Related papers: Self-similarity of bubbles
We numerically study the system of rapidly rotating Bose atoms at the filling factor (ratio of particle number to vortex number) $\nu=1$ with the dipolar interaction. A moderate dipolar interaction stabilizes the incompressible quantum…
In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance…
The interstellar medium is structured as a hierachy of gas clouds, that looks self-similar over 6 orders of magnitude in scales and 9 in masses. This is one of the more extended fractal in the Universe. At even larger scales, the ensemble…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
The shape of the local bubble is modeled in the framework of the thin layer approximation. The asymmetric shape of the local bubble is simulated by introducing axial profiles for the density of the interstellar medium, such as exponential,…
We numerically explore the behavior of repelling and aligning self-propelled polar particles (boids) in 2D enclosed by a damped flexible and elastic loop-shaped boundary. We observe disordered, polar ordered (or jammed) and circulating…
Self-organization of hydrogen bubbles generated by laser-treated areas of an aluminum plate etched in a basic aqueous solution of ammonia is studied experimentally and theoretically. A dynamics of establishment of stationary pattern of gas…
We present similarity solutions for mass-loaded adiabatic bubbles that are blown by winds having time dependent mechanical luminosities. We consider mass-loading through conductive evaporation of clumps. In the limit of little mass loading…
A superbubble which advances in a symmetric Navarro--Frenk--White density profile or in an auto-gravitating density profile generates a thick shell with a radius that can reach 10 kpc. The application of the symmetric and asymmetric image…
We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…
Bubble formation and detachment at a submerged orifice exists widely in both daily life and academic research, and the influence of solid surface on bubble formation and detachment has also been extensively investigated. For example, it has…
We compare the dynamics of a Bose-Einstein condensate in two coupled potential wells with atoms diffracting from a standing light wave. The corresponding Hamiltonians have an identical appearance, but with a different set of commutation…
We generalize the standard computation of homogeneous nucleation theory at zero temperature to a scenario in which the bubble shape is determined self-consistently with its quantum fluctuations. Studying two scalar models in 1+1 dimensions,…
Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial…
Consider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing…
We develop an analytical formalism for studying optical analogues of spherically symmetric black-hole spacetimes. We demonstrate the exact similarity between the electromagnetic wave equations in an inhomogeneous medium in flat spacetime…
To prove presence of chaos for fractals, a new mathematical concept of abstract similarity is introduced. As an example, the space of symbolic strings on a finite number of symbols is proved to possess the property. Moreover, Sierpinski…
From air-sea gas exchange, oil pollution, to bioreactors, the ubiquitous fragmentation of bubbles/drops in turbulence has been modelled by relying on the classical Kolmogorov-Hinze paradigm since the 1950s. This framework hypothesizes that…
We give short proofs of the following two facts: Iterated principal circle bundles are precisely the nilmanifolds. Every iterated circle bundle is almost flat, and hence diffeomorphic to an infranilmanifold.