Related papers: Self-similarity of bubbles
The construction of complex rotation numbers, due to V.Arnold, gives rise to a fractal-like set "bubbles" related to a circle diffeomorphism. "Bubbles" is a complex analogue to Arnold tongues. This article contains a survey of the known…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
In this paper, it is shown that in interaction with an oscillating bubbles cluster the fluid becomes inhomogeneous. The radial variation of the acoustic refractive index of the fluid generates an acoustic lens with spherical symmetry. When…
The paper explores scaling properties of bubbles -- a complex analogue of Arnold tongues, associated to a one-dimensional family of analytic circle diffeomorphisms. Bubbles are smooth loops in the upper half-plane attached at all rational…
In this paper we show that a radial oscillating bubble in a liquid behaves like a convergent acoustic lens.
Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. From pendulum clocks to the behavior of animal groups, self-oscillation is one of the keys to the understanding of…
We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…
Starting from a peculiar image observed below a bubble floating at a water-air interface, the article analyzes several optical properties of these special types of refracting objects (coined \textit{bubble axicons}). Using mainly…
Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not…
We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as $\delta$-quasi-self-similar sets, and some other geometric notions in Euclidean…
An analogy is developed between the bubble universe model and the Young-Laplace equation obtaining an analogic equation and commenting some numerical results produced by its application. The results, even if based on a simple analogy,…
When a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble, it bursts so slowly as to collapse under its own weight simultaneously, and folds into a…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
The spontaneous formation of tiny bubbles in a liquid is at the root of the nucleation mechanism during the liquid-to-vapor transition of a metastable liquid. The smaller the bubbles the larger their probability to appear, and even for…
The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation…
Focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present and cut-off the approach towards the…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
Water usually contains dissolved gases, and because freezing is a purifying process these gases must be expelled for ice to form. Bubbles appear at the freezing front and are then trapped in ice, making pores. These pores come in a range of…
Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also…
The formation of a single bubble from an orifice in a solid surface, submerged in an in- compressible, viscous Newtonian liquid, is simulated. The finite element method is used to capture the multiscale physics associated with the problem…