Related papers: The Space of Planar Soap Bubble Clusters
The most studies on the stability of foam bubbles investigated the mechanical stability of thin films between bubbles due to the drainage by gravity. In the current work, we take an alternative approach by assuming the rupture of bubbles as…
The dense flow of air bubbles in a two-dimensional silo (through an aperture D) filled with a liquid is studied experimentally. A particle tracking technique has been used to bring out the main properties of the flow: displacements of the…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the…
This paper considers the moduli spaces/stacks of parabolic bundles (parabolic logarithmic flat bundles and parabolic logarithmic Higgs bundles with given spectrum) of rank 2 and degree 1 over $\mathbb{P}^1$ with five marked points. The…
The present note contains a review of $p$-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of…
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…
In this work we investigate lump-like solutions in models described by a single real scalar field. We start considering non-topological solutions with the usual lump-like form, and then we study other models, where the bell-shape profile…
Colloidal particles that are confined to an interface such as the air-water interface are an example of a two-dimensional fluid. Such dispersions have been observed to spontaneously form cluster and stripe morphologies in certain systems…
Experiments on generation of 1, 2, 4, and 6 sonoluminescent bubbles in water with an external ultrasound source in an acoustic sphere resonator with glass walls have been carried out. Theoretical examination has shown that the observed…
Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological constant and homogeneous minimally coupled scalar field as a matter sources are…
For a compact manifold with boundary $X$ we introduce the $n$-fold scattering stretched product $X^n_{\text{sc}}$ which is a compact manifold with corners for each $n,$ coinciding with the previously known cases for $n=2,3.$ It is…
The evolution of spherically symmetric unstable scalar field configurations (``bubbles'') is examined for both symmetric (SDWP) and asymmetric (ADWP) double-well potentials. Bubbles with initial static energies $E_0\la E_{{\rm crit}}$,…
This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi…
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we…
We investigate the preferential concentration of particles which are neutrally buoyant but with a diameter significantly larger than the dissipation scale of the carrier flow. Such particles are known not to behave as flow tracers (Qureshi…
We study the soap film capillarity problem, in which soap films are modeled as sets of least perimeter among those having prescribed (small) volume and satisfying a topological spanning condition. When the given boundary is the closed…
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to thirty polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to…
We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…
After a short description of various classical solutions of Plateau's problem, we discuss other ways to model soap films, and some of the related questions that are left open. A little more attention is payed to a more specific model, with…