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We consider the dynamics of monodisperse bubbly fluid confined by two plane solid walls and subjected to small-amplitude high-frequency transversal oscillations. The frequency these oscillations is assumed to be high in comparison with…
We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact…
Using Brakke's Evolver, we numerically verify conjectured optimal planar double bubbles for density $r^p$ and provide conjectures for triple and quadruple bubbles.
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…
We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a consequence, out of the twelve families of non-planar minimal…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.
We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertical fibers minimize vertical surface area among…
The interstellar medium (ISM) is a turbulent, highly structured multi-phase medium. State-of-the-art cosmological simulations of the formation of galactic discs usually lack the resolution to accurately resolve those multi-phase structures.…
Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the…
In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then…
The ostwald ripening of bubbles is studied by molecular dynamics simulations involving up to 679 million Lennard-Jones particles. Many bubbles appear after depressurizing a system that is initially maintained in the pure-liquid phase, and…
The paper addresses the existence of multi-bubble solutions for the well-known Brezis-Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded…
The trajectories of a single bubble rising in the vicinity of a vertical solid wall are experimentally investigated. Distinct initial wall-bubble distances are considered for three different bubble rising regimes, i.e. rectilinear, planar…
We have designed and constructed an experimental system to study gas bubble growth in slightly supersatu- rated liquids. This is achieved by working with carbon dioxide dissolved in water, pressurized at a maximum of 1 MPa and applying a…
The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…
This paper is the second of the series of two papers, which focuses on the derivation of an averaged 1D model for compressible bubbly flows. For this, we start from a microscopic description of the interactions between a large but finite…
We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a…
We study the double bubble problem where the perimeter is taken with respect to the hexagonal norm, i.e. the norm whose unit circle in $\mathbb{R}^2$ is the regular hexagon. We provide an elementary proof for the existence of minimizing…
We investigate the distribution of energy density in a stationary self-reproducing inflationary universe. We show that the main fraction of volume of the universe in a state with a given density at any given moment of proper time t is…