# gst: the way bubbles gallop.

<< ️Bubbles are more than fleeting pockets of air trapped in liquid: they exhibit an ever-expanding repertoire of intriguing behaviors. From da Vinci's sketches of their swirling paths to modern-day studies of their erratic dances under acoustic waves, the rich dynamics of bubbles have long captured the attention of everyday observers, engineers, and scientists alike. When exposed to periodic sound waves, bubbles can shift from regular pulsations to rapid zigzagging, mimicking the randomness of Brownian motion. Under sudden pressure changes, they may collapse violently, producing cavitation—intense shock waves capable of damaging solid surfaces. In extreme cases, the implosion may become so intense that the bubble emits a spark of light. >>

<< ️Bubbles can also challenge common intuition: they may appear to violate Archimedes' principle, sinking against gravity in oscillating fluids, and carbonated drinks. Despite centuries of explorations, new and often surprising bubble phenomena continue to emerge. One such example is the recently discovered “galloping” bubble, introduced in (AA) recent publication. Here, (They) showcase this new mechanism of bubble locomotion, highlighting its rich dynamics and striking visual appeal. >>

Jian H. Guan, Saiful I. Tamim, Connor W. Magoon, et al. The way bubbles gallop. Phys. Rev. Fluids 10, 110507. Nov 20, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/fbdh-fnzv

Gallery of Fluid Motion. https://doi.org/10.1103/APS.DFD.2024.GFM.V2684816

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

Keywords: gst, bubble, galloping bubbles, galloping threshold, galloping motion, galloping mechanism, instability, galloping instability, drops, droplets, droploids, transitions.

# gst: effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop.

<< ️The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this (AA) study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. >>

<< ️Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. >>

<< Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. >>

<< ️Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy. >>

John Matulis, Hitesh Bindra. Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop. Phys. Rev. E 112, 044223. Oct 23, 2025

https://journals.aps.org/pre/abstract/10.1103/42pn-wttx

Also: disorder & fluctuations, turbulence, attractor, chaos, transition, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, turbulence, attractor, chaos, transition, uncertainty, stochasticity, flow instability, chaotic itinerancy, noise-induced transitions.

# gst: experimental observation of hidden multistability in nonlinear systems.

<< ️Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain stable states evade detection via conventional continuous parameter sweeping, has garnered increasing attention due to its elusive nature and promising applications.  >>

<< ️In this Letter, (AA) present the first experimental observation of hidden multistability using a programmable acoustic coupled-cavity platform that integrates competing self-focusing and self-defocusing Kerr nonlinearities. Beyond established bistability, (They) demonstrate semi- and fully-hidden tristabilities by precisely programming system parameters. Crucially, the hidden stable states, typically inaccessible via the traditional protocol, are unambiguously revealed and dynamically controlled through pulsed excitation, enabling flexible transitions between distinct types of stable states. >>

Kun Zhang, Qicheng Zhang, Shuaishuai Tong, et al. Experimental Observation of Hidden Multistability in Nonlinear Systems. arXiv: 2511.04150v1 [nlin.CD]. Nov 6, 2025.

https://arxiv.org/abs/2511.04150

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

Keywords: gst, stability, multistability, hidden multistability, semi- fully-hidden tristabilities, pulsed excitation.

# gst: coupling an elastic string to an active bath: the emergence of inverse damping.

<< ️The interaction between continuous media and particles is a central topic in much of modern physics, and this (AA) paper specifically addresses the transfer of persistence and activity between particles and waves. Indeed, setting up a nonequilibrium dynamics of continuous (field) degrees of freedom requires understanding how that arises from coupling with active matter degrees of freedom. >>

<< ️Within that program, (AA) have studied a system of fast-moving, overdamped, run-and-tumble particles moving on and interacting with a slower string modeled as a scalar Klein-Gordon field. Using time scale separation and weak coupling, (They) have derived an effective fluctuation dynamics for the field after integrating out the active bath. Akin to Landau (inverse) damping, the particles induce friction on the scalar field given by an explicit time correlation for bath observables. >>

<< ️Depending on the level of activity and persistence of the active particles (and their velocity distribution), this friction can be negative, leading to instability. This emergence of negative (linear) friction for an elastic string extends previous results where the probe is a slow inertial particle in an active medium, (..), except that the acceleration (creating transverse waves) is orthogonal to the active motion. >>

Aaron Beyen, Christian Maes, Ji-Hui Pei. Coupling an elastic string to an active bath: The emergence of inverse damping. arXiv: 2505.18665v2 [cond-mat.stat-mech]. Sep 1, 2025.

https://arxiv.org/abs/2505.18665

Phys. Rev. E 112, L042103. Oct 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/g1zm-23sq

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

Keywords: gst, particles, run-and-tumble particles, waves, elasticity, elastic strings, wave-particle interactions.

# gst: nonreciprocity induced spatiotemporal chaos: reactive vs dissipative routes.

<< ️Nonreciprocal interactions fundamentally alter the collective dynamics of nonlinear oscillator networks. Here (AA) investigate Stuart-Landau oscillators on a ring with nonreciprocal reactive or dissipative couplings combined with Kerr-type or dissipative nonlinearities. >>

<< ️Through numerical simulations and linear analysis, (They) uncover two distinct and universal pathways by which enhanced nonreciprocity drives spatiotemporal chaos. Nonreciprocal reactive coupling with Kerr-type nonlinearity amplifies instabilities through growth-rate variations, while nonreciprocal dissipative coupling with Kerr-type nonlinearity broadens eigenfrequency distributions and destroys coherence, which, upon nonlinear saturation, evolve into fully developed chaos. In contrast, dissipative nonlinearities universally suppress chaos, enforcing bounded periodic states. >>

<< ️(AA) findings establish a minimal yet general framework that goes beyond case-specific models and demonstrate that nonreciprocity provides a universal organizing principle for the onset and control of spatiotemporal chaos in oscillator networks and related complex systems. >>

Jung-Wan Ryu. Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes. arXiv: 2509.20992v1 [nlin.CD]. Sep 25, 2025

https://arxiv.org/abs/2509.20992

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

Keywords: gst, networks, instability, chaos, nonreciprocity, nonreciprocal interactions, nonreciprocal reactive-- dissipative couplings.

# gst: instability and self-propulsion of flexible autophoretic filaments; it was observed distinct swimming modes, steadily translating "U" and metastable rotating "S" shapes.

<< ️Over the past decade, autophoretic colloids have emerged as a prototypical system for studying self-propelled motion at microscopic scales, with promising applications in microfluidics, micro-machinery, and therapeutics. Their motion in a viscous fluid hinges on their ability to induce surface slip flows that are spatially asymmetric, from self-generated solute gradients. >>

<<️ Here, (AA) demonstrate theoretically that a straight elastic filament with homogeneous surface chemical properties -- which is otherwise immotile -- can spontaneously achieve self-propulsion by experiencing a buckling instability that serves as the symmetry-breaking mechanism. Using efficient numerical simulations, (They) characterize the nonlinear dynamics of the elastic filament and show that, over time, it attains distinct swimming modes such as a steadily translating "U" shape and a metastable rotating "S" shape when semi-flexible, and an oscillatory state when highly flexible. >>

Ursy Makanga, Akhil Varma, Panayiota Katsamba. Instability and self-propulsion of flexible autophoretic filaments. arXiv: 2509.10153v1 [cond-mat.soft]. Sep 12, 2025.

https://arxiv.org/abs/2509.10153

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

Keywords: gst, colloids, autophoretic colloids, elasticity, instability, buckling instability, symmetry-breaking mechanisms, self-propulsion, transitions.

# gst: falling viscoelastic liquid films on a slippery substrate.

<< This (AA) study develops a weighted-residual model for Oldroyd-B films on slippery substrates at moderate Reynolds number and large slippery length. >>

<< Linear stability analysis reveals that wall slip promotes perturbation growth rates, increases cut-off wave numbers, and accelerates long-wave propagation speed, demonstrating a destabilizing effect. Two distinct families of traveling waves are sought, which demonstrate that varying the slippery length can alter the bifurcation type of traveling wave families. >>

<< Particularly, large slippery length can cause the transition of drag-gravity regime into the drag-inertia regime. In the drag-gravity regime, slippery effect promotes the wave speed and height. However, in the drag-inertia regime, slippery effect can suppress the wave height even though the wave propagates faster. >>

<< Interestingly, plateau-type waves (They)  found in the Oldroyd-B film flow at large slippery length, which has not been reported previously. >>

Zhiwei Song, Zijing Ding. Falling viscoelastic liquid films on a slippery substrate. Phys. Rev. E 112, 025106. Aug 25, 2025. 

https://journals.aps.org/pre/abstract/10.1103/vv3p-cvk2

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

Keywords: gst, slipping, slippery substrates, waves, instability, instability of free-surface flows, transitions.

# gst: apropos of instabilities, stability of co-annular active and passive confined fluids.

<< ️The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. (AA) focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. >>

<< ️Using an active liquid crystal model, (They) employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. >>

<< ️Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. >>

<< ️(AA) also extend (Their) theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. (Their) results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. >>

<< ️The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and the cell nucleus. >>

Tanumoy Dhar, Michael J. Shelley, David Saintillan. Stability of co-annular active and passive confined fluids. Phys. Rev. Fluids 10, 083103. Aug 21, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/m5ck-v2q3

arXiv: 2501.04918v2 [cond-mat.soft]. Jul 25, 2025. 

https://arxiv.org/abs/2501.04918

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

Keywords: gst, drop, droplet, droploid, elasticity, instability, elastic relaxation, interfacial perturbations, capillary, active, elastic, and viscous stresses.

# gst: wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

<< Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. >>

<< To investigate their dynamics, (AA) perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. >>

<< During the early evolution, three well-known nonlocal interactions, the elastic scattering, the induced diffusion, and the parametric subharmonic instability, together with a superharmonic resonance play a prominent role. >>

<< In contrast, local interactions are responsible for anisotropic energy cascade on longer timescales. >>

AA << reveal emergence of a condensate at small horizontal wave vectors that can be interpreted as a pure wave-wave interaction-mediated layering process. >>

Vincent Labarre, Giorgio Krstulovic, Sergey Nazarenko. Wave-Kinetic Dynamics of Forced-Dissipated Turbulent Internal Gravity Waves. Phys. Rev. Lett. 135, 014101. Jul 1, 2025.

https://journals.aps.org/prl/abstract/10.1103/b82h-z21n

arXiv:2407.11469v3 [physics.flu-dyn]. Mar 28, 2025.

https://arxiv.org/abs/2407.11469

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

Keywords: gst, waves, weakness, turbulence, transitions, stratified turbulence, wave-turbulence interactions, weak turbulence.

# gst: turbulence spreading and anomalous diffusion on combs.

<< This (AA) paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process is shown to result universally in a subdiffusive spreading of the wave field. The dispersion of this spreading process is found to depend exclusively on the type of the interaction process (three- or four-wave), but not on a particular underlying instability. The asymptotic transport equations for field spreading are derived with the aid of a specific geometric construction in the form of a comb. >>

<< The results can be summarized by stating that the asymptotic spreading proceeds as a continuous-time random walk (CTRW) and corresponds to a kinetic description in terms of fractional-derivative equations. The fractional indexes pertaining to these equations are obtained exactly using the comb model. >>

<< A special case of the above theory is a situation in which two waves with oppositely directed wave vectors couple together to form a bound state with zero momentum. This situation is considered separately and associated with the self-organization of wave-like turbulence into banded flows or staircases. >>

<< Overall, (AA) find that turbulence spreading and staircasing could be described based on the same mathematical formalism, using the Hamiltonian of inelastic wave-wave interactions and a mapping procedure into the comb space. Theoretically, the comb approach is regarded as a substitute for a more common description based on quasilinear theory. Some implications of the present theory for the fusion plasma studies are discussed and a comparison with the available observational and numerical evidence is given. >>

Alexander V. Milovanov, Alexander Iomin, Jens Juul Rasmussen. Turbulence spreading and anomalous diffusion on combs. Phys. Rev. E 111, 064217 – Published 24 June, 2025

https://journals.aps.org/pre/abstract/10.1103/cmf5-sf8x#d93038b1-6671-419d-be1e-219e5bf78523

Also: waves, turbulence, walk, self-assembly, instability, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, walk, self-assembly, instability, chaos, comb model, inelastic resonant interactions, inelastic wave-wave interactions, continuous-time random walk, self-organization of wave-like turbulence, Lévy flights, Lévy walks

# gst: active drive towards elastic spinodals

<< Active matter, exemplified by adaptive living materials such as the actomyosin cytoskeleton, can navigate material parameter space, leading to unconventional mechanical responses. In particular, it can self-drive toward elastic spinodal regimes, where inhomogeneous floppy modes induce elastic degeneracy and enable a controlled interplay between rigidity loss and recovery. Proximity to such marginal states leads to stress localization and the formation of force chains that can be actively assembled and disassembled. >> 

Here AA << extend the classical notion of spinodal states to active solids and demonstrate how these extreme mechanical regimes can be actively accessed. Moreover, (They) show that in a nonlinear setting, crossing elastic spinodals generates new energy wells and makes force channeling an intrinsic feature of the emerging microstructure. >>

Ayan Roychowdhury, Madan Rao, Lev Truskinovsky. Active drive towards elastic spinodals. Phys. Rev. E 111, 065416. Jun 20, 2025.

https://journals.aps.org/pre/abstract/10.1103/h2yp-d2s2

arXiv: 2403.17517v3 [cond-mat.soft]. May 20, 2025.

https://arxiv.org/abs/2403.17517

Also: elastic, transition, instability, disorder & fluctuations, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, instability, disorder & fluctuations, active matter, elasticity, elastic forces, elastic deformation, elastic spinodals, self-assembly.

# gst: spontaneous flow instability in active nematics; when quiescent and flowing states may coexist.

<< Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly aligned quiescent state. Here, (AA) show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. >>

<< Through a weakly nonlinear analysis and a numerical study, (AA) trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. >>

AA << predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. (AA) predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions. >>

Ido Lavi, Ricard Alert, et al. Nonlinear Spontaneous Flow Instability in Active Nematics. Phys. Rev. Lett. 134, 238301. Jun 9, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.238301 

arXiv: 2403.16841v1 [cond-mat.soft].

https://arxiv.org/abs/2403.16841

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

Also: Active nematics, in A. Doostmohammadi, et al. Nat Comm vol 9, no 3246 (2018). 

https://www.nature.com/articles/s41467-018-05666-8

Keywords: gst, instability, turbulence, transitions, supercritical-- subcritical bifurcations, active nematics.

# gst: unstable fixed points in chaotic networks

<< Understanding the high-dimensional chaotic dynamics occurring in complex biological systems such as recurrent neural networks or ecosystems remains a conceptual challenge. For low-dimensional dynamics, fixed points provide the geometric scaffold of the dynamics. However, in high-dimensional systems, even the location of fixed points is unknown. >>

Here, AA << analytically determine the number and distribution of fixed points for a canonical model of a recurrent neural network that exhibits high-dimensional chaos. This distribution reveals that fixed points and dynamics are confined to separate shells in state space. Furthermore, the distribution enables (AA) to determine the eigenvalue spectra of the Jacobian at the fixed points, showing that each fixed point has a low-dimensional unstable manifold. >>

<< Despite the radial separation of fixed points and dynamics, (They)  find that the principal components of fixed points and dynamics align and that nearby fixed points act as partially attracting landmarks for the dynamics. >>

AA results << provide a detailed characterization of the fixed point geometry and its interplay with the dynamics, thereby paving the way towards a geometric understanding of high-dimensional chaos through their skeleton of unstable fixed points. >>

Jakob Stubenrauch, Christian Keup, et al. Fixed point geometry in chaotic neural networks. Phys. Rev. Research 7, 023203. May 29, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023203

Also: chaos, disorder & fluctuations, instability, transition, network, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, networks, neural networks, ecosystems, fixed points, unstable fixed points.

# gst: defect-free and defective adaptations of crystalline sheets to stretching deformation.

<< The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, (AA) extend this fundamental scientific question to the plastic regime by exploring the adaptations of crystalline sheets to the large uniaxial mechanical stretching. >>

AA << reveal the intermittent plastic shear deformations leading to the complete fracture of the sheets wrapping the cylinder. Specifically, systematic investigations of crystalline sheets of varying geometry show that the fracture processes can be classified into defect-free and defective categories depending on the emergence of topological defects. >>

AA << highlight the characteristic mechanical and geometric patterns in response to the large stretching deformation, including the shear-driven intermittent lattice tilting, the vortex structure in the displacement field, and the emergence of mobile and anchored dislocations as plastic excitations. >>

<< The effects of noise and initial lattice orientation on the plastic deformation of the stretched crystalline sheet are also discussed. These results advance our understanding of the atomic level on the irreversible plastic instabilities of two-dimensional crystals under large uniaxial stretching and may have potential practical implications in the precise engineering of structural instabilities in packings of covalently bonded particulate systems. >>

Ranzhi Sun, Zhenwei Yao. Defect-free and defective adaptations of crystalline sheets to stretching deformation. Phys. Rev. E 111, 055504. May 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.055504

Also: elastic, intermittency, noise, instability, vortex, defect, fracture, crack, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elastic, noise, intermittency, instability, vortex, defect, fracture, crack, stretch, deformation, wrinkles, tilting, plastic instabilities,  plastic excitations.

# gst: like fireflies or neurons, dynamics of pulsating swarmalators on a ring.

AA << study a simple one-dimensional model of swarmalators, a generalization of phase oscillators that swarm around in space as well as synchronize internal oscillations in time. Previous studies of the model focused on Kuramoto-type couplings, where the phase interactions are governed by phase differences. >>

 Here AA << consider Winfree-type coupling, where the interactions are multiplicative, determined by the product of a phase response function  and phase pulse function . This more general interaction (from which the Kuramoto phase differences emerge after averaging) produces rich physics: six long-term modes of organization are found, which we characterize numerically and analytically. >>

Samali Ghosh, Kevin O'Keeffe, et al. Dynamics of pulsating swarmalators on a ring. arXiv: 2504.14912v1 [nlin.AO]. Apr 21, 2025. 

https://arxiv.org/abs/2504.14912

Also: swarm, swarmalators, instability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swarm, swarmalators, instability

# gst: transitions of breakup regimes for viscous droplets in airflow.

In this AA study, << the transitions of breakup regimes for viscous droplets are investigated experimentally using high-speed imaging taken from a side view and a 45 view. Based on the morphology change in the middle of the droplet, the breakup regimes are classified into no-breakup, bag breakup, bag-stamen, low-order multimode, high-order multimode, and shear-stripping breakup. The droplet morphologies in different regimes and the corresponding transitions are discussed in detail. >>

<< The droplet viscosity dissipates the kinetic energy transferred by the airflow during the initial droplet flattening, and affects the development of the Rayleigh-Taylor instability wave after the flattening. Through the analysis of the droplet deformation and the Rayleigh-Taylor instability with the droplet viscosity taken into account, the transition conditions of different regimes are obtained in a regime map. By further considering the relative velocity loss between the droplet and the airflow, the ranges of the dual-bag breakup in the low-order multimode regime and the droplet retraction in the bag-stamen regime are determined. >>

Zhikun Xu, Tianyou Wang, Zhizhao Che. Transitions of breakup regimes for viscous droplets in airflow. arXiv: 2504.14149v1 [physics.flu-dyn]. Apr 19, 2025.

https://arxiv.org/abs/2504.14149

Also: drop, droplet, droploid, transition, instability, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drops, droplets, droploids, viscous droplets, droplet breakup, transitions, instability, waves

# gst: elastic instability of wormlike micelle solution flow in serpentine channels

AA << investigated the flow behavior of a highly elastic, shear-thinning, semi-dilute (Wormlike micelle) WLM solution in serpentine channels at low Reynolds number and moderate Weissenberg numbers. >>

Their << flow visualization experiments revealed three key phenomena: >>

1. << At low Wi, the base flow is steady and laminar but exhibits spatial asymmetry with wall slip, reflecting the shear-thinning and shear banding properties of the WLM solution. Above a critical Wi (..) the flow undergoes an elastic instability and transitions to a 3D unsteady flow state characterized by pronounced spatiotemporal velocity fluctuations. (..). >>

2. << Alongside this unstable bulk flow, dead zones of stagnant fluid form in the downstream portion of halfloops—reflecting the ability of the WLM solution to support shear localization, complementing reports of dead zone formation for other types of complex fluids (..). Due to coupling to the velocity fluctuations in the bulk flow, these dead zones fluctuate in their size; however, they are bounded by a maximalsize that minimizes the fluid streamline curvature, and therefore the generation of elastic stresses. Dead zones also exhibit multistable behavior—forming and persisting in some half-loops, not forming in other half-loops, and randomly switching between these two states. (..). >>

3. << The unstable flow state also features intermittent, 3D “twisting” velocity inversion events amid the spatiotemporally-fluctuating bulk flow. These twisting events reduce the hydrodynamic tortuosity compared to the base flow state, and their geometric structure can also be rationalized as minimizing the fluid streamline curvature, and therefore the generation of elastic stresses. >>

Emily Y. Chen, Sujit S. Datta. Elastic instability of wormlike micelle solution flow in serpentine channels. arXiv: 2504.02951v1 [physics.flu-dyn]. 

https://arxiv.org/abs/2504.02951

Also: elastic, instability, disorder & fluctuations, transition, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elasticity, instability, disorder & fluctuations, transition, behavior, multistable behavior, randomly switch, twisting events, dead zone

# gst: chaotic and time-periodic edge states in square duct flow.

AA << analyse the dynamics within the stability boundary between laminar and turbulent square duct flow with the aid of an edge-tracking algorithm. As for the circular pipe, the edge state turns out to be a chaotic attractor within the edge if the flow is not constrained to a symmetric subspace. The chaotic edge state dynamics is characterised by a sequence of alternating quiescent phases and regularly occurring bursting episodes. These latter reflect the different stages of the well-known streak-vortex interaction in near-wall turbulence: the edge states feature most of the time a single streak with a number of flanking quasi-streamwise vortices attached to one of the four surrounding walls. The initially straight streak undergoes the classical linear instability and eventually breaks in an intense bursting event due to the action of the quasi-streamwise vortices. At the same time, the vortices give rise to a new generation of low-speed streaks at one of the neighbouring walls, thereby causing the turbulent activity to `switch' from one wall to the other. >>

<< When restricting the edge dynamics to a single or twofold mirror-symmetric subspace, on the other hand, the outlined bursting and wall-switching episodes become self-recurrent in time. These edge states thus represent the first periodic orbits found in the square duct. In contrast to the chaotic edge states in the non-symmetric case, the imposed symmetries enforce analogue bursting cycles to simultaneously appear at two parallel opposing walls in a mirror-symmetric configuration. Both localisation of the turbulent activity to one or two walls and wall switching are shown to be a common phenomenon in low Reynolds number duct turbulence. (They) therefore argue that the marginally turbulent trajectories transiently visit the identified edge states during these episodes, so that the edge states become actively involved in the turbulent dynamics. >>️

Markus Scherer, Markus Uhlmann, Genta Kawahara. Chaotic and time-periodic edge states in square duct flow. arXiv: 2503.22519v1 [physics.flu-dyn]. Mar 28, 2025️. 

https://arxiv.org/abs/2503.22519

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

Keywords: gst, turbulence, duct turbulence, chaos, chaotic edge states, vortex, instability, wall-switching episodes, bursting cycles 

# poe: onda di gioco

<<  

Nota a far mescole coll' endogeno docile avo melode /

declamando su traccia nevale di dondolio di geco /

l' evento d' onde nella forma di compressa logica ode /

che, se liberata, s' autoespande in frange d' agile eco.

>>

14.31 13/09/2004

'solebat quid esset litus ita definire: "qua fluctus eluderet"'. In: Cicerone. 'de natura deorum'.

https://inkpi.blogspot.com/2005/03/1782-onda-di-gioco.html  

Anche:  waves, in   

Notes (quasi-stochastic poetry)  https://inkpi.blogspot.com/search?q=onda 

FonT  https://flashontrack.blogspot.com/search?q=waves 

inkgmr.net  https://www.inkgmr.net/kwrds.html 

Anche: World Poetry Day, in

 https://en.m.wikipedia.org/wiki/World_Poetry_Day     https://nationaltoday.com/world-poetry-day

Keywords: poe, poetry, quasi-stochastic poetry, PoetryDay, WorldPoetryDay, InternationalPoetryDay, waves, rogue waves, shock waves, solitons, turbulence, instability

# gst: dynamics of fluid-driven fractures across material heterogeneities.

<< Fracture propagation is highly sensitive to the conditions at the crack tip. In heterogeneous materials, microscale obstacles can cause propagation instabilities. Macroscopic heterogeneities modify the stress field over scales larger than the tip region. >>

 Here AA << experimentally investigate the propagation of fluid-driven fractures through multilayered materials. (They) focus on analyzing fracture profiles formed upon injection of a low-viscosity fluid into a two-layer hydrogel block. >>

<< Experimental observations highlight the influence of the originating layer on fracture dynamics. Fractures that form in the softer layer are confined, with no penetration in the stiffer layer. Conversely, fractures initiated within the stiffer layer experience rapid fluid transfer into the softer layer when reaching the interface. >>

AA << report the propagation dynamics and show that it is controlled by the toughness contrast between neighboring layers, which drives fluid flow. (They) model the coupling between elastic deformation, material toughness, and volume conservation. After a short transient regime, scaling arguments capture the dependence of the fracture geometry on material properties, injection parameters, and time. These results show that stiffness contrast can modify fracture propagation over large length scales and demonstrate the importance of macroscopic scale heterogeneities on fracture dynamics. >>

Sri Savya Tanikella, Marie C. Sigallon, Emilie Dressaire. Dynamics of fluid-driven fractures across material heterogeneities. Phys. Rev. E 111, 025504. Feb 28, 2025.   https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.025504     arXiv: 2407.10298v1 [physics.flu-dyn]. Jul 14, 2024.  https://arxiv.org/abs/2407.10298

Also: fracture, crack, elastic, 

instability, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fracture, crack, elasticity, instability, disorder, transitions