Zobrazeno 1 - 10
of 225
pro vyhledávání: '"Khesin, Boris"'
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality of the angl
Externí odkaz:
http://arxiv.org/abs/2408.03279
Autor:
Khesin, Boris, Saldanha, Nicolau C.
We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain ele
Externí odkaz:
http://arxiv.org/abs/2408.00522
Autor:
Khesin, Boris
The non-transitivity without extra constraints in the Euler equation in any dimension is almost evident and can be derived, e.g., from Morse theory.
Comment: 5 pages, to appear in Nonlinearity
Comment: 5 pages, to appear in Nonlinearity
Externí odkaz:
http://arxiv.org/abs/2402.08836
We consider pairs of point vortices having circulations $\Gamma_1$ and $\Gamma_2$ and confined to a two-dimensional surface $S$. In the limit of zero initial separation $\varepsilon$, we prove that they follow a magnetic geodesic in unison, if proper
Externí odkaz:
http://arxiv.org/abs/2401.08512
We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphisms with a natural metric, which allows a Riemannian submersion to the s
Externí odkaz:
http://arxiv.org/abs/2307.05703
We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an auxiliary proble
Externí odkaz:
http://arxiv.org/abs/2304.09354
Autor:
Khesin, Boris, Modin, Klas
Publikováno v:
Comm. Math. Phys. 401, 1879-1898 (2023)
We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its similarities
Externí odkaz:
http://arxiv.org/abs/2207.10214
Autor:
Izosimov, Anton, Khesin, Boris
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V.Arnold, as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. In this paper we d
Externí odkaz:
http://arxiv.org/abs/2206.01434
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent developments and ac
Externí odkaz:
http://arxiv.org/abs/2205.01143