Related papers: Quantitative stability for hypersurfaces with almo…
We analyze the properties of naturally formed nano-bubbles in Lennard-Jones molecular dynamics simulations of liquid-to-vapor nucleation in the boiling and the cavitation regimes. The large computational volumes provide a realistic…
In 1904, while experimenting with high-speed photography, Lucien Bull recorded a pellet passing through a soap bubble. We investigate the dynamics that allow for a rigid body to pass through a hemispherical soap film without rupturing it.…
Very simple experiments based on an analogy between two theories (gravitation and capillarity) allowed us to construct a two dimension space toy-universe composed of the surface of a three-dimensional water tank with floating soap bubbles…
Sullivan's multi-bubble isoperimetric conjectures in $n$-dimensional Euclidean and spherical spaces assert that standard bubbles uniquely minimize total perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q \leq n+2$.…
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a…
Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct…
Least perimeter solutions for a region with fixed mass are sought in ${\mathbb{R}^d}$ on which a density function $\rho(r) = r^p+a$, with $p>0, a>0$, weights both perimeter and mass. On the real line ($d=1$) this is a single interval that…
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the…
In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data.…
The present paper considers the full nonlinear dynamics of a homogeneous bubble inside an unbounded isentropic compressible inviscid liquid. This model is described by a free-boundary problem of compressible Euler equations with nonlinear…
In this report we discuss and propose a correction to a convergence and stability issue occurring in the work of Da et al.[2015], in which they proposed a numerical model to simulate soap bubbles.
The theory of complete surfaces of (nonzero) constant mean curvature in $\RR^3$ has progressed markedly in the last decade. This paper surveys a number of these developments in the setting of Alexandrov embedded surfaces; the focus is on…
We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the…
In this paper, we prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves Baker's convergence theorem. In particular, we obtain a new differentiable sphere theorem for submanifolds in…
We prove that, for every closed (not necessarily convex) hypersurface $\Sigma$ in $\mathbb{R}^{n+1}$ and every $p>n$, the $L^p$-norm of the trace-free part of the anisotropic second fundamental form controls from above the…
We investigate the creation of scalar particles inside a region delimited by a bubble which is expanding with non-zero acceleration. The bubble is modelled as a thin shell and plays the role of a moving boundary, thus influencing the…
We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants,…
We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The…
We present experimental investigations of antibubbles. Such an unusual fluid object is a thin spherical air shell surrounding a liquid globule. We explain how to produce them and we study their stability. By overweighting antibubbles with a…
Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-\kappa^2$. Using the cone total curvature $TC(\Gamma)$ of a graph $\Gamma$ which was introduced…