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Visualizzazione dei post in ordine di data per la query transitional. Ordina per pertinenza Mostra tutti i post
Visualizzazione dei post in ordine di data per la query transitional. Ordina per pertinenza Mostra tutti i post

giovedì 13 giugno 2024

# gst: helical instabilities from mixed mode transitions in boundary layers

<< Recent (..) direct numerical simulations (DNS) of adverse- and zero-pressure-gradient boundary layers beneath moderate levels of free stream turbulence (𝑇⁢𝑢≤2%) revealed a mixed mode transition regime, intermediate between orderly and bypass routes. >>️

<< In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and both can contribute significantly as these interact. Three-dimensional visualizations of transitional eddies revealed a helical pattern, quite distinct from the sinuous and varicose forms seen in pure bypass transition. This raises the fundamental question of whether the helical pattern could be attributed to a previously unknown instability mode. >>️

In AA work << based on stability analyses, (they) show that it is indeed the case. Two-dimensional stability analyses are performed herein for base flows extracted from DNS flow fields. >>️

Rikhi Bose, Paul A. Durbin. Mixed mode transition in boundary layers: Helical instability. Phys. Rev. Fluids 9, 063905. Jun 12, 2024. 

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

Keywords: gst, instability, transition, turbulence, waves


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martedì 8 agosto 2023

# gst: substrate friction and geometric confinement could act as transitional control parms (in active nematics).


<< Using a minimal continuum model, (AA) investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, (They) observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. (AA) demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. (AA) results show that substrate friction and geometric confinement act as valuable control parameters in active nematics. >> 

Cody D. Schimming, C. J. O. Reichhardt, C. Reichhardt. Friction-mediated phase transition in confined active nematics. Phys. Rev. E 108, L012602. Jul 27, 2023. 



Keywords: gst, transition, friction, friction-mediated phase transition, confinement, nematics




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martedì 21 febbraio 2023

# 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. 

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keyword 'intermittency' in FonT

keyword 'turbulence' in FonT

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


keyword 'transition' | 'transitional' in FonT


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



Keywords: gst, intermittency, turbulence, transition


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lunedì 6 febbraio 2023

# gst: multiphase transitions and existence of bistable modes; how morphoelastic donuts get their wrinkles

<< Many biological structures are toroidal, or donut shaped. These structures often contain intricate wrinkling patterns that change as the object grows or contracts. >>

<< The team found that toroidal structures with large holes typically develop surface wrinkles close to the hole, whereas ones with smaller holes tend to form them away from the hole. Additionally, soft structures often have localized dimples, while stiff ones have bidirectional stripes or a mixture of spiral and axisymmetric stripes. Lastly, moderate-stiffness structures are typically adorned with periodic hexagonal patterns or a combination of hexagonal and labyrinth-like patterns. (AA) also found that their theory can predict wrinkling patterns in some nontoroidal structures, suggesting that it could be applied to a diverse range of objects. >>

Ryan Wilkinson. How Nature’s Donuts Get Their Wrinkles. Physics 16, s5. Jan 25, 2023. 

T. Wang et al. Curvature-regulated multiphase patterns in tori. Phys. Rev. Lett. 130, 048201. Jan 25, 2023.

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keyword 'transition' | 'transitional' in FonT



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




Keywords: gst, morphogenesis, transitions, multiphase transitions, bistability, pattern formation, elastic deformation, mechanical deformation




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mercoledì 21 dicembre 2022

# 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. 

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keyword 'transition' | 'transitional' in FonT



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




keyword 'waves' in FonT


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


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









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giovedì 29 settembre 2022

# life: apropos of transitions, here is an erratic Creature that slightly fluctuates ...

Here is an erratic Creature 

that slightly fluctuates with quasi-stochastic movements in the natural scenario where everything is full of unpredictability;

what is the Creature looking for?

Perhaps a house, perhaps a vision, a perspective, a spark, a glimmer at least, that helps it to face the unstoppable becoming, anzicheforse ...

the Creature ...
cit Erica Snyder, The Download, MIT Tech Rev, Sept 9, 2022. << Watching this ribbon eel swim is mesmerizing. >>️

Also

keyword 'erratico' | 'erratica' in Notes
(quasi-stochastic poetry)



keyword 'erratic' in FonT


Keywords: life, transition, erratics, erratic creature


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venerdì 15 luglio 2022

# life: a proposito di transizioni ...


a proposito di transizioni ... 

<< se si considera la limitatezza del numero degli standards da essi tante volte 'rigenerati'. >> 

<< Il problema qui - in una prospettiva sperimentale - non sembra la generazione (quasistocastica?) delle forme inattese, bensi' inerente la struttura logico- funzionale dei "filtri", dei setacci cioe', capaci di trattenere (e conservare) le soluzioni funzionali al codice, "metastabili" in senso evolutivo, con l'eliminazione di tutto cio' che puo' contribuire alla rigidita' strutturale dell' insieme.  >>

2134 - bizzarrie bop sugli standard. Notes. Apr 29, 2007. 



Also

Keywords: life, transition, evolution, quasi-stochastic,  poetry, quasi-stochastic poetry,  fuzzypoe, droploids.

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giovedì 31 marzo 2022

# gst: apropos of transitions, the vortex dynamics from a twisted baker map

<< A natural approach to understanding complicated systems is to analyze a col­lection of simple examples that retain some essential features of the complexity of the original systems. The baker map (..) is one of the simplest models of chaotic dynamical systems. It divides the unit square into p ≥ 2 equal vertical strips, and maps each strip to a horizontal one by squeezing it vertically by the factor p and stretching it horizontally by the same factor. The horizontal strips are laid out covering the square. Due to the squeezing/stretching, small initial errors get amplified under iteration, and results in an unpredictable long-term behavior. The name “baker” is used since the action of the map is reminiscent of the kneading dough (..). In this paper (AA) introduce a piecewise linear model of an interaction of stretching and twisting that produces vortex dynamics. >>

They << show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space >>

Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke. The twisted baker map. arXiv: 2202.04304v2 [math.DS]. Feb 9, 2022. 


Also

keyword 'transition' | 'transitional' in FonT



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




keyword 'vortex' in FonT


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


keywords: gst, transition, vortex, baker map









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martedì 22 febbraio 2022

# 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. 


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


Also

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


keyword 'black hole' | 'astro' in FonT



keyword 'transition' | 'transitional' in FonT



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




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



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martedì 15 febbraio 2022

# gst: transitional dynamics among gyrotactic (prolate spheroid) swimmers in turbulence


<< In this study, (AA) consider small, elongated, gyrotactic, swimming particles in homogenous isotropic turbulence (..). Many motile phytoplankton species are gyrotactic, i.e., their swimming direction results from the competition between shear-induced viscous torque and the stabilizing torque due to bottom-heaviness. (..)  Moreover, both single phytoplankton cells and multicellular phytoplankton chains can have elongated shapes, which makes the study of gyrotactic active particles with prolate shapes necessary. >>

AA addressed the following problems:
<< (i) How the clustering is affected by the swimming number Φ and the stability number Ψ? In particular, how to characterize the extent of clustering based on the three-dimensional Voronoi analysis?
(ii) How the clustering is related to the flow structures? This question has two perspectives.  From the space perspective, what are the regions that particles accumulate in? From the time perspective, how long do particles exist in an aggregated state? >>

Zehua Liu, Linfeng Jiang, Chao Sun. Accumulation and alignment of elongated gyrotactic swimmers in turbulence. arXiv:2202.04351v1 [physics.flu-dyn]. Feb 9, 2022.


Also

The effect of noise on the dynamics of microswimmers in externally-driven fluid flows.  


keywords 'turbulence' in FonT   


keywords 'turbolento' in Notes (quasi-stochastic poetry)


keywords: transition, swimmers,  gyrotactic swimmers, spheroids,  prolate spheroids, stability, turbulence


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giovedì 10 febbraio 2022

# 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.


Also

keyword 'water' in FonT


keyword 'transition' | 'transitional' in FonT



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




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



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sabato 30 ottobre 2021

# 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. 



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

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giovedì 22 luglio 2021

# life: transitions in the edges; to stimulate a shift in thinking, target small groups of people in the "outer edge" or fringe of a network.

<< social influencers are unlikely to change a person's behavior by example. To stimulate a shift in people's thinking, target small groups of people in the outer edge or fringe of a network. (..) as prominent and revered as social influencers seem to be, in fact, they are unlikely to change a person's behavior by example -- and might actually be detrimental to the cause. >>

<< When social influencers present ideas that are dissonant with their followers' worldviews (..) they can unintentionally antagonize the people they are seeking to persuade because people typically only follow influencers whose ideas confirm their beliefs about the world,"  >> Damon Centola. ️

<< To stimulate a shift in thinking, target small groups of people in the "outer edge" or fringe of a network. >>
️
Study finds surprising source of social influence. University of Pennsylvania.  Jul 20, 2021. 


Douglas Guilbeault, Damon Centola.  Topological measures for identifying and predicting the spread of complex contagions. Nat Commun 12, 4430. doi: 10.1038/ s41467-021-24704-6. Jul 20  2021.


Also

1829 - catalisi d' interferenza periferica (c.i.p.)  Notes. Nov 24, 2004. (quasi-stochastic poetry).


keyword 'transition' | 'transitional' in FonT



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




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lunedì 5 luglio 2021

# gst: apropos of (multitudes) of transitional droplets, when a liquid film collapses in a foam ...

<< Foams have unique properties that distinguish them from ordinary liquids and gases, and are ubiquitously observed in nature, both in biological systems and industrial products. >>
️
<< Once a crack appears near the border and a collapse front is formed, (AA) find that the curvature of the front reverses as it migrates, followed by the emergence and emission of droplets. (they) elucidate the origins of this behavior and discuss the stability of foams, establishing how the characteristic time scales of the process relate to each other. >>️

Naoya Yanagisawa, Marie Tani, Rei Kurita. Dynamics and mechanism of liquid film collapse in a foam. Soft Matter. 17, 1738-1745. Feb 17, 2021.


Also

keyword 'foam' in FonT


keyword 'collapse' in FonT


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







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mercoledì 1 luglio 2020

# life: apropos of transitional blennies

<< Research on blennies, a family of fish that have repeatedly left the sea for land, suggests that being a 'jack of all trades' allows species to make the dramatic transition onto land but adapting into a 'master of one' allows them to stay there. >>

<< a flexible diet and behavior were likely to be instrumental in the transition to land. However, once out of the water, restrictions on the type of food available triggered major evolutionary changes, particularly to their teeth, as land dwelling blennies have become specialists in scraping algae and detritus from rocks. >>

<< having a broad diet or being behaviorally flexible can help you move into a new habitat. But once there, this flexibility becomes eroded by natural selection. This presumably means those highly specialized species are less likely to be able to make further transitions, or cope with abrupt environment changes in their existing habitat. >> Terry Ord.

How fish got onto land, and stayed there. British Ecological Society. Jun 17, 2020.  


Terry J. Ord, Peter J. Hundt. Crossing extreme habitat boundaries: Jack‐of‐all‐trades facilitates invasion but is eroded by adaptation to a master‐of‐one. Funct Ecol. doi: 10.1111/ 1365-2435.13600. Jun 16, 2020.


Also

The multifactorial relationship system evolved in Blenny. FonT. Jun 2, 2017.



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martedì 10 marzo 2020

# gst: apropos of 'transitions', liquid-liquid transitions within a one- component system

<< For a long time, the liquid state of pure substances was believed to be a continuous state in which the component atoms or molecules are all equivalent. However, it has now been widely shown that there can be multiple phases within liquids, even those containing only one component. >>

AA << have devised a model based on two factors that describe the ordering of the liquid; the density, and the local organization of the liquid atoms or molecules at a particular point. >>

<< Our Ginzburg-Landau-type model evaluates the system using two order parameters; one that is conserved-density; and one that is not- local structural order (..) What we found was that the growth of the liquid domain we studied was affected by density changes that cause hydrodynamic fluctuations. >> Kyohei Takae.

<< It was shown that when the density changes as a result of the phase transition, hydrodynamic flow is induced leading to changes in both the rate of domain growth and the long-range interaction between the domains. Hydrodynamic interaction was therefore found to be critical to LLT (liquid-liquid transitions) and the pattern evolution and kinetics. >>

But what about flow? The effect of hydrodynamics on liquid-liquid transitions. University of Tokyo. Feb 10, 2020.

https://phys.org/news/2020-02-effect-hydrodynamics-liquid-liquid-transitions.html

Kyohei Takae, Hajime Tanaka. Role of hydrodynamics in liquid–liquid transition of a single-component substance. PNAS. 117 (9) 4471-4479. doi: 10.1073/pnas.1911544117. Mar 3, 2020.

https://www.pnas.org/content/117/9/4471

Also

more on the weirdness of water, "T" and "non-T" Tetrahedral arrangements. Feb 5, 2020. 

https://flashontrack.blogspot.com/2020/02/chem-more-on-weirdness-of-water-t-and.html

Also

keyword 'transition/al' in FonT

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

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

keyword 'transizione/i' in Notes (quasi-stochastic poetry)

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

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

keyword 'transizionale/i' in Notes (quasi-stochastic poetry)

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

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

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martedì 22 maggio 2018

# zoo: the first look at Oyster's transitional adhesive dynamics

AA << still do not have a clear picture of how these animals attach to surfaces. Efforts described herein provide the first examination of adhesion at the transition from free swimming larvae to initial substrate attachment, through metamorphosis, and on to adulthood. Two different bonding systems were found to coexist >>

Andres M. Tibabuzo Perdomo, Erik M. Alberts, et al.  Changes in Cementation of Reef Building Oysters Transitioning from Larvae to Adults. ACS Appl. Mater. Interfaces. 2018; 10 (17): 14248-53 doi: 10.1021/acsami.8b01305. Apr 13, 2018.

https://pubs.acs.org/doi/10.1021/acsami.8b01305

Kayla Zacharias. Oysters: one animal, two glues. Purdue University. May 7, 2018.

https://m.phys.org/news/2018-05-oysters-animal.html

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giovedì 19 ottobre 2017

# gst: cooperating vs self-serving bacteria in transitional (noise) scenarios

AA << study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity >>

AA << consider two scenarios—one of pure resource competition, and one in which one strain provides a public good—and investigate how environmental randomness (external noise) coupled to demographic (internal) noise determines the population’s fixation properties and size distribution >>

Karl Wienand, Erwin Frey, Mauro Mobilia. Evolution of a Fluctuating Population in a Randomly Switching Environment. Phys. Rev. Lett. 119, 158301 Oct 11, 2017

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.158301

AA << showed that a randomly changing environment can create a level playing field between self-serving bacteria and bacteria that work together >>

<< Cooperating bacterial populations are more likely to survive in changing habitats >>

Fluctuating environments can help cooperating bacteria. Oct 12, 2017

https://m.phys.org/news/2017-10-fluctuating-environments-cooperating-bacteria.html

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martedì 3 maggio 2016

# s-gst: measuring energy levels inside transitional dis-order(s)

<< Vortex  filaments  in  classical  and  quantum  fluids and  DNA  macromolecules,   magnetic  flux  tubes,  phase  defects,  polymers may interact  and  recombine  through reconnection of  neighboring strands.  Details  of  the  process  depend  on specific  local  mechanisms  that  may differ  from  case  to case,  but  certain  qualitative  features  —  such  as  the  preservation  of  the  original  strand  orientation after recombination — are generic and common to all systems. >>

<< The  study of  these  processes  is  clearly of  great  importance,  because  the  change  of  topology is often  accompanied  by a  change  in energy,  entropy and  function. >>

<< (..) HOMFLYPT  polynomial recently  introduced  for  fluid  knots (..) provides a  powerful  tool to  measure  topological  complexity of  various  physical  systems. >>

Liu,  X.,  Ricca,  R.  L.  Knots  cascade  detected  by  a  monotonically decreasing  sequence  of  values.  Sci.  Rep.6,  24118;  doi:  10.1038/srep24118  (2016).

http://www.nature.com/articles/srep24118

Quanta  energia è  nascosta  nel  caos? Bicocca, Milano,  2  maggio  2016

http://www.unimib.it/open/news/Quanta-energia-e-nascosta-nel-caos-Ce-lo-dice-il-polinomio-targato-Bicocca-Beijing-UTech/4936093294137195314

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