# 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. 

# gst: self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions.

<< ️Nonlinear dynamics of runaway electron induced wave instabilities can significantly modify the runaway distribution critical to tokamak operations. Here (AA) present a fully kinetic simulation of runaway-driven instabilities toward nonlinear saturation in a warm plasma where collisional damping is subdominant. >>

<< ️It is found that the slow-X modes grow an order of magnitude faster than the whistler modes, and they parametrically decay to produce whistlers much faster than those directly driven by runaways. These parent-daughter waves, as well as secondary and tertiary wave instabilities, initiate a chain of wave-particle resonances that strongly diffuse runaways to the backward direction. This reduces almost half of the current carried by high-energy runaways, over a time scale orders of magnitude faster than experimental shot duration. These results beyond quasilinear analysis may impact anisotropic energetic electrons broadly in laboratory, space, and astrophysics. >>

Qile Zhang, Yanzeng Zhang, Qi Tang, et al. Self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions. Phys. Rev. E 113, L043203. Apr 20, 2026.

https://journals.aps.org/pre/abstract/10.1103/k3bq-cvjs

arXiv: 2409.15830v2 [physics.plasm-ph]. Mar 7, 2026.

https://arxiv.org/abs/2409.15830

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

Keywords: gst, waves, whistler waves, instability, particles, collisional damping, wave-particle resonance