Related papers: Penrose Tilings as Jammed Solids
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…
Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
The paper studies the modes of vibrations of a lattice with rod-like particles, in a continuum model where the sites of the lattice are the connections among strings and rigid rods. In these structures then, translational and rotational…
We construct a non-commutative scheme that behaves as if it is the space of Penrose tilings of the plane. Let k be a field and B=k<x,y>(y^2). We consider B as the homogeneous coordinate ring of a non-commutative projective scheme. The…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
We define and study two kinds of directional expansiveness, weak and strong, for an action T of \mathbb{R}^d on a compact metric space X. We show that for \mathbb{R}^2 finite local complexity (FLC) tiling dynamical systems, weak and strong…
Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on $d=2$ square lattices. Associated thresholds $p_c^{perc}$ and $p_c^{jam}$ are determined for various needle sizes. Their ratios…
We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot\gamma$ is realized.…
Quasicrystal is now open to search for novel topological phenomena enhanced by its peculiar structure characterized by an irrational number and high-dimensional primitive vectors. Here we extend the concept of a topological insulator with…
We use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction. We show that this system exhibits a number of different commensurability effects when the…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
We study the elastic response of rigid, wire frame particles in concentrated, glassy suspensions to a step strain by applying the simple, geometric methods developed in part I. The wire frame particles are comprised of thin, rigid rods of…
Wave motion is fundamentally constrained by the dispersion properties of the medium, often making it challenging -- or even impossible -- to guide wave packets along desired trajectories, particularly when wave inversion is required. The…
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings--the Penrose, octagonal, and pinwheel tilings are famous examples. We present a…
Classical Landau theory considers structural phase transitions and crystallization as a condensation of several critical density waves whose wave vectors are symmetrically equivalent. Analyzing the simplest nonequilibrium Landau potentials…
We compare the structural and mechanical properties of static packings composed of frictionless convex (ellipses) and concave (rigid dimers) particles in two dimensions. We employ numerical simulations to generate static packings and…
Topological nodal-line semimetals are characterized by symmetry-protected one-dimensional band-touching lines or loops, which give rise to their peculiar Fermi surfaces at low energies. Furthermore, if time-reversal or inversion symmetry…