# gst: labyrinth chaos: revisiting the elegant, chaotic and hyperchaotic walks

<< Labyrinth chaos was discovered by Otto Rossler and Rene' Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, (AA) celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. >>

 << As all Rossler’s pioneering contributions, labyrinth chaos still holds promise for very interesting further developments. Its simplicity and elegance, both in terms of symmetries, topology and feedback-circuit structure, makes it a good candidate to compare it with other nonlinear, cyclically coupled systems, such as the Arabesques, the Lotka-Voltera system and its variants, and the Arnold-Beltrami-Childress  model. >> 

Vasileios Basios, Chris G. Antonopoulos, Anouchah Latifi. Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks. arXiv: 2011.11009v1. Nov 22, 2020.

https://arxiv.org/abs/2011.11009

# gst: complex flow patterns generated by swarms of bubbles

<< When swarms of bubbles are driven upwards through a fluid by their buoyancy, they can generate complex flow patterns in their wake. Named 'pseudo-turbulence,' these patterns are characterized by a universal mathematical relationship between the energy of flows of different sizes, and the frequency of their occurrence. This relationship has now been widely observed through 3-D simulations, but it is less clear whether it would still hold for 2-D swarms of bubbles. >>

AA << show that in 2-D simulated fluids, this pattern changes within larger-scale flows in less viscous fluids. (..) In the past, many studies of pseudo-turbulence have found the statistical properties of 3-D bubble swarms remain universal over a wide range of bubble surface tensions, fluid viscosities, and density ratios between bubbles and fluids. In 2-D fluids, however, an effect named an 'inverse energy cascade' enables energy to be transferred from small- to large-scale flows. >>

Characterising complex flows in 2-D bubble swarms. Springer. Dec 4, 2020

https://phys.org/news/2020-12-characterising-complex-d-swarms.html

Rashmi Ramadugu, Vikash Pandey, Prasad Perlekar. Pseudo-turbulence in two-dimensional buoyancy-driven bubbly flows: A DNS study. The European Physical Journal E. V 43, no. 73. doi: 10.1140/ epje/i2020-11997-0. Nov 25, 2020.

https://link.springer.com/article/10.1140/epje/i2020-11997-0

Also

keyword 'bubble' in FonT

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