# life: apropos of 'dancing at a fixed point'

the last interview to Dr Albert Bourla (Pfizer) about the annual (or maybe semi-annual (?)) shot reiteration of the vaccine against #sars-cov-2   remember to me the 'homoclinic dynamics' that I cited at the 13th Meeting of the Internat Epidemiol Associat - IEA (Sydney, 1993) ... after a large trajectories started at zero point (i.e.  the fixed point), the final point of the dynamic returns at the same zero point ...

<< People will be likely to need to have annual Covid vaccinations for many years to come, the head of Pfizer [Dr Albert Bourla ] has told the BBC >>️

Fergus Walsh. Pfizer boss: Annual Covid jabs for years to come. Dec 2, 2021. 

https://www.bbc.com/news/health-59488848

Who knows if there is a convincing reason that explains why to treat a virus with a high frequency of mutations one should prefer a vaccine approach instead of an antiviral drug ...

to find: 'antiviral drugs covid-19'  

https://pubmed.ncbi.nlm.nih.gov/?term=antiviral+drugs+covid-19&filter=datesearch.y_1

Apropos of 'homoclinic orbits' ...

<< the reinjection of the departing trajectories in the vicinity of an unstable fixed point of the saddle-focus type [..] is frequently associated with the emergence of orbits of a rather exceptional type known as 'homoclinic orbits'. These are trajectories that leave the fixed point but come back to it; in other words, they tend to the same limit when time t goes to +∞ as well as to -∞ . [..]. Homoclinic orbits are very sensitive to variation of parameter [parms] values and are generally destroyed if the [parms] do not satisfy a strict equality (in the terminology of [..] they are structurally unstable). However, for nearby values of the [parms] their disappearance leaves a very rich structure of orbit in phase space, some of which behave chaotically. >>️

Nicolis G., Prigogine I. Exploring complexity. Freeman, NY (1989): 130-131.

https://www.amazon.com/Exploring-Complexity-Introduction-Gregoire-Nicolis/dp/0716718596

Apropos of: [+∞ , -∞] plus infinity, minus infinity; 

<< In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its own tail that has also come to symbolize the infinite, [..] >> 

https://en.m.wikipedia.org/wiki/Infinity_symbol

Also 

Onda omoclina. Notes. Tuesday, Jan  11, 2005 (quasi-stochastic poetry)

<< ed assistere al mutar dell' onda omoclina / (..) >>

️

https://inkpi.blogspot.com/2005/01/1639b-onda-omoclina.html

Also

Inchingolo GM.  Cultural transitions and epidemiology.  Proceedings of the 13th Scientific Meeting of the International Epidemiological Association - IEA, Sydney, Australia, Sept 26-29, 1993: 129.   Med Hypotheses 1994; 43(4): 201-206.

https://pubmed.ncbi.nlm.nih.gov/7838001/

Also

Onda di carambola. Notes. Nov  29, 2004. (quasi-stochastic poetry)

https://inkpi.blogspot.com/2004/11/1619-onda-di-carambola.html

keywords: life, dance, fixed point, homoclinic orbits, instability, chaos,  virus, coronavirus, sars-cov-2,  covid19, 2019ncov, drugs, antiviral drug, vaccine, jabs, Covid jabs.

# gst: small-scale random perturbations, Arnold's cat spontaneously stochastic

<< Multi-scale systems (..) may possess a fascinating property of spontaneous stochasticity: a small-scale initial uncertainty develops into a randomly chosen largescale state in a finite time, and this behavior is not sensitive to the nature and magnitude of uncertainty (..). >>

A << intriguing form is the Eulerian spontaneous stochasticity (ESS) of the velocity field itself: an infinitesimal small-scale noise triggers stochastic evolution of velocity field at finite scales and times. >>

AA << prove that a formally deterministic system with scaling symmetry yields a stochastic process with Markovian properties if it is regularized with a vanishing small-scale random perturbation. Besides its significance for understanding turbulence, (their) model extends the phenomenon of ESS beyond the scope of fluid dynamics: (AA) discuss a prototype of a feasible experiment for observing ESS in optics or electronics, as well as potential applications in other physical systems.>>

Alexei A. Mailybaev, Artem Raibekas. Spontaneously stochastic Arnold's cat. arXiv:2111.03666v1 [nlin.CD]. Nov 5,  2021.

https://arxiv.org/abs/2111.03666

keywords: gst, Arnold's cat, randomness, stochasticity, spontaneous stochasticity, small-scale random perturbations, noise, turbulence, chaos 

# gst: apropos of hybrid nanostructures, the Kondo cloud effects on 'impurities' (inside superconductors).

<< when a metal contains magnetic impurities, conduction electrons can form a screening cloud, which essentially screens the impurity's spin. This physical phenomenon is known as the Kondo effect; thus, the resulting cloud is referred to as a Kondo cloud. >>

<< While the behavior of the Kondo cloud in normal systems is well-understood, its properties in the presence of superconducting materials have not yet been explored in depth. So far, most physicists have believed that the screening of impurity spins in hybrid nanostructures takes place predominantly in the screened, rather than in the unscreened, quantum phase. >>

<< The system we considered exhibits a quantum phase transition when the ground state changes between the Kondo state and the so-called Shiba state, (..) Up to now, it was believed that the screening occurs in the Kondo phase. Quite strikingly, we have however, demonstrated that the Kondo cloud exists also in the unscreened phase. >>  Ireneusz Weymann.

Ingrid Fadelli. Study predicts the behavior of a Kondo cloud in a superconductor. Phys.org. Nov  23, 2021. 

https://phys.org/news/2021-11-behavior-kondo-cloud-superconductor.html

Catalin Pascu Moca, Ireneusz Weymann, et al. Kondo Cloud in a Superconductor.  Phys. Rev. Lett. 127, 186804. Oct 27, 2021.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.186804

keywords: gst, nano, hybrid nanostructure, superconductor, transition, impurity, Kondo cloud, Kondo effect

# gst: apropos of transitions, when collisions can induce coherent dynamics.

<< In this paper (AA)  demonstrate a route to develop coherence in a system of non-driven oscillators. Here, the coherence is brought about via physical collisions through which the oscillators exchange energy. While coherence in the classical situations occurs due to sustained coupling terms in the dynamical equations, collision induced coherence is enabled solely through strong interactions that are of intermittent nature! >>

<< Very few studies (..) have attempted to study the contact dynamics during a collision. (AA) have generalized the framework of these experiments to demonstrate the collision-induced development of coherent dynamics in the simple one-dimensional arrangement of balls known as the Newton’s cradle. >>

Ayanesh Maiti, Shankar Ghosh. Collision-induced coherent dynamics. arXiv:2111.08902v1 [nlin.CD]. Nov 17, 2021. 

https://arxiv.org/abs/2111.08902

keywords: gst, transitions, oscillation, collision 

# gst: predict the wetting of the wedge; why do the teapots always drip?

<<  The "teapot effect" has been threatening spotless white tablecloths for ages: if a liquid is poured out of a teapot too slowly, then the flow of liquid sometimes does not detach itself from the teapot, finding its way into the cup, but dribbles down at the outside of the teapot. >>

<< This phenomenon has been studied scientifically for decades—now a research team at TU Wien has succeeded in describing the "teapot effect" completely and in detail with an elaborate theoretical analysis and numerous experiments: An interplay of different forces keeps a tiny amount of liquid directly at the edge, and this is sufficient to redirect the flow of liquid under certain conditions. >>

<< Although this is a very common and seemingly simple effect, it is remarkably difficult to explain it exactly within the framework of fluid mechanics,  (..) We have now succeeded for the first time in providing a complete theoretical explanation of why this drop forms and why the underside of the edge always remains wetted, >>  Bernhard Scheichl.

<< The sharp edge on the underside of the teapot beak plays the most important role: a drop forms, the area directly below the edge always remains wet. The size of this drop depends on the speed at which the liquid flows out of the teapot. If the speed is lower than a critical threshold, this drop can direct the entire flow around the edge and dribbles down on the outside wall of the teapot. >>

<< The mathematics behind it is complicated—it is an interplay of inertia, viscous and capillary forces. The inertial force ensures that the fluid tends to maintain its original direction, while the capillary forces slow the fluid down right at the beak. The interaction of these forces is the basis of the teapot effect. However, the capillary forces ensure that the effect only starts at a very specific contact angle between the wall and the liquid surface. The smaller this angle is or the more hydrophilic (i.e. wettable) the material of the teapot is, the more the detachment of the liquid from the teapot is slowed down. >>

<< Interestingly, the strength of gravity in relation to the other forces that occur does not play a decisive role. Gravity merely determines the direction in which the jet is directed, but its strength is not decisive for the teapot effect. The teapot effect would therefore also be observed when drinking tea on a moon base, but not on a space station with no gravity at all. >>️

Why teapots always drip. Vienna University of Technology. Nov 08, 2021

https://phys.org/news/2021-11-teapots.html

Scheichl, B., Bowles, R., & Pasias, G. (2021). Developed liquid film passing a smoothed and wedge-shaped trailing edge: Small-scale analysis and the ‘teapot effect’ at large Reynolds numbers. Journal of Fluid Mechanics, 926, A25. doi: 10.1017/jfm.2021.612. Sep 8, 2021. 

http://dx.doi.org/10.1017/jfm.2021.612

keywords: gst, teapot effect, interfacial flows, thin films, boundary layers, Reynolds number, viscosity, viscous–inviscid interaction 

# gst: apropos of oscillations, viscous streaming around an immersed microfeature (e.g. a bubble)

<< Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. >>️

(AA) << demonstrate that a multi-curvature approach in viscous streaming dramatically extends the range of accessible flow topologies. (They) show that numerically predicted, but never experimentally observed, streaming flows can be physically reproduced, computationally engineered, and in turn used to enhance particle manipulation, filtering and separation in compact, robust, tunable and inexpensive devices. >>️

Yashraj Bhosale, Giridar Vishwanathan, et al. Multi-curvature viscous streaming: flow topology and particle manipulation. arXiv: 2111.07184v1 [physics.flu-dyn]. Nov 13, 2021.

https://arxiv.org/abs/2111.07184

keywords: gst, viscosity, viscous streaming, bubble, oscillations, liquid oscillations, flanking vortex, particle manipulation 

# gst: apropos of Cake-cutting, the Art of dividing a cake by countably many cuts

<< Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and edifying. However, different model assumptions are made in its many papers, in particular regarding the set of allowed pieces of cake that are to be distributed among the agents and regarding the agents' valuation functions by which they measure these pieces. >>️

A simple example proposed by AA  <<  shows that a formal mathematical approach to cake-cutting needs to address questions like:

(o) Are (open, closed, half-open) intervals the only possible pieces of cake? 

(o) Do we allow for finitely many or infinitely many cuts (a “cut” being the split of any subset of [0,1] at a single point)? 

(o) Which properties should a valuation function have, and how does it interact with the family of admissible pieces of cake?  >>

<< Among the questions (AA) have tried to answer are: 

(i) Which subsets of [0,1] should be considered as pieces of cake? Only finite unions of intervals or more general sets? 

(ii) If valuation functions are considered as set-functions as studied in measure theory, should they be σ-additive or only finitely additive? 

(iii) more ...

>>️

️

AA << have surveyed the existing rich literature on cake-cutting algorithms and have identified the most commonly used choices of sets consisting of what is allowed as pieces of cake. After showing that these five most commonly used sets are distinct from each other, (they) have discussed them in comparison. >>️

Peter Kern, Daniel Neugebauer, et al. Cutting a Cake Is Not Always a "Piece of Cake": A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory. arXiv: 2111.05402v1 [cs.GT]. Nov 9, 2021. 

https://arxiv.org/abs/2111.05402

keywords: gst, cake, cake-cutting, math.