# 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 

# 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: 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: 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: 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: 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 

# life: Snake Plissken movies revisited, the chaotic escape from Milan, Paris, ...

 "Call me Snake",  the furious chaotic escape of probably conscious "guests",  'cause of 1,2 initial long-range Wuhan sneezing.

<< Everyone we know in Paris who was able to leave the city have done so. >>  

Henry Samuel. Parisian mother on 

escaping the coronavirus lockdown.  Mar 17, 2020

https://www.telegraph.co.uk/news/2020/03/17/dont-know-would-have-done-parisian-mother-escaping-coronavirus/

Also 

"Call me Snake", by Snake Plissken

https://en.m.wikipedia.org/wiki/Snake_Plissken

Also

keyword 'snake' in FonT

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

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

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

# gst: behavior of microswimmers in a vortex with translational and rotational noise

AA << propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices, namely active particles in two- and three-dimensional rotlets. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. (AA) further discover a conserved quantity of motion that allows (..) to map the phase space according to the type of the orbit (bounded vs unbounded). (They) next introduce translational and rotational noise into the system. Using a Fokker--Planck formalism, (AA) quantify the quality of trapping near the centre of the vortex by examining the probability of escape and the mean time of escape from the region of deterministically bounded orbits. (AA) finally show how to use these findings to formulate a prediction for the radius of the depletion zone, which compares favourably with the experiments of Sokolov and Aranson (2016). >>

Ivan Tanasijevic, Eric Lauga. Microswimmers in vortices: Dynamics and trapping. arXiv: 2211.05866v1 [physics.bio-ph].  Nov 10, 2022. 

https://arxiv.org/abs/2211.05866

Also

'microswimmers' in FonT 

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

Keywords: gst, behav, translation,  rotation, trapping, noise, swimmer, swimming,  microswimmers, fluid dynamics, vortex, vortices, vortexes, vorticity

# astro: we have to escape with a speed of 550 km/s

<< When a rocket is launched into space, it is thrown out with a speed of 11 km/s to overcome the Earth's gravitational pull [..] Our home galaxy, the Milky Way, is over a trillion times heavier than our tiny planet Earth so to escape its gravitational pull we have to launch with a speed of 550 km/s. >> Prajwal Kafle.

International Centre for Radio Astronomy Research. Milky Way ties with neighbor in galactic arms race. Feb 14, 2018.

https://m.phys.org/news/2018-02-milky-ties-neighbor-galactic-arms.html  

FonT

intrigante il video che simula la collisione- fusione

# s-astro: the sonic multiverse, by Gavin Starks

<< A project that explores whether there is a musical equivalent to the curvature of spacetime will be presented on Thursday 6 July by Gavin Starks at the National Astronomy Meeting at the University of Hull >>

AA << aim is to test whether mathematical relationships that describe cosmology and quantum mechanics can be applied to a sonic universe , or 'soniverse' >>

Royal Astronomical Society. Adventures in acoustic cosmology. July 6, 2017

https://m.phys.org/news/2017-07-adventures-acoustic-cosmology.html

Gavin Starks. Escape into the multiverse. Jan. 27, 2017

http://www.binarydust.org/2017/01/27/escape-into-the-multiverse/

# gst: elastic instabilities, a morphing model to quickly trap anything (in 100msec), the Venus flytrap (Dionaea muscipula)

<< The Venus flytrap (Dionaea muscipula) takes only 100 milliseconds to trap its prey. Once their leaves, which have been transformed into snap traps, have closed, insects can no longer escape. >>

<< the trap of the carnivorous plant is under mechanical prestress. In addition, its three tissue layers of each lobe have to deform according to a special pattern. >>

<< In order to close correctly, the traps also had to consist of three layers of tissue: an inner which constricts, an outer which expands, and a neutral middle layer. >>

Albert Ludwigs. Biomechanical analyses and computer simulations reveal the Venus flytrap snapping mechanisms. University of Freiburg. Jun 23, 2020.

https://phys.org/news/2020-06-biomechanical-analyses-simulations-reveal-venus.html

Renate Sachse, Anna Westermeier, et al. Snapping mechanics of the Venus flytrap (Dionaea muscipula). PNAS. doi: 10.1073/ pnas.2002707117. Jun 22, 2020. 

https://www.pnas.org/content/early/2020/06/19/2002707117

Also

Dionaea muscipula, with precision. FonT. Feb 2, 2016. 

https://flashontrack.blogspot.com/2016/02/rmx-s-phyto-dionaea-muscipula-with.html

# astro: eight new echoing black hole binaries (in Milky Way)

<< Scattered across our Milky Way galaxy are tens of millions of black holes—immensely strong gravitational wells of spacetime, from which infalling matter, and even light, can never escape. Black holes are dark by definition, except on the rare occasions when they feed. As a black hole pulls in gas and dust from an orbiting star, it can give off spectacular bursts of X-ray light that bounce and echo off the inspiraling gas, briefly illuminating a black hole's extreme surroundings. >>

<< In a study appearing (..) in the The Astrophysical Journal, (AA) report (..) eight new echoing black hole binaries in our galaxy. Previously, only two such systems in the Milky Way were known to emit X-ray echoes. >>️

 << Kara (Erin Kara) and her colleagues are using X-ray echoes to map a black hole's vicinity, much the way that bats use sound echoes to navigate their surroundings. (..)  As a side project, Kara is working with MIT education and music scholars, Kyle Keane and Ian Condry, to convert the emission from a typical X-ray echo into audible sound waves. >>️️

Jennifer Chu. Search reveals eight new sources of black hole echoes. MIT.  May 2, 2022. 

https://phys.org/news/2022-05-reveals-sources-black-hole-echoes.html

https://youtu.be/iIeIag2Ji8k

Jingyi Wang, Erin Kara, et al. The NICER "Reverberation Machine": A Systematic Study of Time Lags in Black Hole X-Ray Binaries. ApJ. 930, 18. May 2, 2022. 

https://iopscience.iop.org/article/10.3847/1538-4357/ac6262

Also

keyword 'black hole' in FonT

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

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: astro, black hole, echoes, waves

# gst: how small particles could reshape an asteroid

<< In January 2019, NASA's OSIRIS-REx spacecraft was orbiting asteroid Bennu when the spacecraft's cameras caught something unexpected: Thousands of tiny bits of material, some just the size of marbles, began to bounce off the surface of the asteroid—like a game of ping-pong in space. Since then, many such particle ejection events have been observed at Bennu's surface. >>

AA have been studying << asteroids for a long time, and no one had ever seen this phenomenon before—these little particles getting shot off of the surface  (..) such seemingly small occurrences may add up over time—perhaps even helping to give the asteroid its telltale shape, which is often compared to a spinning top. >>

<< basic orbital calculations suggest that all of these particles should do one of two things: Jump off the surface and fall right back down or escape from Bennu's gravity and never come back. >>

<< When particles eventually land on Bennu's surface, many appear to disproportionately fall near its equator where the asteroid has a distinct bulge. As a result, these events could be reshaping the asteroid over thousands or millions of years by moving mass from its north and south to its middle. >>

Daniel Strain. How small particles could reshape Bennu and other asteroids. University of Colorado at Boulder. Sep 9, 2020.

https://phys.org/news/2020-09-small-particles-reshape-bennu-asteroids.html 

McMahon Jay W, Scheeres Daniel J, et al. Dynamical Evolution of Simulated Particles Ejected From Asteroid Bennu. J Geophys Res: Planets. 125 (8). doi: 10.1029/ 2019JE006229. May 18, 2020.

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019JE006229 

Scheeres Daniel J, McMahon Jay W, et al. Particle Ejection Contributions to the Rotational Acceleration and Orbit Evolution of Asteroid (101955) Bennu. 

J Geophys Res: Planets. 125 (3). doi: 10.1029/ 2019JE006284. March 11, 2020. 

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019JE006284

# astro: oops? apropos of rapid expansion of trajectories, the nomadic escape propensity of Titan.

As a vision of a fuzzy snooker, << decades of measurements and calculations have revealed that Titan's orbit around Saturn is expanding- meaning, the moon is getting farther and farther away from the planet- at a rate about 100 times faster than expected. The research suggests that Titan was born much closer to Saturn and migrated out to its current distance of 1.2 million kilometers (about 746,000 miles) over 4.5 billion years. >>

<< Titan is expected to gravitationally squeeze Saturn with a particular frequency that makes the planet oscillate strongly, similarly to how swinging your legs on a swing with the right timing can drive you higher and higher. This process of tidal forcing is called resonance locking. Fuller (Jim Fuller) proposed that the high amplitude of Saturn's oscillation would dissipate a lot of energy, which in turn would cause Titan to migrate outward away from the planet at a faster rate than previously thought. >>

<< The resonance locking theory can apply to many astrophysical systems. I'm now doing some theoretical work to see if the same physics can happen in binary star systems, or exoplanet systems, >> Jim Fuller.

Lori Dajose. Titan is migrating away from Saturn 100 times faster than previously predicted. Jun 8, 2020.

https://phys.org/news/2020-06-titan-migrating-saturn-faster-previously.html

Valery Lainey, Luis Gomez Casajus, et al. Resonance locking in giant planets indicated by the rapid orbital expansion of Titan. Nat Astron. doi: 10.1038/ s41550-020-1120-5. Jun 8, 2020.

https://www.nature.com/articles/s41550-020-1120-5   

Also (quasi-stochastic poetry)

1648b - tenuta di rigo della sonda. Notes. Jan 15, 2005.

https://inkpi.blogspot.com/2005/01/1648b-tenuta-di-rigo-della-sonda.html

# gst: bubble phases sliding over periodically modulated substrates

AA << analyze a bubble-forming system composed of particles with competing long-range repulsive and short-range attractive interactions driven over a quasi-one-dimensional periodic substrate. >>️

They << find various pinned and sliding phases as a function of substrate strength and drive amplitude. When the substrate is weak, a pinned bubble phase appears that depins elastically into a sliding bubble lattice. For stronger substrates, (AA) find anisotropic bubbles, disordered bubbles, and stripe phases. Plastic depinning occurs via the hopping of individual particles from one bubble to the next in a pinned bubble lattice, and as the drive increases, there is a transition to a state where all of the bubbles are moving but are continuously shedding and absorbing individual particles. This is followed at high drives by a moving bubble lattice in which the particles can no longer escape their individual bubbles. >>️

<< When the bubbles shrink due to an increase in the attractive interaction term, they fit better inside the pinning troughs and become more strongly pinned, leading to a reentrant pinning phase. For weaker attractive terms, the size of the bubbles becomes greater than the width of the pinning troughs and the depinning becomes elastic with a reduced depinning threshold. >>

️

C. Reichhardt, C.J.O. Reichhardt. Sliding dynamics for bubble phases on periodic modulated substrates. Phys. Rev. Research 6, 023116. May 2, 2024.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.023116

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

Keywords: gst, bubble, pinned bubble, elastic, transition

# life: some scientists hypothesize the possibility of (A) traveling faster than light, (B) visiting the interior of a black hole, (C) being already under observation by alien entities.

(A) traveling faster than light

<< Lentz (Erik Lentz. https://iopscience.iop.org/article/10.1088/1361-6382/abe692 ) proposes one such way we might be able to do this, thanks to what he calls a new class of hyper-fast solitons – a kind of wave that maintains its shape and energy while moving at a constant velocity (and in this case, a velocity faster than light). According to Lentz's theoretical calculations, these hyper-fast soliton solutions can exist within general relativity, and are sourced purely from positive energy densities, meaning there's no need to consider exotic negative- energy- density sources that haven't yet been verified. (..) With sufficient energy, configurations of these solitons could function as 'warp bubbles', capable of superluminal motion, and theoretically enabling an object to pass through space-time while shielded from extreme tidal forces. >>

<< another recent analysis, published only this month ( David Nield.  https://www.sciencealert.com/engineers-have-proposed-the-first-model-for-a-physical-warp-drive  ;  Alexey Bobrick, Gianni Martire. https://iopscience.iop.org/article/10.1088/1361-6382/abdf6e ), which also proposes an alternative model for a physically possible warp drive that doesn't require negative energy to function. >>️️

Peter Dockrill. Faster-Than-Light Travel Is Possible Within Einstein's Physics, Astrophysicist Shows. Mar 11, 2021.

https://www.sciencealert.com/faster-than-light-travel-is-possible-within-einstein-s-physics-astrophysicist-shows

(B) visiting the interior of a black hole

<<  if a person found an isolated supermassive black hole suitable for scientific study and decided to venture in, everything observed or measured of the black hole interior would be confined within the black hole's event horizon.

Keeping in mind that nothing can escape the gravitational pull beyond the event horizon, the in-falling person would not be able to send any information about their findings back out beyond this horizon. Their journey and findings would be lost to the rest of the entire universe for all time. But they would enjoy the adventure, for as long as they survived … maybe …. >>️

Leo Rodriguez, Shanshan Rodriguez. Could a human enter a black hole to study it? A person could travel past (certain) black holes' event horizons without dying immediately — here's how. Feb 7, 2021. 

https://www.salon.com/2021/02/07/could-a-human-enter-a-black-hole-to-study-it_partner/  

(C) being already under observation by alien entities.

<< On June 25 the Pentagon and the Office of the Director of National Intelligence released their much hyped report on unidentified aerial phenomena, or UAP. (..) And while the report did not rule out an extraterrestrial origin for much of the documented UAP, it was short on details or bombshells. >> 

<<  we already know our world is easily detectable by extrasolar observers. A paper published on June 23 in Nature  

(Kaltenegger L., Faherty J.K.  https://www.nature.com/articles/s41586-021-03596-y ) shows that in the past 5,000 years, 1,715 stars have been in the right celestial position to view a populated Earth transiting the sun—with 319 more entering this sweet spot in the next 5,000 years. And seven of these far-off stars are known to have their own orbiting exoplanets that might support life. >>

<< Think of living in a room, and all the windows are open, and you do all your business, and you don’t know that all the windows are open, (..) Would you behave differently if you knew that you are being seen all your life? >>️  René Heller️

️

Tess Joosse. Aliens Might Already Be Watching Us. A new star map reveals more than 2,000 stars, some with their own planets, that have a direct view of our planetary presence. July 1, 2021

https://www.scientificamerican.com/article/aliens-might-already-be-watching-us

# gst: the effect of noise on the dynamics of microswimmers in externally-driven fluid flows.

AA << have quantified the effect of noise on swimmer dynamics in a steady, two-dimensional hyperbolic fluid flow. In such a flow, swimmers are ultimately forced to escape to the left or the right, with their transient dynamics near the passive unstable fixed point determining which way they go. >>

<< Without noise, a swimmer’s fate is sealed based on its position relative to the SwIM (swimming invariant manifolds) in the xθ phase space. With noise, the swimmer’s motion is a stochastic process. >>

AA << calculated the steady-state orientation distributions of diffusive, run-and-tumble, or mixed swimmers in the hyperbolic flow. The fluctuations give some swimmers greater opportunity to cross the SwIM and exit on the opposite side than they would have without noise. There is however a maximal distance that swimmers can get on either side of the passive fixed point and still be able to swim back to the other side—this is where the stable BIMs (burning invariant manifolds) block inward swimming particles. >>

<< Fluctuations make it increasingly likely that a swimmer close to one of these BIMs does indeed end up crossing it, causing irreversible changes to the fluctuating swimmers’ trajectories (assuming negligible translational diffusion).  >>️

Simon A. Berman, Kevin A. Mitchell. Swimmer dynamics in externally-driven fluid flows: The role of noise. arXiv: 2108.10488v1 [physics.flu-dyn]. Aug 24, 2021.

https://arxiv.org/abs/2108.10488

keywords: gst, swimmer, swimming particle, fluid dynamics, chaotic dynamics, rotational diffusion, random fluctuation, tumbling, noise

# GST: the behavior of motile active self-propelling matter

<< From starling aberrations to self-turbulent fluids, 'active systems' encompass a wide family of phenomena in which individual objects propel themselves forward, allowing them to display intriguing collective behaviors. (..) these objects collectively spend most of their time in one of two states, between which some intriguing behaviors can emerge. (..) these collective behaviors are determined by the ability of the self-propelling objects to swim upwards against the gravitational force, and their degrees of bottom-heaviness. For lower values of these quantities, groups of swimmers will sink to the bottom of their container just like inactive dust grains; but higher values will instead collect at the top. In between these states, smaller clusters of swimmers group at the bottom, which are fed by plumes of sinking particles. Also, porous clusters of swimmers can form, which allow individual particles to escape. >>

'Bottom-heavy squirmers' adopt characteristic group behaviours. Springer. May 28, 2020.

https://phys.org/news/2020-05-bottom-heavy-squirmers-characteristic-group-behaviours.html 

Ruhle F., Stark H. Emergent collective dynamics of bottom-heavy squirmers under gravity. Eur. Phys. J. E 43, 26 (2020). doi: 10.1140/epje/ i2020-11949-8. May 25, 2020.

https://link.springer.com/article/10.1140/epje/i2020-11949-8