# gst: networks of pendula with diffusive interactions, chaotic regime seems to emerge at low energies.

AA << study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian; as such, the energy is conserved. >>️

<< The behaviour observed showcases a mechanism for the appearance of chaotic oscillations in conservative systems. For Hamiltonians with two degrees of freedom, it has been shown how chaos can emerge near a saddle-centre equilibrium possessing a homoclinic orbit. (AA) have seen that higher-dimensional systems having mixed equilibria, i.e., generalisations of a saddle-center where the eigenvalues are only imaginary and reals, also show chaotic behaviour close to those points.  >>️

AA << complement the analysis with some numerical simulations showing the interplay between bifurcations of the origin and transitions to chaos of nearby orbits. A key feature is that the observed chaotic regime emerges at low energies. >>

️

Riccardo Bonetto, Hildeberto Jardón-Kojakhmetov, Christian Kuehn. Networks of Pendula with Diffusive Interactions. arXiv: 2408.02352v1 [math.DS]. Aug 5, 2024.

https://arxiv.org/abs/2408.02352

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

Keywords: gst, pendulum, network, transition, chaos, bifurcation

# gst: apropos of synchronization of large bubble clouds, self-oscillating acoustic bubbles that bounce

<< Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. (..) In this study, (AA) consider two closely spaced bubbles pulsating in the kHz range in response to ultrasonic excitation. A translational bouncing motion emerges from their interaction with a much lower frequency than the bubble pulsation frequency. >>

Their analysis << reveals that the observed bubble bouncing exhibits the main features of self-oscillation, such as negative damping and the emergence of a limit cycle. These results highlight unexpected nonlinear effects in the field of microbubbles and give insights into the understanding of synchronization in large bubble clouds. >>️

Gabriel Regnault, Alexander A Doinikov, et al. Phenomenon of self-oscillation in bubble dynamics: Bouncing acoustic bubbles. arXiv: 2404.05822v1 [physics.flu-dyn]. Apr 8, 2024.

https://arxiv.org/abs/2404.05822

Also: bubble, bouncing, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, self-oscillation, bouncing, behavior, collective behavior, bouncing motion, synchronization

# brain: arterial pressure pulsations could modulate neuronal activity.

<< Spontaneous slow oscillations have been described in the rat olfactory bulb local field potential, even in the absence of respiration. What is the origin of these oscillations? >>

AA << discovered a subpopulation of neurons within the olfactory bulb that can directly sense cardiovascular pressure pulsations (..). The modulation of their excitability is transduced by mechanosensitive ion channels. >>

<< Thus, there exists a fast pathway for the interoception of heartbeat whereby arterial pressure pulsations within the brain modulate neuronal activity. >> Peter Stern. ️

Luna Jammal Salameh, Sebastian H. Bitzenhofer, et al. Blood pressure pulsations modulate central neuronal activity via mechanosensitive ion channels. Science. Vol 383, Issue 6682. Feb 2, 2024. 

https://www.science.org/doi/10.1126/science.adk8511

img: https://www.science.org/cms/10.1126/science.adk8511/asset/76a1eaf8-61d3-4233-bc2a-be2276f367cd/assets/images/large/science.adk8511-fa.jpg

Also: brain, pnei, soliton, in https://www.inkgmr.net/kwrds.html  

Keywords: brain, pnei, olfactory bulb, spontaneous slow oscillations, wave, soliton

# gst: kirigami exposed to external flows.

<< Kirigami patterned materials have found several applications in recent years due to their ability to assume complicated shapes and exhibit emergent physical properties when exposed to external forces. >>️

<< Consisting of an array of cuts in a thin material, fabrication of these patterns can be quite simple. Here (AA) show that when they are placed in fluid flow, kirigami cut sheets with various patterns produce a verity of flow patterns in the wake. Through several sets of experiments, (AA) show that the kirigami sheets placed in flow can undergo static or dynamic flow-induced instabilities as a result of which they can buckle or undergo limit cycle oscillations, or they can remain stable while undergoing very large elongations. >>️

<< The ability to create controlled small-scale vortex shedding, induce desired flow-induced instabilities on structures, and form specifically-angled jets will enable several future applications in flow mixing (e.g., by producing small vortices in uniform flow at low Reynolds numbers), flow control (e.g., by controlling the direction and the number of jets that are produced downstream), and underwater soft robotics (e.g., by imposing desired flow-induced oscillations on structures). >>

️

Adrian G. Carleton, Yahya Modarres-Sadeghi. Kirigami Sheets in Fluid Flow.  arXiv: 2311.09381v1 [physics.flu-dyn]. Nov 15, 2023. 

https://arxiv.org/abs/2311.09381

Also: kirigami, origami, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, kirigami, origami, fluid flows, vortex

# gst: emergence of chimeras driven by non-normality

<< The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. >>️

<< Particular attention has been paid to the emergence of chimera states, where subsets of synchronized oscillations coexist with asynchronous ones. Such coexistence of coherence and incoherence is a perfect example where order and disorder can persist in a long-lasting regime. >>

<< Based on a symmetry-breaking mechanism, in this paper, (AA) shed light on the role that non-normality, a ubiquitous structural property of real networks, has in the emergence of several diverse dynamical phenomena, e.g., amplitude chimeras or oscillon patterns. >>️

<< Specifically, (they) demonstrate that the prevalence of source or leader nodes in networks leads to the manifestation of phase chimera states. >>️

Riccardo Muolo, Joseph D. O'Brien, et al. Persistence of chimera states and the challenge for synchronization in real-world networks. arXiv: 2306.00237v1 [nlin.PS]. May 31, 2023.

https://arxiv.org/abs/2306.00237

Also: chimera, network, in: https://www.inkgmr.net/kwrds.html

Keywords: gst, chimera, network, synchronization, swarm, noise, order, disorder, normal

# gst: reconfiguration and oscillations of sheets subject to vortex

<< The dynamics of a thin low-density polyethylene sheet subject to periodic forcing due to Bénard-Kàrmàn vortices in a long narrow water channel is investigated here. In particular, the time-averaged sheet deflection and its oscillation amplitude are considered. >>

<< The former is first illustrated to be well-approximated by the static equilibrium between the buoyancy force, the elastic restoring force, and the profile drag based on the depth-averaged water speed. >>

AA << observations also indicate that the presence of upstream vortices hinder the overall reconfiguration effect, well-known in an otherwise steady flow. For the sheet-tip oscillations, a simple model based on a torsional-spring-mounted flat plate correctly captures the measured tip amplitude δb over a wide range of sheet physical properties and flow conditions. >>

<< Furthermore, a rich phenomenology of structural dynamics including vortex-forced-vibration, lock-in with the sheet natural frequency, and flow-induced vibration due to the sheet wake, multiple-frequency, and modal response is reported. >>

️

J. John Soundar Jerome, Yohann Bachelier, et al. Reconfiguration and oscillations of a vertical, cantilevered sheet subject to vortex shedding behind a cylinder. Phys. Rev. Fluids 8, 093801. Sep 15, 2023. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.093801

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

Keywords: gst, sheet, vortex, Benard-Karman vortices

# gst: stochastic resonance mediated by optimal noise level values; transport of colloidal particles induced by substrate concentration oscillations.

AA << show the existence of a  stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport. >>️

J. D. Torrenegra-Rico, A. Arango-Restrepo, J. M. Rubi. Optimal transport of active particles induced by substrate concentration oscillations. Phys. Rev. E 108, 014134. July 28, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.014134

Img: https://twitter.com/PhysRevE/status/1687119409096089602

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

Keywords: gst, particle, colloids, noise, stochastic resonance, substrate oscillation

# gst: even a tiny noise could self-induce new chimera patterns through stochastic resonance

<< Noise induced order in excitable systems has diverse manifestations, such as coherence resonance (CR) and stochastic resonance. In this context a less explored phenomenon is self-induced stochastic resonance (SISR). Unlike CR, SISR may arise away from the bifurcation threshold and the properties of the induced oscillations depend upon both the noise intensity and the time-scale separation factor. In this work, (AA) report a new chimera pattern in a network of coupled excitable units, namely the self-induced stochastic resonance chimera or SISR-chimera that originates from the SISR phenomenon. (AA) explore the detailed dynamics of the SISR-chimera in the parameter space using proper quantitative measures. (AA) have found that unlike CR chimera, the SISR-chimera pattern strongly depends upon the ratio of time scale and noise intensity. Therefore, this type of chimera pattern can be induced even for a tiny noise intensity if the time scale separation of the activator and inhibitor is large enough. >>️

Taniya Khatun, Tanmoy Banerjee. Genesis of chimera patterns through self-induced stochastic resonance. arXiv:2305.06824v1 [nlin.AO]. May 11, 2023. 

https://arxiv.org/abs/2305.06824

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

Keywords: gst, noise, disorder, chimera, self-induced stochastic resonance chimera 

# gst: intricate transitions in elastoactive structures.

<< The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Among these, spontaneous self-oscillations of mechanical structures is perhaps the simplest and most widespread type of nonequilibrium phenomenon. >>️

<< Here, (AA) introduce a centimeter-sized model system for one-dimensional elastoactive structures. >>️

<< such structures exhibit flagellar motion when pinned at one end, self-snapping when pinned at two ends, and synchronization when coupled together with a sufficiently stiff link. (..) these transitions can be described quantitatively by simple models of coupled pendula with follower forces. >>️

Ellen Zheng, Martin Brandenbourger, et al. Self-Oscillation and Synchronization Transitions in Elastoactive Structures. Phys. Rev. Lett. 130, 178202. April 25, 2023. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.178202

Also:  transition, particle, self-assembly, elastic, pendulum in https://www.inkgmr.net/kwrds.html

Keywords: gst, transition, particle, self-assembly, elastic, pendulum

# gst: even a single bubble can produce creative musical outcomes

<< Producing original and arranging existing musical outcomes is an art that takes years of learning and practice to master. Yet, despite the constant advances in the field of AI-powered musical creativity, production of quality musical outcomes remains a prerogative of the humans. Here we demonstrate that a single bubble in water can be used to produce creative musical outcomes, when it nonlinearly oscillates under an acoustic pressure signal that encodes a piece of classical music. >>️

Ivan S. Maksymov. Musical creativity enabled by nonlinear oscillations of a bubble in water. arXiv:2304.00822v1 [cs.SD]. Apr 3, 2023. 

https://arxiv.org/abs/2304.00822

keyword "bubble" in FonT

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

Keywords: gst, ai, fluid dynamics, bubble, sound, music, audio processing

# gst: apropos of weakly coupled oscillators, a new approach to depict about their spontaneous stochastic activities

<<  Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. >>

<< Here (AA) introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function Q∗1(x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. >>

AA << approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators. >>️

Alberto Pérez-Cervera, Boris Gutkin, et al. A Universal Description of Stochastic Oscillators. arXiv: 2303.03198v1 [nlin.AO]. Feb 27, 2023. 

https://arxiv.org/abs/2303.03198

Also

'oscillations' in FonT

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

Keywords: gst, oscillations, random oscillations, weakly coupled oscillators

# gst: apropos of vibrating pivots, driving a damped coplanar double pendulum.

AA << present results of linear and nonlinear motions of a parametrically driven coplanar double pendulum with velocity-dependent damping. The equations of motion of a damped double pendulum of unequal masses with its pivot vibrated vertically are different from those obtained under gravity modulation. 

Linear stability analysis shows that tongue-shaped marginal stability curves divide the plane of driving parameters into multiple regions of subharmonic and harmonic instabilities. The instability zones for one normal mode overlap with those for the other. 

The double pendulum may oscillate or rotate about its pivot harmonically or subharmonically. The limit cycles corresponding to the normal mode oscillations of a double pendulum of equal masses are squeezed into a line in its configuration space. 

For unequal masses, two marginal curves for subharmonic instabilities merge to form a double-well shaped curve in the presence of damping, which is qualitatively new. The pendulum shows driving amplitude sensitive multi-period complex oscillations for driving parameters near the extrema of the merged instability zones and boundaries of the overlapping zones. 

For larger driving amplitude, the pendulum shows subharmonic, harmonic or chaotic rotations. >>

️

Rebeka Sarkar, Krishna Kumar, Sugata Pratik Khastgir. Parametrically driven damped coplanar double pendulum. arXiv:2208.03292v1 [physics.class-ph]. Aug 2, 2022. 

https://arxiv.org/abs/2208.03292

Also

keyword 'pendulum' in FonT

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

keyword 'pendolo' | 'pendola' in Notes

(quasi-stochastic poetry)

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

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

Keywords: gst, pendulum, double pendulum, instability, chaos, chaotic rotations

# gst: apropos of oscillations, viscous streaming around an immersed microfeature (e.g. a bubble)

<< Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. >>️

(AA) << demonstrate that a multi-curvature approach in viscous streaming dramatically extends the range of accessible flow topologies. (They) show that numerically predicted, but never experimentally observed, streaming flows can be physically reproduced, computationally engineered, and in turn used to enhance particle manipulation, filtering and separation in compact, robust, tunable and inexpensive devices. >>️

Yashraj Bhosale, Giridar Vishwanathan, et al. Multi-curvature viscous streaming: flow topology and particle manipulation. arXiv: 2111.07184v1 [physics.flu-dyn]. Nov 13, 2021.

https://arxiv.org/abs/2111.07184

keywords: gst, viscosity, viscous streaming, bubble, oscillations, liquid oscillations, flanking vortex, particle manipulation 

# geo: apropos of oscillations, a 'true polar wander' (TPW); Earth tip on its side 84 Ma ago.

<< It has been debated for the past few decades whether the outer, solid shell of the Earth can wobble about, or even tip over relative to the spin axis. Such a shift of Earth is called "true polar wander," (TPW) but the evidence for this process has been contentious. New research (..) provides some of the most convincing evidence to date that such planetary tipping has indeed occurred in Earth's past. >>️

<< The Earth is a stratified ball, with a solid metal inner core, a liquid metal outer core, and a solid mantle and overriding crust at the surface which we live on. All of this is spinning like a top, once per day. Because the Earth's outer core is liquid, the solid mantle and crust are able to slide around on top of it.  >>

️

Did the Earth tip on its side 84 million years ago? Tokyo Institute of Technology. Oct 18, 2021. 

https://phys.org/news/2021-10-earth-side-million-years.html

<< a new high-resolution palaeomagnetic record from two overlapping stratigraphic sections in Italy (..) provides evidence for a ~12° TPW oscillation from 86 to 78 Ma. This observation represents the most recent large-scale TPW documented and challenges the notion that the spin axis has been largely stable over the past 100 million years. >>️

Mitchell, R.N., Thissen, C.J.,  et al. A Late Cretaceous true polar wander oscillation. Nat Commun 12, 3629. doi: 10.1038/ s41467-021-23803-8. June 15, 2021. 

https://www.nature.com/articles/s41467-021-23803-8

keywords: gst, geo, geodynamics, geophysics, palaeomagnetism, oscillations, wobble, true polar wander, tpw

# gst: vacuum fluctuations (even in complete darkness)

<< physics is increasingly discovering how our universe is shaped by fluctuations of physical fields, which not only lead to tiny shifts of spectral lines of atoms, but moreover may cause the evaporation of black holes, and are ultimately responsible for the large-scale structure of our universe,  >>

AA  << have now made a large leap toward controlling strongly enhanced vacuum fluctuations much faster than typical timescales of virtual photons. To this end, they created a specialized semiconductor structure in which electrons are extremely strongly coupled to the light fields of tiny antennas designed for the so-called terahertz spectral range. As a result, vacuum fluctuations of light and matter fields participate in the interaction, strongly increasing the presence of virtual photons—even in complete darkness. >>

Understanding vacuum fluctuations in space. University of Regensburg. Aug 10, 2020.

https://phys.org/news/2020-08-vacuum-fluctuations-space.html 

<< The abrupt modification of the vacuum ground state causes spectrally broadband polarization oscillations confirmed by (AA) quantum model. In the future, this subcycle shaping of hybrid quantum states may trigger cavity-induced quantum chemistry, vacuum-modified transport or cavity-controlled superconductivity, opening new scenarios >>

M. Halbhuber, J. Mornhinweg, et al. Non-adiabatic stripping of a cavity field from electrons in the deep-strong coupling regime. Nat. Photonics. doi: 10.1038/ s41566-020-0673-2. Aug 10, 2020.

https://www.nature.com/articles/s41566-020-0673-2

# gst: weird matter, the 'ballistic resonance' paradox; amplitude of mechanical vibrations can grow without external influence

AA << discovered a new physical phenomenon of 'ballistic resonance', where mechanical oscillations can be excited only due to internal thermal resources of the system. >>

<< The discovered phenomenon describes that the process of heat equilibration leads to mechanical vibrations with an amplitude that grows with time. The effect is called ballistic resonance. >>

<< Over the past few years, our scientific group has been looking into the mechanisms of heat propagation at the micro and nano levels. We found out that at these levels, heat doesn't spread in the way we expected it to: for example, heat can flow from cold to hot. This behavior of nanosystems leads to new physical effects, such as ballistic resonance, >> Vitaly Kuzkin.

Scientists have discovered a new physical paradox. Peter the Great Saint-Petersburg Polytechnic University. Jul 13, 2020.

https://phys.org/news/2020-07-scientists-physical-paradox.html

<< coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenomenon is referred to as ballistic resonance. At large times, these mechanical vibrations decay monotonically >>

Vitaly A. Kuzkin, Anton M. Krivtsov. 

Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature. Phys. Rev. E 101, 042209. Apr 16, 2020.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042209

# gst: contactless manipulation of droplets levitating in an acoustic wave

<< A unique, versatile, and material-independent approach to manipulate contactlessly and merge two chemically distinct droplets suspended in an acoustic levitator is reported. Large-amplitude axial oscillations are induced in the top droplet by low-frequency amplitude modulation of the ultrasonic carrier wave, which causes the top sample to merge with the sample in the pressure minimum below. The levitator is enclosed within a pressure-compatible process chamber to enable control of the environmental conditions. The merging technique permits precise control of the substances affecting the chemical reactions, the sample temperature, the volumes of the liquid reactants down to the picoliter range, and the mixing locations in space and time. >>

Stephen J. Brotton, Ralf I. Kaiser. 

Controlled Chemistry via Contactless Manipulation and Merging of Droplets in an Acoustic Levitator. Anal. Chem. 2020, 92, 12, 8371–8377. doi: 10.1021/ acs.analchem.0c00929. Jun 1, 2020. 

https://pubs.acs.org/doi/10.1021/acs.analchem.0c00929#

Levitating droplets allow scientists to perform 'touchless' chemical reactions.  American Chemical Society. Jun 24, 2020.

https://phys.org/news/2020-06-levitating-droplets-scientists-touchless-chemical.html  

# gst: active drops: from steady to chaotic self-propulsion

<< Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. (..) strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. >>

Matvey Morozov, Sebastien Michelin. Nonlinear dynamics of a chemically-active drop: From steady to chaotic self-propulsion. J. Chem. Phys. 150, 044110 (2019). doi: 10.1063/1.5080539. Jan 31, 2019.  https://aip.scitation.org/doi/10.1063/1.5080539

# gst: the complex world of Bacteria; collective oscillations via discontinuous transitions, chemical quorum sensing and brainlike bursts of electricity to communicate.

<< collective oscillations in cell populations can emerge suddenly with nonzero amplitude via a discontinuous transition. >>

Rosa Martinez-Corral, Jintao Liu, et al. Bistable emergence of oscillations in growing Bacillus subtilis biofilms. PNAS Sep 4, 2018;  115 (36) E8333-E8340.  doi: 10.1073/pnas.1805004115

https://www.pnas.org/content/115/36/E8333 

<< As in all communities, cohabiting bacteria need ways to exchange messages. Biologists have known for decades that bacteria can use chemical cues to coordinate their behavior. >>

AA << are now finding that bacteria in biofilms can also talk to one another electrically. Biofilms appear to use electrically charged particles to organize and synchronize activities across large expanses. This electrical exchange has proved so powerful that biofilms even use it to recruit new bacteria from their surroundings, and to negotiate with neighboring biofilms for their mutual well-being. >>

<< Step by step we find that all the things we think bacteria don’t do, they actually do, [..] It’s displacing us from our pedestal. >> Ned Wingreen.

Gabriel Popkin. Bacteria Use Brainlike Bursts of Electricity to Communicate. With electrical signals, cells can organize themselves into complex societies and negotiate with other colonies. Sep 5, 2017

https://twitter.com/QuantaMagazine/status/1071417372500783104

https://www.quantamagazine.org/bacteria-use-brainlike-bursts-of-electricity-to-communicate-20170905/

Also

Gurol M. Suel publ.

http://labs.biology.ucsd.edu/suel/index.html

FonT

intrigante qui l'idea di una Intelligenza Artificiale che, dalle relativamente comode e veloci osservazioni sull'evoluzione di colonie batteriche sotto differenti condizioni, sia in grado di circoscrivere pattern comportamentali di interesse per la modellizzazione (e previsione)  di comunita' altre ...

# gst: periodic oscillations of flexible knots

AA << study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. (..) trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. (..) this motion (..) is accompanied by a very slow rotation around the vertical symmetry axis. (..) this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. (..) the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops. >>

Magdalena Gruziel, Krishnan Thyagarajan, et al. Periodic Motion of Sedimenting Flexible Knots. Phys. Rev. Lett. 121, 127801 Sep 18,  2018. doi: 10.1103/PhysRevLett.121.127801.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.127801

The periodic motion of flexible knots, and the connection to DNA. University of Warsaw. Sep 26, 2018.

https://m.phys.org/news/2018-09-periodic-motion-flexible-dna.html