Remark on an elastic plate interacting with a gas in a semi-infinite tube: periodic solutions

A small remark on the derivation of the plateau angle conditions for the vector-valued Allen-Cahn equation

We clarify a point in arXiv:1210.0231 concerning the derivation of the Plateau angle conditions for the vector-valued Allen-Cahn equation

Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity

Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in $\mathbb{R}^3$ consisting of a thin tube-shaped domain placed upon a thin plate-shaped domain. The problem involves two small parameters, the radius of the cross-section of the tube-shaped domain and the thickness of the plate-shaped domain. We characterize the different limit models, including the limit junction condition, in the membrane-string regime according to the ratio between these two…

A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the 3D incompressible Euler equations, and show that such behavior induces energy cascade in the absence of nonlinear scale-interaction. From this energy cascade, we prove a modified version of the zeroth-law. In the Appendix, we derive Kolmo…

论量子力学中的薛定谔方程与弹性理论中的欧拉-伯努利方程之间的等价性

On the Equivalence Between the Schrodinger Equation in Quantum Mechanics and the Euler-Bernoulli Equation in Elasticity Theory

本文证明了薛定谔方程与欧拉-伯努利方程在数学上的等价性，并探讨了其在量子计算、双缝实验及p-adic方程中的潜在应用。