# gst: topological defects in spiral wave chimera states.

<< ️Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, (AA) introduce a topological analysis method based on winding numbers to characterize the dynamics of spiral wave chimeras in a two-dimensional phase oscillator network. >>

<< ️(Their) investigation reveals distinct scaling laws governing the system's evolution across the phase lag 𝛼. Perturbation analysis in the limit 𝛼→0 demonstrates that the incoherent core radius scales linearly with 𝛼. In contrast, within the stable chimera regime, the average total positive winding number 𝜇 follows a clear exponential growth law 𝜇=𝑎⁢𝑒^(𝑏⁢𝛼). This scaling disparity signals a physical crossover from a regime dominated by geometric core expansion to one driven by active topological excitation. >> 

<< ️Furthermore, (They) identify a statistical transition in the defect distribution from binomial-like to Poisson-like behavior at a critical threshold 𝛼*. These results demonstrate that topological defects possess intrinsic statistical order, establishing 𝜇 as a robust macrovariable for analyzing the structural complexity of chimera states. >>

Lintao Liu, Nariya Uchida. Topological defects in spiral wave chimera states. Phys. Rev. E 113, 054207. May 8, 2026.

https://journals.aps.org/pre/abstract/10.1103/yhbq-ztk8

arXiv: 2511.21058v2 [nlin.AO]. 5 Mar 2026.

https://arxiv.org/abs/2511.21058

Also: chimera, waves, self-assembly, transition, network, defect, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, waves, self-assembly, transition, network, defect, topology, spiral wave chimeras, two-dimensional phase oscillator network, active topological excitations, topological defects. 

# gst: beyond interpolation toward invention, the hypothesis of selective imperfection as a generative framework for analysis, creativity and discovery.

<< ️(AA) introduce materiomusic as a generative framework linking the hierarchical structures of matter with the compositional logic of music. Across proteins, spider webs and flame dynamics, vibrational and architectural principles recur as tonal hierarchies, harmonic progressions, and long-range musical form. >>

<< ️(They) show how sound functions as a scientific probe, an epistemic inversion where listening becomes a mode of seeing and musical composition becomes a blueprint for matter. >>

<< ️Selective imperfection provides the mechanism restoring balance between coherence and adaptability. >>

<< ️(They) show how swarm-based AI models compose music exhibiting human-like structural signatures such as small-world connectivity, modular integration, long-range coherence, suggesting a route beyond interpolation toward invention. (They) show that science and art are generative acts of world-building under constraint, with vibration as a shared grammar organizing structure across scales. >>

Markus J. Buehler. Selective Imperfection as a Generative Framework for Analysis, Creativity and Discovery. arXiv: 2601.00863v1 [cs.LG]. Dec 30,  2025.

https://arxiv.org/abs/2601.00863

Also: jazz, music, clinamen, chaos, defect, error, mistake, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, jazz, music, clinamen, parenklisis, selective imperfection, defect, error, mistake, noise, invention, long-range coherence, chaos.

FonT:  apropos of 'selective imperfection', at one time I was surprised by the structure of a temple gate in Kyoto where one of the elements is installed upside down.

# 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: defects around obstacles, active nematic ratchet in asymmetric arrays

AA << numerically investigate the effect of an asymmetric periodic obstacle array in a two-dimensional active nematic. (They) find that activity in conjunction with the asymmetry leads to a ratchet effect or unidirectional flow of the fluid along the asymmetry direction. The directional flow is still present even in the active turbulent phase when the gap between obstacles is sufficiently small. >>️

AA << demonstrate that the dynamics of the topological defects transition from flow mirroring to smectic-like as the gap between obstacles is made smaller, and explain this transition in terms of the pinning of negative winding number defects between obstacles. >>

️

Cody D. Schimming, C. J. O. Reichhardt, C. Reichhardt. Active nematic ratchet in asymmetric obstacle arrays. Phys. Rev. E 109, 064602. Jun 3, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064602 

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

Keywords: gst, nematic ratchet,  transition, turbulence, defect, error

# gst: controlled creation of point defects in 3D colloidal crystals

<< Crystal defects crucially influence the properties of crystalline materials and have been extensively studied. Even for the simplest type of defect—the point defect—however, basic properties such as their diffusive behavior, and their interactions, remain elusive on the atomic scale. >>️

Here AA << demonstrate in situ control over the creation of isolated point defects in a three-dimensional (3D) colloidal crystal allowing insight on a single-particle level. >>

AA << experimental model system provides a unique opportunity to shed light on the interplay between point defects, on the mechanisms of their diffusion, on their interactions, and on collective dynamics. >>️

Max P. M. Schelling, Janne-Mieke Meijer. Controlled creation of point defects in three-dimensional colloidal crystals. Phys. Rev. E 109, L062601. Jun 4, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.L062601

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

Keywords: gst, colloids, defect, error, transition

# gst: compression and fracture of ordered and disordered droplet rafts

AA << simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. >>

<< For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. >>

<< In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. >>

AA << also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. >>

️

Pablo Eduardo Illing, Jean-Christophe Ono-dit-Biot, et al. Compression and fracture of ordered and disordered droplet rafts. Phys. Rev. E 109, 014610. Jan 17, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.014610

Also: drop, defect, fracture, crack, in https://www.inkgmr.net/kwrds.html

Also:  raft   https://flashontrack.blogspot.com/search?q=raft  

zattera (quasi-stochastic poetry) https://inkpi.blogspot.com/2005/04/1864-onda-di-liberazione.html  

randa (quasi-stochastic poetry) https://inkpi.blogspot.com/search?q=randa

Keywords: gst, drop, droplet, raft, defect, fracture, crack

# gst: intentional defects to trap confined acoustic modes that are protected from perturbation

AA << has discovered how to exploit certain defects to protect confined energy in acoustics systems. Their experimental approach provides a versatile platform to create at-will defects for further theoretical validation and to improve control of waves in other systems, such as light >>

<< We set to understand whether topological defects, such as disclinations, can be created to trap highly confined acoustic modes that are protected from perturbation, (..) Our core insight was that, if we consider the point group symmetry of the disclination, a pair of disclinations modes are prevented from pairing away from zero frequency. This protection mechanism results from the interplay of the symmetry-protected topological phase of the crystalline lattice and the topological charge and symmetry of the disclination. >> Wladimir A. Benalcazar.

<< This is the first work experimentally validating that such protected states exist in the disclination core, >> Yun Jing. 

️

Ashley J. Wennersherron. Researchers find imperfections provide protection for system symmetry. Penn State College of Engineering. May 20, 2022.

https://phys.org/news/2022-05-imperfections-symmetry.html

Sarah Wells. Symmetrical Binding for Topological States. Physics 15, s56. Apr 26, 2022. 

https://physics.aps.org/articles/v15/s56

Yuanchen Deng, Wladimir A. Benalcazar, et al. Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice. Phys. Rev. Lett. 128, 174301. Apr 26, 2022. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.174301

Also

keyword 'acoustic' in FonT

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

Keywords: gst, acoustics, acoustic metamaterials, symmetry, system symmetry, imperfection, defect, topological defects, disclination

# gst: weird nature: the generation of complex (frilly, flexible, and functional) wrinkling patterns by 'defects'

<< A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. >>️

Kenneth K. Yamamoto, Toby L. Shearman, et al. Nature's forms are frilly, flexible, and functional. arXiv: 2103.10509v1. Mar 18, 2021.

https://arxiv.org/abs/2103.10509

Also

keyword 'error' | 'fuzzy' | 'noise'  in FonT 

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

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

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

keywords 'errore' | 'errori' in Notes (quasi-stochastic poetry)

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

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