# gst: apropos of waves that escape trapping; on internal wave whispering gallery modes in channels and critical-slope wave attractors.

<< ️Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and super-attractors in 2D & 3D and the exceptional class of standing global internal wave modes. >>

<< ️However, most of these works did not deal with waves that escape trapping. By using continuous symmetries (AA) analytically prove the existence of internal wave Whispering Gallery Modes (WGMs), internal waves that propagate continuously without getting trapped by attractors. WGMs neutral stability with respect to different perturbations enable whispering gallery beams, a continuum of rays propagating together coherently. The systems' continuous symmetries also enable projection onto 2D planes that yield effective 2D billiards preserving the original dynamics. >>

<< ️By examining rays deviating from these WGMs in parabolic channels (They) discover a new type of wave attractor which is located along the channel instead of across it as in previous works. This new wave attractor leads to a re-understanding of WGMs as sitting at the border between the two basins of attraction. >>

<< ️Finally, both critical-slope wave attractors and whispering gallery beams are used to propose explanations for along-channel energy fluxes in submarine canyons and tidal energy intensification near critical slopes. >>

Nimrod Bratspiess, Eyal Heifetz, Leo R. M. Maas. On internal wave whispering gallery modes in channels and critical-slope wave attractors. arXiv: 2510.07218v1 [physics.flu-dyn]. Oct 8, 2025.

https://arxiv.org/abs/2510.07218

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

Keywords: gst, waves, internal waves, internal wave whispering gallery modes (WGMs), wave attractors, basins of attraction, billiards.

# gst: comparative analysis of detonation and shock waves interacting with droplets.

<< ️The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This (AA) study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. >>

<< ️Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this (AA) study mechanistically explains by the unique postwave conditions. >> 

<< ️A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. >>

<< ️Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone. >>

Hanbing Zou, Xin Jin, Haotian Chen, et al. Comparative analysis of detonation  and shock waves interacting with droplets: Characteristics and mechanisms. Phys. Rev. Fluids 11, 034303. Mar 18, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mp9z-tlk3  

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

Keywords: gst, waves, shock-waves, drop, droplet, droploid, bubble, collapse, vortex, transitions, phase transition, cavitation, detonation wave, detonation front, droplet fragmentation patterns. 

# 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

# 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: apropos of waves perturbed by weak turbulences

<< Wave phenomena are ubiquitous at all scales throughout the Universe, and where there are waves, there’s the potential for wave turbulence. Wave turbulence is the physical state that arises in a continuous medium when a large number of wave modes interact with each other randomly. >>

<< A specific case of wave turbulence in which weakly nonlinear waves propagate in an unbounded space is described by weak turbulence theory. Capturing the dynamics of this regime will be helpful to accurately model large fluid systems. >>

<< In a rotating fluid, the predicted wave spectrum for interacting weakly nonlinear inertial waves is perturbed by the formation of geostrophic modes—columnar vortices aligned with the rotation axis (..) (AA) successfully suppress geostrophic modes with the addition of two honeycomb-patterned plates, allowing them to confirm the predictions of weak turbulence theory. >>

Sergey Nazarenko. Verifying Weak Turbulence Theory.  Physics 13, 194. Dec 14, 2020. 

https://physics.aps.org/articles/v13/194

Eduardo Monsalve, Maxime Brunet, et al. Quantitative Experimental Observation of Weak Inertial-Wave Turbulence. Phys. Rev. Lett. 125, 254502. Dec 14, 2020.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.254502

# gst: to find a separation between plunging and spilling wave breakers

<< While understanding breaking waves is crucial for the development of parametrizations used in ocean wave modeling for both deep and shallow water, the complete process of wave breaking is not well understood. Here (AA) present direct numerical simulations of two-dimensional solitary waves that shoal and break on a uniform beach in shallow water, with the presence of storm surge represented by an inshore region. >>️

They << classify wave breaker types and find a separation between plunging and spilling breakers when scaled by breaking amplitude and depth. (AA) compare energy dissipation during the breaking process with results from the literature without storm surge.  >>️

They << conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse, and further discuss possibilities for a general parametrization of wave breaking valid across different depth regimes. >>️

Hunter Boswell, Guirong Yan, Wouter Mostert. Characterizing energy dissipation of shallow-water wave breaking in a storm surge. Phys. Rev. Fluids 8, 054801. May 5, 2023. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.054801

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

Keywords: gst, waves, soliton, drop 

# gst: nascent water waves induced by the impulsive motion of a solid wall; an unsteady hydraulic jump theory

Fig. 2: Representative cases of the different regimes of impulse waves observed: (a) dispersive wave; (b) solitary-like wave; (c) plunging breaking bore; (d) water jet 

AA << investigated the generation phase of laboratory-scale water waves induced by the impulsive motion of a rigid piston, whose maximum velocity U and total stroke L are independently varied, as well as the initial liquid depth h. By doing so, the influence of two dimensionless numbers is studied: the Froude number Frp (..), with g the gravitational acceleration, and the relative stroke Λp (..) of the piston. >>️

<< For large Froude numbers, an unsteady hydraulic jump theory is proposed, which accurately predicts the time evolution of the wave amplitude at the contact with the piston throughout the generation phase. At the end of the formation process, the dimensionless volume of the bump evolves linearly with Λp and the wave aspect ratio is found to be governed by the relative acceleration γ/g. As the piston begins its constant deceleration, the water bump evolves into a propagating wave and several regimes (such as dispersive, solitary-like and bore waves, as well as water jets) are then reported and mapped in a phase diagram in the (Frp, Λp) plane. While the transition from waves to water jets is observed if the typical acceleration of the piston is close enough to the gravitational acceleration g, the wave regimes are found to be mainly selected by the relative piston stroke Λp while the Froude number determines whether the generated wave breaks or not. >>️

️

Wladimir Sarlin, Zhaodong Niu, et al. Nascent water waves induced by the impulsive motion of a solid wall. arXiv: 2412.08216v1 [physics.flu-dyn]. Dec 11, 2024. 

https://arxiv.org/abs/2412.08216

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

Keywords: gst, waves, soliton

# gst: when a soliton juggles ('catches' and 'throws') droplets

<< Jugglers normally work with solid objects, but a research team has now demonstrated a system that juggles liquid drops. (AA)  have previously shown that liquid drops can bounce in place above the surface of the same liquid—or bounce while moving across the surface—if the container is continuously vibrated (..) In these past experiments, the surface was nearly flat, except for waves generated by the bouncing drop. In the new work by undergraduate student Camila Sandivari of the University of Chile and her colleagues, the vibrations cause the liquid surface to form a large standing wave that actively “catches” and “throws” the drop during each cycle of its oscillation. The trapping of the drop is similar in principle to other types of wave traps, such as laser-based optical tweezers, and the system could potentially lead to new types of traps for larger objects. >>

AA << placed water mixed with a dye and a surface-tension-reducing agent in a 20-cm-long, 2.6-cm-wide basin that supports an unusual type of surface wave when the basin is vibrated in a specific frequency range. In this wave, rather than a series of oscillating peaks and valleys, there is only a single standing wave peak, called a soliton. However, this peak doesn’t oscillate uniformly across the basin’s short dimension (the width). A peak appears at one of the long walls coincident with a valley at the opposite wall, and then the peak and the valley switch places moments later, keeping a relatively flat “node” line along the central long axis of the basin. >>

AA << used a pipette to place a few-millimeter-wide drop of the same fluid just above the oscillating soliton, close to one of the long walls, and found that drops could be juggled for up to 90 minutes. The team attributes this unusual stability in part to a property of the soliton: if the drop wanders off-center, the oscillating surface wave pulls it back toward its center, similar to the way the laser field in optical tweezers is able to stably hold a small particle at its center. >>

David Ehrenstein. Juggling Water Drops. Physics 16, 21. Feb 10, 2023. 

https://physics.aps.org/articles/v16/21

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

https://flashontrack.blogspot.com/search?q=droploids

keyword 'goccia' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=goccia

keyword 'solitons' in FonT

https://flashontrack.blogspot.com/search?q=soliton

https://flashontrack.blogspot.com/search?q=solitons

Keywords: gst, solitons, drop, droplet, droploids, goccia

# gst: triadic instabilities of internal wave standing modes.

<< ️This (AA) article presents (their) experimental study of the nonlinear destabilization of an internal wave standing mode in a uniformly stratified fluid within a rectangular domain. (They) measure the linear response of the system and target its resonances to generate a high-amplitude standing mode, prone to instabilities. Using modal decomposition tools, (They) determine the characteristics of the secondary waves and show that they have a standing-mode spatial structure. Box resonance conditions associated with nonlinear resonance conditions lead to a significant deviation from the internal wave dispersion relation and complex nonlinear interaction dynamics. >>

<< Following previous work, (AA) develop a weakly nonlinear analysis to understand the secondary wave characteristics. This approach, validated by experimental results, shows that the secondary wave characteristics as well as the general nonlinear dynamics are highly sensitive to the domain geometry and to the forcing mode. >>

Julie Deleuze, Ilias Sibgatullin, Philippe Odier, Sylvain Joubaud. Triadic instabilities of internal wave standing modes. Phys. Rev. Fluids 10, 124803. Dec 8, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/2pvv-wkc4

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

Keywords: gst, waves, instability.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

https://arxiv.org/abs/2407.11469

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

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

# gst: random walk model for dual cascades in wave turbulence.

<< Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. >>

<< in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance. >>️️

Oliver Bühler. Random walk model for dual cascades in wave turbulence. Phys. Rev. E 109, 055102. May 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.055102

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

Keywords: gst, waves, turbulence, weak turbulence, random, random walks

# gst: solitary wave billiards

<<  In the present work (AA) introduce the concept of solitary wave billiards. I.e., instead of a point particle, (they) consider a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. >>

J. Cuevas-Maraver, P.G. Kevrekidis, H. Zhang. Solitary wave billiards. arXiv: 2203.09489v1 [nlin.PS]. Mar 17, 2022. 

https://arxiv.org/abs/2203.09489

Also 

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keyword | 'soliton' in FonT

https://flashontrack.blogspot.com/search?q=soliton

keywords: gst, waves, solitons, billiard, chaos 

# gst: self-organized target wave chimeras from asynchronous oscillators in reaction-diffusion media

<< An important development in nonlinear dynamics is the discovery of chimera states that represent the coexistence of synchronized and desynchronized activity in populations of identically coupled oscillators. >>

 Here, AA << unveil a novel chimera state called “self-organized target wave chimera” in reaction-diffusion media where synchronized target waves spontaneously emerge from a pacemaker composed of asynchronous oscillators. This regime contrasts with a widely accepted perspective that synchronized target waves can be generated only by the individuals, which comprise the pacemaker, behaving in a synchronized manner. >>

AA << characterize the features of self-organized target wave chimeras and present a phase diagram of existence of such a regime. >>

Bing-Wei Li, Jie Xiao, et al. Self-Organized Target Wave Chimeras in Reaction-Diffusion Media. Phys. Rev. Lett. 133, 207203. Nov 15, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.207203

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

Keywords: gst, chimera, self-assembly, waves, self-organized target wave chimera, asynchronous oscillators

# phys: the qu-wave of the natural antibiotic gramicidin

<< One of the great counterintuitive puzzles of quantum mechanics is wave-particle duality. This is the phenomenon in which objects behave both like particles and like waves. >>

AA << for the first time, have demonstrated quantum interference in molecules of gramicidin, a natural antibiotic made up of 15 amino acids. Their work paves the way for the study of the quantum properties of  biomolecules and sets the scene for experiments that exploit the quantum nature of enzymes, DNA, and perhaps one day simple life forms such as viruses. >>

A natural biomolecule has been measured acting like a quantum wave for the first time. Mit Tech Rew - Emerging Technology from the arXiv. Nov 9, 2019. 

https://www.technologyreview.com/s/614688/a-natural-biomolecule-has-been-measured-acting-in-a-quantum-wave-for-the-first-time/

Armin Shayeghi, Philipp Rieser, et al. Matter-wave interference of a native polypeptide. arXiv:1910.14538v1 [quant-ph]. Oct 31, 2019.

https://arxiv.org/abs/1910.14538

Also

keyword "quantum" in FonT

https://flashontrack.blogspot.com/search?q=quantum

# phys: probing quantum mechanics with nanoparticle matter-wave interferometry.

<< ️The quantum superposition principle is a fundamental concept of physics and the basis of numerous quantum technologies. Yet, it is still often regarded counterintuitive because we do not observe its key features on the macroscopic scales of our daily lives. It is, therefore, interesting to ask how quantum properties persist or change as we increase the size and complexity of objects. >>

<< ️A model test for this question can be realized by matter-wave interferometry, in which the motion of individual massive particles becomes delocalized and needs to be described by a wave function that spans regions far larger than the particle itself. Over the years, this has been explored with a series of objects of increasing mass and complexity and a growing community aims at pushing this to ever larger limits. >>

<< ️Here (AA) present an experimental platform that extends matter-wave interference to large metal clusters, a qualitatively new material class for quantum experiments. (They) specifically demonstrate quantum interference of sodium nanoparticles, which can each contain more than 7,000 atoms at masses greater than 170,000 Da. They propagate in a Schrödinger cat state with a macroscopicity of μ = 15.5, surpassing previous experiments by an order of magnitude. >>

Sebastian Pedalino, Bruno E. Ramírez-Galindo, Richard Ferstl, et al. Probing quantum mechanics with nanoparticle matter-wave interferometry. Nature 649, 866–870. Jan 21, 2026.

https://www.nature.com/articles/s41586-025-09917-9

Also: keyword 'quantum' in FonT

https://flashontrack.blogspot.com/search?q=quantum

Keywords: particles, quantum mechanics, quantum superposition.

# gst: degrees of universality in wave turbulence

<< ️Turbulence of weakly interacting waves displays a great deal of universality: independence of the details of the interaction and of the pumping and dissipation scales. Here (AA) study how inverse turbulent cascades (from small to large scales) transition from weak to strong. (They) find that while one-loop corrections can be dependent on excitation and dissipation scales, new types of universality appear in strong turbulence. (They) contrast turbulence of spin waves in ferromagnets with turbulent cascades in the Nonlinear Schrödinger Equation (NSE) and in an MMT-like (Majda-McLaughlin-Tabak) model in higher dimensions having a multiplicative interaction vertex: vertex renormalization gives rise to dependence on the pumping (UV scale) in the former but not in the latter. >>

<< ️As a result of this spectral nonlocality, spin-wave turbulence stops being weak if one is sufficiently far from the pumping scale, even when the interaction of waves with comparable wavenumbers is weak. (AA) paraphrase this as: nonlocality enhances nonlinearity. >>

<< ️(AA) then describe strong turbulence in a multi-component version of these models with a large number of components. (They) argue that strong spin-wave turbulence is similar to turbulence of the focusing NSE, as it realizes a critical-balance state. However, UV nonlocality causes the level of spin-wave turbulence at large scales to decrease with increasing pumping level, culminating in a state that is independent of the level of pumping. >>

Jiasheng Liu, Vladimir Rosenhaus, Gregory Falkovich. Degrees of universality in wave turbulence. arXiv: 2512.04866v1 [cond-mat.stat-mech]. Dec 4, 2025.

https://arxiv.org/abs/2512.04866

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

Keywords: gst, waves, turbulence, transitions.

# gst: "diffusing wave paradox", synthetic microswimmers can mimic the behavior of Amoeba

<< Amoeba are unusual creatures that form when a dispersed population of cells spontaneously comes together and reorganizes itself into a multicellular macroscopic organism. To do this, a few leader cells emit chemical pulses that cause the other individual cells to move in the direction opposite to that of the traveling pulses (the "diffusing wave paradox," ), leading to the formation of dense clusters. >>

<< In experiments, the researchers used spherical particles that are half-coated by a carbon cap and placed in a viscous liquid. When illuminated by light, the particles propel themselves forward with the cap in front. >>

<< At low pulse speeds, the particles have enough time to reorient themselves, if needed, so that their caps are facing in the same direction as that of the traveling pulses. This orientation ensures that the particles travel in the same direction as the pulses. >>

<< At high pulse speeds, on the other hand, the pulses come too quickly for the particles to reorient themselves before the next one comes. This is because the speed of the particles' rotation is limited by the friction of the viscous liquid. So if the particles' caps are initially facing the oncoming pulses, the particles will move counter to the direction of the traveling pulses, resembling the behavior of amoeba in the diffusing wave paradox. >>

Lisa Zyga. Diffusing wave paradox may be used to design micro-robotics. Jun 12, 2019.

https://m.phys.org/news/2019-06-diffusing-paradox-micro-robotics.html

Celia Lozano, Clemens Bechinger. Diffusing wave paradox of phototactic particles in traveling light pulses. Nature Communications 10, Article number: 2495.  Jun 7, 2019.

https://www.nature.com/articles/s41467-019-10535-z

# 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. 

# s-gst: vortex knots in wave systems

<< Waves  surround  us  all  the  time:  sound waves in  the  noise  around  us, light  waves enabling  us  to see,  and  according  to  quantum  mechanics,  all  matter  has  a  wave  nature.  Most  of  these  waves, however,  do  not  resemble  the  regular  train  of  waves  at  the  shore  of  the  ocean—the  pattern  is much  more  chaotic.  Most  significantly,  the  whirls  and  eddies  form  lines  in  space  called  vortices. Along  these  lines,  the  wave  intensity  is  zero,  and  natural  wave  fields  -  light,  sound  and  quantum matter  -  are  filled  with  a  dense  tangle  of  these  null  filaments >>

Knots  in  chaotic  waves. July  29,  2016.

http://m.phys.org/news/2016-07-chaotic.html

Alexander J. Taylor & Mark R. Dennis. Vortex knots in tangled quantum eigenfunctions. Nature Communications. Published 29 Jul 2016 DOI: 10.1038/ncomms12346 OPEN

http://www.nature.com/ncomms/2016/160729/ncomms12346/full/ncomms12346.html