# 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: 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: experimental investigation of turbulence modulation by deformable bubbles

<< In this work (AA) experimentally investigate the turbulence modulation in the wake of deforming bubbles in homogeneous and isotropic turbulence, in the regime where the turbulence fluctuation is stronger than or comparable to the bubble rising velocity. >>

<< In a quiescent or weak turbulence, the wake has a persistent direction due to the buoyancy. In turbulence, however, (Their) results suggest that the decorrelation time for the slip velocity roughly equals the bubble-sized eddy turn over time. It suggests that, when turbulence becomes intense enough, the slip velocity changes its direction and magnitude so frequently that a wake barely has time to develop. >>

<< As a result, both the intensity and length of the wake are significantly modified. Nevertheless, with sufficient bubble Reynolds number, the wake, albeit limited, can still modulate surrounding turbulence. >>

<< The results suggest that the local turbulence is augmented by the bubble wake, and the amount of augmentation depends heavily on the bubble Reynolds number, the orientation of the bubble semimajor axis relative to the slip velocity, and the bubble deformation. >>️

Xu Xu, Shiyong Tan, et al. Experimental investigation of turbulence modulation by deformable bubbles. Phys. Rev. Fluids 10, 033605. March 31, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.033605

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

Keywords: gst, bubble, deformable bubbles, bubble wake, bubble-bubble interaction, disorder & fluctuations, turbulence, turbulence modulation, surrounding turbulence, vortex, slip velocity, buoyancy

# gst: when homogeneous systems meet dissipation and disorder.

AA << investigate the localization and topological properties of the non-equilibrium steady state (NESS) in a one-dimensional homogeneous system. (Their) results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. >>

<< Conversely, for an initially flat-band system with compactly localized wave functions, the NESS is delocalized. >>

<< Furthermore, (They) find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, (AA) systematically characterize the impact of disorder on the localization and topological properties of the NESS. >>

<< The phase diagram reveals that the NESS can be topologically non-trivial even when the initial state is topologically trivial, and that the topological triviality of the initial state weakens the topological non-triviality of the NESS. >>

Xixi Feng, Ao Zhou, et al. When Homogeneous Systems Meet Dissipation and Disorder. arXiv: 2502.11383v1 [cond-mat.dis-nn]. Feb 17, 2025. 

https://arxiv.org/abs/2502.11383

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

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# 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: intrinsic disorder bars intruders (from biomolecular condensates)

<< It was recently discovered that eukaryotic cells are host to a multiplicity of biomolecular condensates. These condensates typically contain protein and/or RNA components with intrinsically disordered regions (IDRs). While IDRs have been proposed and demonstrated to play many roles in condensate biology, (AA) suggest here an additional crucial role of IDRs, which is to exclude unwanted “intruders” from condensates. This exclusion effect arises from the large conformational entropy of IDRs; i.e., there is a high free-energy cost to occupying space that would otherwise be available to the IDRs. By combining polymer theory with sticker-spacer simulations, (They) show that the relevant insertion free energy increases with the concentration of IDRs in the condensate as well as with intruder size, attaining a linear scaling with surface area for large intruders. >>

AA << find that at realistic IDR concentrations, particles as small as the size of an average protein (4 nm in diameter) can be 97% excluded from condensates. To overcome this entropic barrier, molecules must interact favorably with condensate components to be recruited as clients. Application of the developed size-exclusion theory to biological condensates suggests that condensate IDRs may play a generic exclusionary role across organisms and types of condensates. >>️

Vladimir Grigorev, Ned S. Wingreen, Yaojun Zhang. Conformational Entropy of Intrinsically Disordered Proteins Bars Intruders from Biomolecular Condensates. PRX Life 3, 013011. Feb 14, 2025.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.3.013011

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

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# gst: necklacelike pattern of vortex bound states

<< A vortex is a topological defect in the superconducting condensate when a magnetic field is applied to a type-II superconductor, (..). Because of the confinement of the quasiparticles by a vortex, it exhibits a circular-shaped pattern of bound states with discrete energy levels, (..) >>

 Here, AA << report a completely new type of vortex pattern which is necklacelike in an iron-based superconductor (..). (AA) theoretical analysis shows that this necklacelike vortex pattern arises primarily from selective off-shell interference between vortex bound states of opposite angular momenta in the presence of rotational symmetry breaking due to disorders. >>

<< This fascinating effect can be observed in a system with a small Fermi energy and wave vector, conditions fortuitously met in (Their) samples. (AA) results not only disclose a novel vortex structure, but also unravel a completely new quantum phenomenon in the superconducting condensate. >>️

Zhiyong Hou, Kailun Chen, et al. Necklacelike Pattern of Vortex Bound States. Phys. Rev. X 15, 011027. Feb 7, 2025.   https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011027   arXiv: 2407.08547v1 [cond-mat.supr-con]. Jul 11, 2024.    https://arxiv.org/abs/2407.08547

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

Keywords: gst, vortex, vortex bound states, symmetry breaking, disorder, disorder & fluctuations, necklacelike patterns

# gst: apropos of subdiffusive behaviors, the boomerang effect in classical stochastic models.

<< The phenomenon of Anderson localization, occurring in a disordered medium, significantly influences the dynamics of quantum particles. A fascinating manifestation of this is the “quantum boomerang effect” (QBE), observed when a quantum particle, propelled with a finite initial velocity, reverses its average trajectory, eventually halting at its starting point. >>

AA << uncover evidence of a similar effect in classical systems, characterized by the absence of typical diffusion processes. (Their) investigation encompasses both simplified probabilistic models and more complex phenomenological models that link classical with quantum mechanics. The results indicate that the boomerang effect is not confined to the quantum realm and may also be present in diverse systems exhibiting subdiffusive behavior. >>️

Santiago Zamora, Lisan M. M. Durao, et al. Boomerang effect in classical stochastic models. Phys. Rev. E 111, 024104. Feb 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.024104 

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

Keywords: gst, behavior, particles, disorder, disorder & fluctuations, stocasticity, boomerang effect

# gst: criticality and multistability in quasi-2D turbulence

       Fig. 1(a) Helmholtz resonators

<< Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior, whose study is hindered by the long spatial and temporal scales involved. >>

Here AA << experimentally study turbulence in periodically driven nanofluidic channels with a high aspect ratio using superfluid helium. (They) find a multistable transition behavior resulting from cascading bifurcations of large-scale vorticity and critical behavior at the transition to quasi-2D turbulence consistent with phase transitions in periodically driven many-body systems. >>

AA << demonstrate that quasi-2D turbulent systems can undergo an abrupt change in response to a small change in a control parameter, consistent with predictions for large-scale atmospheric or oceanic flows. >>️

Filip Novotny, Marek Talir, et al. Critical behavior and multistability in quasi-two-dimensional turbulence. arXiv: 2406.08566v1 [physics.flu-dyn]. Jun 12, 2024.

https://arxiv.org/abs/2406.08566

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

Keywords: gst, order, disorder, disorder & fluctuations, criticality, turbulence, transition