Related papers: Isoperimetric bubbles in spaces with density $r^p …
Let $u$ be a nonnegative, local, weak solution to the porous medium equation for $m\ge2$ in a space-time cylinder $\Omega_T$. Fix a point $(x_o,t_o)\in\Omega_T$: if the average \[…
In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the…
The $l\!=\!+1.\!\!^\circ3$ region in the Galactic center is characterized by multiple shell-like structures and their extremely broad velocity widths. We revisit the molecular superbubble hypothesis for this region, based on high resolution…
We study stationary hollow vortices with surface tension in two dimensions. Such objects solve an overdetermined elliptic free boundary problem in an exterior domain, with an additional boundary condition involving mean curvature and the…
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…
The nucleation and evolution of bubbles are investigated in the model of an $O(3)$-symmetric scalar field coupled to gravity in the high temperature limit. It is shown that, in addition to the well-known bubble of which the inside region is…
We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher, de Gennes, and Au-Yang ($[$C. R. Acad.…
A model is proposed for the interior of a neutral non-rotating black hole. It consists of an ideal fluid with density $\r$ and a negative pressure $p$, obeying an equation of state $p=-\xi\r$. In order to have a solution, $\xi$ must lie in…
We introduce a versatile and spatially resolved morphological characterisation of binary fields, rooted in the opening transform of mathematical morphology. We subsequently apply it to the thresholded ionization field in simulations of…
We hypothesise that dust rings in protoplanetary discs formed by an embedded planet should have properties that reflect the planet's mass. We use 2D hydrodynamical simulations of planet-disc interactions to investigate this, focusing on…
Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is…
In an earlier paper we developed a QCD inspired theoretical parton bubble model (PBM) for RHIC/LHC. The PBM quantitatively agreed with the strong charged particle pair correlations observed by the STAR collaboration at RHIC in the highest…
With the aim of studying the properties of Galactic IR bubbles and their impact in massive star formation, we present a study of the IR bubble S169, associated with the massive star forming region IRAS12326-6245. We used…
Bubbles play an important role in the transport of chemicals and nutrients in many natural and industrial flows. Their dispersion is crucial to understand the mixing processes in these flows. Here we report on the dispersion of millimetric…
In the present manuscript we address and solve for the first time a nonlocal discrete isoperimetric problem. We consider indeed a generalization of the classical perimeter, what we call a nonlocal bi-axial discrete perimeter, where, not…
The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally…
The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the volume under constraint on the product between boundary area and radius. The goal of the paper is to investigate such mixed…
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.…