# gst: geometric dynamics of turbulence; a minimal oscillator structure from non-local closure

<< ️Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on high-dimensional statistical representations, without identifying a minimal set of dynamical variables governing the cascade response. >>

<< ️Here (AA) show that the non-local stress response implied by the Navier-Stokes equations admits a systematic reduction onto a low-dimensional anisotropic sector of the turbulent cascade. This reduction leads to a minimal dynamical system with the structure of a damped oscillator, arising from the coupling between the leading angular mode and its nonlinear transfer to higher-order sectors. >>

<< ️Within this framework, classical turbulent behaviors -- including inertial-range scaling, shear-driven transport, and wall-bounded logarithmic profiles -- emerge as different realizations of the same underlying dynamical structure. Universal quantities such as the Kolmogorov constant and the von Kármán constant appear as leading-order consequences of internal consistency conditions applied across homogeneous and shear-driven regimes. >>

<< ️These results suggest that turbulence admits a minimal dynamical backbone governed by non-local cascade response, providing a unified perspective that connects spectral transfer, anisotropy, and mean-flow interaction within a single reduced framework. >>

Alejandro Sevilla. Geometric Dynamics of Turbulence: A Minimal Oscillator Structure from Non-local Closure. arXiv: 2603.18913v3 [physics.flu-dyn]. Mar 24, 2026. 

https://arxiv.org/abs/2603.18913

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

Keywords: gst, turbulence, cascade response, non-local stress response, damped oscillators, inertial-range scaling, shear-driven transport, wall-bounded log profiles, spectral transfer, anisotropy, mean-flow interaction.

# brain: entraining chimeras, the effect of driving with regular, irregular, and real-world phases.

<< ️Chimera states in coupled oscillator networks are paradigmatic examples of partial synchronization in nonlinear systems, with direct relevance to real-world network dynamics, such as neuronal dynamics. Since real-world networks are not isolated, but embedded in larger interacting systems, chimeras have also been studied under the influence of other networks and external signals. In particular, most prior work has treated periodic forcing of chimeras in the thermodynamic limit. >>

<< ️As a consequence, it remains unclear how chimera states respond to external driving in finite-size networks, where they can spontaneously collapse into full synchronization. It is also largely unknown how realistic noisy drivers, rather than periodic signals, affect driver-response synchronization. >>

<< ️To address these open questions, (AA) drive a finite-size oscillator network that exhibits a chimera state with constant-angular-frequency phases and with the same phases superimposed with noise. (They) find that, for a specific range of angular-frequency mismatch and driving strength, (They) can entrain chimeras without causing them to collapse into full synchronization. Adding noise, in turn, reduces entrainment and facilitates collapses. >>

<< ️As a real-world application of the driven chimera state framework, (AA) also drive chimeras with phases from focal and nonfocal electroencephalography (EEG) signals recorded during seizure-free periods in patients with epilepsy. (They) observe that focal signals yield higher entrainment power, within-network coherence, and collapse power than nonfocal signals when the driver EEG's dominant frequency is close to the chimera's mean angular frequency. Away from this regime, nonfocal signals yield higher values of all three measures. The observed differences not only characterize focal and nonfocal signals, but may also provide additional insight into the seizure-free brain dynamics of epilepsy patients. >>

<< ️In conclusion, beyond quantifying how external driving signals, with or without noise, affect the dynamics of chimera states that can collapse into full synchronization, this (AA) work further bridges the study of chimera states and epilepsy research. >>

Jacopo Epifanio, Martin Brešar, Ralph G. Andrzejak. Entraining chimeras: The effect of driving with regular, irregular, and real-world phases. Phys. Rev. E 113, 034214. Mar 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/vczh-r59d

Also: brain, chimera, noise, transition, collapse, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, chimeras, noise, transitions, collapse, networks, coupled oscillator networks, epilepsy, synchronization, driver-response synchronization. 

# gst: redirecting counter-moving swarms through collision.

<< ️Multi-swarm systems, where two or more swarms of mobile agents occupy the same region of space with different parameters and goals, occur in a variety of biological, engineering, and defense applications. Composites of multiple swarms can produce hybrid spatiotemporal patterns, which compared to single swarming systems, are relatively unexplored. >>

<< ️In this work, (AA) develop a framework for studying the collision of counter-moving swarms, each with its own preferred, stable velocity before collision. (They) show that redirection of such swarms after collision occurs when a stable velocity synchronized state of the multi-swarm composite exists. Using a rigid-body approximation, (They) are able to extract how scatter-redirection transitions scale with swarm parameters in a variety of scenarios from reciprocal and non-reciprocal systems to symmetric and antagonistic parameter values. (They) results compare well to simulations of both particle modeled agents and wheeled robots. >>

Jason Hindes, Chinthan B. Prasad, Loy McGuire, et al. Redirecting counter-moving swarms through collision. arXiv: 2603.12002v1 [nlin.AO]. Mar 12, 2026.

https://arxiv.org/abs/2603.12002

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

Keywords: gst, swarms, particles, transitions, scatter-redirection transitions, multi-swarm systems, collisions, collision of counter-moving swarms.

# gst: apropos of ab.normal criticalities, a hypothetical scenario of non-normal route to chaos.

<< ️Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. (AA) show that this paradigm is incomplete in dimensions d>1.  >>

<< ️(They) construct a bounded 3D dynamical system whose Jacobian is pointwise spectrally contracting, namely all instantaneous eigenvalues remain strictly inside the stability region, yet the system develops a positive maximal Lyapunov exponent and undergoes a transition to chaos as a non-normality index increases at fixed spectral radius. The mechanism relies on the repeated regeneration of transient non-normal amplification through endogenous switching that reinjects trajectories into amplifying non-orthogonal directions. >>

<< ️Although demonstrated here for a discrete-time map, the mechanism is geometric and applies more broadly to deterministic dynamical systems. These results show that chaos can emerge without spectral criticality and identify non-normality as an independent route to deterministic chaos. >>

D. Sornette, V.R. Saiprasad, V. Troude. Non-Normal Route to Chaos. arXiv: 2603.08191v1 [nlin.CD]. Mar 9, 2026.

https://arxiv.org/abs/2603.08191

Also:  Virgile Troude, Sandro Claudio Lera, Ke Wu, Didier Sornette. Illusions of Criticality: Crises Without Tipping Points. arXiv: 2412.01833v5 [nlin.CD]. Oct 3, 2025. https://arxiv.org/abs/2412.01833

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

Keywords: gst, chaos, criticality, transitions, non-normality, transient non-normality, reinjection via endogenous switch.

# gst: geometry of contraction-induced flows.

<< ️Peristalsis is the driving mechanism behind a broad array of biological and engineered flows. In peristaltic pumping, a wavelike contraction of the tube wall produces local changes in volume which induce flow. Net flow arises due to geometric nonlinearities in the momentum equation, which must be properly captured to compute the flow accurately. >>

<< ️While most previous models focus on radius-imposed peristalsis, they often neglect longitudinal length changes—a natural consequence of radial contraction in elastic materials. In this paper, to capture a more accurate picture of peristaltic pumping, (AA) calculate the flow in an elastic vessel undergoing contractions in the transverse and longitudinal directions simultaneously, keeping the geometric nonlinearities arising in the strain. >>

<< ️(They) demonstrate that transverse and longitudinal contractions induce instantaneous flows at the same order in wall strain but in opposite directions. (They) investigate the influence of the wall's Poisson ratio on the flow profile. Incompressible walls suppress flow by minimizing local volume changes, whereas auxetic walls enhance flow. For radius-imposed peristaltic waves, wall incompressibility reduces both reflux and particle trapping. In contrast, length-imposed waves typically generate backflow, although trapping can still occur at large amplitudes for some Poisson ratios. >>

Aaron Winn, Eleni Katifori. Geometry of contraction-induced flows. Phys. Rev. Fluids 11, 033101. Mar 12, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/pw9s-vvf4

arXiv: 2510.24016v1 [physics.flu-dyn]. Oct 28, 2025.

https://arxiv.org/abs/2510.24016

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

Keywords: gst, waves, elasticity, networks, peristalsis, peristaltic pumping, peristaltic waves, wavelike contractions, transverse and longitudinal contractions, longitudinal length changes, instantaneous flows, auxetic walls, backflows.

# gst: from fluttering to drifting: inertialess sedimentation of an achiral particle.

<< ️There has been much recent interest in the chiral motion of achiral particles that sediment in a viscous fluid in a regime where inertial effects can be neglected. This occurs in a broad range of applications such as those involving biological objects like algae, ultrathin graphene flakes, or colloidal suspensions. It is known that particles with two planes of symmetry can be categorized as “settlers,” “drifters,” or “flutterers,” where the latter sediment along chiral trajectories despite their achiral shapes. >>

<< ️Previous work investigated the sedimentation of circular disks bent into a U-shape and identified them as “flutterers.” In this work (AA) analyze the change in behavior of such particles when (They) break one of their symmetries by pinching the disks isometrically along their axis, a shape change that can arise during the sedimentation of thin elastic sheets. The “fluttering” behavior is found to be robust to such shape changes, with the trajectories now evolving toward helical paths. However, the behavior changes when the degree of pinching becomes too strong, at which point the particles become “drifters” which sediment steadily without rotation. >>

<< ️(AA) establish criteria for the transition between the two types of behavior and confirm (Their) predictions in experiments. Finally, (AA) discuss the implications of (Their) observations for the dispersion of dilute suspensions made of such particles. >>

Christian Vaquero-Stainer, Tymoteusz Miara, Anne Juel, et al. From fluttering to drifting: Inertialess sedimentation of an achiral particle. Phys. Rev. Fluids 11, 034102. March 10, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/scj8-6lpf

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

Keywords: gst, behaviors, particles, achiral particles, settlers, drifters, flutterers.

# gst: prolate and oblate nematic shells under equal and hybrid alignments.

<< ️Using the Landau–de Gennes free-energy formalism with the fast inertial relaxation engine relaxation method, (AA) investigate the role of geometry and anchoring conditions in nematic liquid crystal shells. Both prolate and oblate geometries are explored for four distinct anchoring configurations: degenerate planar on both surfaces, homeotropic on both surfaces, and hybrid cases with planar-homeotropic and homeotropic-planar alignments. (Their) simulations reveal a rich variety of topological defect arrangements, including bipolar configurations with boojums; tetrahedral patterns featuring disclination lines, boojums, and hedgehogs; Saturn-ring structures; and twisted director fields in the equatorial plane. >>

<< ️Detailed energy analyses demonstrate that elastic distortions—splay, bend, and twist—are strongly influenced by parameters such as inner and outer radii, shell thickness, and aspect ratio, which in turn dictate the stabilization of specific defect structures. ️These findings provide insights into the curvature-driven mechanisms that control the formation of defects in nematic shells. >>

F. C. Cruz, E. K. Lenzi, Q. Li, et al. Prolate and oblate nematic shells under equal and hybrid alignments. Phys. Rev. E 113, 035403. Mar 4, 2026.

https://journals.aps.org/pre/abstract/10.1103/3ynk-2nsp

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

Keywords: gst, spheroids, elasticity, nematic liquid crystal shells, prolate and oblate geometries, topological defects, elastic distortions, curvature-driven mechanisms.