Related papers: Tiling Billards on Triangle Tilings, and Interval …
The tidally tilted pulsators are a new type of oscillating star in close binary systems that have their pulsation axis in the orbital plane because of the tidal distortion caused by their companion. We describe this group of stars on the…
Transformation optics, a recent geometrical design strategy of controlling light by combining Maxwell's principles of electromagnetism with Einstein's general relativity, promises without precedent an invisibility cloaking device that can…
In this second paper, we study the case of substitution tilings of R^d. The substitution on tiles induces substitutions on the faces of the tiles of all dimensions j=0, ..., d-1. We reconstruct the tiling's equivalence relation in a purely…
Directional motion is commonly observed in various living active systems, such as bacterial colonies moving through confined environments. In these systems, the dynamics arise from the collective effects of mutual interactions between…
We study the properties of a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time…
The axial propagation of circularly polarized light in an optically active structurally chiral medium is exactly solved via full electromagnetic analysis. Some symmetries of the system's characteristic matrix reveal new insights, which are…
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature…
The growing use of triaxial particles in microfluidic, microrobotic, and biological systems makes it essential to understand how their rotational dynamics couples with lateral migration in microscale flows. Our experiments in inertial…
Expressions corresponding to the transmission of a uniaxial optically active crystal platelet are provided for an optical axis parallel and perpendicular to the plane of interface. The optical activity is taken into account by a consistent…
We present a one dimensional model for the nonlinear response of a colloidal crystal to intense light illumination along a high symmetry direction. The strong coupling between light and the colloidal lattice, via the electric gradient force…
The trinomial transform of a sequence is a generalization of the well-known binomial transform, replacing binomial coefficients with trinomial coefficients. We examine Pascal-like triangles under trinomial transform, focusing on the ternary…
Recently it has been shown that surface plasmons supported by an interface between a 3+1 dimensional topological insulator and a metal or between a 3+1 dimensional topological insulator with residual bulk charge carriers and vacuum have a…
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
A three-wave Budden model with two resonance layers is constructed that allows recirculation of energy fluxes along a quadrangle in ray phase space. The transmission, reflection, and conversion coefficients for this extended Budden problem…
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based on partitions of triangles or rectangles. The fractal example…
We study the depinning transition of driven interfaces in thin ferromagnetic films driven by external magnetic fields. Approaching the transition point the correlation length increases with decreasing driving. If the correlation length…
A quantitative model of the mobility of functionalized particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles anchored through…
We experimentally study the mixing of binary granular systems in a horizontal rotating cylinder. When materials have the same size and differ by dynamic angle of repose only, we observe an axial transport of matter that generates transient…
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…