# gst: multiparticle dispersion in rotating-stratified turbulent flows (when stratification increases turbulent fluctuations may not be weaker)

AA << study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably stratified Boussinsesq equations, with Brunt-Väisälä frequency 𝑁 and Coriolis parameter 𝑓. >>

<< In all cases considered, (AA) demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backward in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when 𝑁 and 𝑓  increase. (They) also find evidence for the formation of shear layers, which become more pronounced as 𝑁 and 𝑓  become larger. Finally, (They) show that the irreversibility on the dispersion of a set of particles initially forming a regular tetrahedron becomes weaker when the influence of stratification and rotation increases, a property that (They) relate to that of the perceived rate-of-strain tensor. >>️

<< Unexpectedly, (AA) observe that the higher moments of particle separation, in particular the normalized fourth-order central moment of the separation (the kurtosis Kr) is an increasing function of stratification and rotation. This is surprising, as when stratification increases the turbulent fluctuations are expected to be weaker, (..) >>️

Sebastian Gallon, Fabio Feraco, et al. Multiparticle dispersion in rotating-stratified turbulent flows. Phys. Rev. Fluids 10, 034605. Mar 17, 2025. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.034605

Also: particle, turbulence, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, turbulence, disorder, fluctuations

# gst: conventional and anomalous mobility edges in a quasiperiodic chain.

<< Mobility edges (MEs) constitute the energies separating the localized states from the extended ones in disordered systems. Going beyond this conventional definition, recent proposal suggests for an ME which separates the localized and multifractal states in certain quasiperiodic systems - dubbed as the anomalous mobility edges (AMEs). >>

<< In this study, (AA) propose an exactly solvable quasiperiodic system that hosts both the conventional and anomalous mobility edges under proper conditions. (They) show that with increase in quasiperiodic disorder strength, the system first undergoes a delocalization to localization transition through an ME of conventional type. >>

<< Surprisingly, with further increase in disorder, (They) obtain that a major fraction of the localized states at the middle of the spectrum turn multifractal in nature. Such unconventional behavior in the spectrum results in two AMEs, which continue to exist even for stronger quasiperiodic disorder. >>

AA << numerically obtain the signatures of the coexisting MEs complement it through analytical derivation using Avila's global theory. In the end (They) provide important signatures from the wavepacket dynamics. >>️

Sanchayan Banerjee, Soumya Ranjan Padhi, Tapan Mishra. Emergence of distinct exact mobility edges in a quasiperiodic chain. arXiv: 2503.19834v1 [cond-mat.quant-gas]. Mar 25, 2025.️

https://arxiv.org/abs/2503.19834

Also: edge, order, disorder, waves, transition,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, edge, order, disorder, waves, transition 

# gst: when a phase transition could be controlled by a fixed point of infinite disorder

AA << apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First (They) recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for arbitrary size of the block. For the model with three-spin couplings (They) calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. (AA) have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus this model represents a new infinite disorder universality class. >>️

Ferenc Iglói, Yu-Cheng Lin. Random quantum Ising model with three-spin couplings. arXiv:2503.18690v1 [cond-mat.dis-nn]. Mar 24, 2025.

https://arxiv.org/abs/2503.18690

Also: disorder, order, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, order, transition

# qubit: stability of classical shadows under gate-dependent noise

<< Expectation values of observables are routinely estimated using so-called classical shadows—the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow estimation in practice, it is crucial to understand the behavior of the estimators under realistic noise. >>

<< In this Letter, (AA) prove that any shadow estimation protocol involving Clifford unitaries is stable under gate-dependent noise for observables with bounded stabilizer norm—originally introduced in the context of simulating Clifford circuits. In contrast, (They) demonstrate with concrete examples that estimation of “magic” observables can lead to highly misleading results in the presence of miscalibration errors and a worst case bias scaling exponentially in the system size. >>

AA << further find that so-called robust shadows, aiming at mitigating noise, can introduce a large bias in the presence of gate-dependent noise compared to unmitigated classical shadows. Nevertheless, (AA) guarantee the functioning of robust shadows for a more general noise setting than in previous works. On a technical level, (They) identify average noise channels that affect shadow estimators and allow for a more fine-grained control of noise-induced biases. >>️

Raphael Brieger, Markus Heinrich, et al. Stability of Classical Shadows under Gate-Dependent Noise. Phys. Rev. Lett. 134, 090801. Mar 4, 2025. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.090801  arXiv: 2310.19947v3 [quant-ph]. Feb 19, 2025.   https://arxiv.org/abs/2310.19947

Also: qubit, in FonT  https://flashontrack.blogspot.com/search?q=qubit  noise, ai (artificial intell) (bot), in https://www.inkgmr.net/kwrds.html   

Keywords: qubit, noise, realistic noise, shadows, robust shadows

# gst: emergent flocking in mixtures of antialigning self-propelled particles.

FIG. 4. (c) Mean field phase diagram with disorder (green triangles), polarized moving bands (blue circles), and polarized patches (orange squares).

AA << observe a flocking mechanism, the emergence of a state with global polar order, in mixed systems of self-propelled particles with purely antialigning interactions, i.e., the ground state for any pair of particles is to be opposedly oriented. In binary mixtures, (They) find that flocking can be realized by cross-species antialigning that is dominant compared to intraspecies antialignment. >>

<< While the key mechanism can be understood within a mean-field description, beyond mean-field (AA) develop an asymptotically exact Boltzmann-scattering theory from first principles.  This theory yields analytical predictions for the flocking transition and shows excellent quantitative agreement with simulations of dilute systems. For large systems, (They) find either microphase separation or static patterns with patches or stripes that carry different polarization orientations. >>️

Rüdiger Kürsten, Jakob Mihatsch, Thomas Ihle. Emergent flocking in mixtures of antialigning self-propelled particles. Phys. Rev. E 111, L023402. Feb 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L023402

Also: particle, flock, flocking, swarm, order, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, self-propelled particles, flock, flocking, swarm, order, disorder, transitions

# gst: apropos of the impact of noise, stochastic Kuramoto oscillators with inertia and higher-order interactions.

<< The impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, (AA) study stochastic second-order coupled Kuramoto oscillators with higher-order interactions and show that as noise strength increases, the critical points associated with synchronization transitions shift toward higher coupling values. By employing the perturbation analysis, (They) obtain an expression for the forward critical point as a function of inertia and noise strength. Further, for overdamped systems, (AA) show that as noise strength increases, the first-order transition switches to second-order even for higher-order couplings. >>

️

Priyanka Rajwani, Sarika Jalan. Stochastic Kuramoto oscillators with inertia and higher-order interactions. Phys. Rev. E 111, L012202. Jan 13, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L012202   arXiv: 2407.14874v1 [nlin.AO]. Jul 20, 2024. https://arxiv.org/abs/2407.14874 

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

Keywords: gst, noise, transition, coupled oscillators, synchronization transition

# gst: when homogeneous systems meet dissipation and disorder.

AA << investigate the localization and topological properties of the non-equilibrium steady state (NESS) in a one-dimensional homogeneous system. (Their) results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. >>

<< Conversely, for an initially flat-band system with compactly localized wave functions, the NESS is delocalized. >>

<< Furthermore, (They) find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, (AA) systematically characterize the impact of disorder on the localization and topological properties of the NESS. >>

<< The phase diagram reveals that the NESS can be topologically non-trivial even when the initial state is topologically trivial, and that the topological triviality of the initial state weakens the topological non-triviality of the NESS. >>

Xixi Feng, Ao Zhou, et al. When Homogeneous Systems Meet Dissipation and Disorder. arXiv: 2502.11383v1 [cond-mat.dis-nn]. Feb 17, 2025. 

https://arxiv.org/abs/2502.11383

Also: order, disorder, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# gst: order and chaos in systems of coaxial vortex pairs

Fig. B.12: Ex. with 4 interact. vortex pairs

AA << have analyzed interactions between two and three coaxial vortex pairs, classifying their dynamics as either ordered or chaotic based on strengths, initial sizes, and initial horizontal separations.  >>️

They << found that periodic cases are scattered among chaotic ones across different initial configurations. Quasi-periodic leapfrogging typically occurs when the initial distances between the vortex pairs are small and cannot coexist with vortex-pair overtake. When the initial configuration splits into two interacting vortex pairs and a single propagating vortex pair, the two interacting pairs consistently exhibit periodic leapfrogging. For the smallest initial horizontal separations, the system predominantly exhibits chaotic or quasi-periodic motions rather than periodic leapfrogging with a single frequency. This behavior is due to the strong coupling between all three vortex pairs. When the pairs are in close proximity, more complex and chaotic dynamics emerge instead of periodic motion. >>

Their << findings indicate that quasi-periodic leapfrogging and chaotic interactions generally occur when the three vortex pairs have similar strengths and initial sizes. Conversely, discrepancies in these parameters cause the system to disintegrate into two subsystems: a single propagating vortex pair and two periodically leapfrogging pairs. >>️

️

Christiana Mavroyiakoumou, Wenzheng Shi. Order and Chaos in Systems of Coaxial Vortex Pairs. arXiv: 2502.07002v1 [physics.flu-dyn]. Feb 10, 2025. ️

https://arxiv.org/abs/2502.07002

Also: chaos, vortex, order, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, vortex, order, disorder, disorder & fluctuations

# gst: intrinsic disorder bars intruders (from biomolecular condensates)

<< It was recently discovered that eukaryotic cells are host to a multiplicity of biomolecular condensates. These condensates typically contain protein and/or RNA components with intrinsically disordered regions (IDRs). While IDRs have been proposed and demonstrated to play many roles in condensate biology, (AA) suggest here an additional crucial role of IDRs, which is to exclude unwanted “intruders” from condensates. This exclusion effect arises from the large conformational entropy of IDRs; i.e., there is a high free-energy cost to occupying space that would otherwise be available to the IDRs. By combining polymer theory with sticker-spacer simulations, (They) show that the relevant insertion free energy increases with the concentration of IDRs in the condensate as well as with intruder size, attaining a linear scaling with surface area for large intruders. >>

AA << find that at realistic IDR concentrations, particles as small as the size of an average protein (4 nm in diameter) can be 97% excluded from condensates. To overcome this entropic barrier, molecules must interact favorably with condensate components to be recruited as clients. Application of the developed size-exclusion theory to biological condensates suggests that condensate IDRs may play a generic exclusionary role across organisms and types of condensates. >>️

Vladimir Grigorev, Ned S. Wingreen, Yaojun Zhang. Conformational Entropy of Intrinsically Disordered Proteins Bars Intruders from Biomolecular Condensates. PRX Life 3, 013011. Feb 14, 2025.

https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.3.013011

Also: order, disorder, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, transitions

# gst: criticality and multistability in quasi-2D turbulence

       Fig. 1(a) Helmholtz resonators

<< Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior, whose study is hindered by the long spatial and temporal scales involved. >>

Here AA << experimentally study turbulence in periodically driven nanofluidic channels with a high aspect ratio using superfluid helium. (They) find a multistable transition behavior resulting from cascading bifurcations of large-scale vorticity and critical behavior at the transition to quasi-2D turbulence consistent with phase transitions in periodically driven many-body systems. >>

AA << demonstrate that quasi-2D turbulent systems can undergo an abrupt change in response to a small change in a control parameter, consistent with predictions for large-scale atmospheric or oceanic flows. >>️

Filip Novotny, Marek Talir, et al. Critical behavior and multistability in quasi-two-dimensional turbulence. arXiv: 2406.08566v1 [physics.flu-dyn]. Jun 12, 2024.

https://arxiv.org/abs/2406.08566

Also: order, disorder, disorder & fluctuations, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, criticality, turbulence, transition 

# gst: quadrupolar stress drives collapse of nematic order on frictional substrates.

<< The field of active nematics has traditionally employed descriptions based on dipolar activity, with interactions that align along a single axis. However, it has been theoretically predicted that interactions with a substrate, prevalent in most biological systems, would require novel forms of activity, such as quadrupolar activity, that are governed by hydrodynamic screening. >>

<< Here, by combining experiments and numerical simulations, (AA) show that upon light-induced solidification of the underlying medium, microtubule-kinesin mixtures undergo a transformation that leads to a biphasic active suspension. Using an active lyotropic model, (They) prove that the transition is governed by screening effects that alter the dominant form of active stress. Specifically, the combined effect of friction and quadrupolar activity leads to a hierarchical folding that follows the intrinsic bend instability of the active nematic layer. >>

AA << results demonstrate the dynamics of the collapse of orientational order in active nematics and present a new route for controlling active matter by modifying the activity through changing the surrounding environment. >>️

Aleksandra Ardaseva, Ignasi Velez-Ceron, et al. Beyond Dipolar Activity: Quadrupolar Stress Drives Collapse of Nematic Order on Frictional Substrates. arXiv: 2407.03723v3 [cond-mat.soft]. Jan 14, 2025. 

https://arxiv.org/abs/2407.03723

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

Keywords: gst, transition, collapse, active nematics, stress 

# gst: acceleration of enzymatic reactions due to nearby inactive binding sites.

<< Many biological molecular motors and machines are driven by chemical reactions that occur in specific catalytic sites. (AA) study whether the arrival of molecules to such an active site can be accelerated by the presence of a nearby inactive site.  >>️

AA << identify two parameter regimes in which the reaction is accelerated. >>️

<< In the first regime, the inactive site stores a molecule in order to release it following a reaction, when the neighboring catalytic site is empty. >>

<< In the second regime, the inactive site releases a molecule when the catalytic site is full, in order to impede the molecules from leaving the active site before they react. For the storage mechanism, which is more likely to be biologically relevant, the acceleration can reach up to 15%, depending on parameters. >>️

Hila Katznelson, Saar Rahav. Acceleration of enzymatic reactions due to nearby inactive binding sites. arXiv: 2501.01662v1 [cond-mat.stat-mech]. Jan 3, 2025.

https://arxiv.org/abs/2501.01662  

Phys. Rev. Research 6, 043330. Dec 30, 2024. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043330

Keywords: gst, enzymes, enzymatic catalysis, catalytic sites, inactivity, inactive binding sites

# gst: apropos of dances, drops that dance following snake- and ouroboros-shaped trajectories on lubricated surfaces.

<< Recently, (AA) observed a curious breath figure pattern when water condenses on solid surfaces coated with a thin lubricant oil film. Water drops of various sizes, ranging from tens of microns to several millimetres, start to perform a self-avoiding, serpentinelike dance. As the drop moves, it consumes smaller droplets along its path, converting interfacial energy into kinetic energy to sustain its motion. These self-avoiding drops preferentially avoid crossing their own paths as well as the paths of other drops; they can only intersect their previous paths once sufficient recondensation has occurred. This self-avoiding behavior arises because the previous path (..) contains little to no water content to fuel self-propulsion, so the drops continually seek areas with higher local water content. >>️

<< This intricate serpentine dance is driven by short-range interactions between droplets, mediated by overlapping menisci, similar to the Cheerios effect. Remarkably, long-range order spontaneously emerges from these short-range interactions, with the collective motion exhibiting self-similarity—breath figure patterns appear roughly similar across different scales. >>

<< The serpentine motions of the drops, which can span distances many times their diameters, eventually deplete the local lubricant film, causing a transition from serpentine to circular motion. This circular motion can be seen as a unique form of serpentine motion occurring in lubricant-poor regions. As the drops move, they continually redistribute the lubricant across the substrate, leading to a dynamic interplay between serpentine and circular motions. This ongoing redistribution can be visualized by illuminating the surface with diffused white light and capturing the resulting interference patterns with a digital camera. Variations in lubricant thickness produce different hues, creating a vibrant, colorful canvas and an intricate dance floor for the condensing drops. >>️

<< The phenomenon described in (AA) paper represents a fascinating example of active matter driven by condensation, rather than the more commonly observed chemical reactions or Marangoni effects. >>

Marcus Lin, Fauzia Wardani, Dan Daniel. Dancing drops on lubricated surfaces. Phys. Rev. Fluids 9, 110504. Nov 22, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.110504

Marcus Lin, Solomon Adera, Joanna Aizenberg, Yao Xi, Dan Daniel. V0030: Serpents and Ouroboros: Emergent collective motion of condensate droplets. 76th Annual Meeting of the APS Division of Fluid Dynamics. Nov 19-21, 2023.

https://gfm.aps.org/meetings/dfd-2023/64ff56f3199e4c1bbe725834

Also: drop, droplet, droploid, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, dance

# gst: curiosity-driven search for novel behaviors.

<< One of the first exciting things to do with a new physical system is to go exploring—to tune parameters and see what unexpected behaviors the system is capable of. >>️

AA << combine active and unsupervised learning for automated exploration of nonequilibrium systems with unknown order parameters. (They) iteratively use active learning based on current order parameters to expand the library of behaviors and relearn order parameters based on this expanded library. (They) demonstrate the utility of this approach in Kuramoto models of increasing complexity. In addition to reproducing known phases, (AA) reveal previously unknown behavior and related order parameters, and demonstrate how to align search with human intuition. >>️

Martin J. Falk, Finnegan D. Roach, et al. Curiosity-driven search for novel nonequilibrium behaviors. Phys. Rev. Research 6, 033052. Jul 11, 2024. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.033052  

Also: curiosity, behav, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, curiosity, behav, transition

# gst: apropos of the transition of order from chaos, a universal behavior near a critical point.

<< As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, (AA) observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. >>️

AA << study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system.   >>️

<< the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. (AA) results show that the observed emergence of order from chaos is a continuous phase transition (..) the critical exponents characterizing this transition fall in the universality class of directed percolation. >>️

The << paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point. >>️

Sivakumar Sudarsanan, Amitesh Roy, et al. Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system. Phys. Rev. E 109, 064214. Jun 20, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064214

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

Keywords: gst, order, chaos, transition 

# gst: apropos of avoidance, packing of stiff rods on ellipsoids; the effects of self-avoidance

AA << study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. >>

<< Within a mean-field approximation, (AA) show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. (They)  find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. >>

<< While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. >>

<< the critical behavior of this system is in fact related to the butterfly catastrophe model. >>

Doron Grossman, Eytan Katzav. Effects of self-avoidance on the packing of stiff rods on ellipsoids. Phys. Rev. E 109, 054111. May 9, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.054111

Also: spheroids, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, ellipsoids, spheroids,  oblate- prolate spheroids, avoidance, self-avoidance

# gst: apropos of uncertainty, notes on uncertainty, information, and classical dynamics.

<< Survival in this world is an adventure because we are so ignorant and everything around us seems so uncertain. In fact, it is hard to think of any realistic phenomenon that is completely free from one of the three kinds of uncertainty—deterministic (chaotic), stochastic, and quantum; more often than not, all of the three are present in various degrees. Thus, in order to gain any knowledge about any realistic system, one must understand how to characterize, quantify, and interpret these uncertainties. >>️

Sagar Chakraborty. Eclectic Notes on Uncertainty, Information, and Classical Dynamics. arXiv: 2404.13511v1 [physics.class-ph]. Apr 21, 2024.

https://arxiv.org/abs/2404.13511

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

Keywords: gst, information, uncertainty, ambiguity, noise, error 

# gst: apropos of collective behaviors, a visual model to reproduces swarming, schooling, and milling.

<< Animal collective behavior is often modeled with self-propelled particles, assuming each individual has “omniscient” knowledge of its neighbors. Yet, neighbors may be hidden from view and we do not know the effect of this information loss. To address this question, (AA) propose a visual model of collective behavior where each particle moves according to bioplausible visual cues, in particular the optic flow. This visual model successfully reproduces three classical collective behaviors: swarming (no orientational order), schooling (high orientational order), and milling (the group coordinately swirls in a circular pattern). >>️

Diego Castro, Franck Ruffier, Christophe Eloy. Modeling collective behaviors from optic flow and retinal cues. Phys. Rev. Research 6, 023016. Apr 4, 2024. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.023016

Also: swarm, flock, behav, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swarming, flocking, behavior, particle, self-propelled particles

# gst: an analogy between geometrical frustrations and nonreciprocal systems

<< A system is geometrically frustrated when its members cannot find a configuration that simultaneously minimizes all their interaction energies, (..). A nonreciprocal system is one whose members have conflicting, asymmetric goals, as exemplified by an ecosystem of predators and prey. >>️

<< Ryo Hanai (..) has identified a powerful mathematical analogy between those two types of dynamical systems. >>️

Peter Littlewood. Nonreciprocal Frustration Meets Geometrical Frustration. Physics 17, 32. Feb 26, 2024. 

https://physics.aps.org/articles/v17/32

Ryo Hanai. Nonreciprocal Frustration: Time Crystalline Order-by-Disorder Phenomenon and a Spin-Glass-like State. Phys. Rev. X 14, 011029. Feb 26, 2024. 

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.011029

Also: order, disorder, disorder & fluctuations, noise, analogy, in https://www.inkgmr.net/kwrds.html

Keywords: gst, analogy, order, disorder, noise

# gst: feedback systems with switches that actuate after a preset delay.

AA << study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. >>

AA << are able to show that slowly oscillating solutions are always stable if they exist. (They) also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions. >>

Lucas Illing, Pierce Ryan, Andreas Amann. ️Dynamics of a time-delayed relay system. Phys. Rev. E 109, 014223. Jan 23, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.014223

Keywords: gst, feedback, relay, switch