Related papers: Isoperimetric bubbles in spaces with density $r^p …

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…

We present a new high signal-to-noise (S/N) observations of the Diffuse Interstellar Bands (DIBs) in the Local Bubble and its surroundings. We observed 432 sightlines and obtain the equivalent widths of $\lambda$5780 and $\lambda$5797 \AA\…

We prove that a subset of the hypercube $(0,1)^d$ with volume sufficiently close to $\frac12$ has (relative) perimeter greater than or equal to $1$. This settles a conjecture by Brezis and Bruckstein. We also prove that, in contrast with…

Based on the molecular emission in the $^{12}$CO(2-1) and $^{13}$CO(2-1) lines, and the continuum emission in the MIR and FIR towards the S21 IR dust bubble, we analyze the physical characteristics of the gas and dust linked to the nebula…

Consider a set of integers $\mathscr A$ having finite diameter $X$, and a system of simultaneous polynomial equations to be solved over $\mathscr A$. In many circumstances, it is known that the number of solutions of this system is…

We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles…

Let $\Delta$ be the optimal packing density of $\mathbb R^n$ by unit balls. We show the optimal packing density using two sizes of balls approaches $\Delta + (1 - \Delta) \Delta$ as the ratio of the radii tends to infinity. More generally,…

Motivated by Gamow's liquid drop model in the large mass regime, we consider an isoperimetric problem in which the standard perimeter $P(E)$ is replaced by $P(E)-\gamma P_\varepsilon(E)$, with $0<\gamma<1$ and $P_\varepsilon$ a nonlocal…

Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is…

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…

If energy is suddenly released in a localized region of space uniformly filled with identical stationary hard spheres, the outcome is a blast with an asymptotically spherical shock wave separating moving and stationary hard spheres. The…

This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…

We prove that for a symmetric, strictly log-convex density on the real line, there are four possible types of perimeter-minimizing triple bubbles. This extends the work of Bongiovanni et al., which shows that there are two possible types of…

We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material…

We prove a vertex isoperimetric inequality for the $n$-dimensional Hamming ball $\mathcal{B}_n(R)$ of radius $R$. The isoperimetric inequality is sharp up to a constant factor for sets that are comparable to $\mathcal{B}_n(R)$ in size. A…

We consider the isoperimetric inequality involving the $s$-perimeter and the $t$-perimeter with $0<s<t<1$, and show that the ball is a local minimizer of the (scale-invariant) isoperimetric ratio $\mathcal{F}(E):=P_t(E)^{\frac{1}{n-t}}/…

Locally isoperimetric $N$-partitions are partitions of the space $\mathbb R^d$ into $N$ regions with prescribed, finite or infinite measure, which have minimal perimeter (which is the $(d-1)$-dimensional measure of the interfaces between…

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant $\Lambda,$ which are regular at the centre, and we investigate the influence of $\Lambda$ on the bound of M/R, where M is the…

We present an analysis of wind-blown, parsec-sized, mid-infrared bubbles and associated star-formation using GLIMPSE/IRAC, MIPSGAL/MIPS and MAGPIS/VLA surveys. Three bubbles from the Churchwell et al. (2006) catalog were selected. The…

Transient microstructure in the diffuse interstellar medium has been observed towards galactic and extragalactic sources for decades, usually in lines of atoms and ions, and, more recently, in molecular lines. Evidently, there is a…