# gst: describing a universal critical behavior in a transition from order to chaos.

<< ️(AA) present a comprehensive discussion of a transition from integrability to nonintegrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter 𝜀, which modifies the boundary shape from circular, corresponding to 𝜀=0 and an integrable dynamics, to oval for 𝜀≠0, where nonintegrability emerges. >>

<< ️The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, (They) characterize the diffusive spreading of ensembles of trajectories and identify an observable, 𝜔_(rms,sat), which plays the role of an order parameter for the transition. >>

<< For small deformations, the saturation value of the diffusion obeys the scaling law 𝜔_(rms,sat)∝𝜀^(˜𝛼), with a critical exponent ˜𝛼=0.507⁢(2), vanishing continuously as 𝜀→0. The associated susceptibility, 𝜒=𝑑⁢𝜔_(rms,sat)/𝑑⁢𝜀, diverges in the same limit, signaling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. >>

Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo, et al. Describing a universal critical behavior in a transition from order to chaos. Phys. Rev. E 113, 054220. May 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/7231-j7zv

arXiv: 2602.17810v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17810

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

Keywords: gst, billiard, oval billiard, transitions, order, disorder, elementary excitations, small deformations, topological defects, criticality, chaotic stripes, chaos.

# gst: orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow.

<< ️(AA) perform an unstable periodic orbit (UPO) analysis of moderately developed Couette turbulence with large-eddy simulations (LES) using a static eddy viscosity model. >>

<< ️(They) find that spanwise vortices, stretched between streamwise rolls, approach the walls, over which new spanwise vortices are generated. The stretching of these vortices is driven by strong shear layers induced by the streamwise rolls. This vortex-generation mechanism, as revealed by the LES UPOs, is a significant dynamical process in LES turbulence at high Reynolds numbers. >>

<< ️By computing local Lyapunov exponents, which quantify the least stable perturbation growth rates along the UPOs, (They) show that the stretching process amplifies their growth. The corresponding Lyapunov vectors highlight the instability of prominent shear layers through which the stretched spanwise vortices emerge between the rolls. >>

<< ️(Their) results suggest that high-strain-rate structures in developed turbulence play a central role in shaping the geometrical structure of turbulent orbits in phase space. >>

Eiichi Sasaki, Javier Jiménez, Genta Kawahara. Orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow. Phys. Rev. Fluids 11, 054603. May 14, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mtw2-29r3

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

Keywords: gst, instability, turbulence, vortex, spanwise vortices, eddy viscosity model, unstable periodic orbit (UPO), streamwise rolls, stretching process.

# gst: apropos of interfacial contact events, bounce or coalescence, a physical learning frame.

<< ️In this study, (AA) develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes interfacial coalescence and bouncing through the fusion and generation of multiple volume-of-fluid fields. When adjacent interfaces are predicted to coalesce, multiple VOF fields are collapsed into a single VOF field. When approaching interfaces are predicted to bounce, a single VOF field is regenerated into multiple VOF fields, allowing the interfaces to continue evolving independently. >>

<< With this treatment, the difficulties associated with topological transition, regime-map identification, increasing computational demand, and stochastic behavior during interfacial approach are separated from the interface-tracking procedure. These decisions are instead assigned to a physics-guided machine-learning model with strong adaptability. This strategy avoids the direct resolution of an ultrathin gas film and reduces the dependence on empirical molecular-force parameters. >>

<< ️Simulations of droplet--droplet collisions show that the proposed framework can reproduce both coalescence and bouncing over different impact conditions. By further introducing a drainage-time criterion, the framework is extended to the simulation of droplet impact on a liquid surface. For this problem, the numerical results agree well with both previous experimental observations and the present experiments. >>

<< ️Moreover, the framework captures the complete sequence of bouncing followed by subsequent coalescence within a single simulation, These (AA) results demonstrate that the proposed framework has strong adaptability for interfacial contact problems and provides a unified modeling route for droplet coalescence, bouncing. >>

J.H. Xu, Z.L. Wang. Bounce or coalescence: a physical learning frame. arXiv: 2605.15844v1 [physics.flu-dyn]. May 15, 2026. 

https://arxiv.org/abs/2605.15844

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

Keywords: gst, drops, droplets, droploids, coalescence, bouncing, volume-of-fluid (VOF) field, transitions, topological transitions, stochasticity, droplet--droplet collisions, interfacial contact events, 

# gst: multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling.

<< ️Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the so-called clusters) are formed, and these coexist with a set of desynchronized oscillators. >>

<< ️For phase oscillators on a ring with nonlocal piecewise linear repulsive coupling that also involves a phase lag, (AA) find that in the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n. >>

<< ️This is in contrast to multi-cluster chimeras that are formed with nonlocal attractive coupling. The synchronized solutions are studied numerically as well as analytically and by analysing their stability, (They) identify the parameter regions where these can be observed. (Their) numerical results are validated by dimensional reduction using the Ott-Antonsen analysis. >>

Ayushi Saxena, Sangeeta Rani Ujjwal, Ram Ramaswamy. Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling. arXiv: 2605.15628v1 [nlin.AO]. May 15, 2026.

https://arxiv.org/abs/2605.15628

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

Keywords: gst, chimera, stability, coupled oscillators, repulsive coupling, multi-cluster chimeras. 

# gst: formation of mechanical rogue waves.

<< ️Rogue waves, characterized by their abrupt and extreme localization in space and time, have evolved from maritime folklore to subjects of intense study across diverse fields, from hydrodynamics and nonlinear optics to plasmas and condensed matter physics. In mechanical systems, however, experimental realization remains elusive despite theoretical and numerical predictions. This gap stems from the stringent requirements for controllable nonlinearity, the high-fidelity initialization of the system, and the necessity to overcome inherent energy dissipation. >>

<< ️Here, (AA) report the experimental formation of mechanical rogue waves in a precisely engineered one-dimensional metamaterial lattice with tailored nonlinearity and minimal dissipative losses. Using a precision electromagnetic release system, (They) prescribe initial strain profiles that trigger a transition from dispersive decay to extreme wave focusing. >>

<< ️(Their) parametric analysis reveals that the emergence of these extreme events is strictly contingent upon a synergy between high nonlinearity and a broad spatial energy reservoir within the initial seed. Crucially, neither factor alone is sufficient to overcome dispersion and trigger the observed focusing. >> 

<< ️These findings establish a robust platform for studying transient nonlinear wave focusing phenomena in mechanical systems and offer insights for harnessing extreme wave localization for applications such as energy harvesting, waveguiding, and mechanical signal processing. >>

Yasuhiro Miyazawa, Christopher Chong, Panayotis G. Kevrekidis, et al. Formation of mechanical rogue waves. arXiv: 2605.18518v1 [nlin.PS]. May 18, 2026.

https://arxiv.org/abs/2605.18518

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

Keywords: gst, waves, rogue waves, mechanical rogue waves, transitions.

# gst: spin-hair induced chaos of spinning test particles in rotating hairy black holes.

<< ️(AA) investigate the finite-time instability of massive spinning test particles around a rotating hairy black hole generated through gravitational decoupling. (They) show that spin–curvature coupling and the hairy geometry can shift the evolved orbit away from the requested seed parameters, making the empirical orbital map essential for interpreting the dynamics. >>

<< Small-spin and geodesic trajectories remain close to regular behavior, whereas large-spin trajectories show stronger finite-time growth. A scan of the (S,β) plane shows that the instability does not grow monotonically, but appears in localized regions where the particle spin and the radial profile of the hair act cooperatively. Thus, the hairy background does not simply rescale the Kerr result; it reorganizes the strong-field phase-space region sampled by spinning particles. >>

Surojit Dalui, Xian-Hui Ge. Spin-Hair Induced Chaos of Spinning Test Particles in Rotating Hairy Black Holes. arXiv: 2605.19673v1 [gr-qc]. May 19, 2026.

https://arxiv.org/abs/2605.19673

Also: black hole, instability, particle, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, black hole, instability, particle, chaos, rotating hairy black hole.

# gst: free-surface deformations induced by three-dimensional turbulence.

<< ️(AA) report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, (They) perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. >>

<< ️The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (−2.5), suggesting the advection of turbulent structures at the free surface. >> 

<< ️(They) develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (−7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold. >>

Michaël Berhanu, Eric Falcon. Free-surface deformations induced by three-dimensional turbulence. arXiv: 2605.13654v1 [physics.flu-dyn]. May 13, 2026.

https://arxiv.org/abs/2605.13654

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

Keywords: gst, free-surface turbulence, free-surface deformations, subsurface velocity fluctuations, wave-turbulent damping, surface-breaking threshold.

# gst: apropos of control by noise, diffusive transport from spatially correlated random phase kicks.

<< ️(AA) study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in driven quantum systems. >>

<< ️Using a momentum-space formulation, (They) show that the evolution is governed by an accumulated phase whose structure determines the spreading of the wave packet. (They) find that the phase kicks strongly suppress ballistic transport and induce diffusion at long times. (They) derive an explicit analytical expression for the diffusion coefficient as a function of the correlation length, in excellent agreement with numerical simulations. >>

<< (Their) results uncover a simple mechanism by which spatially correlated phase noise controls quantum transport, and provide a quantitatively testable prediction for diffusion in periodically driven lattice systems. Possible experimental realizations in cold-atom platforms are discussed. >>

Pei Wang. Diffusive transport from spatially correlated random phase kicks. arXiv: 2605.06701v1 [cond-mat.mes-hall]. May 5, 2026.

https://arxiv.org/abs/2605.06701

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

Keywords: gst, particle, waves, randomness, noise, single-particle wave packet, periodic random phase kicks, spatially correlated phase noise, quantum transport.

# music: rhythm as an ordered phase of sound; how musical meter emerges in a statistical mechanical model.

<< ️(AA) develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. >>

<< ️By mapping these competing preferences onto analogous quantities in statistical physics, (They) define an effective free energy which is minimized in the grand canonical ensemble. Using a mean field approximation, (They) observe phase transitions in the model from disordered events in time to orderings that closely reproduce those seen in music. >>

<< ️(They) then compare the range of rhythmic characteristics predicted by the model to a data set drawn from compositions by Johann Sebastian Bach, finding generally good quantitative agreement. The results provide a lens through which to study musical rhythm and a method for generatively producing rhythms. >>

Robert St. Clair, Jesse Berezovsky. Rhythm as an ordered phase of sound: How musical meter emerges in a statistical mechanical model. Phys. Rev. E 113, 054116. May 11, 2026.

https://journals.aps.org/pre/abstract/10.1103/kjfs-v245

arXiv: 2604.07476v1 [cond-mat.stat-mech]. Apr 8,2026.

https://arxiv.org/abs/2604.07476

Also: music, sound, jazz, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: music, sound, jazz, brain, musical rhythms, perceiving repeated patterns, desire for variety and complexity, phase transitions, disordered events, J.S. Bach.

# gst: from chaos to synchrony in recurrent excitatory-inhibitory networks with target-specific inhibition.

<< ️Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. >>

<< ️Here, (AA) extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, (They) derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. (They) show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. >>

<< Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics. >>

Carles Martorell, Rubén Calvo, Alessia Annibale, et al. From Chaos to Synchrony in Recurrent Excitatory-Inhibitory Networks with Target-Specific Inhibition. arXiv: 2605.14916v1 [cond-mat.dis-nn]. May 14, 2026.

https://arxiv.org/abs/2605.14916

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

Keywords: gst, networks, fluctuations, instability, transitions, chaos, biological neural networks, random recurrent networks, asynchronous chaos, excitation--inhibition balance, target-specific inhibition.

# gst: rigorous ultimate scaling in rapidly rotating steady convection.

<< ️Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, (AA) obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. >>

<< (They) show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales. >>

Gabriel Hadjerci, Shingo Motoki, Genta Kawahara. Rigorous ultimate scaling in rapidly rotating steady convection. arXiv: 2605.05574v1 [physics.flu-dyn]. May 7, 2026.

https://arxiv.org/abs/2605.05574

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

Keywords: gst, waves, vortex, convection, convection cells, Rayleigh-Bénard convection, bulk and boundary-layer structure, rotation, rotating convection.

# gst: delay-induced chimera transitions via mode selection in a multiplex FitzHugh Nagumo network.

<< ️(AA) investigate delay-induced collective dynamics in a two-layer multiplex FitzHugh Nagumo network with nonlocal intra layer coupling and delayed inter layer interactions. While delay effects are often treated as secondary, (They) show that deterministic inter-layer delay alone can act as a control mechanism for spatial coherence. >>

<< ️Through systematic numerical simulations, (They) observe a clear transition as the delay parameter increases: fragmented incoherence evolves into chimera-like partial coherence, and eventually into a coherent traveling-wave state. This transition is consistently captured by spatial snapshots, space-time plots, and mean phase velocity profiles. >>

<< ️To explain this behavior, (They) analyze the stability of spatial Fourier modes and show that the delay term introduces a mode-dependent exponential factor in the characteristic equation. This term induces non-monotonic changes in modal stability, effectively acting as a mode-selection mechanism: intermediate delays selectively destabilize a subset of modes, producing chimera-like coexistence, while larger delays suppress incoherent modes and restore global coherence. >>

<< ️(Their) results demonstrate that inter-layer delay provides a simple and robust mechanism for controlling pattern formation in multiplex excitable networks, offering new insight into delay driven synchronization phenomena. >>

Hui Wu. Delay-induced chimera transitions via mode selection in a multiplex FitzHugh Nagumo network. arXiv: 2605.04430v1 [physics.bio-ph]. May 6, 2026.

https://arxiv.org/abs/2605.04430

Also: chimera, network, transition, waves, pause, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, networks, transitions, waves, pause, delay, inter-layer delay, delay-induced collective dynamics, two-layer multiplex excitable network.

# gst: apropos of dissipation of fast tides, turbulent damping of fast tidal oscillations by three-dimensional Rayleigh-Bénard convection with a radiating free surface.

<< ️(AA) present three-dimensional Dedalus simulations of Rayleigh–Benard convection with a blackbody-radiating free upper surface, subject to a low-amplitude oscillatory forcing that mimics tidal perturbations in convective envelopes of stars and planets. The forcing period is 10–100 times shorter than the convective timescale, tconv. Using a Reynolds decomposition of the velocity field averaged over one oscillation period, in which the tidal oscillations naturally constitute the fluctuating field and xconvection the mean flow, (They) elucidate the kinetic energy exchange between the two. >>

<< ️Provided the oscillatory Reynolds number exceeds a modest threshold, (They) find that the oscillations systematically transfer kinetic energy to the mean flow at a volume-averaged rate D_R∼u′^(2)t^−1_conv, where u′ is the rms fluctuation velocity. This reflects strong, order-unity correlations between the fluctuation velocities and the mean flow. These arise because the oscillatory forcing displaces fluid elements that are then redirected by buoyancy and incompressibility in the same manner as the mean flow. >>

<< The transfer is dominated by correlations involving vertical velocity fluctuations and vertical gradients of the mean flow. The resulting energy transfer rate is consistent, within the equilibrium-tide framework, with the observed tidal circularisation of solar-type binaries and with the orbital evolution of moons of Jupiter and Saturn. This validates the formalism proposed by Terquem (2021) for the dissipation of fast tides, a longstanding problem. Replacing the free surface with a rigid upper boundary significantly and artificially modifies the correlations. >>

Caroline Terquem, Alexander Boone, Enrico Martinez. Turbulent damping of fast tidal oscillations by three-dimensional Rayleigh-Bénard convection with a radiating free surface. arXiv: 2605.05108v1 [astro-ph.SR]. May 6, 2026.

https://arxiv.org/abs/2605.05108

Also: turbulence, fluctuations, dissipation,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, fluctuations, dissipation, turbulent damping, tidal oscillations, tidal perturbations, Rayleigh-Bénard convection, dissipation of fast tides.

# gst: apropos of packing regimes, understanding the dynamics of evaporation-driven colloidal self-assembly.

<< ️Complex colloidal cluster morphologies are desirable for the fabrication of advanced materials, such as photonic crystals and meta-materials, and can be formed through evaporation-driven packing. By coupling lattice Boltzmann and discrete element methods, here (AA) elucidate the rich interplay between fluid and particle dynamics during evaporation-driven self-assembly of spherical colloidal particles. >>

<< ️(They) construct a regime diagram for a wide range of evaporation rates, interparticle friction coefficients, and particle numbers, identifying parameter regimes for open, closed, and minimal moment of inertia cluster configurations. >>

<< ️Analyzing the competition between capillary, hydrodynamic, normal, and friction forces, (They) show that interparticle friction can exert a disproportionately strong influence on the final packing outcome despite being considerably smaller in magnitude than other forces at play. (Their) simulation results further highlight the potential for tuning colloidal cluster configurations via their dynamic trajectories. >>

Junyu Yang, Abhinav Naga, Xitong Zhang, et al. Understanding the Dynamics of Evaporation-Driven Colloidal Self-Assembly. arXiv: 2605.04878v1 [cond-mat.soft]. May 6, 2026.

https://arxiv.org/abs/2605.04878

Also: particle, self-assembly, evaporation, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, self-assembly, evaporation, spherical colloidal particles, complex colloidal clusters, evaporation-driven packing, evaporation-driven self-assembly, interparticle friction coefficients, minimal moment of inertia, tuning colloidal cluster configurations.

# gst: critical parameters of an oval billiard with an elliptical component.

<< ️(AA) explore the critical parameters responsible for the transition from integrability to chaos in a family of billiards combining elliptical and oval deformations. Unlike standard oval billiards, where a known critical parameter governs the destruction of the last invariant curve, the introduction of an integrable elliptic component yields a second deformation axis. >>

<< (They) derive an analytical expression for the critical parameter in this combined system and validate it numerically using Slater's theorem, showing that increasing the elliptical component lowers the critical threshold for global chaos. >>

<< ️Moreover, (They) uncover a previously unexplored regime: when the two deformation components are in phase, the elliptic contribution progressively suppresses chaos, leading to the restoration of invariant curves and periodic orbits. A first-order analytical approximation confirms this behavior, supported by numerical validation. >>

<< ️(Their) results reveal how the interplay between distinct boundary deformations enriches phase-space organization and offers enhanced controllability of chaotic dynamics in billiard systems. >>

Anne Kétri P. da Fonseca, Joelson D. V. Hermes, Edson D. Leonel. Critical parameters of an oval billiard with an elliptical component. arXiv: 2605.00145v1 [nlin.CD]. Apr 30, 2026. 

https://arxiv.org/abs/2605.00145

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

Keywords: gst, billiard, transition, chaos, criticality, elliptical and oval deformations. 

# gst: topological defects in spiral wave chimera states.

<< ️Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, (AA) introduce a topological analysis method based on winding numbers to characterize the dynamics of spiral wave chimeras in a two-dimensional phase oscillator network. >>

<< ️(Their) investigation reveals distinct scaling laws governing the system's evolution across the phase lag 𝛼. Perturbation analysis in the limit 𝛼→0 demonstrates that the incoherent core radius scales linearly with 𝛼. In contrast, within the stable chimera regime, the average total positive winding number 𝜇 follows a clear exponential growth law 𝜇=𝑎⁢𝑒^(𝑏⁢𝛼). This scaling disparity signals a physical crossover from a regime dominated by geometric core expansion to one driven by active topological excitation. >> 

<< ️Furthermore, (They) identify a statistical transition in the defect distribution from binomial-like to Poisson-like behavior at a critical threshold 𝛼*. These results demonstrate that topological defects possess intrinsic statistical order, establishing 𝜇 as a robust macrovariable for analyzing the structural complexity of chimera states. >>

Lintao Liu, Nariya Uchida. Topological defects in spiral wave chimera states. Phys. Rev. E 113, 054207. May 8, 2026.

https://journals.aps.org/pre/abstract/10.1103/yhbq-ztk8

arXiv: 2511.21058v2 [nlin.AO]. 5 Mar 2026.

https://arxiv.org/abs/2511.21058

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

Keywords: gst, chimera, waves, self-assembly, transition, network, defect, topology, spiral wave chimeras, two-dimensional phase oscillator network, active topological excitations, topological defects. 

# gst: apropos of smallest amplitude perturbations that trigger transition to turbulence, the minimal seeds in the Stokes boundary layer.

<< ️Minimal seeds, the smallest amplitude perturbations that trigger transition to turbulence, are presented in the Stokes boundary layer, the oscillating flow of a viscous fluid above a flat plate. The minimal seed trajectories are dominated by the Stokes boundary layer's large linear transient growth at early times, but only 73% of the initial energy is formed from the linearly optimal growing mode; the remainder ensures that nonlinear interaction transfers energy from spanwise- to streamwise- independent structures, and makes up for a timing mismatch between the end of linear transient growth and the production phase of the edge state (the saddle point separating laminar and turbulent basins of attraction). >>

Tom Eaves. Minimal seeds in the Stokes boundary layer. arXiv: 2604.23213v1 [physics.flu-dyn]. Apr 25, 2026.

https://arxiv.org/abs/2604.23213

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

Keywords: gst, turbulence, transitions, minimal seeds, laminar and turbulent basins of attraction.

# gst: capillary slinky; equilibrium and dynamics of a droplet in a soft spring.

<< ️Springs can be found in many applications and biological systems, and when these are soft, they easily deform. At small scales, capillarity can induce a force leading to spring deformations when the elastocapillary number is small. >>

<< ️ (AA) demonstrate through experiments the nontrivial equilibrium-shape liquid droplets adopt in these soft springs, which form an annulus, eruciform, and spherical shapes. When these droplets are set in motion, they display different flow regimes with significant dissipation generated by the internal rotational flow. >>

<< ️The static and dynamics of droplets in such a capillary slinky are also used to demonstrate how surface tension can actuate springs by stretching/compression, while providing a way for active flow control in soft springs. >>

Bidisha Bhatt, Andreas Carlson. Capillary slinky: Equilibrium and dynamics of a droplet in a soft spring. Phys. Rev. Fluids 11, 043607. Apr 29, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/p9j4-hp5h

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

Keywords: gst, drops, droplets, droploids, capillarity, capillary slinky, spring deformations, annulus, eruciform, spherical shapes, rotational flows.

# gst: apropos of unsteady two-dimensional flows, the Lagrangian rotating contracting structures.

<< ️(AA) identify materially defined regions in unsteady two-dimensional flows that combine finite-time contraction with elevated accumulated intrinsic rotation along trajectories, which (They) term Lagrangian rotating contracting structures (LRCS). These regions are detected using existing objective diagnostics—the Lagrangian-averaged vorticity deviation (LAVD) together with direct tests of material contraction—without relying on the geometry of LAVD level sets. >>

<< ️In strongly deforming flows, LAVD maxima need not correspond to vortical regions or be enclosed by regular level sets, rendering geometry-based identification unreliable. Nevertheless, regions exhibiting inward spiraling motion and contraction can be extracted by combining LAVD with a contraction criterion. >>

<< ️Applications to atmospheric and oceanic flows show that such behavior arises both in twisted LAVD fields generated at submesoscales and in mesoscale flows where it is enhanced by inertial effects, with finite-time contraction providing the dynamical constraint that isolates materially organized regions with elevated intrinsic rotation. >>

F.J. Beron-Vera. Lagrangian Rotating Contracting Structures. arXiv: 2604.25036v1 [nlin.CD]. Apr 27, 2026.

https://arxiv.org/abs/2604.25036

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

Keywords: gst, vortex, instability, finite-time contraction, accumulated intrinsic rotation, Lagrangian rotating contracting 

structures, inward spiraling motion.

# gst: chaotic billiard lasers.

<< ️This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. >>

<< ️(AA) begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. >>

<< ️(They) discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. >>

<<️ Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, (They) establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. >>

<< ️By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources. >>

Takahisa Harayama. Chaotic Billiard Lasers. arXiv: 2604.23614v1 [quant-ph]. 26 Apr 26, 2026.

https://arxiv.org/abs/2604.23614

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

Keywords: gst, billiard, billiard laser, waves, transitions, chaos, quantum chaos, chaotic billiard, chaos-assisted light emission, chaos-assisted tunneling.