Related papers: Surface fraction of random close packing in two di…
Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is…
Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis,…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle and the density profile of the…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less…
In this paper, we perform molecular dynamics (MD) simulations to study the two-dimensional packing process of both monosized and random size particles with radii ranging from $1.0 \, \mu m$ to $7.0 \, \mu m$. The system was allowed to…
We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particular we show that if P has volume 1,…
We provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a disk is 0.5. This implies that any set of (not necessarily equal) disks of total area…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a…
We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…
In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, with respect to fractional Brownian motion with Hurst parameter $H \in (1/2,1)$, for a large class of convex functions $f$ is considered. In…
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation…
We study the upper and lower regularity dimensions in relation to the notions of doubling and uniformly perfect. These two regularity properties are closely related which is quantified thanks to the regularity dimensions. The regularity…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
We investigate next nearest neighbor correlations of the contact number in simulations of polydisperse, frictionless packings in two dimensions. We find that discs with few contacting neighbors are predominantly in contact with discs that…
Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…