# 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: 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?

# gst: random interaction in active matter models; critical changes in Vicsek's scenario.

<< Randomness plays a key role in the order transition of active matter but has not yet been explicitly considered in pairwise interaction connection. In this paper, (AA) introduce the perception rate 𝑃 into the Vicsek model as the probability of the interaction connections and model the connections as superposition states. (They) show that with increasing 𝑃, the polar order number undergoes an order transition and then saturation. >>

<< The order transition is a first-order phase transition with band formation, and the effect of 𝑃 is different from density. The change of the order number is linked with the interaction structure. The order transition, order saturation, and phase separation correspond to different critical changes in the local interaction number. >>

<< The global interaction structure is further analyzed as a network. The decrease of 𝑃 is comparable to random edge removal, under which the network experiences modal transitions near the critical points of the order number, and the network exhibits surprising robustness.  (AA) results suggest that random interaction can be a new important factor in active matter models, with potential applications in robotic swarms and social activities. >>

Ruizhi Jin, Kejun Dong. Role of random interaction connection in the order transition of active matter based on the Vicsek model. Phys. Rev. E 111, 064122. Jun 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/9rdd-tbn7

arXiv: 2501.10669v1 [cond-mat.soft]. Jan 18, 2025. 

https://arxiv.org/abs/2501.10669

Also: network, random, perception, transition, swarm, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, active matter, network, randomness, perception, criticality, transitions, swarm.

# gst: interactive anisotropic walks in 2D generated from a 3-state opinion dynamics model.

<< A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. >>

In this article AA has performed the mapping << in such a way that the walk is directed along the 𝑌 axis while it can move either way along the 𝑋 axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. >>

<< For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power-law behavior, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents. >>

Surajit Saha, Parongama Sen. Interactive anisotropic walks in two dimensions generated from a three-state opinion dynamics model. Phys. Rev. E 111, 064123. Jun 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/5c2y-yj1z

arXiv: 2409.10413v3 [cond-mat.stat-mech]. Apr 28, 2025. 

https://arxiv.org/abs/2409.10413

Also: walk, noise, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, walk, walking, random walk, randomness, noise, transitions, noise-induced transitions, criticality.

# gst: active drive towards elastic spinodals

<< Active matter, exemplified by adaptive living materials such as the actomyosin cytoskeleton, can navigate material parameter space, leading to unconventional mechanical responses. In particular, it can self-drive toward elastic spinodal regimes, where inhomogeneous floppy modes induce elastic degeneracy and enable a controlled interplay between rigidity loss and recovery. Proximity to such marginal states leads to stress localization and the formation of force chains that can be actively assembled and disassembled. >> 

Here AA << extend the classical notion of spinodal states to active solids and demonstrate how these extreme mechanical regimes can be actively accessed. Moreover, (They) show that in a nonlinear setting, crossing elastic spinodals generates new energy wells and makes force channeling an intrinsic feature of the emerging microstructure. >>

Ayan Roychowdhury, Madan Rao, Lev Truskinovsky. Active drive towards elastic spinodals. Phys. Rev. E 111, 065416. Jun 20, 2025.

https://journals.aps.org/pre/abstract/10.1103/h2yp-d2s2

arXiv: 2403.17517v3 [cond-mat.soft]. May 20, 2025.

https://arxiv.org/abs/2403.17517

Also: elastic, transition, instability, disorder & fluctuations, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, instability, disorder & fluctuations, active matter, elasticity, elastic forces, elastic deformation, elastic spinodals, self-assembly.

# gst: spontaneous flow instability in active nematics; when quiescent and flowing states may coexist.

<< Active nematics exhibit spontaneous flows through a well-known linear instability of the uniformly aligned quiescent state. Here, (AA) show that even a linearly stable uniform state can experience a nonlinear instability, resulting in a discontinuous transition to spontaneous flows. In this case, quiescent and flowing states may coexist. >>

<< Through a weakly nonlinear analysis and a numerical study, (AA) trace the bifurcation diagram of striped patterns and show that the underlying pitchfork bifurcation switches from supercritical (continuous) to subcritical (discontinuous) by varying the flow-alignment parameter. >>

AA << predict that the discontinuous spontaneous flow transition occurs for a wide range of parameters, including systems of contractile flow-aligning rods. (AA) predictions are relevant to active nematic turbulence and can potentially be tested in experiments on either cell layers or active cytoskeletal suspensions. >>

Ido Lavi, Ricard Alert, et al. Nonlinear Spontaneous Flow Instability in Active Nematics. Phys. Rev. Lett. 134, 238301. Jun 9, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.238301 

arXiv: 2403.16841v1 [cond-mat.soft].

https://arxiv.org/abs/2403.16841

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

Also: Active nematics, in A. Doostmohammadi, et al. Nat Comm vol 9, no 3246 (2018). 

https://www.nature.com/articles/s41467-018-05666-8

Keywords: gst, instability, turbulence, transitions, supercritical-- subcritical bifurcations, active nematics.

# aibot: noise balance and stationary distribution of stochastic gradient descent.

<< The stochastic gradient descent (SGD) algorithm is the algorithm (is used) to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. >>

<< In this work, (AA) show that the minibatch noise of SGD regularizes the solution towards a noise-balanced solution whenever the loss function contains a rescaling parameter symmetry. Because the difference between a simple diffusion process and SGD dynamics is the most significant when symmetries are present, (AA) theory implies that the loss function symmetries constitute an essential probe of how SGD works. (They) then apply this result to derive the stationary distribution of stochastic gradient flow for a diagonal linear network with arbitrary depth and width. >>

<< The stationary distribution exhibits complicated nonlinear phenomena such as phase transitions, broken ergodicity, and fluctuation inversion. These phenomena are shown to exist uniquely in deep networks, implying a fundamental difference between deep and shallow models. >>

Liu Ziyin, Hongchao Li, Masahito Ueda. Noise balance and stationary distribution of stochastic gradient descent. Phys. Rev. E 111, 065303. Jun 6, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.065303

Also: ai (artificial intell) (bot), network, noise, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: ai, artificial intelligence, noise, stochasticity, networks, neural networks, deep learning,stochastic gradient descent (SGD), transitions, phase transitions, broken ergodicity, fluctuation inversion

# gst: double burst transition in hypergraphs.

Fig.2 - Bifurcation diagram. A two-parameter stability diagram in K2-d_th space depicting the different synchronization transition regimes. Blue, gray, cyan, red, light green, magenta, and dark gray present the regimes for continuous, tiered, classical explosive, forward and  backward double jump, forward double jump, explosive with stable middle states, and backward double jump synchronization transitions, respectively. 

This AA study << aims to develop a generalized concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. >>

AA << found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. >>

<< To reinforce numerical observations, (They) employed the Ott-Antonsen ansatz. (AA) observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition. >>

Sangita Dutta, Prosenjit Kundu, et al. Double explosive Kuramoto transition in hypergraphs. Phys. Rev. Research 7, L022049. June 2, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.L022049

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

Keywords: gst, transitions, phase transitions.

# gst: symmetry breaking in time-dependent billiards.

AA << investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When inelastic collisions are introduced between the particle and the boundary, the velocity reaches a plateau after the crossover iteration. The system presents the expected behavior for this type of transition, including scale invariance, critical exponents related by scaling laws, and an order parameter approaching zero in the crossover iteration. >>

AA << analyze the velocity spectrum and its averages for dissipative and conservative dynamics. The transition point in velocity behavior caused by the physical limit of the boundary velocity and by the introduced dissipation coincides with the crossover interaction obtained from the Vrms (root mean sq V) curves. Additionally, (they) examine the velocity distributions, which lose their symmetry once the particle's velocity approaches the lower limit imposed by the boundary's motion and the system's control parameters. This distribution is also characterized analytically by an expression P(V,n), which attains a stationary state, with a well-defined upper bound, only in the dissipative case. >>

Anne Kétri Pasquinelli da Fonseca, Edson Denis Leonel. Symmetry breaking in time-dependent billiards. arXiv: 2505.20488v1 [nlin.CD]. May 26, 2025.

https://arxiv.org/abs/2505.20488

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

Keywords: gst, billiard, particles, transitions, dissipation, symmetry breaking, inelastic collisions.

# gst: apropos of ambiguous scenarios, very persistent random walkers reveal transitions in landscape topology

AA << study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical glass transition, but persistent walks remain ergodic at lower energies. >>

<< In models where the energy landscape is thoroughly understood, (They) show that, in the limit of infinite persistence time, the ergodicity-breaking transition coincides with a transition in the topology of microcanonical configuration space. (They) conjecture that this correspondence generalizes to other models, and use it to determine the topological transition energy in situations where the landscape properties are ambiguous. >>

Jaron Kent-Dobias. Very persistent random walkers reveal transitions in landscape topology. arXiv: 2505.16653v2 [cond-mat.dis-nn]. May 23, 2025. 

https://arxiv.org/abs/2505.16653

Also: random, walk, walking, disorder, transition, in https://www.inkgmr.net/kwrds.html

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

Keywords: mean-field disordered systems, disorder, randomness, random walker, transitions, topological transition energy, ambiguity.

# gst: dynamic expulsion of magnetic flux by vortices.

AA << study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. (They)  concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. >>

<< Within the context of a weak background field, (AA) are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. >>

<< Furthermore, in the case of a row of vortices, (AA) show that the orientation of the background field significantly influences the evolution, especially at higher field strengths. >>

Jonathan Tessier, Francis J. Poulin, David W. Hughes. Dynamic expulsion of magnetic flux by vortices. Phys. Rev. Fluids 10, 053702. May 19, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.053702

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

Keywords: gst, vortex, transitions, flux expulsion, vortex disruption.

# gst: toy model of turbulent shear flow using vortons.

AA << introduce a toy model for shear flows, exploiting the spatial intermittency and the scale separation between large-scale flows and small-scale structures. The model is highly sparse, focusing exclusively on the most intense structures, which are represented by vortons—dynamically regularized quasisingularities that experience rapid distortion from the large-scale shear. The vortons, in turn, influence the large-scale flow through the subgrid stress tensor. >>

<< Despite its simplicity, the model displays an interesting transition between two distinct regimes: (i) a laminar regime, where dissipation is entirely attributed to the large-scale flow and the vortons dynamics is essentially diffusive, and (ii) a turbulent regime, in which most of the dissipation arises from the vortons. These regimes correspond to different scalings of dissipation and the Grashof number as functions of the Reynolds number, with power-law relationships that resemble those observed in classical turbulence. >>

Wandrille Ruffenach, Lucas Fery, Bérengère Dubrulle. Toy model of turbulent shear flow using vortons. Phys. Rev. Fluids 10, 054601. May 1, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.054601

arXiv:2501.05779v2 [physics.flu-dyn]. 

https://arxiv.org/abs/2501.05779

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

Keywords: gst, turbulence, intermittency, transitions, vortons

# life: to protect freedoms, not just funding.

<< At Harvard University in Cambridge, Massachusetts, and Columbia University in New York City, cuts to previously granted federal research funds have been accompanied by demands from the government. If enacted, the changes to departmental oversight, disciplinary procedures, campus police and governance structures would allow the government to dictate hiring, student admissions and disciplinary decisions. >>

<< So far, the US science community has been outspoken about the threats that funding cuts pose to health, innovation and the economy. Yet, few researchers have decried the devastation wreaked on science by attacks on civil liberties and the rule of law. >>

Andrew M. Leifer, Andrea J. Liu, Sidney R. Nagel. US researchers must stand up to protect freedoms, not just funding. Nature 641, 592-593. May 13, 2025.

https://www.nature.com/articles/d41586-025-01466-5

Also: people who turn career into a game playing ... FonT. May 31, 2017.

https://flashontrack.blogspot.com/2017/05/s-game-people-who-turn-career-into-game.html

Also: minimal risk, in FonT 

https://flashontrack.blogspot.com/search?q=minimal+risk

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

Also:  dance, game, transition, sars* covid* (aka 1or2achoos), forms of power, Mr. Donald, are you ready, in https://www.inkgmr.net/kwrds.html 

Also: nefst (e.g. not embedded, freestyle thinker) 

https://quod.lib.umich.edu/m/middle-english-dictionary/dictionary/MED20173/track

Keywords: life, acad, game, dance, transitions, nefst, 1or2achoos, minimal risk, turn career, forms of power, Mr. Donald, are you ready.

# gst: emergent scattering regimes in disordered metasurfaces near critical packing.

<< Disordered metasurfaces provide a versatile platform for harnessing near- and far-field scattered light. Most research has focused on either particulate topologies composed of individual, well-identified metaatoms or, to a lesser extent, semi-continuous aggregate topologies without well identified inclusions. >>

Here, AA << uncover an intermediate critical packing regime characterized by metasurface morphologies in which a significant fraction of metaatoms begin to connect. (They) experimentally demonstrate that, at this threshold, the properties of the scattered light abruptly change and interpret this change as a marked transition in the statistics of the photon density of states. >>

<< Unlike percolation metal films, this transition affects not only the specular but also the diffuse components of the scattered light in a profound way. (AA)  results introduce critical packing topologies as a novel design strategy for manipulating the spectral and angular characteristics of light using ultrathin optical coatings. Emergent functionalities include color shifts in diffuse light driven by multiple scattering and surface whitening, >>

Miao Chen, Adrian Agreda, et al. Emergent scattering regimes in disordered metasurfaces near critical packing. arXiv: 2505.02244v1 [physics.optics]. May 4, 2025.

https://arxiv.org/abs/2505.02244

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

Keywords: gst, disorder, fluctuations, transitions, disordered metasurfaces, ultrathin optical coatings, near- far- field scattered light, critical packing regime.

# gst: elasticity of fibers prefers the chaos of turbulence.

<< The dynamics of fibers, modeled as a sequence of inertial beads linked via elastic springs, in turbulent flows is dictated by a nontrivial interplay of inertia and elasticity. Such elastic, inertial fibers preferentially sample a three-dimensional turbulent flow in a manner that is qualitatively similar to that in two dimensions [R. Singh et al., Phys. Rev. E 101, 053105 (2020)]. >>

<< Both these intrinsic features have competing effects on fiber dynamics: Inertia drives fibers away from vortices while elasticity tends to trap them inside. However, these effects swap roles at very large values. A large inertia makes the fibers sample the flow more uniformly while a very large elasticity facilitates the sampling of straining regions. >>

<< This complex sampling behavior is further corroborated by quantifying the chaotic nature of sampled flow regions. This is achieved by evaluating the maximal Lagrangian Lyapunov Exponents associated with the flow along fiber trajectories. >>

Rahul K. Singh. Elasticity of fibers prefers the chaos of turbulence. Phys. Rev. E 111, L053101. May 5, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L053101

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

Keywords: gst, elasticity, turbulence, chaos, transitions

# gst: hyperchaos and complex dynamical regimes in N-d neuron lattices.

AA << study the dynamics of N-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. (They) consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. >>

<< As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. >>

<< For lattices in higher spatial dimensions, (AA) discover dynamical effects arising from the ``destructive interference'' of many connected neurons and miniature ``phase transitions'' from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, (They) observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. >>

<< These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems. >>

Brandon B. Le, Dima Watkins. Hyperchaos and complex dynamical regimes in N-dimensional neuron lattices. arXiv: 2505.03051v1 [nlin.CD]. May 5, 2025.

https://arxiv.org/abs/2505.03051

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

Keywords: gst, brain, network, behavior, cooperation, cooperative behavior, chaos, hyperchaos, transitions, phase transitions, transition thresholds,  synchrony, dimensionality, topology of connectivity, intermittent bursting activity, interference, destructive interference.

# gst: overcoming overly simplistic representations, chaos and regularity in an anisotropic soft squircle billiard.

<< A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. >>

<< Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. >>

AA << study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. (AA) characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. (They) characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squarness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. >>

AA << expect (Their) work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards. >>

A. González-Andrade, H. N. Núñez-Yépez, M. A. Bastarrachea-Magnani. Chaos and Regularity in an Anisotropic Soft Squircle Billiard. arXiv: 2504.20270v1 [nlin.CD]. Apr 28, 2025.

https://arxiv.org/abs/2504.20270

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

Keywords: gst, billiard, soft billiard, soft-wall squircle billiard, particles, smooth boundary,  specular collisions, transitions, chaos

# gst: apropos of critical transitions, a new approach to extreme events.

FIG. 1. Dynamics of excitable complex networks [coupling topologies: random (RN); small-world (SW); scale-free (SF); all-to-all (complete; CP)]. 

<< Unexpected and often irreversible shifts in the state or the dynamics of a complex system often accumulate in extreme events with likely disastrous impact on the system and its environment. Detection, understanding, and possible prediction of such critical transitions are thus of paramount importance across a variety of scientific fields. >>

<< The rather modest improvement achieved so far may be due previous research mostly concentrating on either particular subsystems, considered to be of vital importance for the generating mechanism of a critical transition, or on the system as a whole. These approaches only rarely take into account the intricate, time-dependent interrelatedness of subsystems that can essentially determine emerging behaviors underlying critical transitions. >> 

AA << uncover subsystems, network vertices, and the interrelatedness of certain subsystems, network edges, as tipping elements in a networked dynamical system, forming a time-evolving tipping subnetwork. (They)  demonstrate the existence of tipping subnetworks in excitable complex networks and in human epileptic brains. These systems can repeatedly undergo critical transitions that result in extreme events. >>

AA << findings reveal that tipping subnetworks encapsulate key properties of mechanisms involved in critical transitions. >>

Timo Bröhl, Klaus Lehnertz. Emergence of a tipping subnetwork during a critical transition in networked systems: A new avenue to extreme events. Phys. Rev. Research 7, 023109. May 1, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023109

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

Keywords: gst, networks, excitable complex networks, network edges, network vertices, subnetwork, tipping subnetworks, small-worlds, unexpected shifts, transitions, critical transition, extreme events, interrelatedness, time-dependent interrelatedness.

# gst: apropos of adaptation of simple organisms to changing environments, self-organization and memory in a disordered entity to random driving.

AA << consider self-organization and memory formation in a mesoscopic model of an amorphous solid subject to a protocol of random shear confined to a strain range ±𝜖max. (They) develop proper readout protocols to show that the response of the driven system self-organizes to retain a memory of the strain range, which can be subsequently retrieved. >>

AA << findings generalize previous results obtained upon oscillatory driving and suggest that self-organization and memory formation of disordered materials can emerge under more general conditions, such as a disordered system interacting with its fluctuating environment. Self-organization results in a correlation between the dynamics of the system and its environment, providing thereby an elementary mechanism for sensing. >>

AA << conclude by discussing (Their)  results and their potential relevance for the adaptation of simple organisms lacking a brain to changing environments. >>

Muhittin Mungan, Dheeraj Kumar, et al. Self-Organization and Memory in a Disordered Solid Subject to Random Driving. Phys. Rev. Lett. 134, 178203. April 30, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.178203

arXiv: 2409.17096v2 [cond-mat.soft]. 

https://arxiv.org/abs/2409.17096

Also: disorder & fluctuations, 

self-assembly, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, self-assembly, self-organization, transitions

# gst: transitions of breakup regimes for viscous droplets in airflow.

In this AA study, << the transitions of breakup regimes for viscous droplets are investigated experimentally using high-speed imaging taken from a side view and a 45 view. Based on the morphology change in the middle of the droplet, the breakup regimes are classified into no-breakup, bag breakup, bag-stamen, low-order multimode, high-order multimode, and shear-stripping breakup. The droplet morphologies in different regimes and the corresponding transitions are discussed in detail. >>

<< The droplet viscosity dissipates the kinetic energy transferred by the airflow during the initial droplet flattening, and affects the development of the Rayleigh-Taylor instability wave after the flattening. Through the analysis of the droplet deformation and the Rayleigh-Taylor instability with the droplet viscosity taken into account, the transition conditions of different regimes are obtained in a regime map. By further considering the relative velocity loss between the droplet and the airflow, the ranges of the dual-bag breakup in the low-order multimode regime and the droplet retraction in the bag-stamen regime are determined. >>

Zhikun Xu, Tianyou Wang, Zhizhao Che. Transitions of breakup regimes for viscous droplets in airflow. arXiv: 2504.14149v1 [physics.flu-dyn]. Apr 19, 2025.

https://arxiv.org/abs/2504.14149

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

Keywords: gst, drops, droplets, droploids, viscous droplets, droplet breakup, transitions, instability, waves