Related papers: Surface fraction of random close packing in two di…
Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of…
We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a…
Often experimentalists study colloidal suspensions that are nominally monodisperse. In reality these samples have a polydispersity of 4-10%. At the level of an individual particle, the consequences of this polydispersity are unknown as it…
The probability density function of the random flight with isotropic initial conditions is obtained by an expansion in the number of collisions and the in the spatial harmonics of the solution, as in a Fourier series. The method holds for…
We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any choice of lift of the dynamics to the real line, and prove that…
The notion of random close packings of a bulk static collection of ball bearings or sand grains was introduced in the 1960's by G.D. Scott and J.D. Bernal. There have been numerous attempts to understand the packings. We give a short…
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion. This process has been introduced by the second author…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
We consider the two-dimensional discrete scan statistic generated by a block-factor type model obtained from i.i.d. sequence. We present an approximation for the distribution of the scan statistics and the corresponding error bounds. A…
We study the packing fraction of clusters in free-falling streams of spherical and irregularly shaped particles using flash X-ray radiography. The estimated packing fraction of clusters is low enough to correspond to coordination numbers…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in $\mathbb{R}^n$. Let $\overset{\sim}{x} \in {[0,1]}^n$ be a…
Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…
We present numerical simulations that allow us to compute the number of ways in which $N$ particles can pack into a given volume $V$. Our technique modifies the method of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and outperforms…
Packing is a complex phenomenon of prominence in many natural and industrial processes (liquid crystals, granular materials, infiltration, melting, flow, sintering, segregation, sedimentation, compaction, etc.). A variety of computational…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and…