# gst: transient and steady-state chaos in dissipative quantum systems.

<< Dissipative quantum chaos plays a central role in the characterization and control of information scrambling, non-unitary evolution, and thermalization, but it still lacks a precise definition. >>

AA << properly restore the quantum-classical correspondence through a dynamical approach based on entanglement entropy and out-of-time-order correlators (OTOCs), which reveal signatures of chaos beyond spectral statistics. Focusing on the open anisotropic Dicke model, (They) identify two distinct regimes: transient chaos, marked by rapid early-time growth of entanglement and OTOCs followed by low saturation values, and steady-state chaos, characterized by high long-time values. >>

AA << introduce a random matrix toy model and show that Ginibre spectral statistics signals short-time chaos rather than steady-state chaos. (Their) results establish entanglement dynamics and OTOCs as reliable diagnostics of dissipative quantum chaos across different timescales. >>

Debabrata Mondal, Lea F. Santos, S. Sinha. Transient and steady-state chaos in dissipative quantum systems. arXiv: 2506.05475v1 [quant-ph]. Jun 5, 2025. 

https://arxiv.org/abs/2506.05475

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

Keywords: gst, information scrambling, entropy, chaos, transient chaos, steady-state chaos.

# 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: far-from-equilibrium complex landscapes

<< Systems with a complex dynamics like glasses or models of biological evolution are often pictured in terms of a complex landscape, with a large number of possible collective states. (AA) show on the example of a stochastic spin model with nonreciprocal and heterogeneous interactions how the complex landscape picture can be generalized far from equilibrium, where collective states may become time-dependent and exhibit, e.g., spontaneous oscillations, often hidden by the presence of disorder. >>

AA << identify relevant observables, like the density of entropy production rate, to unveil the spontaneous collective time dependence, and  determine a configurational entropy which counts the number of oscillating collective states when this number grows exponentially with system size. >>

Laura Guislain, Eric Bertin. Far-from-equilibrium complex landscapes. Phys. Rev. E 111, L062101 Jun 16, 2025.

https://journals.aps.org/pre/abstract/10.1103/93tr-phkw

arXiv: 2405.08452v1 [cond-mat.dis-nn]. May 14, 2024.

https://arxiv.org/abs/2405.08452

Also: evolution, order, disorder, disorder & fluctuations, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, evolution, complexity, entropy, configurational entropy, order, disorder, disorder & fluctuations, spontaneous oscillations, chaos.

# gst: a note on spinning billiards and chaos

AA << investigate the impact of internal degrees of freedom - specifically spin - on the classical dynamics of billiard systems. While traditional studies model billiards as point particles undergoing specular reflection, (AA) extend the paradigm by incorporating finite-size effects and angular momentum, introducing a dimensionless spin parameter that characterizes the moment of inertia. Using numerical simulations across circular, rectangular, stadium, and Sinai geometries, (AA) analyze the resulting trajectories and quantify chaos via the leading Lyapunov exponent. >>

<< Strikingly, (They) find that spin regularizes the dynamics even in geometries that are classically chaotic: for a wide range of α, the Lyapunov exponent vanishes at late times in the stadium and Sinai tables, signaling suppression of chaos. This effect is corroborated by phase space analysis showing non-exponential divergence of nearby trajectories. >>

AA << results suggest that internal structure can qualitatively alter the dynamical landscape of a system, potentially serving as a mechanism for chaos suppression in broader contexts. >>

Jacob S. Lund, Jeff Murugan, Jonathan P. Shock. A Note on Spinning Billiards and Chaos. arXiv: 2505.15335v1 [nlin.CD]. May 21, 2025.

https://arxiv.org/abs/2505.15335

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

Keywords: gst, billiard, spinning billiards, chaos.

# 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: elasticity of fibers prefers the chaos of turbulence.

<< The dynamics of fibers, modeled as a sequence of inertial beads linked via elastic springs, in turbulent flows is dictated by a nontrivial interplay of inertia and elasticity. Such elastic, inertial fibers preferentially sample a three-dimensional turbulent flow in a manner that is qualitatively similar to that in two dimensions [R. Singh et al., Phys. Rev. E 101, 053105 (2020)]. >>

<< Both these intrinsic features have competing effects on fiber dynamics: Inertia drives fibers away from vortices while elasticity tends to trap them inside. However, these effects swap roles at very large values. A large inertia makes the fibers sample the flow more uniformly while a very large elasticity facilitates the sampling of straining regions. >>

<< This complex sampling behavior is further corroborated by quantifying the chaotic nature of sampled flow regions. This is achieved by evaluating the maximal Lagrangian Lyapunov Exponents associated with the flow along fiber trajectories. >>

Rahul K. Singh. Elasticity of fibers prefers the chaos of turbulence. Phys. Rev. E 111, L053101. May 5, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L053101

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

Keywords: gst, elasticity, turbulence, chaos, transitions

# gst: hyperchaos and complex dynamical regimes in N-d neuron lattices.

AA << study the dynamics of N-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. (They) consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. >>

<< As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. >>

<< For lattices in higher spatial dimensions, (AA) discover dynamical effects arising from the ``destructive interference'' of many connected neurons and miniature ``phase transitions'' from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, (They) observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. >>

<< These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems. >>

Brandon B. Le, Dima Watkins. Hyperchaos and complex dynamical regimes in N-dimensional neuron lattices. arXiv: 2505.03051v1 [nlin.CD]. May 5, 2025.

https://arxiv.org/abs/2505.03051

Also: brain, network, behavior, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, network, behavior, cooperation, cooperative behavior, chaos, hyperchaos, transitions, phase transitions, transition thresholds,  synchrony, dimensionality, topology of connectivity, intermittent bursting activity, interference, destructive interference.

# gst: overcoming overly simplistic representations, chaos and regularity in an anisotropic soft squircle billiard.

<< A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. >>

<< Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. >>

AA << study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. (AA) characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. (They) characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squarness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. >>

AA << expect (Their) work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards. >>

A. González-Andrade, H. N. Núñez-Yépez, M. A. Bastarrachea-Magnani. Chaos and Regularity in an Anisotropic Soft Squircle Billiard. arXiv: 2504.20270v1 [nlin.CD]. Apr 28, 2025.

https://arxiv.org/abs/2504.20270

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

Keywords: gst, billiard, soft billiard, soft-wall squircle billiard, particles, smooth boundary,  specular collisions, transitions, chaos

# gst: emergent oscillations and chaos in noncompliant microfluidic networks.

<< Incompressible fluids in microfluidic networks with nonrigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC (resistor, inductor, capacitor) circuits. This is due to the elastic deformation of channel walls that can store and release fluid, as electric capacitors can store and release electric charges. This property is quantified through the compliance of the system, defined as the volume change relative to the pressure change. >>

<< In systems with rigid walls and incompressible fluid, compliance vanishes, and no oscillations can occur through this mechanism. >>

Here, AA << show that not only oscillations but also chaos can emerge in the flow-rate dynamics of noncompliant microfluidic networks with incompressible fluid. Notably, these dynamics emerge spontaneously, even under time-independent driving pressures. The underlying mechanism is governed by the effect of fluid inertia, which becomes relevant at moderate Reynolds numbers observed in microfluidic systems exhibiting complex flow patterns. >>

<< The results are established using a combination of direct numerical simulations and a reduced model derived from modal analysis. This approach enables (AA) to determine the onset of oscillations, the associated bifurcations, the oscillation frequencies and amplitudes, and their dependence on the driving pressures. >>

Yanxuan Shao, Jean-Regis Angilella, Adilson E. Motter. Emergent oscillations and chaos in noncompliant microfluidic networks. Phys. Rev. Fluids 10, 054401. May 1, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.054401

arXiv: 2505.00068v1 [physics.flu-dyn]. 

https://arxiv.org/abs/2505.00068

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

Keywords: gst, networks, microfluidic networks, noncompliant networks with incompressible fluid, fluid inertia, 

driving pressures, elasticity, chaos.

# gst: period-doubling route to chaos in viscoelastic flows

<< Polymer solutions can develop chaotic flows, even at low inertia. This purely elastic turbulence is well studied, but little is known about the transition to chaos. In two-dimensional (2D) channel flow and parallel shear flow, traveling wave solutions involving coherent structures are present for sufficiently large fluid elasticity. >>

AA << numerically study 2D periodic parallel shear flow in viscoelastic fluids, and (They) show that these traveling waves become oscillatory and undergo a series of period-doubling bifurcations en-route to chaos. >>

Jeffrey Nichols, Robert D. Guy, Becca Thomases. Period-doubling route to chaos in viscoelastic Kolmogorov flow. Phys. Rev. Fluids 10, L041301. Apr 17, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.L041301

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

Keywords: gst, chaos, waves, traveling waves, elasticity, viscoelastic fluids, turbulence, elastic turbulence, period-doubling bifurcations, transitions

# gst: strange attractors in complex networks

<< Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean architectures with hidden symmetries, hinting at spontaneous order. Finding low-dimensional embeddings that reveal network patterns and link them to dimensionality that governs universal behavior remains a fundamental open challenge, as it needs to bridge the gap between microscopic disorder and macroscopic regularities. >>

<< Here, the minimal space revealing key network properties is introduced, showing that non-integer dimensions produce chaotic-like attractors. >>

Pablo Villegas. Strange attractors in complex networks. Phys. Rev. E 111, L042301. Apr 15, 2025. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L042301.  

arXiv: 2504.08629v1 [cond-mat.stat-mech] . Apr 11, 2025.

https://arxiv.org/abs/2504.08629

Also: disorder, disorder & fluctuations, noise, network, attractor, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, disorder & fluctuations, noise, networks, attractors, self-similarity, chaos 

# gst: weird quasiperiodic attractors

AA << consider a class of n-dimensional, n≥2, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may appear chaotic, (They)  prove that chaos cannot occur. The considered class of n-dimensional maps allows for any finite number of partitions, separated by various types of discontinuity sets. The key characteristic, beyond discontinuity, is that all functions defining the map have the same real fixed point. These maps cannot have hyperbolic cycles other than the fixed point itself. >>

Laura Gardini, Davide Radi, et al. Abundance of weird quasiperiodic attractors in piecewise linear discontinuous maps. arXiv: 2504.04778v1 [math.DS]. Apr 7, 2025.

https://arxiv.org/abs/2504.04778

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

Keywords: gst, attractors, weird attractors, chaos

# 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 

# epidem: societal self-regulation appears to induce complex infection dynamics and chaos.

<< Classically, endemic infectious diseases are expected to display relatively stable, predictable infection dynamics. Accordingly, basic disease models such as the susceptible-infected-recovered-susceptible model display stable endemic states or recurrent seasonal waves. However, if the human population reacts to high infection numbers by mitigating the spread of the disease, then this delayed behavioral feedback loop can generate infection waves itself, driven by periodic mitigation and subsequent relaxation. >>

AA << show that such behavioral reactions, together with a seasonal effect of comparable impact, can cause complex and unpredictable infection dynamics, including Arnold tongues, coexisting attractors, and chaos. >>

<< Importantly, these arise in epidemiologically relevant parameter regions where the costs associated to infections and mitigation are jointly minimized. By comparing (Their) model to data, (AA) find signs that COVID-19 was mitigated in a way that favored complex infection dynamics. (AA)  results challenge the intuition that endemic disease dynamics necessarily implies predictability and seasonal waves and show the emergence of complex infection dynamics when humans optimize their reaction to increasing infection numbers. >>️

Joel Wagner, Simon Bauer, et al.  Societal self-regulation induces complex infection dynamics and chaos. Phys. Rev. Research 7, 013308. Mar 24, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013308

Also: virus, sars* covid* (aka 1or2achoos), waves, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: epidemiology, virus, sars, covid-19, chaos

# gst: synchronization and chaos in complex systems with delayed interactions.

<< Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables. >>

AA << consider a general framework to model the dynamics of species-rich communities under the effects of external environmental factors, showing that it naturally leads to delayed interactions between species, and analyze the impact of such memory effects on population dynamics. >>

<< Employing the generalized Lotka-Volterra equations with time delays and random interactions, (AA) characterize the resulting dynamical phases in terms of the statistical properties of community interactions. (Their) findings reveal that memory effects can generate persistent and synchronized oscillations in species abundances in sufficiently competitive communities. This provides an additional explanation for synchronization in large communities, complementing known mechanisms such as predator-prey cycles and environmental periodic variability. >>

<< Furthermore, (AA) show that when reciprocal interactions are negatively correlated, time delays alone can induce chaotic behavior. This suggests that ecological complexity is not a prerequisite for unpredictable population dynamics, as intrinsic memory effects are sufficient to generate long-term fluctuations in species abundances. >>

Francesco Ferraro, Christian Grilletta, et al. Synchronization and chaos in complex ecological communities with delayed interactions. arXiv: 2503.21551v1 [q-bio.PE]. Mar 27, 2025.

https://arxiv.org/abs/2503.21551

Also: pause, silence, random, chaos, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, pause, silence, random, chaos, chaotic behavior, network, delay, time delay, delayed interactions, random interactions, memory effect 

# gst: apropos of multiple delays, transitions to intermittent chaos in quorum sensing-inspired dynamics.

<< This study analyses the dynamical consequences of heterogeneous temporal delays within a quorum sensing-inspired (QS-inspired) system, specifically addressing the differential response kinetics of two subpopulations to signalling molecules. >>️

<< The analysis reveals the critical role of multiple, dissimilar delays in modulating system dynamics and inducing bifurcations. Numerical simulations, conducted in conjunction with analytical results, reveal the emergence of periodic self-sustained oscillations and intermittent chaotic behaviour. These observations emphasise the intricate relationship between temporal heterogeneity and the stability landscape of systems exhibiting QS-inspired dynamics. This interplay highlights the capacity for temporal variations to induce complex dynamical transitions within such systems. >>️

AA << findings show that the presence of multiple delays, particularly when characterised by significant disparities in magnitude, can dramatically alter the system’s stability features and promote the emergence of complex nonlinear oscillatory behaviour. >>️

<< Upon explicitly incorporating distinct delays for different state-components, (AA) have shown how temporal factors can dramatically influence system stability and give rise to a spectrum of complex dynamical behaviours, including intermittent chaos. >>

Anahí Flores, Marcos A. González, Víctor F. Breña-Medina. Transitions to Intermittent Chaos in Quorum Sensing Dynamics. arXiv: 2503.14363v2 [nlin.CD]. Mar 19, 2025.

https://arxiv.org/abs/2503.14363

Also: intermittency, pause, silence, transition, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, intermittency, pause, silence, transitions, chaos 

# gst: 'jazzy' intermittency, its onset and multiscaling in active turbulence.

<< Recent results suggest that highly active, chaotic, nonequilibrium states of living fluids might share much in common with high Reynolds number, inertial turbulence. (AA) now show, by using a hydrodynamical model, the onset of intermittency and the consequent multiscaling of Eulerian and Lagrangian structure functions as a function of the bacterial activity. (Their) results bridge the worlds of low and high Reynolds number flows as well as open up intriguing possibilities of what makes flows intermittent. >>️

AA << believe that (Their) work significantly understands the dynamics of dense bacterial suspensions in ways which isolates the truly turbulent effects from those stemming from simpler chaotic motion. More intriguingly, and at a broader conceptual framework, this study yet again underlines that intermittency can be an emergent phenomena in flows where the nonlinearity does not, trivially, dominate the viscous damping. Indeed, there is increasing evidence of intermittency emerging in systems which are not turbulent in the classical sense. Examples include flows with modest Reynolds number of∼O(10e2) showing intermittent behaviour characteristic of high Reynolds turbulence, self-propelling active droplets with intermittent fluctuations, active matter systems of self-propelled particles, which undergo a glass transition, with an intermittent phase before dynamical arrest, and perhaps most pertinently, in elastic turbulence. Thus, (AA) believe, (Their) work will contribute further to understanding what causes flows to turn intermittent. Answers to such questions will also help in understanding fundamental questions in high Reynolds number turbulence. >>️

Kolluru Venkata Kiran, Kunal Kumar, et al. Onset of Intermittency and Multiscaling in Active Turbulence. Phys. Rev. Lett. 134, 088302. Feb 28, 2025. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.088302  arXiv: 2408.06950v2 [cond-mat.soft].  https://arxiv.org/abs/2408.06950

Also: intermittency, transition, fluctuations, drop, droplet, droploid, elastic, turbulence, chaos, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, intermittency, transitions, fluctuations, drops, droplets, droploids, elasticity, turbulence, chaos, jazz

# gst: order and chaos in systems of coaxial vortex pairs

Fig. B.12: Ex. with 4 interact. vortex pairs

AA << have analyzed interactions between two and three coaxial vortex pairs, classifying their dynamics as either ordered or chaotic based on strengths, initial sizes, and initial horizontal separations.  >>️

They << found that periodic cases are scattered among chaotic ones across different initial configurations. Quasi-periodic leapfrogging typically occurs when the initial distances between the vortex pairs are small and cannot coexist with vortex-pair overtake. When the initial configuration splits into two interacting vortex pairs and a single propagating vortex pair, the two interacting pairs consistently exhibit periodic leapfrogging. For the smallest initial horizontal separations, the system predominantly exhibits chaotic or quasi-periodic motions rather than periodic leapfrogging with a single frequency. This behavior is due to the strong coupling between all three vortex pairs. When the pairs are in close proximity, more complex and chaotic dynamics emerge instead of periodic motion. >>

Their << findings indicate that quasi-periodic leapfrogging and chaotic interactions generally occur when the three vortex pairs have similar strengths and initial sizes. Conversely, discrepancies in these parameters cause the system to disintegrate into two subsystems: a single propagating vortex pair and two periodically leapfrogging pairs. >>️

️

Christiana Mavroyiakoumou, Wenzheng Shi. Order and Chaos in Systems of Coaxial Vortex Pairs. arXiv: 2502.07002v1 [physics.flu-dyn]. Feb 10, 2025. ️

https://arxiv.org/abs/2502.07002

Also: chaos, vortex, order, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, vortex, order, disorder, disorder & fluctuations

# gst: alignment-induced self-organization of autonomously steering microswimmers: turbulence, clusters, vortices, and jets.

<< Microorganisms can sense their environment and adapt their movement accordingly, which gives rise to a multitude of collective phenomena, including active turbulence and bioconvection. In fluid environments, collective self-organization is governed by hydrodynamic interactions. >>

<< By large-scale mesoscale hydrodynamics simulations, (AA) study the collective motion of polar microswimmers, which align their propulsion direction by hydrodynamic steering with that of their neighbors. The simulations of the employed squirmer model reveal a distinct dependence on the type of microswimmer—puller or pusher—flow field. No global polar alignment emerges in both cases. Instead, the collective motion of pushers is characterized by active turbulence, with nearly homogeneous density and a Gaussian velocity distribution; strong self-steering enhances the local coherent movement of microswimmers and leads to local fluid-flow speeds much larger than the individual swim speed. >>

<< Pullers exhibit a strong tendency for clustering and display velocity and vorticity distributions with fat exponential tails; their dynamics is chaotic, with a temporal appearance of vortex rings and fluid jets. >>

AA << results show that the collective behavior of autonomously steering microswimmers displays a rich variety of dynamic self-organized structures. >>

Segun Goh, Elmar Westphal, et al. Alignment-induced self-organization of autonomously steering microswimmers: Turbulence, clusters, vortices, and jets. Phys. Rev. Research 7, 013142. Feb 7, 2025. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013142 

Also: swim, microswimmer, particle, turbulence, chaos, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swim, swimmer, microswimmers, particle, turbulence, chaos, noise

# gst: chaotic billiards inside mixed curvatures

<< The boundary of a billiard system dictates its dynamics, which can be integrable, mixed, or fully chaotic. >>️

This AA study << introduces two such billiards: a bean-shaped billiard and a peanut-shaped billiard, the latter being a variant of Cassini ovals. Unlike traditional chaotic billiards, these systems incorporate both focusing and defocusing regions along their boundaries, with no neutral segments. >>

AA << examine both classical and quantum dynamics of these billiards and observe a strong alignment between the two perspectives. For classical analysis, the billiard flow diagram and billiard map reveal sensitivity to initial conditions, a hallmark of classical chaos. In the quantum domain, (AA) use nearest-neighbour spacing distribution and spectral complexity as statistical measures to characterise chaotic behaviour. >>

<< Both classical and quantum mechanical analysis are in firm agreement with each other. One of the most striking quantum phenomena (They) observe is the eigenfunction scarring (both scars and super-scars). Scarring phenomena serve as a rich visual manifestation of quantum and classical correspondence, and highlight quantum suppression chaos at a local level. >>

Pranaya Pratik Das, Tanmayee Patra, Biplab Ganguli. Manifestations of chaos in billiards: the role of mixed curvature. arXiv: 2501.08839v1 [nlin.CD]. Jan 15, 2025.

https://arxiv.org/abs/2501.08839

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

Keywords: gst, billiard, chaos