Related papers: Tiling Billards on Triangle Tilings, and Interval …

The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the…

By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width. Efficiencies of the main transformation…

We study the thermal rectification phenomenon in ``billiard'' systems with interacting particles. This interaction induces a local dynamical response of the billiard to an external thermodynamic gradient. To explain this dynamical effect we…

We investigate a dynamically triangulated random surface action that consists of a gaussian term plus the modulus of the intrinsic scalar curvature. We find that the flips are frozen out and the internal geometry is regularized as the…

For substitution satisfying Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in construction of a stepped surface and Rauzy fractal. In this paper we will extend the method to hyperbolic automorphisms on the…

An inverse Doppler shift occurs in a photonic crystal (PC) bounded by a moving wall. The interpretation of this result has stirred some controversy. In this paper, we address the problem using a diagrammatic approach. This visual…

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo…

The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable…

There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the…

Despite much interest and progress in optical spatial cloaking, a three-dimensional (3D), transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. Here we experimentally demonstrate such a cloak…

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…

We study experimentally the interactions between normal solitons and tilted beams in glass waveguide arrays. We find that as a tilted beam, traversing away from a normally propagating soliton, coincides with the self-defocusing regime of…

We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional…

Aperiodic tiling is a well-know area of research. First developed by mathematicians for the mathematical challenge they represent and the beauty of their resulting patterns, they became a growing field of interest when their practical use…

We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically…

We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and…

An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union of N triangles congruent to T, overlapping only at their boundaries. The triangle T is the "tile". The tile may or may not be similar to ABC. In this paper we…

We study structural transitions in a system of interacting particles arranged as a crystalline bilayer, as a function of the density $\rho$ and the distance $d$ between the layers. As $d$ is decreased a sequence of transitions involving…

It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n=2,3,4,5,6,8. The proof for dense tile orientations uses a general result about irrationality of angles in certain…