相关论文: Champagne subdomains with unavoidable bubbles

As a fluid object breaks, it often leaves behind satellite fragments. Here we show that satellite formation can follow universal dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid…

We consider a collection of balls in Euclidean space and the problem of determining if Brownian motion has a positive probability of avoiding all the balls

The main purpose of this paper is to explore the structure of regular subspaces of 1-dim Brownian motion. As outlined in \cite{FMG} every such regular subspace can be characterized by a measure-dense set $G$. When $G$ is open, $F=G^c$ is…

Let $X$ be a nondegenerate Peano unicoherent continuum. The family $CB(X)$ of proper subcontinua of $X$ with connected boundaries is a $G_\delta$-subset of the hyperspace $C(X)$ of all subcontinua of $X$. If every nonempty open subset of…

Let $E$ be a bounded open subset of $\mathbb{R}^n$. We study the following questions: For i.i.d. samples $X_1, \dots, X_N$ drawn uniformly from $E$, what is the probability that $\cup_i \mathbf{B}(X_i, \delta)$, the union of $\delta$-balls…

Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have…

We consider a branching Brownian motion in $\mathbb{R}^d$. We prove that there exists a random subset $\Theta$ of $\mathbb{S}^{d-1}$ such that the limit of the derivative martingale exists simultaneously for all directions $\theta \in…

We consider an n-dimensional Brownian Motion trapped inside a bounded convex set by normally-reflecting boundaries. It is well-known that this process is uniformly ergodic. However, the rates of this ergodicity are not well-understood,…

Let $G$ be a finite abelian group and $A$ a subset of $G$. The spectrum of $A$ is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime…

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…

When a drop impacts at very low velocity onto a pool surface it is cushioned by a thin layer of air, which can be stretched into a hemispheric shape. We use ultra-high-speed video imaging to show how this thin air-layer ruptures. The number…

Benjamini, Burdzy and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component processes of the coupling staying a positive…

The pressure threshold for 1/2 order subharmonic (SH) emissions and period doubling during the oscillations of ultrasonically excited bubbles is thought to be minimum when the bubble is sonicated with twice its resonance frequency (fr).…

For a Euclidean building $X$ of type $A_{2}$, we classify the 0-dimensional subbuildings $A$ of $\partial_{T}X$ that occur as the asymptotic boundary of closed convex subsets. In particular, we show that triviality of the holonomy of a…

We extend the phase diagram of SU(N) gauge-fermion theories as function of number of flavours and colours to the region in which asymptotic freedom is lost. We argue, using large $N_f$ results, for the existence of an ultraviolet…

In the effective field theory framework, we consider the effect of supersymmetry breaking via gaugino condensation and supergravity in the hidden sector gauge group on the hidden sector vacuum angle $\theta_h$. The $\theta_h$ parameter…

We study spherical completeness of ball spaces and its stability under expansions. We introduce the notion of an ultra-diameter, mimicking diameters in ultrametric spaces. We prove some positive results on preservation of spherical…

Bubbles and droplets are ubiquitous in many areas of engineering, including microfluidics where they can serve as microreactors for screening of chemical reactions. They are often formed out of a constriction (a microfluidic channel or a…

We present a simple four-dimensional model in which anomaly mediated supersymmetry breaking naturally dominates. The central ingredient is that the hidden sector is near a strongly-coupled infrared fixed-point for several decades of energy…

We suggest a systematic procedure to study D- and F-flat directions in a large class of models with an anomalous U(1). This class of models is characterized by the existence of a vacuum that breaks all Abelian gauge symmetries connecting…