Related papers: Return Radius and volume of recrystallized materia…
Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative…
In this paper, we obtain some additional probabilistic properties of the renewal process $\{\hat{N}_{\alpha}(t)\}_{t\ge0}$, $0<\alpha\le 1$ introduced by Beghin and Orsingher (2010). A time-changed relationship connecting…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
The residual gas within newly formed star clusters is expelled through stellar feedback on timescales ~ 1 Myr. The subsequent expansion of the cluster results in an unbinding of a fraction of stars before the remaining cluster members can…
We consider the following problem in one-dimensional diffusion-limited aggregation (DLA). At time $t$, we have an "aggregate" consisting of $\Bbb{Z}\cap[0,R(t)]$ [with $R(t)$ a positive integer]. We also have $N(i,t)$ particles at $i$,…
The mean matter density within the turnaround radius, which is the boundary that separates a nonexpanding structure from the Hubble flow, was recently proposed as a novel cosmological probe. According to the spherical collapse model, the…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
We introduce in this paper a strategy to prove gradient estimates for some infinite-dimensional diffusions on $L_2$-Wasserstein spaces. For a specific example of a diffusion on the $L_2$-Wasserstein space of the torus, we get a…
By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $\epsilon=\Omega^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth…
We consider the one-dimensional linear free space Schr\"odinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudoperiodic boundary conditions, the solution of the…
We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole…
Influence of volume capture on a process of volume reflection of ultrarelativistic particles moving in bent single crystals was considered analytically. Relations describing various distributions of particles involving in the process, the…
We investigate the surface width $W$ of solid-on-solid surfaces in the vicinity of the roughening temperature $T_r$. Above $T_r$, $W^2$ is expected to diverge with the system size $L$ like $\ln L$. However, close to $T_r$ a clean $\ln{L}$…
The evolution of RHEED reflexes intensity during reconstructed transitions characterizes (often implicitly) reconstructed surface state peculiarities. The approaches of a correct RHEED data interpretation, aimed at obtaining information…
We consider the three-dimensional radial Stefan problem which describes the evolution of a radial symmetric ice ball with free boundary \begin{equation*} \left\{\begin{aligned} &\partial_{t}u-\partial_{rr}u-\frac{2}{r}\partial_{r}u=0 \quad…
A continuum growth model is introduced. The state at time $t$, $S_t$, is a subset of $\mathbb{R}^d$ and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs…
Here we consider the strong evolution experienced by the matter reinserted by massive stars, both in giant star forming regions driven by a constant star formation rate, and in massive and coeval superstar clusters. In both cases we take…
Large-scale circulation (LSC) quasi-stably emerges in the turbulent Rayleigh-B\'{e}nard convection, and intermittently reverses its rotational direction in two-dimensional turbulent convection. In this paper, direct numerical simulations of…
We examine the growth of crystals from vapor. We assume that the Wulff shape is a prism with a hexagonal base. The Gibbs-Thomson correction on the crystal surface is included in the model. Assuming that the-initial crystal has an admissible…
In this paper we prove the Kneser-Poulsen conjecture for the case of large radii. Namely, if a finite number of points in Euclidean space $E^n$ is rearranged so that the distance between each pair of points does not decrease, then there…