# gst: intensity landscapes in elliptic and oval billiards with a circular absorbing region.

<< ️Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi)permeable walls and internal holes have been used to study open systems. >>

<< ️Here (AA) introduce a billiard model containing an internal region with partial absorption. The absorption does not change the trajectories but instead reduces an intensity variable associated with each trajectory. The value of the intensity can be tracked as a function of the initial configuration and the number of reflections from the wall and depicted in intensity landscapes over the Poincaré phase space. >>

<< ️This is similar in spirit to escape time diagrams that are often considered in dynamical systems with holes.  >>

<< ️(AA) analyze the resulting intensity landscapes for three different geometries: a circular, elliptic, and oval billiard, respectively, all with a centrally placed circular absorbing region. The intensity landscapes feature increasingly more complex structures, organized around the sets of points in phase space that intersect the absorbing region in a given iteration, which (They) study in some detail. On top of these, the intensity landscapes are enriched by effects arising from multiple absorption events for a given trajectory. >>

Katherine Holmes, Joseph Hall, Eva-Maria Graefe. Intensity landscapes in elliptic and oval billiards with a circular absorbing region. Phys. Rev. E 112, 034202. Sep 2, 2025.

https://journals.aps.org/pre/abstract/10.1103/9bv6-4npn 

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

Keywords: gst, billiard, particle, escape.

# gst: hidden qu-classical correspondence in chaotic billiards revealed by mutual information.

<< ️Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. >>

<< ️(AA) show that, contrary to this expectation, increasing chaos in quantum billiards enhances mutual information between conjugate phase space variables, revealing nontrivial correlations. Using an information-theoretic decomposition of eigenstate entropy, (They) demonstrate that spatial delocalization may coincide with increased mutual information between position and momentum. >>

<< These correlations track classical invariant structures in phase space and persist beyond the semiclassical regime, suggesting a robust information-theoretic manifestation of quantum-classical correspondence. >>

Kyu-Won Park, Soojoon Lee, Kabgyun Jeong. Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information. Phys. Rev. E 112, 024209. Aug 13, 2025.

https://journals.aps.org/pre/abstract/10.1103/qpxx-csdj

arXiv:2505.08205v1 [nlin.CD]. May 13, 2025.

https://arxiv.org/abs/2505.08205

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

Keywords: gst, billiard, chaos, qu-chaos, waves, quantum-to-classical transition

# gst: extreme event precursor prediction in turbulence.

<< ️(AA) present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks (CNN) to identify precursors to extreme events. >>

<< ️(They) evaluate the framework across three distinct testbed systems: a triad turbulent interaction model, a prototype stochastic anisotropic turbulent flow, and the Kolmogorov flow. This method offers three key advantages: (1) a threshold-free classification strategy that eliminates subjective parameter tuning, (2) efficient training using only O (100) recurrence matrices, and (3) ability to generalize to unseen systems. >>

<< ️The results demonstrate robust predictive performance across all test systems: 96% detection rate for the triad model with a mean lead time of 1.8 time units, 96% for the anisotropic turbulent flow with a mean lead time of 6.1 time units, and 93% for the Kolmogorov flow with a mean lead time of 22.7 units. >> 

Rahul Agarwal, Mustafa A. Mohamad. Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis. arXiv: 2508.04301v1 [cs.CE]. Aug 6, 2025.

https://arxiv.org/abs/2508.04301

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

Keywords: gst, turbulence, chaos, extreme events, convolutional neural networks (CNN).

# gst: transition to chaos with conical billiards.

<< ️(AA) adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane, with tilt angle γ. >>

<< ️(They) explore the dynamics as a function of γ and the cone deficit angle χ that controls the sharpness of the apex, where a point source of positive Gaussian curvature is concentrated. >>

<< ️(AA) find regions of the (γ,χ) plane where, depending on the initial conditions, either (A) the trajectories sample the entire cone base and avoid the apex region; (B) sample only a portion of the base region while again avoiding the apex; or (C) sample the entire cone surface much more uniformly, suggestive of ergodicity. >>

<< ️The special case of an untilted cone displays only type A trajectories which form a ring caustic at the distance of closest approach to the apex. However, (They) observe an intricate transition to chaotic dynamics dominated by Type (C) trajectories for sufficiently large χ and γ. A Poincaré map that summarizes trajectories decomposed into the geodesic segments interrupted by specular reflections provides a powerful method for visualizing the transition to chaos. (AA) then analyze the similarities and differences of the path to chaos for conical billiards with other area-preserving conservative maps. >>

Lara Braverman, David R. Nelson. Transition to chaos with conical billiards. arXiv: 2508.02786v1 [nlin.CD]. Aug 4, 2025.

https://arxiv.org/abs/2508.02786

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

Keywords: gst, billiard, particles, transitions, chaos. 

# gst: fluctuations around turbulence

<< ️Numerical simulations of turbulent flows at realistic Reynolds numbers generally rely on filtering out small scales from the Navier Stokes equations and modeling their impact through the Reynolds stress tensor τ_ij. Traditional models approximate τ_ij solely as a function of the filtered velocity gradient, leading to deterministic subgrid scale closures. However, small scale fluctuations can locally exhibit instantaneous values whose deviation from the mean can have a significant influence on flow dynamics. >>

<< ️In this work, (AA) investigate these effects by employing direct numerical simulations combined with Gaussian filtering to quantify subgrid scale effects and evaluating the local energy flux in both space and time. The mean performance of the canonical Clark model is assessed by conditioning the energy flux distributions on the invariants of the filtered velocity gradient tensor, Q and R. The Clark model captures to a good degree the mean energy flux. However, the fluctuations around these mean values for given (Q, R) are of the order of the mean displaying fat tailed distributions. ️To become more precise, (AA) examine the joint distributions of true energy flux and the predictions from both the Clark and the Smagorinsky models. >>

<< ️This approach mirrors the strategy adopted in early stochastic subgrid scale models. Clear non Gaussian characteristics emerge from the obtained distributions, particularly through the appearance of heavy tails. The mean, the variance, the skewness and flatness of these distributions are quantified. (Their) results emphasize that fluctuations are an integral component of the small scale feedback onto large scale dynamics and should be incorporated into subgrid scale modeling through an appropriate stochastic framework. >>

Flavio Tuteri, Alexandros Alexakis, Sergio Chibbaro. Fluctuations around Turbulence Models. arXiv: 2507.17575v1 [physics.flu-dyn]. Jul 23, 2025. 

https://arxiv.org/abs/2507.17575

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

Keywords: gst, disorder & fluctuations, turbulence.

# gst: reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing.

AA << ️describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence of the transition, infinitesimal parameter variations allow switching between uniform distribution and clusters in single-species models, and between mixed and sorted states in multi-species contexts, without hysteresis. >>

Their << main technical contribution is a universal expansion for the size of vacuum bubbles that arise in this phase transition and a quantitative analysis of the effect of noise. >>

Arnd Scheel, Angela Stevens. Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing. arXiv: 2507.10406v1 [math.DS]. Jul 14, 2025.

https://arxiv.org/abs/2507.10406

Also: particle, bubble, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, bubbles, noise, short-range repulsion, long-range attraction, phase transitions.

# gst: breakdown of stochastic resonance in complex networks

<< ️In networked systems, stochastic resonance (SR) occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external periodic signal, and the intensity of stochastic fluctuations, the maintenance of stochastic resonance also crucially depends on the resonance capacity of each oscillator composing the network. This scenario raises the question: Can local defects in the ability of oscillators to resonate break down the stochastic resonance phenomenon in the entire network?  >>

Jonah E. Friederich, Everton S. Medeiros, et al. Breakdown of stochastic resonance in complex networks. Phys. Rev. E 112, 014218. Jul 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/fc2t-275m

<< ️First, (AA) found that the combinations of network coupling and noise intensity for the maintenance of SR form tongue-like structures, specifying different optimal values of these parameters depending on the number of non-resonant units. Subsequently, (They) verified that, counter-intuitively, increasing the network coupling intensity causes SR to globally fail in the presence of a few non-resonant oscillators. Additionally, the upper limit of the coupling intensity diminishes as the number of nonresonant units increases. Moreover, (They) observed that for the maintenance of SR in (Their) network, the number of non-resonant oscillators is a nonlinear function of their dissimilarity level. >>

arXiv: 2502.06626v1 [nlin.AO]. Feb 10, 2025. 

https://arxiv.org/abs/2502.06626

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

Keywords: gst, networks, coupled oscillators, stochasticity, stochastic resonance

# gst: impact of spinning droplets onto superhydrophobic surfaces: asymmetric tumbling rapid rebound.

<< ️The impact dynamics of spinning droplets onto superhydrophobic surfaces was studied by using Volume-of-Fluid simulations, covering broad ranges of Weber number (We) and dimensionless angular velocity (Ω). >>

<< ️Results show that, the spinning motion of droplets leads to two novel rebound scenarios. Specifically, the front-raise tumbling rebound occurs at a lower (Ω) and is caused by the unsymmetrical Laplace pressure, while the rear-raise tumbling rebound emerges at a higher (Ω) and is attributed to the rotational inertia. The angular momentum of the spinning droplet is dissipated or even reversed, while its direction upon detachment is inconsistent with the visually observed spinning motion. >>

<< ️With the increase of the angular velocity, the droplet-wall contact time is largely reduced, which is attributed to the asymmetric spreading by the spinning motion rather than the increased kinetic energy. A theoretical model was also established to predict asymmetric spreading and the contact time and validated against numerical results in wide ranges of (We) and (Ω).  >>

Jinyang Wang, Feifei Jia, et al. Impact of Spinning Droplets onto Superhydrophobic Surfaces: Asymmetric Tumbling Rapid Rebound. arXiv: 2507.13150v1 [physics.flu-dyn]. Jul 17, 2025. 

https://arxiv.org/abs/2507.13150

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

Keywords: gst, drops, droplets, droploids

# gst: the turbulence development at its initial stage, a scenario based on the idea of vortices decay.

<< ️In this paper, a model of the development of a quantum turbulence in its initial stage is proposed. The origin of the turbulence in the suggested model is the decay of vortex loops with an internal structure. >>

AA << ️consider the initial stage of this process, before an equilibrium state is established. As result of (Their) study, the density matrix of developing turbulent flow is calculated. The quantization scheme of the classical vortex rings system is based on the approach proposed by the author earlier. >>

S.V. Talalov. The turbulence development at its initial stage: a scenario based on the idea of vortices decay. arXiv: 2303.05908v3 [physics.flu-dyn]. Feb 16, 2024.

https://arxiv.org/abs/2303.05908

Also: << Lo "smoothing" e', nell' essenziale, un atteggiamento, un comportamento piu' o meno automatico, una tecnica, una prassi. (..) tutte le volte che uno "smoother" livella un vortice (piu' verosimilmente crede di aver circoscritto un vortice per livellarlo), se non e' accorto (non lo e' quasi mai) mentre cerca di spianare lo potenzia e, allo stesso tempo - questo e' il fatto curioso - puo' avere inconsapevolmente generato i presupposti per accenderne in prospettiva almeno un' altro. Oppure altri due. Oppure 'n'. >> In: Smoothers. Notes (quasi-stochastic poetry). Mar 27, 2006.

http://inkpi.blogspot.com/2006/03/1980-smoothers.html

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

Keywords: gst, turbulence, vortex.

# gst: self-feedback delay induces extreme events in the theoretical Brusselator system.

AA << ️present a study of the theoretical Brusselator model with time-delayed self-feedback, demonstrating its ability to induce extreme events when delays in reaction processes significantly influence subsequent dynamics, with and without diffusion. >>

<< ️Stability analyses reveal the mechanisms driving this behavior with respect to the delay time. The occurrence of extreme events is validated using various numerical and statistical tools, including phase portraits, time series, probability distribution functions, return periods, and spatiotemporal evolution. >>

<< ️A comprehensive two-parameter scan delineates the parameter regimes where the extreme events emerge, alongside the identification of transient chaos within specific regions of the parameter space. To confirm these numerical findings, (AA) constructed an analog electronic circuit that emulates the model, providing experimental validation of the predicted dynamics. >>

S. V. Manivelan, S. Sabarathinam, et al. Self-feedback delay induces extreme events in the theoretical Brusselator system. Phys. Rev. E 112, 014202. Jul 1, 2025.

https://journals.aps.org/pre/abstract/10.1103/v1h2-42w1

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

Keywords: gst, Brusselator system, self-feedback, delay, chaos, transient chaos, transitions, extreme events.

# gst: additional jamming transition in two-dimensional bidisperse granular packings.

AA << ️present a jamming diagram for two-dimensional bidisperse granular systems, capturing two distinct jamming transitions. The first occurs as large particles form a jammed structure, while the second, emerging at a critical small-particle concentration, 𝑋*_S ≈0.21, and size ratio, 𝛿*≈0.25, involves small particles jamming into the voids of the existing large-particle structure upon further compression. >>

<< ️Below this threshold, small particles fill voids within the large-particle network, increasing packing density. Beyond this point, excess small particles disrupt efficient packing, resulting in looser structures. These results, consistent with previous three-dimensional studies, demonstrate that the second transition occurs at a well-defined point in the (𝑋_S,𝛿) plane, independent of dimensionality, likely driven by the geometric saturation of available space around particles, void closure, and structural arrangement. >>

<< ️The second transition reveals that jamming in mixtures of differently sized particles does not occur through a single, unified process. Instead, it can involve multiple, distinct transitions, each associated with a specific particle size and contributing uniquely to the emergence of rigidity through excluded area effects and spatial organization. >>

Juan C. Petit, Matthias Sperl. Additional jamming transition in two-dimensional bidisperse granular packings. Phys. Rev. Research 7, L022073. Jun 20, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/mtcv-dbpd

Also: particle, jamming, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, granular packing, jamming, disorder, transitions. 

# gst: chimera states with multiple coexisting solutions.

AA << ️report on the emergence of chimera states in extended systems characterized by the coexistence of more than two spatiotemporal solutions. Specifically, (They) show that three-domain chimeras may generically appear in reaction-diffusion systems under three conditions, with a crucial role played by the existence of a Maxwell point. >>

AA << verify the universality of (their) findings by analyzing five different models, and demonstrate that such new chimeras are independent of the boundary conditions imposed. >>

Gui-Quan Sun, Zhi-Chao Xue, et al. Chimera states with multiple coexisting solutions. Phys. Rev. Research 7, 023289. Jun 20, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/y3t8-bk24

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

Keywords: gst, chimera, chaos, transitions.

# gst: energy spectra and fluxes of 2D turbulent quantum droplets.

AA << explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. >>

<< ️Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. >>

Their << ️findings offer insights into the turbulent response of exotic phases of matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics. >>

Shawan Kumar Jha, Mahendra K. Verma, et al. Energy spectra and fluxes of two-dimensional turbulent quantum droplets. Phys. Rev. Fluids 10, 064618. Jun 25, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/pj6n-3w6p

arXiv:2501.01771v1 [cond-mat.quant-gas]. Jan 3, 2025.

https://arxiv.org/abs/2501.01771

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

Keywords: gst, drop, droplet, droploid, turbulence, vortex, harmonic trap, quantum fluctuations, exotic phases of matter, self-similar nonequilibrium dynamics

# gst: the evasion of tipping; pattern formation near a Turing-fold bifurcation

<< ️Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses') from a preferred state to a less desirable one. In ecosystems, the emergence of spatial patterns has traditionally been interpreted as a possible 'early warning signal' for tipping. More recently, however, pattern formation has been proposed to serve a fundamentally different role: as a mechanism through which an (eco)system may 'evade tipping' by forming stable patterns that persist beyond the tipping point. >>

<< ️Mathematically, tipping is typically associated with a saddle-node bifurcation, while pattern formation is normally driven by a Turing bifurcation. Therefore, (AA) study the co-dimension 2 Turing-fold bifurcation and investigate the question: 'When can patterns initiated by the Turing bifurcation enable a system to evade tipping?' >>

AA << develop (their) approach for a class of phase-field models and subsequently apply it to -component reaction-diffusion systems -- a class of PDEs often used in ecosystem modeling. (AA) demonstrate that a two-component system of modulation equations governs pattern formation near a Turing-fold bifurcation, and that tipping will be evaded when a critical parameter, β, is positive. (They) derive explicit expressions for β, allowing one to determine whether a given system may evade tipping. Moreover, (They) show numerically that this system exhibits rich behavior, ranging from stable, stationary, spatially quasi-periodic patterns to irregular, spatio-temporal, chaos-like dynamics. >>

Dock Staal, Arjen Doelman. The evasion of tipping: pattern formation near a Turing-fold bifurcation. arXiv: 2506.22251v1 [math.DS]. Jun 27, 2025.

https://arxiv.org/abs/2506.22251

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

Keywords: gst, disorder & fluctuations, pattern formation, Turing-fold bifurcation, transitions, tipping, collapse

# gst: allosteric lever: toward a principle of specific allosteric response.

<< ️Allostery, the phenomenon by which the perturbation of a molecule at one site alters its behavior at a remote functional site, enables control over biomolecular function. >>

<< ️However, a general principle of allostery, i.e., a set of quantitative and transferable “ground rules,” remains elusive. It is neither a set of structural motifs nor intrinsic motions. >>

<< ️Focusing on elastic network models, (AA) here show that an allosteric lever—a mode-coupling pattern induced by the perturbation—governs the directional, source-to-target, allosteric communication: A structural perturbation of an allosteric site couples the excitation of localized hard elastic modes with concerted long-range soft-mode relaxation. >>

<< ️Perturbations of nonallosteric sites instead couple hard and soft modes uniformly. The allosteric response is shown to be generally nonlinear and nonreciprocal, and allows for minimal structural distortions to be efficiently transmitted to specific changes at distant sites. Allosteric levers exist in proteins and “pseudoproteins”—networks designed to display an allosteric response. >>

<< ️Interestingly, protein sequences that constitute allosteric transmission channels are shown to be evolutionarily conserved. >>

Maximilian Vossel, Bert L. de Groot, Aljaž Godec. Allosteric Lever: Toward a Principle of Specific Allosteric Response. Phys. Rev. X 15, 021097. Jun 20, 2025

https://journals.aps.org/prx/abstract/10.1103/wv2k-676p

Also: allostery in FonT https://flashontrack.blogspot.com/search?q=allostery

Also: allosterico in Notes (quasi-stochastic poetry) https://inkpi.blogspot.com/search?q=allosterico

Keywords: gst, allostery, allosteric lever, elasticity, networks, elastic networks.

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

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

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

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

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

https://arxiv.org/abs/2506.05475

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

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

# gst: chimera states on m-directed hypergraphs.

<< Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted a lot of interest and has been widely studied, revealing several types of chimeras. Most cases involve reciprocal pairwise couplings, where each oscillator exerts and receives the same interaction, modeled via networks. >>️

<< However, real-world systems often have non-reciprocal, non-pairwise (many-body) interactions. From previous studies, it is known that chimera states are more elusive in the presence of non-reciprocal pairwise interactions, while easier to be found when the latter are reciprocal and higher-order (many-body). >>️

<< In this work, (AA) investigate the emergence of chimera states on non-reciprocal higher-order structures, called m-directed hypergraphs, and (They) show that, not only the higher-order topology allows the emergence of chimera states despite the non-reciprocal coupling, but also that chimera states can emerge because of the directionality. >>️

<< Finally, (AA) compare the latter results with the one resulting from non-reciprocal pairwise interactions: their elusiveness confirms that the observed phenomenon is thus due to the presence of higher-order interactions. The nature of phase chimeras has been further validated through phase reduction theory. >>️

Rommel Tchinda Djeudjo, Timoteo Carletti, et al. Chimera states on m-directed hypergraphs. arXiv: 2506.12511v1 [nlin.PS]. Jun 14, 2025. 

https://arxiv.org/abs/2506.12511

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

Keywords: gst, chimera, networks, non-reciprocal pairwise interactions, non-reciprocal higher-order structures, m-directed hypergraphs.

# gst: nonstationary critical phenomena: expanding the critical point.

<< A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic behaviours are nonstationary and involve persistent fluxes. >>

<< To do so, (AA) construct an effective field theory with a single order-parameter -- a nonstationary analogue of active Model B -- that reflects the fact that different properties of bQSAPs can only be interpreted in terms of passive thermodynamics in appropriately chosen inertial frames. This codifies the movement of phase boundaries due to nonequilibrium fluxes between coexisting bulk phases in terms of a difference in effective chemical potentials and therefore an 'unequal' tangent construction on a bulk free energy density. >>

<< The result is both an anomalous form of coarsening and, more generally, an exotic phase structure; binodals are permitted to cross spinodal lines so that criticality is no longer constrained to a single point. >>

<< Instead, criticality, with exponents that are seemingly unchanged from symmetric QSAPs, is shown to exist along a line that marks the entry to an otherwise forbidden region of phase space. The interior of this region is not critical in the conventional sense, but retains certain features of criticality, which (AA) term pseudo-critical. >>

<< Whilst an inability to satisfy a Ginzburg criterion implies that fluctuations remain relevant at macroscopic scales, finite-wavenumber fluctuations grow at finite rates and exhibit non-trivial dispersion relations. The interplay between the growth of fluctuations and the speed at which they move relative to the bulk results in distinct regimes of micro- and meso-phase separation. >>

Richard E. Spinney, Richard G. Morris. Nonstationary critical phenomena: expanding the critical point. Phys. Rev. E 111, 064129. Jun 23, 2025.

https://journals.aps.org/pre/abstract/10.1103/hx6n-9qsk

arXiv: 2412.15627v2 [cond-mat.stat-mech]. Jun 25, 2025. 

https://arxiv.org/abs/2412.15627

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

Keywords: gst, particles, active particles, disorder & fluctuations, criticality, pseudo-criticality, transitions.

# 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: topological phase transition under infinite randomness

<< In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. >>

Here AA << investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, (AA) show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. >>

<< Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. (AA) work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder. >>

Saikat Mondal, Adhip Agarwala. Topological Phase Transition under Infinite Randomness. arXiv: 2506.19913v1 [cond-mat.dis-nn]. Jun 24, 2025.

https://arxiv.org/abs/2506.19913

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

Keywords: gst, order, disorder, disorder & fluctuations, randomness, criticality, transitions, forms of power

FonT: who knows if during some master's courses on the organization and evolution of social enclosures, held by the legendary "Frattocchie School" ( https://it.m.wikipedia.org/wiki/Scuola_delle_Frattocchie ) during the early 80s (but also early 90s) some bizarre theoretician advanced the imaginative, up in the air, absolutely unfounded hypothesis (here it is emphasized: absolutely), about the possibility of an immediate cracking of a social structure due to the action of idiots (?) disguised as idiots until the complete, universal, ontheback breakthrough anzicheforse?