# gst: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

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

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# gst: oscillating concentrations suppress condensate coarsening.

<< ️Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. >>

<< ️To understand how oscillating signals affect condensates, (AA) analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, (They) find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. (They) thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications. >>

Mathias S. Heltberg, Lukas H. Kristensen, Mogens H. Jensen, David Zwicker. Oscillating concentrations suppress condensate coarsening. arXiv: 2606.16614v1 [physics.bio-ph]. Jun 15, 2026.

https://arxiv.org/abs/2606.16614

Also: drop, droplet, droploid, self-assembly, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, self-assembly, disorder & fluctuations, chemically active droplets, spatially concentration, nuclear condensate. 

# gst: chiral packings in cylinders are ultrasensitive to confinement deformation.

<< ️Sphere packings in circular cylinders have attracted substantial research interest, among which the discovery of chiral helical structures is the most iconic. However, recent experimental results on zebrafish do not match the known packing structures in circular cylinders. >>

<< ️To account for the inherent imperfections of biological tubes, (AA) take elliptic cylinders as the canonical deformation of circular cylinders and investigate the densest packings of hard spheres in them using simulation, theory, and experiments. Starting from the chiral structures in circular cylinders, (They) demonstrate that even a weak cross-sectional deformation can trigger entirely new phases, including ones that either eliminate global chirality or significantly complicate the chiral structures. ️This reveals the significant effect of cylindrical anisotropy. >>

<< ️The new helical phases under anisotropic confinement remain chiral and develop hierarchical periodic structures, which are difficult to obtain by simulations but are predicted by our newly developed theory for helical phases in elliptic cylinders. >> 

<< ️The theory also predicts double oscillated-chain phases without chirality, which perfectly match the simulations. (Their) work offers fresh insights into understanding packings in anisotropic cylinders, which will help researchers to design new materials and to understand many living systems. >>

Xuebin Wang, Jiahao Guo, Yao Li. Chiral Packings in Cylinders are Ultrasensitive to Confinement Deformation. arXiv: 2606.19082v1 [cond-mat.soft]. Jun 17, 2026.

https://arxiv.org/abs/2606.19082

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

Keywords: gst, chirality, transitions, packings, chiral helical structures, elliptic cylinders, cylindrical anisotropy, double oscillated-chain phases. 

# gst: rotation sets and topological entropy for random circle endomorphisms.

<< ️(AA) study the topological dynamics of random circle endomorphisms of degree one over an ergodic measure-preserving dynamical system. Under an integrability assumption, (They) prove that the random rotation set is almost surely the compact interval whose endpoints are the mean random rotation numbers of the associated lower and upper random maps. (They) also show that the natural orbitwise versions of the random rotation set agree almost surely, and on the same full-measure set, every value in this interval is realised as the asymptotic average displacement along an individual orbit. >>

<< ️In addition, every closed subinterval of the random rotation set is realised, on a full-measure set, as the set of accumulation values of the displacement averages along a single orbit. ️Finally, (AA) prove that a positive length of the random rotation set implies a positive random topological entropy, in contrast to random monotone maps, which have zero random topological entropy. (They) illustrate the theory by computing the random rotation set and random topological entropy for a piecewise linear example. >>

Zixu Li, Simon Lloyd, Sergio Romaña. Rotation Sets and Topological Entropy for Random Circle Endomorphisms. arXiv: 2606.16498v1 [math.DS]. Jun 15, 2026.

https://arxiv.org/abs/2606.16498

Keywords: gst, randomness, random rotations, entropy.

# gst: on the geometry of spreading puddles.

<< ️(AA) develop a geometric model for the spreading of shallow, viscous puddles of arbitrary shape, building on the recent 'capillary current' model for axisymmetric droplets. In short, (They) assume that a spreading puddle remains close to instantaneous mechanical equilibrium as it spreads, with hydrostatic pressure balanced by surface curvature. In turn, its contact line advances so as to maximize the rate of energy loss subject to viscous dissipation. >>

<< ️The resulting system yields a natural geometric evolution equation for both the two-dimensional footprint and the three-dimensional depth profile of a spreading puddle. In appropriate limits, it recovers the classical spreading laws for axisymmetric droplets, a local version of the Hoffman-Voinov-Tanner law for small non-axisymmetric puddles, and a nonlocal Hele-Shaw-like description for large, relatively regular puddles. >>

David Darrow. On the Geometry of Spreading Puddles. arXiv: 2606.13893v1 [physics.flu-dyn]. Jun 11, 2026.

https://arxiv.org/abs/2606.13893

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

Keywords: gst, drops, droplets, droploids, spreading puddle, axisymmetric droplets, surface curvature, viscous dissipation.

# gst: dissipation-coherence tradeoff for stochastic oscillations.

<< ️Autonomous noisy oscillations in biochemical and mesoscopic systems require nonequilibrium driving and therefore dissipation. A striking conjecture by Oberreiter, Barato, and Seifert (OBS) proposes a universal lower bound on the entropy produced per oscillation period in terms of the coherence number of the slowest oscillatory mode (L. Oberreiter et al. [Phys. Rev. E 106, 014106 (2022)]). >>

<< ️Here (AA) derive a weaker but rigorous lower bound that preserves the OBS structure while introducing a mode-uniformity factor that quantifies how evenly the oscillatory eigenmode is distributed across states in the steady-state inner product. The result makes explicit that an eigenvalue-only prefactor can fail when the dominant oscillatory mode is localized. >>

<< ️(They) also outline a proof-of-principle route for estimating this factor from low-dimensional data under single-mode dominance and sufficiently informative measurements, and derive an eigenvector-free corollary using only the smallest stationary probability. >>

<< ️Translation-invariant Markov jump processes on a ring provide a symmetry-protected class with 𝜂=1, so the refinement reduces to the OBS form; the drift-diffusion limit on a circle saturates the bound. >>

Jie Gu. Dissipation-coherence tradeoff for stochastic oscillations. Phys. Rev. E 113, 064130.  Jun 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/zxw1-zdb7

arXiv: 2606.05498v1 [cond-mat.stat-mech]. Jun 3, 2026.

https://arxiv.org/abs/2606.05498

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

Keywords: gst, noise, disorder, dissipation, entropy, stochasticity, stochastic processes, autonomous noisy oscillations, stochastic oscillations, disorder-induced localization, time series analysis, transitions.

# life: apropos of singular, bizarre, un.expected convergences, here an asymptotic, extreme, double 'quasistochastic tit-for-tat' exploit (within the same time window).

(A1)

<< “There were no moments of friction or disagreement,” Italian Prime Minister Giorgia Meloni said at a press conference Wednesday. “I found that, overall, there was a desire to work together, and that’s not something to be taken for granted.” >>. 

Myah Ward, Clea Caulcutt, Giorgio Leali. Trump clears low bar for G7 summit in France. Jun 17, 2026.

https://www.politico.com/news/2026/06/17/trump-and-allies-keep-the-peace-at-the-g7-summit-after-months-of-tumult-00966117

(A2)

<< However, Trump has since given a phone interview with Italy's La7 TV channel in which he alleged: "She begged me to take a photo with her; I felt sorry for her." >>. 

Paul Kirby, Europe digital editor, Davide Ghiglione, Rome, James Landale, Diplomatic correspondent. Italy's Meloni says Trump 'made up' story that she 'begged' him for photo at G7. BBC. Jun 19, 2026. 

https://www.bbc.com/news/articles/c20y1ygn707o

(B) 

<< Donald Trump arrived in France yesterday for this morning’s G7

summit and promptly confirmed America’s capitulation to Iran. >>

Tom Nichols. Trump Does Not Understand the War He Lost. The Atlantic Daily. Jun 16, 2026.

https://www.theatlantic.com/newsletters/2026/06/trump-g7-comments-misunderstsand-middle-east/687569/

(A&B)

<< qui i due estremi: era modicamente non cooperatore e ha ricevuto come reazione una "bastonata"; era assolutamente ostile e ha ricevuto la classica "pacca sulla spalla" ... >>

Donald, what he can do (with less than four lines ...). FonT. May 23, 2016.

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html 

FonT

Ultimately, here too one could hypothesize another case of historic, singular checkmate of 'one against all'. Anzicheforse?

Also: Mr. Donald, tit-for-tat, game, dance, in https://www.inkgmr.net/kwrds.html

Also: here's another checkmate (FonT. Dec 4, 2024)

https://flashontrack.blogspot.com/2024/12/life-apropos-of-saliva-healers-herd.html 

Keywords: Mr. Donald, tit-for-tat, game, dance