Related papers: Double Interlacing in Random Tiling Models
A \textit{domino} is a $2\times 1\times 1$ parallelepiped formed by the union of two unit cubes and a \textit{slab} is a $2\times 2\times 1$ parallelepiped formed by the union of four unit cubes. We are interested in tiling regions formed…
We consider the interaction between two rods embedded in a fluctuating surface. The modification of fluctuations by the rods leads to an attractive long-range interaction between them. We consider fluctuations governed by either surface…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Previous works for a liquid suddenly contacting a gas at a supercritical pressure show the coexistence of both phases and the generation of diffusion layers on both sides of the liquid-gas interface due to thermodynamic phase equilibrium. A…
In the paper arXiv:1803.11463, the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for…
The existence of normal deterministic diffusion in dynamical systems with a two-dimensional phase space tiled by regular triangles (or their unions into regular hexagons) is proven.
We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley…
Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the…
We study two-dimensional turbulence in a square no-slip domain without bottom drag using direct numerical simulations. The dynamics are shown to depend strongly on the torque $M$ of the external forcing. When $M$ is relatively large, a…
Self-organized regular patterns are ubiquitous in nature, and one of their most celebrated manifestations is the Abrikosov vortex lattice: under an applied magnetic field, the homogeneous superconductivity becomes unstable and cast itself…
We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will contain a domino covering a given pair of…
Two-dimensional colloidal suspensions subject to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction [J. Mikhael et al.,…
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science and…
Nodal chain is a typical topological phase in nodal line semimetals. Here, we propose a new topological phase -- interlocking nodal chains, in which two sets of nodal chains are interlocked each other. It includes one- (1D), two- (2D) and…
The phase diagram and the thermodynamics of the random field Ising model (RFIM) defined on a family of diamond hierarchical lattices of arbitrary dimension and scaling factor $b=2$ is investigated. The phase diagram is studied considering…
We consider domino tilings of $3$-dimensional cubiculated regions. A three-dimensional domino is a 2x2x1 rectangular cuboid. We are particularly interested in regions of the form $R_N = D \times [0,N]$ where $D$ is a fixed quadriculated…
Many engineering and environmental surfaces exhibit spatial heterogeneity in the spanwise direction and encompass multiple surface length scales. When the dominant spanwise length scale is on the order of the largest flow scales (e.g., the…
Natural materials often feature a combination of soft and stiff phases, arranged to achieve excellent mechanical properties, such as high strength and toughness. Many natural materials have even independently evolved to have similar…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path…