# gst life: apropos of critical points, love (at first sight and love from liking or friendship) might be a second-order phase transition.

<< The hypothesis of the human brain operation in vicinity of a critical point has been a matter of a hot debate in the recent years. >>

<< In this work, (AA) suggest that love might be an example of a second-order phase transition occurring in the brain. (They) show that this hypothesis explains a lot of well-known properties of love. Analyzing several most famous literature examples and a private diary, (they) show that the intensity of feelings exhibits a universal scaling behavior, distinguishing two cases: love at first sight and love developing from liking or friendship (friends first), both being studied in psychology. >>

The theory of second-order phase transitions developed by L.D. Landau (1980) << has inspired a lot of activity in physics, because it turned out that such transitions are characterized by a universal scaling behavior. Independently of the nature of the system, their parameters exhibit power law dependencies on the dimensionless parameter (temperature). >>

<< The key hypothesis of the present work is that love is a second-order phase transition occurring in the human brain under the influence of hormones, such as dopamine and serotonin (..). The brain switches from the normal operation in the critical regime to the supercritical regime because of the increase of the excitation (more dopamine) and reduction of the inhibition (less serotonin) (..). The order parameter of the transition is the intensity of feelings: before the transition, the subject has no particular feelings, while after the transition the feelings are non-zero. The most direct consequence is that the order parameter should exhibit a universal power law behavior: the feelings should grow as a square root of time α ∼√ >>

<< Since it is impossible to analyze the human feelings directly during such uncontrollable phenomenon as ”love at first sight”, (AA) have decided to perform a quantitative study of the intensity of feelings depicted in the literature. (..) (They) have chosen three well-known books for this analysis: ”Romeo and Juliet” (W. Shakespeare), ”The Lily of the Valley” (H. de Balzac, (..)), and ”Martin Eden” (J. London). >>

<< the case of a non-zero external ”bias”, which is a situation that occurs more often than love at first sight. Indeed, one usually knows several persons better than all the others, and thus some positive feelings towards some of them can be present before the transition occurs. (..) To study this transition quantitatively, (AA) have chosen another well-known book, ”Jane Eyre” by Charlotte Bronte. This books is also quite autobiographic, and famous for the psychological details, that got its author the title of ”first historian of the private consciousness”. The delay between the initial acquaintance and love is now of several weeks (about 45 days).

Dmitry Solnyshkov, Guillaume Malpuech. Love might be a second-order phase transition. arXiv: 2203.13246v1 [cond-mat.stat-mech]. Mar 24, 2022. 

https://arxiv.org/abs/2203.13246

Also

keyword 'transition' in FonT: 

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

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

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

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

keywords: gst, life, love, transitions,  critical point, phasetransition, second-order phase transition, brain, mind, behavior.

# gst: liquid–liquid phase transition, the two forms of liquid water (mixed with the natural antifreeze trehalose)

<< Liquids are structurally disordered, so it’s not immediately obvious how they can support two distinct structures with different densities. But that does seem to be possible for liquids in which some degree of directional bonding, such as hydrogen bonds between adjacent water molecules, makes distinct local structures possible. Liquid–liquid transitions have been reported, for example, in silicon, gallium, phosphorus and silicates. But finding one in supercooled water has proved very challenging. There have been previous claimed observations of a liquid–liquid transition in aqueous solutions at ambient pressure, (..) where the solute, such as the sugar glycerol, sometimes used as a cryoprotectant, lowers the freezing point. But such claims have been disputed.(..) Other researchers have reported liquid-like behaviour as the two well-established high- and low-density forms of amorphous (glass-like) ice interconvert. (..) >>

<< In 2014 Yoshiharu Suzuki (..) working with veteran water researcher Osamu Mishima, reported possible signs of a liquid–liquid transition, ending in a critical point where the two liquid states become indistinguishable, in emulsified, supercooled solutions of glycerol. (..) They saw signs of two distinct disordered states with different densities at a temperature of 150K. But there was no direct evidence that both were liquids, rather than amorphous ice. >>

<< Suzuki has now explored the same approach using trehalose as the solute – a sugar produced as a natural cryoprotectant by some organisms, such as insects, that experience extreme cold, to prevent their blood from freezing. He pressurised dilute emulsified solutions to about 0.6GPa at a range of temperatures below 159K, and then decompressed them again.  >>

<< Such hysteresis – whereby the density jumps at different pressures on compression and decompression – is normal for a first-order transition where a parameter such as density changes discontinuously. It reflects the fact that the transition has to start with the chance formation of a ‘nucleus’ of the new phase, which then grows. >>

<< Suzuki is not yet sure why trehalose stabilises water so well against crystallisation, compared with glycerol – but this might help explain why life uses it as an antifreeze. >>

Philip Ball. Direct evidence emerges for the existence of two forms of liquid water. Feb 1, 2022.

https://www.chemistryworld.com/news/direct-evidence-emerges-for-the-existence-of-two-forms-of-liquid-water/4015144.article  

Also

keyword 'water' in FonT

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

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

keywords: gst, transition, liquid-liquid transition, water

# gst: discontinuous transitions to active nematic turbulence.

<< Active fluids exhibit chaotic flows at low Reynolds number known as active turbulence. Whereas the statistical properties of the chaotic flows are increasingly well understood, the nature of the transition from laminar to turbulent flows as activity increases remains unclear. Here, through simulations of a minimal model of unbounded active nematics, (AA) find that the transition to active turbulence is discontinuous. (They) show that the transition features a jump in the mean-squared velocity, as well as bistability and hysteresis between laminar and chaotic flows. >>

<< From distributions of finite-time Lyapunov exponents, (AA) identify the transition at a value A∗≈4900 of the dimensionless activity number. Below the transition to chaos, (They) find subcritical bifurcations that feature bistability of different laminar patterns. These bifurcations give rise to oscillations and to chaotic transients, which become very long close to the transition to turbulence. Overall, (Their) findings contrast with the continuous transition to turbulence in channel confinement, where turbulent puffs emerge within a laminar background. >>

AA << propose that, without confinement, the long-range hydrodynamic interactions of Stokes flow suppress the spatial coexistence of different flow states, and thus render the transition discontinuous. >>️

Malcolm Hillebrand, Ricard Alert. Discontinuous Transition to Active Nematic Turbulence. arXiv: 2501.06085v1 [cond-mat.soft]. Jan 10, 2025.

https://arxiv.org/abs/2501.06085

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

Keywords: gst, chaos, transition, turbulence, jumps, active nematics

# gst: apropos of transitions, perspectives on viscoelastic flow instabilities; the 'porous individualism'

<< given the observation that disorder can suppress the transition to elastic turbulence in 2D porous media (..), it has been unclear whether and how this transition manifests in disordered 3D media — though elastic turbulence has been speculated to underlie the long-standing observation that the macroscopic flow resistance of an injected polymer solution can abruptly increase above a threshold flow rate in a porous medium, but not in bulk solution >>️

AA << found that the transition to unstable flow in each pore is continuous, arising due to the increased persistence of discrete bursts of instability above a critical value of the characteristic (Weissenberg no.) Wi; however, the onset value varies from pore to pore. This observation that single pores exposed to the same macroscopic flow rate become unstable in different ways provides a fascinating pore-scale analog of “molecular individualism” [P.  De Gennes, Molecular individualism. Science 276, 1999–2000 (1997)], in which single polymers exposed to the same extensional flow elongate in different ways; the authors therefore termed it “porous individualism”, although it is important to note that here, this effect is still at the continuum (not molecular) scale. Thus, unstable flow is spatially heterogeneous across the different pores of the medium, with unstable and laminar regions coexisting >>

AA << quantitatively established that the energy dissipated by unstable pore-scale fluctuations generates an anomalous increase in flow resistance through the entire medium that agrees well with macroscopic pressure drop measurements. >>

Sujit S. Datta, Arezoo M. Ardekani, et al. Perspectives on viscoelastic flow instabilities and elastic turbulence. arXiv: 2108.09841v1 [physics.flu-dyn]. Aug 22, 2021. 

https://arxiv.org/abs/2108.09841

Also

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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keywords: gst, droplet, fluctuations, disorder, instability, viscoelastic flow instability, turbulence, elastic turbulence, individualism, porous individualism, transition

# gst: apropos of transitions, scrambling trajectories in a radiative random unitary circuit.

AA << study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment (..). As a result, initially localized quantum information  not only spreads within the system, but also spills into the environment. >>

<< The transition is also easily extended to higher dimensions, where higher-dimensional DP (directed percolation) universality classes will control the critical behavior. >>

<<  The transition in operator spreading  coincides with an information-theoretic 3 transition, which can be framed by  viewing (AA) circuit as a toy model for an evaporating black hole (..). >>️

<< Depending on the initial state of the swapped-in qubits, (AA) observe a corresponding entanglement transition in the coherent information into the environment. >>

️

Zack Weinstein, Shane P. Kelly, Jamir Marino, Ehud Altman. Scrambling Transition in a Radiative Random Unitary Circuit. arXiv:2210.14242v1 [quant-ph]. Oct 25, 2022.

https://arxiv.org/abs/2210.14242

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

Keywords: transition, quantum information, entanglement transition, scrambling, directed percolation

# gst: the hypothesis of a first order phase transition (a type of abrupt phase transition) to originate black holes observed by LIGO/Virgo in binary mergers.

<<  To summarize, motivated by the ~10 M* (mass similar to that of the sun) black holes observed by LIGO/Virgo in binary mergers, (AA) entertained the possibility that the quark-gluon confinement phase transition was first order due to the effect of 6 light quarks. The larger number of light quarks, compared to the standard case, pushes the transition temperature below ∼100 MeV. The first order nature of the transition significantly improves the likelihood of forming primordial black holes and its lower temperature suggests that these black holes can potentially be as heavy as ∼10 M*, compared to ∼M* for the standard QCD transition. >>

Hooman Davoudiasl.  LIGO/Virgo Black Holes from a First Order Quark Confinement Phase Transition. Phys. Rev. Lett. 123, 101102. Sep 6, 2019.   https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.101102  

Ingrid Fadelli. Theory proposes that LIGO/Virgo black holes originate from a first order phase transition. Sep 23, 2019.    https://m.phys.org/news/2019-09-theory-ligovirgo-black-holes-phase.html  

QCD = quantum chromodynamic  
https://en.m.wikipedia.org/wiki/Standard_Model

# gst: breakthrough in unstable growth processes, shorter branches can revive when a striking transition of the leading branch reaches the boundary of the system.

<< Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They often emerge as a result of unstable growth processes, in which growing branches compete for the available flux. This leads to effective repulsion between the branches and screening of the shorter ones. (AA) show that a striking transition in growth dynamics takes place as the leading branch reaches the boundary of the system. The shorter branches revive then and grow toward the leading one forming loops. These effects are observed both in living and inanimate systems. >>

Stanisław Zukowski, Annemiek Johanna Maria Cornelissen, et al. Finger revival and reconnections near breakthrough in unstable growth processes. arXiv: 2212.08878v1 [physics.flu-dyn]. Dec 17, 2022.

https://arxiv.org/abs/2212.08878

Also

keyword 'transition' in FonT: 

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

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

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

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

Keywords: gst, transition, growth, growth dynamics, transport networks, spatial networks

# gst: apropos of transitions, rich behaviors from chimeras or solitary states to traveling waves

AA << study numerically the spatiotemporal dynamics of a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. >>

<< It is shown that the discretized oscillator exhibits a richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Such regimes as the coexistence of multichimera state/traveling wave and solitary state are revealed for the first time and studied in detail. >>

<< It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient towards the purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, observation time, initial conditions, and influence of external noise. >>

Elena Rybalova, Sishu Muni, Galina Strelkova. Transition from chimera/solitary states to traveling waves. arXiv: 2212.07990v1 [nlin.AO]. Dec 15, 2022. 

https://arxiv.org/abs/2212.07990

Also

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

keyword 'waves' in FonT

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

keyword 'onda' in Notes (quasi-stochastic poetry)

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

Keywords: gst, behavior, van der Pol oscillator, transition, chimera state, solitons, solitary state, waves, noise

# gst: simultaneous presence of attraction and repulsion in quantum self-sustained oscillators

AA << study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. >>

They << discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. >>

<< Remarkably, (they) find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. >>

Bulti Paul, Biswabibek Bandyopadhyay, Tanmoy Banerjee. Attractive-repulsive interaction in coupled quantum oscillators. Phys. Rev. E 110, 034210. Sept 19, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.034210

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

Keywords: gst, transition, symmetry-breaking transition, noise, attractive-repulsive interaction, coupled qu-oscillator

# 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: apropos of bubble rearrangements, transition from slip to scraping as critical-like behavior in foam dynamics.

<< Jamming systems, including colloids, emulsions, foams, and biological tissues, undergo significant deformation during processes like material scraping or wound self-healing. To adequately spread a foam or cream over a surface, external force must be applied to artificially scrape it. Notably, the transition from slip to scraping when foam is manipulated using a rigid plate remains poorly understood. >>

<< Systematic observations of the internal foam structure during scraping were conducted, and the scraping length was qualitatively analyzed by varying the scraping velocity. (AA) study reveals that the transition from slip to scraping is driven by the sequential propagation of bubble rearrangements. Furthermore, the scraping length diverges towards the transition point, with a critical exponent of approximately 0.61. >>

<< These findings align with directional percolation theory, underscoring the robustness of the theoretical framework. >>

Masaya Endo, Rei Kurita. Critical-like behavior in foam dynamics: Transition from slip to scraping. Phys. Rev. Research 7, 023013. Apr 3, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023013

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

Keywords: gst, bubble, bubble rearrangements, foam, jamming, transition, criticality, scraping,  percolation

# 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: 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: apropos of a immaginary transition (with a tipping point), which simulates the chaotic interactions of three black holes.

<< The interactions between three bodies such as stars or planets or black holes cannot be predicted with an elegant formula. Moerman (Arend Moerman) therefore used a computer that calculates what happens for a short period of time and then uses the result for the next period of time. >>

AA << varied the masses of the three interacting black holes. They started with one solar mass and went up to a billion times the mass of the sun. >>

<< Around ten million solar masses, there appeared to be a tipping point. In the simulations, black holes that are lighter than about ten million solar masses mostly eject each other through a gravitational slingshot. Black holes heavier than about ten million solar masses start to merge. First, two black holes merge. The third black hole will follow later. The black holes merge because they lose kinetic energy and that is because they emit gravitational waves. >>

<< Arend's work (..) has led to a new understanding of how black holes become supermassive. In the simulations, we see that heavy black holes no longer endlessly move around each other, but that, if they are heavy enough, they collide pretty much instantly. >> Simon Portegies Zwart. 

Simulating chaotic interactions of three black holes. Netherlands Research School for Astronomy. Oct 20, 2021. 

https://phys.org/news/2021-10-simulating-chaotic-interactions-black-holes.html

Tjarda C. N. Boekholt, Arend Moerman, Simon F. Portegies Zwart. Relativistic Pythagorean three-body problem. Phys. Rev. D 104, 083020. 14 Oct 14,  2021. 

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.083020

Also

more on the three-body problem (695 families of collisionless orbits). FonT. Oct 16, 2017. 

https://flashontrack.blogspot.com/2017/10/gst-more-on-three-body-problem-695.html

keyword 'black hole' | 'astro' in FonT

https://flashontrack.blogspot.com/search?q=black+hole

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

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

keywords: gst, black hole, three-body problem, transition, chaos, chaotic interaction, tipping point.

# gst: apropos of the transition of order from chaos, a universal behavior near a critical point.

<< As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, (AA) observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. >>️

AA << study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system.   >>️

<< the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. (AA) results show that the observed emergence of order from chaos is a continuous phase transition (..) the critical exponents characterizing this transition fall in the universality class of directed percolation. >>️

The << paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point. >>️

Sivakumar Sudarsanan, Amitesh Roy, et al. Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system. Phys. Rev. E 109, 064214. Jun 20, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064214

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

Keywords: gst, order, chaos, transition 

# gst: self-organization to multicriticality; when a system can self-organize to a new type of phase transition while staying on the verge of another.

<< Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, (AA) show that the dynamics inside the self-organized critical state are fundamentally far more versatile than previously recognized, to the extent that a system can self-organize to a new type of phase transition while staying on the verge of another. >>

<< In this first demonstration of self-organization to multicriticality, (AA) investigate a model of coupled oscillators on a random network, where the network topology evolves in response to the oscillator dynamics. (They) 

 show that the system first self-organizes to the onset of oscillations, after which it drifts to the onset of pattern formation while still remaining at the onset of oscillations, thus becoming critical in two different ways at once. >>

 

<< The observed evolution to multicriticality is robust generic behavior that (AA) expect to be widespread in self-organizing systems. Overall, these results offer a unifying framework for studying systems, such as the brain, where multiple phase transitions may be relevant for proper functioning.>>

Silja Sormunen, Thilo Gross, Jari Saramäki. Self-organization to multicriticality. arXiv: 2506.04275v1 [nlin.AO]. Jun 4, 2025. 

https://arxiv.org/abs/2506.04275

Also: network, random, self-assembly, transition, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, random, self-assembly, transition, phase transition, multiple phase transitions, self-organizing systems, self-organized criticality, multicriticality, brain.

# gst: apropos of transitions to turbulence, pulsatility delays the transition to sustained turbulence in quasi-2D shear flows

<< Two-dimensional disturbances require high Reynolds numbers to incite transition from a steady base flow, as transient growth is modest. With the addition of an oscillatory base flow component, (AA) work shows that the transient growth experienced by two-dimensional initial perturbations is often well above that provided by the steady component. >>

<< However, as has been shown for three-dimensional flows [B. Pier and P. J. Schmid, J. Fluid Mech. 926, A11 (2021)], the transient growth is almost entirely composed of modal intracyclic growth, rather than a transient mechanism which takes advantage of non-normality. This lack of transient growth, relative to the severe decay induced by the favorable pressure gradient during the acceleration phase of the oscillatory base flow, only ever delays the transition to sustained turbulence. >>

<< Thus, a nonoscillatory driving force remains the most efficient strategy for sustained turbulence in quasi-two-dimensional shear flows. The only benefit provided by pulsatility is that the amplitude of the initial condition required to trigger intermittent turbulence is orders of magnitude smaller. >>️

Christopher J. Camobreco, Alban Pothérat, Gregory J. Sheard. Pulsatility delays the transition to sustained turbulence in quasi-two-dimensional shear flows. Phys. Rev. Fluids 10, 023905. Feb 25, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.023905

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

Keywords: gst, pause, transition, turbulence, vortex

# gst: towards (insights into) intermittency and inhomogeneity of turbulent mixing

<< Fluid elements deform in turbulence by stretching and folding. In this work, by projecting the material deformation tensor onto the largest stretching direction, the dynamics of folding is depicted through the evolution of the material curvature. Results from direct numerical simulation (DNS) show that the curvature growth exhibits two regimes, first a linear stage dominated by folding fluid elements through a persistent velocity Hessian which then transitions to an exponential growth driven by the stretching of already strongly bent fluid elements. This transition leads to strong curvature intermittency at later stages, which can be explained by a proposed curvature-evolution model. The link between velocity Hessian to folding provides a new way to understand the crucial steps in energy cascade and mixing in turbulence beyond the classical linear description. >>

Yinghe Qi, Charles Meneveau, Greg Voth, Rui Ni. Folding dynamics and its intermittency in turbulence. arXiv: 2301.10341v1 [physics.flu-dyn]. Jan 24, 2023. 

https://arxiv.org/abs/2301.10341

Also

keyword 'intermittency' in FonT

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

keyword 'turbulence' in FonT

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

keyword 'turbolento' | 'turbolenza' in Notes (quasi-stochastic poetry)

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

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

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

Keywords: gst, intermittency, turbulence, transition

# gst: apropos of prolate- oblate spheroid transition, the chaotic behavior of a spinless entity around a black hole.

AA << investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. (AA) do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method. >>️

Ricardo A. Mosna, Fernanda F. Rodrigues, Ronaldo S. S. Vieira. Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole. arXiv: 2207.04341v1 [gr-qc]. Jul 9, 2022. 

https://arxiv.org/abs/2207.04341

Phys. Rev. D 106, 024016 (2022). 

https://doi.org/10.1103/PhysRevD.106.024016

Also - Oblate and Prolate Spheroid.  

<< The shape of the earth is that of a round ball or sphere slightly flattened at two opposite sides. Such a body is termed a spheroid. There are two kinds of spheroids-oblate and prolate; the former as the shape of an orange, the latter that of a lemon.  >>️

Oblate and Prolate Spheroid.  

https://etc.usf.edu/clipart/30500/30587/spheroid_30587.htm

img    https://etc.usf.edu/clipart/30500/30587/spheroid_30587_sm.gif

Also

keyword 'transition' in FonT: 

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

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

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

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

Keywords: gst, spheroid, behavior, chaos, transition, black hole

# gst: the complex dynamics of a transition

<< The transition state is a central concept of chemistry (..) Everything we think about in reactions really hinges on the structure of the transition state, which we cannot directly observe. >> Robert Field.

<< there are two different mechanisms competing for transition states, >>

<< there are additional reaction mechanisms beyond those two, >>

Chemists glimpse the fleeting 'transition state' of a reaction. 

Massachusetts Institute of Technology. Dec 16, 2019.

https://m.phys.org/news/2019-12-chemists-glimpse-fleeting-transition-state.html