# gst: asymptotic scaling in a one-dimensional billiard

<< The emergence of power laws that govern the large-time dynamics of a one-dimensional billiard of N point particles is analysed. In the initial state, the resting particles are placed in the positive half-line x≥0 at equal distances. Their masses alternate between two distinct values. The dynamics is initialized by giving the leftmost particle a positive velocity. >>

<< Due to elastic inter-particle collisions the whole system gradually comes into motion, filling both right and left half-lines. As shown by S. Chakraborti, et al. (2022), an inherent feature of such a billiard is the emergence of two different modes: the shock wave that propagates in x≥0 and the splash region in x<0. >>

<< Moreover, the behaviour of the relevant observables is characterized by universal asymptotic power-law dependencies. In view of the finite size of the system and of finite observation times, these dependencies only start to acquire a universal character. To analyse them, (AA) set up molecular dynamics simulations using the concept of effective scaling exponents, familiar in the theory of continuous phase transitions. (They) present results for the effective exponents that govern the large-time behaviour of the shock-wave front, the number of collisions, the energies and momentum of different modes and analyse their tendency to approach corresponding universal values. >>️

<< A characteristic feature of the billiard problem (AA) have considered (..) is the lack of a priori randomness, neither in the distribution of masses nor in the inter-particle distances. Therefore, the emergence of the hydrodynamic power-law asymptotics– pointing to the stochastic background of the underlying process– may be interpreted as a kind of self-averaging in the system.  >>️

Taras Holovatch, Yuri Kozitsky, et al. Effective and asymptotic scaling in a one-dimensional billiard problem. arXiv: 2503.20476v1 [cond-mat.stat-mech]. Mar 26, 2025.

https://arxiv.org/abs/2503.20476

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

Keywords: gst, billiard, randomness 

# gst: First-passage-time statistics of active Brownian particles: a perturbative approach.

AA << study the first-passage-time (FPT) properties of active Brownian particles to reach an absorbing wall in two dimensions. Employing a perturbation approach (They) obtain exact analytical predictions for the survival and FPT distributions for small Péclet numbers, measuring the importance of self-propulsion relative to diffusion. >>

<< While randomly oriented active agents reach the wall faster than their passive counterpart, their initial orientation plays a crucial role in the FPT statistics. Using the median as a metric, (AA) quantify this anisotropy and find that it becomes more pronounced at distances where persistent active motion starts to dominate diffusion. >>️

Yanis Baouche, Magali Le Goff, et al. First-passage-time statistics of active Brownian particles: a perturbative approach. arXiv: 2503.05401v1 [cond-mat.soft]. Mar 7, 2025.

https://arxiv.org/abs/2503.05401

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

Keywords: gst, particles, active particles, perturbation approach, randomness, stochasticity, stochastic resetting, rotational diffusion, anisotropy

# behav: the benefit of ignorance for traffic through a random congestible network.

<< When traffic is routed through a network that is susceptible to congestion, the self-interested decisions made by individual users do not, in general, produce the optimal flow. This discrepancy is quantified by the so-called "price of anarchy." >>

AA << consider whether the traffic produced by self-interested users is made better or worse when users have uncertain knowledge about the cost functions of the links in the network, and define a parallel concept that (They) call the "price of ignorance."  >>

AA << introduce a simple model in which fast, congestible links and slow, incongestible links are mixed randomly in a large network and users plan their routes with finite uncertainty about which of the two cost functions describes each link. >>

<< One of (Their) key findings is that a small level of user ignorance universally improves traffic, regardless of the network composition. Further, there is an optimal level of ignorance which, in (the) model, causes the self-interested user behavior to coincide with the optimum. Many features of (AA) model can be understood analytically, including the optimal level of user ignorance and the existence of critical scaling near the percolation threshold for fast links, where the potential benefit of user ignorance is greatest. >>️

Alican Saray, Calvin Pozderac, et al. The benefit of ignorance for traffic through a random congestible network. arXiv: 2503.09684v1 [cond-mat.dis-nn]. Mar 12, 2025.

https://arxiv.org/abs/2503.09684

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

Keywords: gst, networks, behavior,  randomness, uncertainty, price of anarchy, price of ignorance

# gst: like steering a marble through a tilting labyrinth, randomness seems to quickly deliver specific outcomes.

<< According to the infinite monkey theorem, a monkey randomly hitting the keys of a typewriter will eventually write something worth reading—but it might take a few trillion years of trying. For those lacking the patience to wait, (AA)  now show that randomness can deliver specific outcomes much more quickly.  Simulating a 2D nanocluster of a dozen particles, (they) determine the temperature at which thermal fluctuations can most quickly rearrange those particles into a predetermined shape. They find that this time can be dramatically cut by applying an appropriate macroscopic force to the particles. >>

<< The duo also simulated nanoclusters that were subject to a macroscopic force field, for example, metallic nanoparticles in an electric field. Like steering a marble through a tilting labyrinth, they found the optimal global force to apply at each iteration such that the nanocluster navigated the space of possible configurations several orders of magnitude more quickly. >>️️

Marric Stephens. Rearranging Nanoclusters Using Randomness. Physics 15, s83. Jun 22, 2022. 

https://physics.aps.org/articles/v15/s83

Francesco Boccardo, Olivier Pierre-Louis. Controlling the Shape of Small Clusters with and without Macroscopic Fields. Phys. Rev. Lett. 128, 256102. Jun 22, 2022.  

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.256102

Also

keyword 'random' in FonT:

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

keyword 'error' | 'fuzzy' | 'noise'  in FonT 

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

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

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

keywords 'errore' | 'errori' in Notes (quasi-stochastic poetry)

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

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

keywords 'jelly roll' in FonT

https://flashontrack.blogspot.com/search?q=jelly+roll

Keywords: gst, nano, nanocluster, fluctuations, randomness, noise

# evol: spontaneous, immediate asymmetry, the chiral twist

<< When holding a right hand in front of a mirror, one can see a reflected image of a left hand and vice versa. In 1848, Louis Pasteur discovered that organic molecules are much like our hands: they come in mirror-image pairs of left- and right-handed variants. Nowadays, we know that this handedness or chirality (from the Greek word for "hand") is a hallmark of organic molecules. >>

<< Organic molecules are rich in carbon atoms, which form bonds to create either a right or a left "nano-hand." Yet, puzzlingly, life almost always selects to exclusively use one of the two mirror-image twins—a phenomenon called homochirality. For example, terrestrial life is based on left-handed amino acids and right-handed sugars. >>️️

<< A model now proposes a novel explanation for the emergence of homochirality in life—a longstanding puzzle about the origin of life on Earth. >>️

<< Homochirality emerges spontaneously in prebiotic chemical networks that adapt to optimize energy harvesting from the environment. Previously, it was believed that chiral symmetry breaking requires multiple loops of auto-catalysis, which increasingly produces one enantiomer of a molecule while inhibiting the formation of the other. However, the IBS team's results showed that the underlying mechanism of symmetry breaking is very general, as it can occur in large reaction systems with many random molecules and does not require sophisticated network architectures. It was found that this sharp transition to homochirality stems from the self-configuration of the reaction network in order to achieve more efficient harvesting of energy from the environment. >>️

Learning chemical networks give life a chiral twist. Institute for Basic Science. Apr 26, 2022. 

https://phys.org/news/2022-04-chemical-networks-life-chiral.html

William D. Pineros, Tsvi Tlusty. Spontaneous chiral symmetry breaking in a random driven chemical system. Nat Commun 13, 2244. doi: 10.1038/ s41467-022-29952-8. Apr 26, 2022.

https://www.nature.com/articles/s41467-022-29952-8

Also

keyword 'chiral' in FonT

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

keyword 'self-assembly' in FonT

https://flashontrack.blogspot.com/search?q=self-assembly

Keywords: evolution, gst, randomness, self-assembly, self-configuration, break symmetry, asymmetry, chiral, chirality  

# evol: the hypothesis of quasi-stochastic 'jazzy' metamechanics of biological evolution (in Arabidopsis thaliana)

<< Mutations occur when DNA is damaged and left unrepaired, creating a new variation. The scientists wanted to know if mutation was purely random or something deeper. What they found was unexpected. >>️

<< We always thought of mutation as basically random across the genome, (..) It turns out that mutation is very non-random and it's non-random in a way that benefits the plant. It's a totally new way of thinking about mutation. >> Grey Monroe. ️

Study challenges evolutionary theory that DNA mutations are random. UC Davis. Jan 12, 2022.

https://phys.org/news/2022-01-evolutionary-theory-dna-mutations-random.html

Monroe JG, Srikant T, et al. Mutation bias reflects natural selection in Arabidopsis thaliana. Nature. doi: 10.1038/ s41586-021-04269-6. Jan 12, 2022.

https://www.nature.com/articles/s41586-021-04269-6

FonT 

for a long time I have developed the suspicion that the small plant cared for by grandmother on the windowsill could be a not trivial image of (r)evolution ... 

The three ways of the plastoquinone inside the photosystem II complex. May 23, 2017.

https://flashontrack.blogspot.com/2017/05/s-phyto-three-ways-of-plastoquinone.html

Also

keyword 'evolution'  in FonT

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

keyword 'evolution' | 'evoluzione'  in Notes (quasi-stochastic poetry)

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

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

keyword 'jazz' in FonT

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

keyword 'jazz' in Notes (quasi-stochastic poetry):

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

keywords: evol, dna, mutations, randomness, quasi-stochasticity, jazz

# gst: small-scale random perturbations, Arnold's cat spontaneously stochastic

<< Multi-scale systems (..) may possess a fascinating property of spontaneous stochasticity: a small-scale initial uncertainty develops into a randomly chosen largescale state in a finite time, and this behavior is not sensitive to the nature and magnitude of uncertainty (..). >>

A << intriguing form is the Eulerian spontaneous stochasticity (ESS) of the velocity field itself: an infinitesimal small-scale noise triggers stochastic evolution of velocity field at finite scales and times. >>

AA << prove that a formally deterministic system with scaling symmetry yields a stochastic process with Markovian properties if it is regularized with a vanishing small-scale random perturbation. Besides its significance for understanding turbulence, (their) model extends the phenomenon of ESS beyond the scope of fluid dynamics: (AA) discuss a prototype of a feasible experiment for observing ESS in optics or electronics, as well as potential applications in other physical systems.>>

Alexei A. Mailybaev, Artem Raibekas. Spontaneously stochastic Arnold's cat. arXiv:2111.03666v1 [nlin.CD]. Nov 5,  2021.

https://arxiv.org/abs/2111.03666

keywords: gst, Arnold's cat, randomness, stochasticity, spontaneous stochasticity, small-scale random perturbations, noise, turbulence, chaos 

# gst: when randomly-timed external impulses can synchronize

<< Random perturbations applied in tandem to an ensemble of objects can synchronize their motion. (AA) study multiple copies of an object in periodic motion such as a firing neuron, each with an arbitrary phase. Randomly-timed external impulses can synchronize these phases. For impulses slightly too strong to synchronize, (they) find remarkable erratic synchronization, with stochastic fluctuations from near-perfect to more random synchronization. The sampled entropies of these phase distributions themselves form a steady-state ensemble. A stochastic dynamics model for the entropy's evolution accounts for the observed exponential distribution of entropies and the stochastic synchronization. >>

<< One general virtue of noise-induced synchronization is that one may use it to induce synchronization without

specific knowledge about the limit cycle being synchronized, such as the phase map function or the cycle time.(..) As noted in the Introduction, synchronization of a remote oscillator enables transmission of information.

Stochastic synchronization appears to have comparable ability, potentially useable by technology or biology. >>️

<< The stochastic synchronization phenomenon explored above seems to be a distinctive mode of organization. It can be produced via broad classes of driving, and creates striking fluctuations of randomness. This model may aid understanding of other puzzling systems showing erratic fluctuations, such as strong turbulence. >>️

️

Yunxiang Song, Thomas A. Witten. Stochastic synchronization induced by noise. arXiv:2108.13172v1 [cond-mat.stat-mech]. Aug 16, 2021.

https://arxiv.org/abs/2108.13172

Also

<< stabilizzare il volo del fascio di aquiloni  >> in: ️2149 - onda di predazione (to knock seals off the ice).  Notes. Dec 17, 2007. (quasi-stochastic poetry)

https://inkpi.blogspot.com/2007/12/2149-onda-di-predazione-to-knock-seals.html

keyword 'noise' | 'fuzzy' in FonT

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

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

# gst: apropos of transitions, randomness can stabilize edge states in short- lifetime regions of disordered periodically-driven systems

<< lifetimes of the edge states exhibit universal behavior when random potentials exist since the edge- and bulk- dominant eigenstates are mixed, leading to that lifetimes are prolonged by random potentials in the region II (short- lifetime region) and shortened in the region I (long- lifetime region). >>

<<  it is an intriguing phenomenon that random potentials tend to stabilize edge states in the region II (short- lifetime regions). >>

Ken Mochizuki, Kaoru Mizuta, Norio Kawakami. Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems. arXiv: 2108.00649 (nlin). Aug 2, 2021.

https://arxiv.org/abs/2108.00649

Also

keyword 'random' in FonT

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

keyword 'disorder' in FonT

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

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

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