# gst: floating droplets excited with Faraday waves

<< The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. (AA) study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. (AA) develop a theoretical model for the evolution of the boundary of the droplet, thus allowing to simulate its full transient motion toward steady state. >>

<< By changing the forcing frequency and amplitude of (the) system, (They) observe a variety of stable droplet shapes. (..) Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, (They) touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity. >>️

L. Mazereeuw. Theoretical and experimental investigation of the shapes formed by floating droplets excited with Faraday waves. Phys. Rev. Fluids 9, 124404. Dec 19, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.124404

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

Keywords: drops, droplets, droploids, waves, instability, Faraday instability, transitions   

# gst: soliton dynamics over a disordered topography

AA << report on the dynamics of a soliton propagating on the surface of a fluid in a 4-m-long canal with a random or periodic bottom topography. Using a full space-and-time resolved wave field measurement, (They) evidence, for the first time experimentally, how the soliton is affected by the disorder, in the context of Anderson localization, and how localization depends on nonlinearity. >>

<< For weak soliton amplitudes, the localization length is found in quantitative agreement with a linear shallow-water theory. For higher amplitudes, this spatial attenuation of the soliton amplitude is found to be enhanced. >>

<< Behind the leading soliton slowed down by the topography, different experimentally unreported dynamics occur: fission into backward and forward nondispersive pulses for the periodic case, and scattering into dispersive waves for the random case. >>

Guillaume Ricard, Eric Falcon. Soliton Dynamics over a Disordered Topography. Phys. Rev. Lett. 133, 264002. Dec 27, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.264002

Also: soliton, waves, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, soliton, waves, disorder

# gst: self-organized critical dynamic on the Sierpinski carpet.

<< Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions.  >>️

In this paper, AA << explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power law with a noninteger exponent, i.e., a fractal. To achieve this, (They) proposed an Ising–bond-correlated percolation model as the foundation for investigating critical dynamics.  >>️

<< Within this framework, (AA) outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice.  >>️

Viviana Gomez, Gabriel Tellez. Self-organized critical dynamic on the Sierpinski carpet. Phys. Rev. E 110, 064141. Dec 20, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.064141 

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

Keywords: gst, self-assembly, criticality, self-organized critical dynamics, transitions.