances the stability of an insect swarm, as it interferes with pair formation. >>

<< Finally, (AA) demonstrate that a specific species of malarial mosquito produces swarms that reside on the edge of a transition to instability. (Their) study shows that fairly simple local interaction rules can be sufficient to describe the collective behavior of swarming biological systems. >>

Justin Faber, Annabelle Boots, Dolores Bozovic. Noise-induced stability of insect swarms. arXiv: 2608.00314v2 [physics.bio-ph]. Aug 7, 2026.

https://arxiv.org/abs/2608.00314

Also: swarm, behavior, noise, instability, transition, sound, jazz, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: behavior, swarm, noise, instability, transitions, sound, jazz, dance, flying insects, collective behavior, acoustic communication, weighted mean field of neighbors.

# gst: survival probability of particles inside the lemon billiard.

<< ️(AA) study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, (They) explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. >>

<< ️(AA) find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. (Their) results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. >>

<< ️(They) also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases. >>

Daniel Borin, Edson Denis Leonel, Diego Fregolent Mendes de Oliveira. Survival probability of particles inside the lemon billiard. Phys. Rev. E 114, 014224. Jul 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/md5j-ggyd

arXiv: 2601.13000v1 [nlin.CD]. Jan 19, 2026.

https://arxiv.org/abs/2601.13000

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

Keywords: gst, billiard, particles, chaos, transitions, survival probability, two-stage decay pattern, stickiness effect, scaling behavior, scaling laws of complex systems. 

# gst: apropos of bluff-body wakes, effect of centerline separation on a vortex dominated wake.

<< A previously undocumented Reynolds-number-dependent transition is identified in the wake of a rounded-edge slanted afterbody, from a centerline-separated to a novel centerline-attached vortex state. The transition produces a pronounced drag reduction through the collapse of the centerline recirculation region as the upstream boundary layer becomes turbulent. These (AA) findings explore experimental evidence linking laminar separation bubble dynamics, shear-layer instability, and wake-state transitions in this canonical bluff-body geometry. >> ( APS Editor, https://journals.aps.org/prfluids/recent/ )

Rhylan A. Huss, Farrukh S. Alvi. Effect of centerline separation on a vortex dominated wake. Phys. Rev. Fluids 11, 074702. Jul 28, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/bn64-wtlz

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

Keywords: gst, vortex, transition, 

bubble, laminar separation bubble dynamics, shear-layer instability, wake-state transitions.

# gst: on the scaling of bubble interactions in dynamic turbulence; theoretical, numerical, and experimental study.

<< This (AA) study investigates dilute bubbly decaying homogeneous isotropic turbulence at high Reynolds number using theory, direct numerical simulation, and experiments. The turbulent kinetic energy and dissipation rate follow power-law decay, while the bubble population reorganizes relative to the evolving Hinze scale. When the dissipation decays sufficiently rapidly, the Hinze scale grows faster than the characteristic bubble diameter, driving the population from super-Hinze toward sub-Hinze sizes. The system passes through a mixed regime in which coalescence dominates but breakup remains active, followed by a pure-coalescence regime. Residual breakup in the mixed regime increases the number of small bubbles and enhances coalescence, leading to faster growth of the characteristic bubble size. DNS of dilute bubble-laden turbulence shows decay exponents close to single-phase turbulence and a bubble-size distribution that shifts toward smaller diameter relative to the Hinze scale. >>

<< Before the transition, the distribution exhibits two power-law ranges associated with capillary effects and inertial breakup; after the transition, it approaches a single capillary-dominated scaling. Theory and DNS predict distinct growth laws for bubble diameter in the mixed and pure-coalescence regimes, together with corresponding scalings for number density, interfacial area, and coalescence rate. These predictions are further assessed in a spatially developing pump-driven bubbly duct flow at higher Reynolds number. Despite confinement, inhomogeneity, and wall production, the measured trends agree with the theoretical and DNS-based scalings. >>

<< The (AA) results identify Hinze-scale drift as the organizing mechanism for bubble interactions in both idealized and practical decaying turbulent flows, and provide guidance for population-balance and interfacial-area-transport models. >>

Vivek Kumar, Prasoon Suchandra, Shivam Prajapati, et al. On the scaling of bubble interactions in dynamic turbulence: theoretical, numerical, and experimental study.  arXiv: 2607.25251v1 [physics.flu-dyn]. Jul 28, 2026.

https://arxiv.org/abs/2607.25251

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

Keywords: gst, bubble, transitions, dilute bubbly decaying, coalescence, mixed- pure-coalescence regimes, dilute bubble-laden turbulence, capillary effects, inertial breakup, decaying turbulent flows.  

# gst: the origins of transient bimodality

<< Many dynamical systems exhibit diverse modes of behavior. In biology, such modes can represent individual or cell fates. While the emergence of multimodality is commonly studied, transient bimodality is much less well understood. Under transient bimodality, a system moving from a well-defined initial to a final state transiently undergoes a bifurcation into multiple probability modes. This noise-driven phenomenon can significantly impact processes such as cell differentiation and speciation in the presence of changing environmental conditions. >>

<< (AA) detail a theoretical approach for understanding transient bimodality connecting results from ecology, optics, chemical reaction networks and cell biology, propose a ``minimal model'' of transient bimodality and derive a general criterion for its presence. (They) show that fast-to-slow dynamics can lead to transient bimodality in addition to the well-known case of slow-to-fast dynamics. Finally, (AA)  discuss the role of transient bimodality across the scientific literature, with emphasis on biochemical kinetics and gene regulation. >>

Kaan Öcal, Augustinas Sukys, Aanjaneya Kumar, et al. The Origins of Transient Bimodality. arXiv: 2607.16531v1 [q-bio.SC]. Jul 17, 2026.

https://arxiv.org/abs/2607.16531

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

Keywords: gst, noise, uncertainty, transitions, transient bimodality, bifurcations, multimodality, noise-driven phenomenon, fast-to-slow dynamics. 

# gst: interwoven long-range order induced by random fields.

<< (AA) propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by random-field disorder that couples to a composite vestigial order parameter. >>

<< The proposed ``implectic'' phase is characterized by spontaneous symmetry breaking on the background of the spatially interwoven domain structure created by the random fields. (They) explicitly demonstrate the existence of this phase in a layered J1−J2 Ising magnet by means of large-scale Monte Carlo simulations. (AA) then discuss numerous potential applications in systems featuring charge and spin density wave order including frustrated magnets, cuprate and iron-based superconductors, and ultracold atoms. >>

Jeremiah Bender, Thomas Vojta. Interwoven long-range order induced by random fields. arXiv: 2607.10337v1 [cond-mat.dis-nn]. Jul 11, 2026.

https://arxiv.org/abs/2607.10337

Also: particle, waves, order, disorder, fracture, crack, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, waves, order, disorder, fracture, crack, transitions, impurities, defects, locally break, spontaneous symmetry breaking, random-field disorder, implectic long-range ordered phases.

# life: apropos of bifurcations from stable consensus to periodic multiconsensus, consensus-breaking global Hopf bifurcation in memory-based Multi-Agent Systems.

<< ️This (AA) dissertation provides the first systematic study of symmetric consensus-breaking bifurcation to periodic multiconsensus in multi-agent systems. It analyzes this for three classes of multi-agent systems based on three different types of memory, whose closed-loop dynamics equations form delay differential equations of retarded type, neutral type, and pseudoneutral type - a subclassification of retarded type equations introduced in this dissertation which bridges retarded and neutral type delay equations. >>

<< ️Equivariant twisted degree is used to analyze the symmetric global Hopf bifurcation problem in these systems, i.e. bifurcation from a stable consensus to periodic multiconsensus. This shows how the effects of memory allow self-organizing agents to move beyond mere stationary consensus. Theoretical results for the global Hopf bifurcation and symmetric classification of periodic multiconsensus solutions across all three systems are provided, and numerical results are conducted to both validate and enhance the theoretical predictions by providing stability information on the branches which is not obtainable by the degree alone. >>

<< These principles are demonstrated in three real-world applications: one involving the control of formations of UAVs (Unmanned Aerial Vehicles), allowing them to maintain their overall spatial relationships while dancing in complex selectable oscillations; and two more in networked asset markets featuring different traders with different memory-based strategies, showing how similar mechanisms can be responsible for economic cycles of bubbles and crashes. >>

<< Finally, (AA) also numerically investigate resonant double Hopf bifurcations in the neutral delay system, showing strong evidence of a breakdown to chaos via the Ruelle-Takens-Newhouse scenario and the existence of riddled basins. >>

Casey Maikalani Crane. Consensus-Breaking Global Hopf Bifurcation in Memory-Based Multi-Agent Systems. Dissertation. The University of Texas at Dallas. Aug 2026. Supervising Professor: Wieslaw Krawcewicz, Chair.  arXiv: 2607.02388v1 [math.DS]. Jul 2, 2026.

https://arxiv.org/abs/2607.02388

Also: network, swarm, bubble, crack, chaos, transition, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: life, gst, networks, swarm, bubbles, crack, chaos, transitions, dance, multi-agent systems, symmetric consensus-breaking bifurcation, stable consensus, periodic multiconsensus, symmetric global Hopf bifurcation, self-organizing agents, economic cycles of bubbles and crashes, riddled basins.