April 11th, 2019

лошадь, диаграмма, Фейнман

Полет в сверхтекучей жидкости

Симпатичная статейка с формулками и картинками:)

Flying in a superfluid: starting flow past an airfoil: https://arxiv.org/abs/1904.04908

We investigate the development of superfluid flow around an airfoil accelerated to a finite velocity from rest. Using both simulations of the Gross-Pitaevskii equation and analytical calculations we find striking similarities to viscous flows: from the production of starting vortices to the convergence of the airfoil circulation onto a quantized version of the classical Kutta-Joukowski circulation. Using a phenomenological argument we predict the number of vortices nucleated by a given foil and find good agreement with numerics. Finally we analyze the lift and drag acting on the airfoil.

5 pages of main text with 4 figures, 5 pages of supplementary information with 3 figures
лошадь, диаграмма, Фейнман

Метод изображений живет и развивается!

Four-dimensional reflection groups and electrostatics: https://arxiv.org/abs/1904.04655

We start from the observation that the two-element cyclic group consisting of the identity and a sphere inversion can be viewed as a stereographic image of a one-mirror reflection group in 4D. This allows us to identify 19 three-parametric families of finite groups formed by four (or less) sphere inversions. Exactly as in the single sphere case, each member of each of the 19 families generates a solvable electrostatics problem of a charge inside a piecewise-spherical cavity with grounded conducting walls. We present a worked example of a member of the D4 family: a cavity formed by three mutually orthogonal planes (i.e. spheres of infinite radius) and a spherical segment at 60∘ to each of the flat walls. In this particular case, generating the induced potential requires 191 image charges.

9 pages, 3 figures