# gst: complexity of a flat-foldings random origami

AA << give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. >>️

<< In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. >>️

Chihiro Nakajima. An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami. arXiv: 2409.03240v1 [cond-mat.stat-mech]. Sep 5, 2024.

https://arxiv.org/abs/2409.03240

Also: origami, kirigami, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, origami, kirigami 

# life: anyone could now run small AIs privately on their laptops

<< Artificial-intelligence models are typically used online, but a host of openly available tools is changing that. Here’s how to get started with local AIs. >>️

Matthew Hutson. Forget ChatGPT: why researchers now run small AIs on their laptops. Nature 633, 728-729 (2024). Sep 16, 2024. Correction: Sep 24,  2024. 

https://www.nature.com/articles/d41586-024-02998-y

Also: ai (artificial intell), Donald, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, ai, artificial intelligence, life, Donald

FonT: In a completely bizarre hypothesis, with the right personal AI consultant, even a medieval history professor could be absolutely operational in other fields, for example in the agri-food sector (here we underline: absolutely).

In case of serious mistakes, the AI ​​entity can be held entirely responsible, or it can be blamed on an unfortunate malfunction due to hacking, anzicheforse. 

Also: << Asked if Strohschneider (Peter Strohschneider) wrote the report himself, the spokesperson said he “was able to propose language” for it and that a “limited number of staff” helped Strohschneider write it. >> Balazs Ujvari. 

Eddy Wax. Von der Leyen budgeted €149K to pay medieval history professor for farming report. Politico.eu. Sep 26, 2024 4:20 am CET. 

https://www.politico.eu/article/ursula-von-der-leyen-farming-agriculture-italy/

# gst: apropos of intermittent switchings, presence of chaotic saddles in fluid turbulence.

<< Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. >>️

Here AA << demonstrate the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, (they) confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model. >>️

Hibiki Kato, Miki U Kobayashi, et al. A laminar chaotic saddle within a turbulent attractor. arXiv: 2409.08870v1 [nlin.CD]. Sep 13, 2024. 

https://arxiv.org/abs/2409.08870

Also: transition, turbulence, intermittency, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, turbulence, intermittency, chaos

# gst: simultaneous presence of attraction and repulsion in quantum self-sustained oscillators

AA << study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. >>

They << discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. >>

<< Remarkably, (they) find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. >>

Bulti Paul, Biswabibek Bandyopadhyay, Tanmoy Banerjee. Attractive-repulsive interaction in coupled quantum oscillators. Phys. Rev. E 110, 034210. Sept 19, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.034210

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

Keywords: gst, transition, symmetry-breaking transition, noise, attractive-repulsive interaction, coupled qu-oscillator

# gst: a body of revolution with a cat’s toy mechanism.

AA << introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. >>

️

They << prove that (this system can be) integrable if the generalized momentum M is vertical (i.e. parallel to γ) and exhibit numerical evidence that it is chaotic otherwise. >>️

M. Costa Villegas, L.C. García-Naranjo. Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane. arXiv: 2409.08072v1 [math-ph]. Sep 12, 2024. 

https://arxiv.org/abs/2409.08072

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

Keywords: gst, transition, chaos

# gst: vortex structures under dimples and scars in turbulent free-surface flows

<< Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. >>️

AA << explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. >>️

<< The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale λT, this probability is independent of Reynolds and Weber number. >>️

<< Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately λT/4. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. >>️

AA << findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes. >>

Jørgen R. Aarnes, Omer Babiker, et al. Vortex structures under dimples and scars in turbulent free-surface flows. arXiv: 2409.05409v1 [physics.flu-dyn]. 

9 Sep 2024.

https://arxiv.org/abs/2409.05409

Also: vortex, turbulence, waves, bubble, drop, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, turbulence, waves, bubble, drop, transition

# gst: overlapping substitutions and tilings.

AA << generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. For such a substitution, the substitution matrix may have non-integer entries. (They) also show that the expansion constant is an algebraic integer under mild conditions. In general, overlapping substitutions may yield a patch with contradictory overlaps of tiles, even if it is locally consistent. >>

AA << give a sufficient condition for an overlapping substitution to be consistent, that is, no such contradiction will emerge. (They) also give many one-dimensional examples of overlapping substitution. (AA) finish by mentioning a construction of overlapping substitutions from Delone multi-sets with inflation symmetry. >>️

Shigeki Akiyama, Yasushi Nagai, Shu-Qin Zhang. Overlapping substitutions and tilings. arXiv: 2407.18666v2 [math.CO]. Aug 30, 2024. 

https://arxiv.org/abs/2407.18666

Also

keyword 'tile', in FonT

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

keyword 'overlap', 'overlapping', in FonT

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

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

Keywords: gst, tiles, overlap, overlapping