# gst: singular bifurcations, an approach

<< Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. >>

AA << then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked. >>️

Alexander Farutin, Chaouqi Misbah. Singular bifurcations and regularization theory. Phys. Rev. E 109, 064218. Jun 27, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064218

Alexander Farutin, Chaouqi Misbah. Singular Bifurcations : a Regularization Theory. arXiv: 2112.12094v2 [cond-mat.soft]. Jan 6, 2022. 

https://arxiv.org/abs/2112.12094 

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

Keywords: gst, transition, singularity, bifurcation

# gst: pulse-to-crack transition, unsteady slip pulses under spatially-varying prestress scenarios.

AA << study the effects of a spatially-varying prestress τb(x) on 2D slip pulses, initially generated under a uniform τb along a rate-and-state friction fault. (They) consider periodic and constant-gradient prestress τb(x) around the reference uniform τb. For a periodic τb(x), pulses either sustain and form quasi-limit cycles in the L−c plane or decay predominantly monotonically along the L(c) line, depending on the instability index of the initial pulse and the properties of the periodic τb(x).  >>️

<< For a constant-gradient τb(x), expanding/decaying pulses closely follow the L(c) line, with systematic shifts determined by the sign and magnitude of the gradient. (They) also find that a spatially-varying τb(x) can revert the expanding/decaying nature of the initial reference pulse.  >>

<< Finally, (AA) show that a constant-gradient τb(x), of sufficient magnitude and specific sign, can lead to the nucleation of a back-propagating rupture at the healing tail of the initial pulse, generating a bilateral crack-like rupture. This pulse-to-crack transition, along with the above-described effects, demonstrate that rich rupture dynamics merge from a simple, nonuniform prestress. >>️️

Anna Pomyalov, Eran Bouchbinder. Unsteady slip pulses under spatially-varying prestress. arXiv: 2407.21539v1 [cond-mat.mtrl-sci]. Jul 31, 2024.

https://arxiv.org/abs/2407.21539

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

Keywords: gst, transition, instability, crack 

# gst: apropos of transverse instabilities, from chimeras to extensive chaos

<< Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can thus expect complex dynamics to arise in networks of such populations. >>️

Here AA << analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators, and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. >>️

Pol Floriach, Jordi Garcia-Ojalvo, Pau Clusella. From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations. arXiv: 2407.20408v2 [nlin.CD]. Oct 11, 2024.

https://arxiv.org/abs/2407.20408

Also: chimera, instability, chaos, network, in 

https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, instability, chaos, network

# gst: apropos of bubbles, the case of bubbles collapsing near a wall.

AA << study examines the pressure exerted by a cavitation bubble collapsing near a rigid wall. A laser-generated bubble in a water basin undergoes growth, collapse, second growth, and final collapse. Shock waves and liquid jets from non-spherical collapses are influenced by the stand-off ratio γ, defined as the bubble centroid distance from the wall divided by the bubble radius. (AA) detail shock mechanisms, such as tip or torus collapse, for various γ values. High-speed and Schlieren imaging visualize the microjet and shock waves. The microjet's evolution is tracked for large γ, while shock waves are captured in composite images showing multiple shock positions. Quantitative analyses of the microjet interface, shock wave velocities, and impact times are reported. Wall-mounted sensors and a needle hydrophone measure pressure and compare with high-speed observations to assess the dominant contributions to pressure changes with γ, revealing implications for cavitation erosion mechanisms. >>️

Roshan Kumar Subramanian, Zhidian Yang, et al. Bubble collapse near a wall. Part 1: An experimental study on the impact of shock waves and microjet on the wall pressure. arXiv: 2408.03479v2 [physics.flu-dyn]. Aug 8, 2024. 

https://arxiv.org/abs/2408.03479

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

Keywords: gst, bubble, bubble collapse 

# life: don't worry folks! Mr Donald will not run again in 2028. Anzicheforse?

<< In September, Donald Trump said he would run for president again in 2028 if he didn't win this week's general election. >>️

<< But on Tuesday, Donald Trump won the vote to become the 47th president of the United States. So, can he still run for office in 2028? >>️

<< And just a few months before that, at the NRA's annual meeting in May, Trump mentioned running for a third term. >>️

<< Here's what to know about term limits and if Trump can run for president a third time, now that he's won twice. >>

<< The 22nd Amendment to the Constitution ... >>️️

Lianna Norman, Joyce Orlando. Can Trump run for president again in 2028? Here’s what to know about term limits. USA TODAY NETWORK, Florida. Nov 7, 2024. 

https://eu.floridatoday.com/story/news/2024/11/07/trump-run-again-term-limits-22nd-amendment-constitution/76087581007/

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

Keywords: life, Donald, potus, potus race

# gst: phase transitions in anisotropic turbulence.

<<  

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres, oceans and stars, its manifestations can vary considerably between different physical systems. For instance, three-dimensional (3D) turbulent flows display a forward energy cascade from large to small scales, while in two-dimensional (2D) turbulence, energy cascades from small to large scales. In a given physical system, a transition between such disparate regimes of turbulence can occur when a control parameter reaches a critical value. The behavior of flows close to such transition points, which separate qualitatively distinct phases of turbulence, has been found to be unexpectedly rich. Here, (AA) survey recent findings on such transitions in highly anisotropic turbulent fluid flows, including turbulence in thin layers and under the influence of rapid rotation. (They) also review recent work on transitions induced by turbulent fluctuations, such as random reversals and transitions between large-scale vortices and jets, among others. The relevance of these results and their ramifications for future investigations are discussed.

>>️

Adrian van Kan. Phase Transitions in Anisotropic Turbulence. arXiv: 2408.02844v1 [physics.flu-dyn]. Aug 5, 2024. 

https://arxiv.org/abs/2408.02844

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

Keywords: gst, turbulence, vortex

# brain: mosaic evolution of a learning and memory circuit in Heliconiini butterflies.

<< A species of tropical butterfly with unusually expanded brain structures display a fascinating mosaic pattern of neural expansion linked to a cognitive innovation. >>

<< The study (..) investigates the neural foundations of behavioural innovation in Heliconius butterflies, the only genus known to feed on both nectar and pollen. As part of this behaviour, they demonstrate a remarkable ability to learn and remember spatial information about their food sources—skills previously connected to the expansion of a brain structure called the mushroom bodies, responsible for learning and memory. >>️

Butterfly brains reveal the tweaks required for cognitive innovation. University of Bristol. Oct 18, 2024. 

https://www.bristol.ac.uk/news/2024/october/butterfly-brains.html

Max S. Farnworth, Theodora Loupasaki, et al. Mosaic evolution of a learning and memory circuit in Heliconiini butterflies. Curr. Biol. doi: 10.1016/ j.cub.2024.09.069. Oct 18, 2024. 

https://www.cell.com/current-biology/fulltext/S0960-9822(24)01337-X

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

Keywords: gst, brain, evolution