# gst: apropos of transitions, the vortex dynamics from a twisted baker map

<< A natural approach to understanding complicated systems is to analyze a col­lection of simple examples that retain some essential features of the complexity of the original systems. The baker map (..) is one of the simplest models of chaotic dynamical systems. It divides the unit square into p ≥ 2 equal vertical strips, and maps each strip to a horizontal one by squeezing it vertically by the factor p and stretching it horizontally by the same factor. The horizontal strips are laid out covering the square. Due to the squeezing/stretching, small initial errors get amplified under iteration, and results in an unpredictable long-term behavior. The name “baker” is used since the action of the map is reminiscent of the kneading dough (..). In this paper (AA) introduce a piecewise linear model of an interaction of stretching and twisting that produces vortex dynamics. >>

They << show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space >>

Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke. The twisted baker map. arXiv: 2202.04304v2 [math.DS]. Feb 9, 2022. 

https://arxiv.org/abs/2202.04304

Also

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

keyword 'vortex' in FonT

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

keyword 'vortice' in Notes

 (quasi-stochastic poetry)

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

keywords: gst, transition, vortex, baker map

# gst: apropos of 'strange' transitions to self-assemble into an egg; the coordinated elastic behavior to swirl in a vortex (D. melanogaster)

 << At the end of its first week of development, a striking change occurs in a fruit-fly egg cell. The cell’s internal fluid motion transitions from a disordered mix of small-scale flows to a single vortex that encompasses the entire cell. >> 

 << Given the fluid’s incompressibility, those forces can give rise to what the researchers call a  "swirling" instability, and the flow switches to a cell-spanning rotation. The threshold of molecular motor activity for the transition depends on the buckling of individual microtubules, which are treated as elastic rods. >> 

A Vortex in an Egg Cell. Physics 14, s1. Jan 13, 2021.  

https://physics.aps.org/articles/v14/s1

David B. Stein, Gabriele De Canio, et al. Swirling Instability of the Microtubule Cytoskeleton. Phys. Rev. Lett. 126, 028103.  doi: 10.1103/ PhysRevLett.126.028103. Jan 13, 2021.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.028103  

# phys: stable vortex loops intersected by point singularities (in magnets)

<< Vortex rings are remarkably stable structures that occur in a large variety of systems (..) Although vortex rings have also been predicted to exist in ferromagnets, they have not yet been observed. >>

AA << imaged three-dimensional structures forming closed vortex loops in a bulk micromagnet. The cross-section of these loops consists of a vortex–antivortex pair and, on the basis of magnetic vorticity (they) identify these configurations as magnetic vortex rings. >>

<< In addition, (they) observe stable vortex loops intersected by point singularities at which the magnetization within the vortex and antivortex cores reverses. >>

Claire Donnelly, Konstantin L. Metlov, et al. Experimental observation of vortex rings in a bulk magnet. Nature Physics. doi: 10.1038/ s41567-020-01057-3. Nov 30,  2020.

https://www.nature.com/articles/s41567-020-01057-3

Magnetic vortices come full circle. 

Paul Scherrer Institute. Nov 30, 2020.

https://phys.org/news/2020-11-magnetic-vortices-full-circle.html

# gst: as a Lorenz's butterfly, even small disturbances can trigger catastrophic storms

<< meteorologists still have questions about how hurricanes develop. Now, Florida State University researchers have found that even the smallest changes in atmospheric conditions could trigger a hurricane, >>

Researchers find even small disturbances can trigger catastrophic storms. Florida State University. May 13, 2020.

https://phys.org/news/2020-05-small-disturbances-trigger-catastrophic-storms.html   

Jacob D. Carstens,  Allison A. Wing. Tropical Cyclogenesis From Self‐Aggregated Convection in Numerical Simulations of Rotating Radiative‐Convective Equilibrium. Journal of Advances in Modeling Earth Systems. Vol 12, Issue 5. doi: 10.1029/ 2019MS002020. Apr 24, 2020.

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019MS002020   

Also

Edward Lorenz. Deterministic nonperiodic flow. Journal of Atmospheric Sciences. Vol.20 130—141. 1963. in:  Lynn M. Resler. Edward N Lorenz’s 1963 paper, “Deterministic nonperiodic flow”, in Journal of the Atmospheric Sciences, Vol 20, pages 130–141: Its history and relevance to physical geography. Progress in Physical Geography: Earth and Environment. Vol 40 issue 1,  175-180. doi: 10.1177/ 0309133315623099. Jan 21, 2016. 

https://journals.sagepub.com/doi/full/10.1177/0309133315623099

# gst: apropos of turbulences close to a wall, the repetitive structure of a vortex

<< At the boundary where a fluid flows over a fixed structure, a turbulent boundary layer is created where the fluid interacts with the wall, creating eddies in the current. These eddies may seem to be random on first glance, but they actually create distinct patterns, with countless tiny eddies close to the wall; fewer but larger eddies located a little farther out; and even fewer, but still larger, eddies beyond those. >>

<< "We knew that, underlying these very complicated structures, there had to be a very simple pattern. We just didn't know what that pattern was until now," says McKeon, who next plans to dig deeper into the model to quantify just how many eddies should be included to create an accurate representation of the whole. >>

Engineers exploit the repeating structure of turbulence to create a more complete model of the phenomenon. California Institute of Technology. Nov 6, 2019.

https://m.phys.org/news/2019-11-exploit-turbulence-phenomenon.html

Beverley J. McKeon. Self-similar hierarchies and attached eddies. Phys. Rev. Fluids 4, 082601(R). Aug 26, 2019.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.4.082601