# gst: gigantic dynamical spreading and anomalous diffusion of jerky active particles.

<< ️Jerky active particles are Brownian self-propelled particles which are dominated by “jerk,” the change in acceleration. They represent a generalization of inertial active particles. In order to describe jerky active particles, a linear jerk equation of motion which involves a third-order derivative in time, Stokes friction, and a spring force (AA) combined with activity modeled by an active Ornstein-Uhlenbeck process. This equation of motion (They) solved analytically and the associated mean-square displacement (MSD) is extracted as a function of time. >>

<< ️For small damping and small spring constants, the MSD shows an enormous superballistic spreading with different scaling regimes characterized by anomalous high dynamical exponents 6, 5, 4, or 3 arising from a competition among jerk, inertia, and activity. When exposed to a harmonic potential, the gigantic spreading tendency induced by jerk gives rise to an enormous increase of the kinetic temperature and even to a sharp localization-delocalization transition, i.e., a jerky particle can escape from harmonic confinement. >>

<< ️The transition can be either first or second order as a function of jerkiness. Finally (AA)  shown that self-propelled jerky particles governed by the basic equation of motion can be realized experimentally both in feedback-controlled macroscopic particles and in active colloids governed by friction with memory. >>

Hartmut Löwen. Gigantic dynamical spreading and anomalous diffusion of jerky active particles. Phys. Rev. E 112, 045412. Oct 17, 2025.

https://journals.aps.org/pre/abstract/10.1103/976t-qry7

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

Keywords: gst, particles, colloids, self-propelled particles, active Brownian particles, Jerky active particles, jerkiness, transitions, superballistic spreading, escape.

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

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

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

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

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

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

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

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

Keywords: gst, billiard, particle, escape.

# gst: apropos of diffusive anomalies, anomalous diffusion of active Brownian particles in responsive elastic gels.

Here, AA << examine via extensive computer simulations the dynamics of SPPs (self-propelled particles) in deformable gellike structures responsive to thermal fluctuations. (AA) treat tracer particles comparable to and larger than the mesh size of the gel. (They) observe distinct trapping events of active tracers at relatively short times, leading to subdiffusion; it is followed by an escape from meshwork-induced traps due to the flexibility of the network, resulting in superdiffusion. >>

AA << thus find crossovers between different transport regimes. (They) also find pronounced nonergodicity in the dynamics of SPPs and non-Gaussianity at intermediate times. The distributions of trapping times of the tracers escaping from “cages” in (..)  quasiperiodic gel often reveal the existence of two distinct timescales in the dynamics. At high activity of the tracers these timescales become comparable. >>

<< Furthermore, (AA) find that the mean waiting time exhibits a power-law dependence on the activity of SPPs (in terms of their Péclet number). (Their) results additionally showcase both exponential and nonexponential trapping events at high activities. Extensions of this setup are possible, with the factors such as anisotropy of the particles, different topologies of the gel network, and various interactions between the particles (also of a nonlocal nature) to be considered. >>

Koushik Goswami, Andrey G. Cherstvy, et al. Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times. Phys. Rev. E 110, 044609. Oct 29, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.044609

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

Keywords: gst, particle, random, random walks, escape, network

# gst: isles of regularity (depending on the initial setup) in a sea of chaos amid the gravitational three-body problem.

AA << study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP (three-body problem) and assesses their impact on statistical escape theories. >>

AA << analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. >>

Alessandro Alberto Trani, Nathan W.C. Leigh, et al. Isles of regularity in a sea of chaos amid the gravitational three-body problem. A&A, 689, A24, Jun 25, 2024.

https://www.aanda.org/articles/aa/full_html/2024/09/aa49862-24/aa49862-24.html

"Islands" of Regularity Discovered in the Famously Chaotic Three-Body Problem. University of Copenhagen. Oct 11, 2024.

https://science.ku.dk/english/press/news/2024/islands-of-regularity-discovered-in-the-famously-chaotic-three-body-problem/

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

Keywords: gst, three balls, escape, chaos, transition 

# gst: relativistic chaotic scattering, scaling laws for trapped trajectories.

AA << study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the Hénon-Heiles Hamiltonian, (They) numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. >>

<< In all cases, fractal structures are present, and the escaping dynamics is characterized. In every case a scaling law is numerically obtained in which the percentage of the trapped trajectories as a function of the relativistic parameter β and the energy is obtained. >>

Their << work could be useful in the context of charged particles which eventually can be trapped in the magnetosphere, where the analysis of these structures can be relevant. >>️

Fernando Blesa, Juan D. Bernal, et al. Relativistic chaotic scattering: Unveiling scaling laws for trapped trajectories. Phys. Rev. E 109, 044204. Apr 5, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044204

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

Keywords: gst, chaos, chaotic, escape, escape trajectories

# gst: Lévy flights and Lévy walks under stochastic resetting.

<< Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. (AA)  demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also in the presence of heavy-tailed, Lévy-type, α

-stable noise. However, the width of the domain where resetting is beneficial depends on the value of the stability index α determining the power-law decay of the jump length distribution. For heavier (smaller α) distributions, the domain becomes narrower in comparison to lighter tails. >>

<< Additionally, (AA) explore connections between Lévy flights (LFs) and Lévy walks (LWs) in the presence of stochastic resetting. First of all, (They) show that for Lévy walks, the stochastic resetting can also be beneficial in the domain where the coefficient of variation is smaller than 1. Moreover, (They) demonstrate that in the domain where LWs are characterized by a finite mean jump duration (length), with the increasing width of the interval, the LWs start to share similarities with LFs under stochastic resetting. >>️

Bartosz Żbik, Bartłomiej Dybiec. Lévy flights and Lévy walks under stochastic resetting. Phys. Rev. E 109, 044147. April 22, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044147

Also: keyword Lévy in FonT

https://flashontrack.blogspot.com/search?q=Lévy&m=1

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

Keywords: gst, escape, noise, stochastic resetting, Lévy

# gst: wandering domains: a hypothetical scenario with bounded orbits.

<< A significant open question in transcendental dynamics asks if it is possible for a point, and thus all points, of a wandering domain to have a bounded orbit. >>

<< In other words, is there a transcendental entire function f with a wandering domain U such that its forward orbit, U_n≥0 f^n(U), is bounded? >>

AA << give a partial answer to this question by constructing an example of a such a wandering domain U which has a nearly bounded orbit; >>

<< In other words, the set of natural numbers n for which f^n(U) is contained in D has upper (and lower) natural density one. >>

<< This is in particularly strong contrast to all existing examples of wandering domains, for which the quantity (..) is equal to zero for any choice of bounded domain D. >>

Leticia Pardo-Simon, David J. Sixsmith. Wandering domains with nearly bounded orbits. arXiv: 2307.16682v1 [math.DS]. Jul 31, 2023. 

https://arxiv.org/abs/2307.16682

Also: Unbounded fast escaping wandering domains. https://arxiv.org/abs/2210.13350 ; Escaping sets of continuous functions. https://arxiv.org/abs/1601.04010 

Also: 'escape', in FonT: https://flashontrack.blogspot.com/search?q=escape

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

Keywords: gst, wandering domain, escape 

# gst: apropos of transitions, escape inside a noisy layered system

<< Noisy layered systems can exhibit amplified fluctuation patterns depending on their connectivity. Here (AA) showed that noise originally injected in one layer may induce faster basin escape in connected layers. This is both due to the amplification of the noise amplitude and the system specific correlations that the noise acquire while going through the first layer. Indeed, (..) one sees that the noise in the second is correlated in both space and time with clear dependence on the network structure. For networks with low algebraic connectivity, (AA) numerically showed that the first escape time is shorter in the two cases where (i) fluctuations are amplified in the second layer and (ii) noise in the second layer is rescaled in order to have the same variance in both layers. While point (i) is rather intuitive, i.e. larger fluctuations lead to shorter first escape times, point (ii) is more involved. Indeed, this indicates that noise with spatial and temporal correlations (..) selects directions that enable faster exits from the initial basin of attraction. >>

Melvyn Tyloo. Faster network disruption from layered oscillatory dynamics. arXiv: 2210.01180v1 [nlin.AO]. Oct 3, 2022. 

https://arxiv.org/abs/2210.01180

Also

keyword 'escape' in FonT

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

keyword 'escape' | 'fuga' in Notes 

(quasi-stochastic poetry)

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

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

Keywords: gst, transitions, escape, noise, noisy layered systems