Related papers: The Rayleigh collapse of two spherical bubbles
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
We construct solutions of Schr\"odinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero $L^2$ norms, and are…
In 1993 Foisy et al. proved that the optimal Euclidean planar double bubble---the least-perimeter way to enclose and separate two given areas---is three circular arcs meeting at 120 degrees. We consider the plane with density $r^p$, joining…
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 Rayleigh criterion determines the resolution limit of a periodogram, which is the minimum frequency separation required to barely resolve two sinusoids. Failing to consider the Rayleigh criterion may result in incorrect interpretations…
The impact of a sessile droplet with a moving meniscus, as encountered in processes such as dip-coating, generically leads to the entrapment of small air bubbles. Here we experimentally study this process of bubble formation by looking…
The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by first of its kind, continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited…
Using a self-similar approach a general nonsteady theory is elaborated for the case of the diffusion growth of a gas bubble in a supersaturated solution of gas in liquid. Due to the fact that the solution and the bubble in it are physically…
The seminal work \cite{bm} by Brezis and Merle showed that the bubbling solutions of the mean field equation have the property of mass concentration. Recently, Lin and Tarantello in \cite{lt} found that the "bubbling implies mass…
In this work, we established a novel theory for the dynamics of oscillating bubbles such as cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we proposed bubble dynamics equations that can simultaneously…
The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always…
Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary…
We study the matching conditions for a collapsing anisotropic cylindrical perfect fluid, and we show that its radial pressure is non zero on the surface of the cylinder and proportional to the time dependent part of the field produced by…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in…
Presented here are experiments clarifying how the deformation of cavitation bubbles affects their rebound. Rebound bubbles carry the remaining energy of a bubble following its initial collapse, which dissipates energy mainly through shock…
We study an inertial chiral active fluid, formed by repulsive particles that transfer angular momentum through odd interactions, i.e. transverse forces. Chirality induces an inhomogeneous phase, consisting of rotating bubbles, whose…
The impact of a drop onto a liquid layer and the subsequent splash has important implications for diverse physical processes such as air-sea gas transfer, cooling, and combustion. In the {\it crown splash} parameter regime, the splash…
The classical isoperimetric inequality in R^3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of…