# gst: unstable fixed points in chaotic networks

<< Understanding the high-dimensional chaotic dynamics occurring in complex biological systems such as recurrent neural networks or ecosystems remains a conceptual challenge. For low-dimensional dynamics, fixed points provide the geometric scaffold of the dynamics. However, in high-dimensional systems, even the location of fixed points is unknown. >>

Here, AA << analytically determine the number and distribution of fixed points for a canonical model of a recurrent neural network that exhibits high-dimensional chaos. This distribution reveals that fixed points and dynamics are confined to separate shells in state space. Furthermore, the distribution enables (AA) to determine the eigenvalue spectra of the Jacobian at the fixed points, showing that each fixed point has a low-dimensional unstable manifold. >>

<< Despite the radial separation of fixed points and dynamics, (They)  find that the principal components of fixed points and dynamics align and that nearby fixed points act as partially attracting landmarks for the dynamics. >>

AA results << provide a detailed characterization of the fixed point geometry and its interplay with the dynamics, thereby paving the way towards a geometric understanding of high-dimensional chaos through their skeleton of unstable fixed points. >>

Jakob Stubenrauch, Christian Keup, et al. Fixed point geometry in chaotic neural networks. Phys. Rev. Research 7, 023203. May 29, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023203

Also: chaos, disorder & fluctuations, instability, transition, network, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, networks, neural networks, ecosystems, fixed points, unstable fixed points.

# gst: apropos of weakness, weak but influential; nonlinear contributions of structural connectivity to human cognitive abilities and brain functions.

<< Diverse human cognitive abilities are rooted in brain structural connectivity which has weights spanning several orders of magnitude. However, due to false-positive challenges in tractography, weak connectivity has been often treated as noise and ignored - despite its prevalence across mammalian brains. >>

Here AA show << that weak connectivity significantly predicts human cognitive abilities and supports brain functions through amplification of its small weight in a nonlinear manner. >>

AA found that << weak connectivity involves high individual variability and significantly predicts general cognitive ability and memory in individuals, and it is also critical for whole-brain dynamic simulation and structure-function coupling. Importantly, fusing two post-tractography filtering methods of streamlines potentially results in more reliable connectivity that preserves weak links and outperforms conventional thresholding in predicting cognitive abilities and functional connectivity. >>

<< At the network level, weak connectivity expands the operational capacity of brain networks to enhance both global integration and fine-grained segregation, thereby supporting a functional balance essential for cognitive abilities. >>

<< Finally, (AA) identified a specific type of weak connectivity mainly linking visual/motor to limbic areas with negative gene co-expression, which has a disproportionately large impact on cognitive predictions and network dynamics. >>

Rong Wang, Zhao Chang, et al. Weak but influential: Nonlinear contributions of structural connectivity to human cognitive abilities and brain functions. arXiv: 2505.24125v1 [q-bio.NC]. May 30, 2025.

https://arxiv.org/abs/2505.24125

Also: brain, network, weak, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, network, noise,  weakness, weak connectivity,  brain structural connectivity, tractography, multiple tractography algorithms, cognitive ability and memory, individual variability, global integration, fine-grained segregation, limbic areas.

# gst: collective behavior based on topological vision.

<< The collective dynamics of active particles with topological vision are investigated. The topological vision, defined as a combination of the visual field and topological neighborhoods, breaks the action-reaction symmetry, thereby indicating that active particles exhibit the nonreciprocal topological interactions. >>

<< Furthermore, (AA) model considers position-based attractive force, wherein moving particles navigate using instantaneous visual information from neighboring particles within the topological vision, distinct from conventional models based on the velocity-velocity alignment. (They) demonstrate that the competition between the noise and the nonreciprocal topological interactions results in the emergence of four typical phases: gas phase, ordered phase, nematic bands, and aggregate traveling polar band. >>

<< Moreover, the nonreciprocal topological interactions impact both anomalous diffusion and ergodicity breaking. Specifically, the weak nonreciprocal topological interactions lead to ergodic subdiffusion, while the strong nonreciprocal topological interactions give rise to nonergodic superdiffusion. These findings provide a theoretical basis for understanding the nonequilibrium collective transport of active particles with topological vision. >>

Hongda Shi, Luchun Du, Wei Guo. Collective behavior based on topological vision. Phys. Rev. Research 7, 023234. Jun 6, 2025. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023234

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

Keywords: gst, particles, active 

particles, noise, topological vision, 

reciprocal- nonreciprocal topological interactions, gas phase, ordered phase, nematic bands, aggregate traveling polar band.

# gst: double burst transition in hypergraphs.

Fig.2 - Bifurcation diagram. A two-parameter stability diagram in K2-d_th space depicting the different synchronization transition regimes. Blue, gray, cyan, red, light green, magenta, and dark gray present the regimes for continuous, tiered, classical explosive, forward and  backward double jump, forward double jump, explosive with stable middle states, and backward double jump synchronization transitions, respectively. 

This AA study << aims to develop a generalized concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. >>

AA << found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. >>

<< To reinforce numerical observations, (They) employed the Ott-Antonsen ansatz. (AA) observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition. >>

Sangita Dutta, Prosenjit Kundu, et al. Double explosive Kuramoto transition in hypergraphs. Phys. Rev. Research 7, L022049. June 2, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.L022049

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

Keywords: gst, transitions, phase transitions.

# gst: symmetry breaking in time-dependent billiards.

AA << investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When inelastic collisions are introduced between the particle and the boundary, the velocity reaches a plateau after the crossover iteration. The system presents the expected behavior for this type of transition, including scale invariance, critical exponents related by scaling laws, and an order parameter approaching zero in the crossover iteration. >>

AA << analyze the velocity spectrum and its averages for dissipative and conservative dynamics. The transition point in velocity behavior caused by the physical limit of the boundary velocity and by the introduced dissipation coincides with the crossover interaction obtained from the Vrms (root mean sq V) curves. Additionally, (they) examine the velocity distributions, which lose their symmetry once the particle's velocity approaches the lower limit imposed by the boundary's motion and the system's control parameters. This distribution is also characterized analytically by an expression P(V,n), which attains a stationary state, with a well-defined upper bound, only in the dissipative case. >>

Anne Kétri Pasquinelli da Fonseca, Edson Denis Leonel. Symmetry breaking in time-dependent billiards. arXiv: 2505.20488v1 [nlin.CD]. May 26, 2025.

https://arxiv.org/abs/2505.20488

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

Keywords: gst, billiard, particles, transitions, dissipation, symmetry breaking, inelastic collisions.

# gst: spreading and retraction dynamics of drop impact onto elastic surfaces.

In this study, AA << numerically investigate the impact of droplets on elastic plates using a two-phase lattice Boltzmann method, with a particular focus on how vertical surface movements influence the spreading and retraction dynamics of the droplet. >>

<< The results show that, during the spreading phase, the spreading diameter is smaller on elastic surfaces compared to rigid ones due to the vertical velocity of the surface. A universal linear evolution of the drop spreading is derived for the early stage across both rigid and elastic substrates, accounting for the surface motion by rescaling time, and this relationship is in good agreement with the numerical results. >>

<< In the retraction phase, unlike the nearly constant retraction speed observed on rigid surfaces, the retraction speed 𝑉ret oscillates with the vibrations of the elastic surface, with the oscillation period remaining relatively consistent. Further analysis reveals that the variation in 𝑉ret is not influenced by the surface's velocity but rather by its acceleration, as additional inertia is introduced during surface acceleration. >>

<< Based on this understanding, a predictive model for 𝑉ret during droplet impacts on moving surfaces is proposed, which demonstrates strong agreement with the numerical findings. >>

Yufei Ma, Haibo Huang. Spreading and retraction dynamics of drop impact onto elastic surfaces. Phys. Rev. Fluids 10, 053607. May 15, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.053607

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

Keywords: gst, drops, droplets, droploids, elasticity, elastic surfaces, surface acceleration, vertical surface movements, spreading phase, retraction phase.

# gst: disorder, chimera state, traveling chimera state, and synchronization by weak temporal couplings.

<< The mechanisms of self-sustained oscillations of brain rhythms have been studied for a long time and it is revealed that the emergence of a pacemaker loop takes a key role for these rhythms. However, it is unclear how this pacemaker loop plays a role in the resting state of the brain, where the characteristic slow-wave activities show a multi-scaled feature and can switch easily between different dynamics states. >>

<< To study this problem, herein (AA) present a neural model of pacemaker looplike network, with a weak temporal electrical coupling to mark the resting state of the brain. (They) find that different dynamics patterns can be generated by this model, including the disorder, traveling chimera state, chimera state, and synchronization. >>

<< Interestingly, (AA) observe a sensitive switching effect between the region of traveling chimera state and that of chimera state, which may provide new insights to the mechanism of quickly switching between different rhythms of the brain in the resting state. >>

<< Further, (AA) introduce an index 𝑄 to describe the fluctuations of the local order parameter of network and conjecture that there is a new regularity caused by the fluctuations. (They) find that 𝑄 is optimally dependent on the matching of parameters and thus confirms the conjecture. Moreover, (they) show that the observed traveling chimera state is robust to different forms of temporal couplings. >>

Wenbin Mao, Guoshen Liang, Zonghua Liu. Traveling chimera states by weak temporal couplings. Phys. Rev. E 111, 054220. May 27, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.054220

Also: network, brain, disorder & fluctuations, waves, chimera, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, brain, disorder & fluctuations, waves, chimera, brain rhythms, brain resting state, self-sustained oscillations, pacemaker loop network, traveling chimera state, temporal coupling.

# gst: diffusion and decay of an expanding turbulent blob; the cascade can leave an indelible footprint far into the decay process

<< Turbulence, left unforced, decays and invades the surrounding quiescent fluid. Though ubiquitous, this simple phenomenon has proven hard to capture within a simple and general framework. >>

Here, AA << circumvent these issues by creating a spatially-localized blob of turbulent fluid using eight converging vortex generators focused towards the center of a tank of water, and observe its decay and spread over decades in time, using particle image velocimetry with a logarithmic sampling rate. >>

<< The blob initially expands and decays until it reaches the walls of the tank and eventually transitions to a second regime of approximately spatially uniform decay. (AA) interpret these dynamics within the framework of a nonlinear diffusion equation, which predicts that the ideal quiescent-turbulent fluid boundary is sharp and propagates non-diffusively, driven by turbulent eddies while decaying with characteristic scaling laws. >>

AA << find direct evidence for this model within the expansion phase of (their) turbulent blob and use it to account for the detailed behavior (they) observe, in contrast to earlier studies. (AA) work provides a detailed spatially-resolved narrative for the behavior of turbulence once the forcing is removed, and demonstrates unexpectedly that the turbulent cascade leaves an indelible footprint far into the decay process. >>

Takumi Matsuzawa, Minhui Zhu, et al. Nonlinear Diffusion and Decay of an Expanding Turbulent Blob. arXiv: 2505.22737v2 [physics.flu-dyn]. May 30, 2025

https://arxiv.org/abs/2505.22737

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

Keywords: gst, quiescence, quiescent fluids, blobs, turbulent blobs, turbulent eddies, turbulent cascade, expansion and decay.

# gst: apropos of double-wells, stabilizing role of multiplicative noise in nonconfining potentials.

AA << provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. (They) focus on a large class of one-dimensional stochastic differential equations in which the deterministic drift pushes trajectories toward infinity. (AA) show that increasing the multiplicative noise intensity surprisingly causes the mass of the stationary probability distribution to become increasingly concentrated around the points of minimal multiplicative noise strength. Under quite general conditions the trajectory exhibits intermittent burstlike jumps away from these minima. (AA) framework relies on first-term expansions, which become more accurate for larger noise intensities. >>

<< In this work (AA) show that the full width at half maximum in addition to the maximum is appropriate for quantifying the stationary probability distribution (instead of the mean and variance, which are often undefined). (They) define a corresponding kind of weak-sense stationarity. (AA) end by applying these results to the problem of a double-well potential with multiplicative noise, where noise stabilizes unstable fixed points. >>

Ewan T. Phillips, Benjamin Lindner, Holger Kantz. Stabilizing role of multiplicative noise in nonconfining potentials. Phys. Rev. Research 7, 023146. May 14, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023146

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

Keywords: gst, noise, multiplicative noise intensity, intermittency, intermittent burstlike jumps, stationary probability distribution, weak-sense stationarity, double-well potential.

# gst: defect-free and defective adaptations of crystalline sheets to stretching deformation.

<< The elastic response of the crystalline sheet to the stretching deformation in the form of wrinkles has been extensively investigated. In this work, (AA) extend this fundamental scientific question to the plastic regime by exploring the adaptations of crystalline sheets to the large uniaxial mechanical stretching. >>

AA << reveal the intermittent plastic shear deformations leading to the complete fracture of the sheets wrapping the cylinder. Specifically, systematic investigations of crystalline sheets of varying geometry show that the fracture processes can be classified into defect-free and defective categories depending on the emergence of topological defects. >>

AA << highlight the characteristic mechanical and geometric patterns in response to the large stretching deformation, including the shear-driven intermittent lattice tilting, the vortex structure in the displacement field, and the emergence of mobile and anchored dislocations as plastic excitations. >>

<< The effects of noise and initial lattice orientation on the plastic deformation of the stretched crystalline sheet are also discussed. These results advance our understanding of the atomic level on the irreversible plastic instabilities of two-dimensional crystals under large uniaxial stretching and may have potential practical implications in the precise engineering of structural instabilities in packings of covalently bonded particulate systems. >>

Ranzhi Sun, Zhenwei Yao. Defect-free and defective adaptations of crystalline sheets to stretching deformation. Phys. Rev. E 111, 055504. May 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.055504

Also: elastic, intermittency, noise, instability, vortex, defect, fracture, crack, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elastic, noise, intermittency, instability, vortex, defect, fracture, crack, stretch, deformation, wrinkles, tilting, plastic instabilities,  plastic excitations.

# gst: dynamic expulsion of magnetic flux by vortices.

AA << study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. (They)  concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. >>

<< Within the context of a weak background field, (AA) are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. >>

<< Furthermore, in the case of a row of vortices, (AA) show that the orientation of the background field significantly influences the evolution, especially at higher field strengths. >>

Jonathan Tessier, Francis J. Poulin, David W. Hughes. Dynamic expulsion of magnetic flux by vortices. Phys. Rev. Fluids 10, 053702. May 19, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.053702

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

Keywords: gst, vortex, transitions, flux expulsion, vortex disruption.

# gst: apropos of attractive-- repulsive potentials in free boundary movements, stochastic and deterministic dynamics of free boundaries atop turbulent convection

AA << present a low-dimensional model that explains the coupled dynamics of floating boundaries that interact with turbulent flows in thermal convection. >>

<< The model consists of Langevin-type, stochastic differential equations, which captures the deterministic and stochastic movements of boundaries shown in an earlier experiment J.-Q. Zhong et al. [Phys. Rev. E 75, 055301(R) (2007)]. From the displacement, speed, and acceleration of the boundaries, (They) construct the force potentials that underlie two distinct boundary-size-dependent behaviors. >>

<< Namely, (AA) find a repulsive potential (when the boundary is small) that leads to an oscillatory state and an attractive potential (when the boundary is large) that leads to a trapped state. >>

<< The boundary movements, which are subject to thermal convection underneath, also inform us of the mean speed and turbulent fluctuations of the flows. >>

Wen-Tao Wu, Jun Zhang, Jin-Qiang Zhong. Stochastic and deterministic dynamics of free boundaries atop turbulent convection. Phys. Rev. Fluids 10, 053504. May 9, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.053504

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

Keywords: gst, convection, floating 

boundaries, turbulence, turbulent flows, turbulent fluctuations, disorder & fluctuations, trapped states

# gst: apropos of absorbing targets, persistence exponents of self-interacting random walks

<< The persistence exponent, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. >> 

In their Letter, AA << consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time 𝑡 with the territory already visited at earlier times 𝑡′ <𝑡. (AA)  compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, (They) also determine the splitting probability of these processes. >>

<< Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and nonreversible Monte Carlo methods. >>

J. Brémont, L. Régnier, et al. Persistence Exponents of Self-Interacting Random Walks. Phys. Rev. Lett. 134, 197103. May 16, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.197103

arXiv:2410.18699v1 [cond-mat.stat-mech]. 

https://arxiv.org/abs/2410.18699

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

Keywords: gst, walk, walking, self-interacting random walk, walker self-repulsion, walker self-attraction, stochasticity, absorbing targets.

# gst: toy model of turbulent shear flow using vortons.

AA << introduce a toy model for shear flows, exploiting the spatial intermittency and the scale separation between large-scale flows and small-scale structures. The model is highly sparse, focusing exclusively on the most intense structures, which are represented by vortons—dynamically regularized quasisingularities that experience rapid distortion from the large-scale shear. The vortons, in turn, influence the large-scale flow through the subgrid stress tensor. >>

<< Despite its simplicity, the model displays an interesting transition between two distinct regimes: (i) a laminar regime, where dissipation is entirely attributed to the large-scale flow and the vortons dynamics is essentially diffusive, and (ii) a turbulent regime, in which most of the dissipation arises from the vortons. These regimes correspond to different scalings of dissipation and the Grashof number as functions of the Reynolds number, with power-law relationships that resemble those observed in classical turbulence. >>

Wandrille Ruffenach, Lucas Fery, Bérengère Dubrulle. Toy model of turbulent shear flow using vortons. Phys. Rev. Fluids 10, 054601. May 1, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.054601

arXiv:2501.05779v2 [physics.flu-dyn]. 

https://arxiv.org/abs/2501.05779

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

Keywords: gst, turbulence, intermittency, transitions, vortons

# gst: accelerated first detection in discrete-time quantum walks using sharp restarts.

<< Restart is a common strategy observed in nature that accelerates first-passage processes, and has been extensively studied using classical random walks. In the quantum regime, restart in continuous-time quantum walks (CTQWs) has been shown to expedite the quantum hitting times [Phys. Rev. Lett. 130, 050802 (2023)]. >>

 Here, AA << study how restarting monitored discrete-time quantum walks (DTQWs) affects the quantum hitting times. (They) show that the restarted DTQWs outperform classical random walks in target searches, benefiting from quantum ballistic propagation, a feature shared with their continuous-time counterparts. >>

Kunal Shukla, Riddhi Chatterjee, C. M. Chandrashekar. Accelerated first detection in discrete-time quantum walks using sharp restarts. Phys. Rev. Research 7, 023069. Apr 21, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023069

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

Keywords: gst, networks, randomness, walk, random walk, quantum walk, stochasticity, sharp restart.

# gst: biased random walks on networks with stochastic resetting.

<< This study explores biased random walk dynamics with stochastic resetting on general networks. (AA) show that the combination of biased random walks and stochastic resetting makes significant contributions by analyzing the search efficiency. (They) derive two analytical expressions for the stationary distribution and the mean first passage time, which are related to the spectral representation of the probability transition matrix of a biased random walk without resetting. These expressions can be used to determine the capacity of a random walker to reach the specific target and probe a finite network. >>

AA << apply the analytical results to two types of networks, pseudofractal scale-free webs and T-fractals, which are constructed through an iterative process. (They) also extend a strategy to explore other complex structure networks or larger networks by leveraging the spectral properties. >>

Anlin Li, Xiaohan Sun. Biased random walks on networks with stochastic resetting. Phys. Rev. E 111, 054309. May 16, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.054309

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

Keywords: gst, networks, randomness, random walk, stochasticity, stochastic resetting.

# gst: emergent scattering regimes in disordered metasurfaces near critical packing.

<< Disordered metasurfaces provide a versatile platform for harnessing near- and far-field scattered light. Most research has focused on either particulate topologies composed of individual, well-identified metaatoms or, to a lesser extent, semi-continuous aggregate topologies without well identified inclusions. >>

Here, AA << uncover an intermediate critical packing regime characterized by metasurface morphologies in which a significant fraction of metaatoms begin to connect. (They) experimentally demonstrate that, at this threshold, the properties of the scattered light abruptly change and interpret this change as a marked transition in the statistics of the photon density of states. >>

<< Unlike percolation metal films, this transition affects not only the specular but also the diffuse components of the scattered light in a profound way. (AA)  results introduce critical packing topologies as a novel design strategy for manipulating the spectral and angular characteristics of light using ultrathin optical coatings. Emergent functionalities include color shifts in diffuse light driven by multiple scattering and surface whitening, >>

Miao Chen, Adrian Agreda, et al. Emergent scattering regimes in disordered metasurfaces near critical packing. arXiv: 2505.02244v1 [physics.optics]. May 4, 2025.

https://arxiv.org/abs/2505.02244

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

Keywords: gst, disorder, fluctuations, transitions, disordered metasurfaces, ultrathin optical coatings, near- far- field scattered light, critical packing regime.

# gst: elasticity of fibers prefers the chaos of turbulence.

<< The dynamics of fibers, modeled as a sequence of inertial beads linked via elastic springs, in turbulent flows is dictated by a nontrivial interplay of inertia and elasticity. Such elastic, inertial fibers preferentially sample a three-dimensional turbulent flow in a manner that is qualitatively similar to that in two dimensions [R. Singh et al., Phys. Rev. E 101, 053105 (2020)]. >>

<< Both these intrinsic features have competing effects on fiber dynamics: Inertia drives fibers away from vortices while elasticity tends to trap them inside. However, these effects swap roles at very large values. A large inertia makes the fibers sample the flow more uniformly while a very large elasticity facilitates the sampling of straining regions. >>

<< This complex sampling behavior is further corroborated by quantifying the chaotic nature of sampled flow regions. This is achieved by evaluating the maximal Lagrangian Lyapunov Exponents associated with the flow along fiber trajectories. >>

Rahul K. Singh. Elasticity of fibers prefers the chaos of turbulence. Phys. Rev. E 111, L053101. May 5, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.L053101

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

Keywords: gst, elasticity, turbulence, chaos, transitions

# gst: hyperchaos and complex dynamical regimes in N-d neuron lattices.

AA << study the dynamics of N-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. (They) consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. >>

<< As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. >>

<< For lattices in higher spatial dimensions, (AA) discover dynamical effects arising from the ``destructive interference'' of many connected neurons and miniature ``phase transitions'' from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, (They) observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. >>

<< These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems. >>

Brandon B. Le, Dima Watkins. Hyperchaos and complex dynamical regimes in N-dimensional neuron lattices. arXiv: 2505.03051v1 [nlin.CD]. May 5, 2025.

https://arxiv.org/abs/2505.03051

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

Keywords: gst, brain, network, behavior, cooperation, cooperative behavior, chaos, hyperchaos, transitions, phase transitions, transition thresholds,  synchrony, dimensionality, topology of connectivity, intermittent bursting activity, interference, destructive interference.

# gst: overcoming overly simplistic representations, chaos and regularity in an anisotropic soft squircle billiard.

<< A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. >>

<< Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. >>

AA << study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. (AA) characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. (They) characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squarness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. >>

AA << expect (Their) work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards. >>

A. González-Andrade, H. N. Núñez-Yépez, M. A. Bastarrachea-Magnani. Chaos and Regularity in an Anisotropic Soft Squircle Billiard. arXiv: 2504.20270v1 [nlin.CD]. Apr 28, 2025.

https://arxiv.org/abs/2504.20270

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

Keywords: gst, billiard, soft billiard, soft-wall squircle billiard, particles, smooth boundary,  specular collisions, transitions, chaos