Tootfinder

The Snapshot Problem for the Euler-Poisson-Darboux Equation
Fulton Gonzalez, Jue Wang, Jens Christensen, Tomoyuki Kakehi
https://arxiv.org/abs/2507.13257 h…

The Snapshot Problem for the Euler-Poisson-Darboux Equation
The generalized Euler-Poisson-Darboux (EPD) equation with complex parameter $α$ is given by $$ Δ_x u=\frac{\partial^2 u}{\partial t^2}+\frac{n-1+2α}{t}\,\frac{\partial u}{\partial t}, $$ where $u(x,t)\in \mathscr E(\mathbb R^n\times \mathbb R)$, with $u$ even in $t$. For $α=0$ and $α=1$ the solution $u(x,t)$ represents a mean value over spheres and balls, respectively, of radius $|t|$ in $\mathbb R^n$. In this paper we consider existence and uniqueness results for the following t…

Apropos HŸyre og Peter FrŸlich sine angrep på fag de ikke forstår eller kan kvantifisere nytteverdien av — jeg var inne på temaet på bloggen forleden: https://filmschoolteacher.info/fredsnotes/2025/07/25/why-we-ar-t/
(Jobber med en norsk versjon, men d…

Energy minimization for skyrmions on planar thin films
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius, Valeriy Slastikov
https://arxiv.org/abs/2509.23495 https://

Energy minimization for skyrmions on planar thin films
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmetric exchange as well as an anisotropy term. We devise an algorithm for energy minimization in the continuous case and show weak convergence of a subsequence towards a solution of the corresponding Euler--Lagrange equation. Furthermore, an algorithm for numerical energy minimization is presented. We show empirically th…

Super homology groups of differential forms and vector fields on Euclidean line
Kentaro Mikami, Tadayoshi Mizutani
https://arxiv.org/abs/2509.04698 https://

Super homology groups of differential forms and vector fields on Euclidean line
The arXiv:2105.09738 claims several stuffs. In particular, we recall the following two. (1) Vector fields and differential forms become a Lie superalgebra structure for each manifold. (2) For an n-dimensional Euclidean space, vector fields and differential forms with polynomial coefficients become a double weighted Lie uperalgebra. By using Euler vector field, the Betti numbers are 0 except the last one if the primary weight and the secondary weight are different. Now, a simple question arises:…

On the inextensibility assumption in the stability of elastic rings: overhaul of a traditional paradigm
Federico Guarracino, Ida Mascolo
https://arxiv.org/abs/2509.02738 https:/…

On the inextensibility assumption in the stability of elastic rings: overhaul of a traditional paradigm
One of the oldest and most common structural engineering issues is the elastic buckling of circular rings under external pressure, which has a fundamental importance in a number of applications in general mechanics, engineering and bio-physics, just to name a few. Levy is considered to have provided the first significant solution to this problem in 1884, and most stability text-books make reference to this original solution, which is based on the Euler-Bernoulli beam model. Following this incip…

On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Theodore D. Drivas, Tarek M. Elgindi, Daniel Ginsberg
https://arxiv.org/abs/2510.02955

On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as such, all the orbits of the velocity are closed. Different from Lortz, our construction has a discrete m-fold symmetry and is foliated by invariant cylindrical level sets of a non-degenerate Bernoulli pressure. Such examples narrow the scope of validity of Gr…