Related papers: Complex rotation numbers: bubbles and their inters…
An inverse turbulent cascade in a periodic square box produces a coherent system-sized vortex dipole. We study the statistics of its motion by carrying out direct numerical simulations performed for various bottom friction $\alpha$, pumping…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
The aim of this paper (inspired from a problem of Habegger) is to describe the set of cubical decompositions of compact manifolds mod out by a set of combinatorial moves analogous to the bistellar moves considered by Pachner, which we call…
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral…
Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about…
We propose a phenomenological model of vortex tube reconnection at high Reynolds numbers. The basic picture is that squeezed vortex lines, formed by stretching in the region of closest approach between filaments, interact like dipoles…
Analytical considerations and potential flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, $r_n$, decreases as $\tau\propto r_n^2 \, (-\ln{r_n^2})^{1/2}$, where $\tau$ is…
This work reveals that the dynamic response of a spherical cap bubble in contact with a rigid wall depends on the effective contact angle at the instant prior to collapse. This parameter allows us to discriminate between two regimes in…
The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction…
Consider a real algebraic variety, $\R X$, of dimension $d$. If its complexification, $\C X$, is a rational homology manifold (at least in a neighborhood of $\R X$), then the intersection form in $\C X$ defines a bilinear form in…
We report on the nucleation of bubbles on solids that are gently rubbed against each other in a liquid. The phenomenon is found to depend strongly on the material and roughness of the solid surfaces. For a given surface, temperature, and…
Incompressible, inviscid, irrotational, and unsteady flows with circulation $\Gamma$ around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a…
Given any Liouville number $\alpha$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation number $\alpha$.
Oblique collision of solid particles with surfaces has been a topic of extensive study in Newtonian mechanics, which also explains the motion of bubbles and droplets to some extent. Here, we observe that air bubbles exhibit a backflipping…
In this paper, we study multi-rotation orbits on the unit circle. We obtain a natural generalization of a classical result which says that orbits of irrational rotations on the unit circle are dense. It is possible to show that this result…
Topological defects can naturally be formed soon after bubble nucleation in the open inflation scenario. The defects are not completely diluted away by the subsequent period of inflation in the bubble interior and can produce observable…
Patterns of convection in internally heated, self-gravitating rotating spherical fluid shells are investigated through numerical simulations. While turbulent states are of primary interest in planetary and stellar applications the present…
We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and…
This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic…
We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…