Related papers: On regular and random two-dimensional packing of c…
Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary…
In jammed packings, it is usually thought that local structure only plays a significant role in specific regimes. The standard deviation of the relative excess coordination, $\sigma_Z/ Z_\mathrm{c}$, decays like $1/\sqrt{d}$, so that local…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Relaxation of the packing of elongated particles (discorectangles) aligned on a line was studied numerically. The aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;50]$. The initial…
By combining computer simulations and a unit cell model approach, we study the apparent bimodality of local structural ordering in a system of confined hard disks. It is shown that a two-dimensional (2D) array of hard disks confined…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of…
Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…
The shape of the cross section of a dense fiber bundle is related to the symmetry of its molecular packing. However, this statement might be belied by type I collagen fibrils which have a rounded section of high symmetry while structural…
The packing of hard-core particles in contact with their neighbors offers the statically determinate problem which allows analytical investigation of the stress tensor distribution. We construct the stress probability functional and derive…
By rectangle packing we mean putting a set of rectangles into an enclosing rectangle, without any overlapping. We begin with perfect rectangle packing problems, then prove two continuity properties for parallel rectangle packing problems,…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with…
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…