Tootfinder

Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus
Peng Gao, Hung D. Nguyen
https://arxiv.org/abs/2508.01794 https://arxiv…

Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus
In this paper, we study the large-time behaviors of the Kuramoto-Sivashinsky equation (KSE) on the 1D torus while being subjected to random perturbation via additive Gaussian noise. It is well-known that under suitable assumptions on the stochastic forcing, the KSE admits a unique invariant probability measure. In this work, we make further progress on the topic of ergodicity by addressing the issue of convergence rate toward equilibrium. In comparison with the previous results, we can prove th…

I see no Constitutional reason why SCOTUS is precluded from revisiting a prior decision and amending it.
We issue updates for software, why not for decisions?
Yes, it could lead to uncertainties if used more than rarely.
But imagine if the court could re-open the Dred Scott or Korematsu decisions and change the original?
Git hubs could accommodate this.

ICYMI, I still have my FREE Pride, Progress Pride, Trans and Bi Backgrounds for iPhone, iPad, 1080p, 4K and Ultrawide on my Ko-fi store!
#Pride #Backgrounds

The size of the sync basin resolved
Pablo Groisman, Cecilia De Vita, Juli\'an Fern\'andez Bonder, Yuanzhao Zhang
https://arxiv.org/abs/2506.03419 h…

The size of the sync basin resolved
Sparsely coupled Kuramoto oscillators offer a fertile playground for exploring high-dimensional basins of attraction due to their simple yet multistable dynamics. For $n$ identical Kuramoto oscillators on cycle graphs, it is well known that the only attractors are twisted states, whose phases wind around the circle with a constant gap between neighboring oscillators ($θ_j = 2πq j/n$). It was conjectured in 2006 that basin sizes of these twisted states scale as $e^{-kq^2}$ to the winding numbe…

On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains
V\'ictor Hern\'andez-Santamar\'ia, Subrata Majumdar
https://arxiv.org/abs/2508.00812

On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains
In this article, we investigate null controllability of the Kuramoto-Sivashinsky (KS) equation on a cylindrical domain $Ω=Ω_x\times Ω_y$ in $\mathbb R^N$, where $Ω_x=(0,a),$ $a>0$ and $Ω_y$ is a smooth domain in $\mathbb R^{N-1}$. We first study the controllability of this system by a control acting on $\{0\}\times ω$, $ω\subset Ω_y$, through the boundary term associated with the Laplacian component. The null controllability of the linearized system is proved using a combination of two …

🇺🇦 #NowPlaying on BBCRadio3's #MusicMap
Kerry Andrew & You Are Wolf:
🎵 Reynardine
#KerryAndrew #YouAreWolf

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Kermit the Frog:
🎵 The Rainbow Connection
#KermittheFrog
https://annereburn.bandcamp.com/track/rainbow-connection-kermit-the-frog-cover

Researchers uncover cause of uranium groundwater contamination #environment

Researchers uncover cause of uranium groundwater contamination
A new study published in the journal Environmental Science & Technology and led by researchers at Columbia University Mailman School of Public Health identifies the hidden geological mechanisms behind widespread uranium contamination in Eastern Karnataka, India, where 78% of tested groundwater exceeds safe drinking limits for uranium, and some groundwater uranium contamination reaches levels 75 times the U.S. EPA limit. Uranium exposure can affect the kidneys, bones, and the liver, yet contamin…

After long presenting heatwaves as fun episodes, with pictures of young people in fountains and swimming pools, European media are now realizing it's not funny anymore.
French TV talked about the worst day instead of the warmest day, and Le Parisien had "Torture" as headline. https://nos.nl/l/2573263

Zweten in Frankrijk, Spanje en Italië, Franse krant noemt hittegolf 'marteling'
In zuidelijk Europa worden temperaturen van 40 graden en meer bereikt. Onze correspondenten doen verslag.

This https://arxiv.org/abs/2402.15311 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Scaling Limit of the Kuramoto Model on Random Geometric Graphs
We consider the Kuramoto model on a graph with nodes given by $n$ i.i.d. points uniformly distributed on the $d$ dimensional torus. Two nodes are declared neighbors if they are at distance less than $ε$. We prove a scaling limit for this model in compact time intervals as $n\to\infty$ and $ε\to 0$ such that $ε^{d+2}n/\log n \to \infty$. The limiting object is given by the heat equation. On the one hand this shows that the nonlinearity given by the sine function disappears under this scaling …