Related papers: Isoperimetric bubbles in spaces with density $r^p …
We study the radial relaxation dynamics toward equilibrium and time-periodic pulsating spherically symmetric gas bubbles in an incompressible liquid due to thermal effects. The asymptotic model ([A. Prosperetti, J. Fluid Mech., 1991] and…
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…
Dissolving armored bubbles stabilize with nonspherical shapes by jamming the initially Brownian particles adsorbed on their interfaces. In a gas-saturated solution, these shapes are characterized by planar facets or folds for decreasing…
This paper is concerned with volume-constrained minimization problems derived from Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter term and repulsive nonlocal potentials. We consider a large class…
The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet…
The reverse isoperimetric problem asks for existence and properties of bounded convex sets in a Riemannian manifold which maximise the perimeter under all those sets of fixed volume which roll freely in a ball of some given radius. If the…
Given a sphere of any radius $r$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average…
We find the first smooth microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial…
Interstellar bubbles are structures in the interstellar medium with diameters of a few to tens of parsecs. Their progenitors are stellar winds, intense radiation of massive stars, or supernova explosions. Star formation and young stellar…
Investigating the bubbles generated by the interaction between asymptotic giant branch stellar outflows and the interstellar medium (ISM) is pivotal for elucidating the mechanism by which evolved low- to intermediate-mass stars enrich the…
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…
We consider isoperimetric sets, i.e., sets with minimal vertex boundary for a prescribed volume, of the infinite cluster of supercritical site percolation on the triangular lattice. Let $p$ be the percolation parameter and let $p_c$ be the…
At each point of a Poisson point process of intensity $\lambda$ in the hyperbolic place, center a ball of bounded random radius. Consider the probability $P_r$ that from a fixed point, there is some direction in which one can reach distance…
Forming macroscopic solid bodies in circumstellar discs requires local dust concentration levels significantly higher than the mean. Interactions of the dust particles with the gas must serve to augment local particle densities, and…
Bishop's volume comparison theorem states that a compact $n$-manifold with Ricci curvature larger than the standard $n$-sphere has less volume. While the traditional proof uses geodesic balls, we present another proof using isoperimetric…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
To explain the puzzling situation in the observed bulk flows on scales $\sim 150 h^{-1}$ Mpc ($H_0 = 100 h^{-1}$ km sec$^{-1}$ Mpc$^{-1}$), we consider the observational behavior of spherically symmetric inhomogeneous cosmological models,…
Average distance between two points in a unit-volume body $K \subset \mathbb{R}^n$ tends to infinity as $n \to \infty$. However, for two small subsets of volume $\varepsilon > 0$ the situation is different. For unit-volume cubes and…
We consider a very simple toy model for a spatially varying `cosmological constant', where we are inside a spherical bubble (with a given set of cosmological parameters) that is surrounded by a larger region where these parameters are…
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…