Related papers: Enumeration of octagonal tilings
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference…
In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…
We classify edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^4b$ and with any irrational angle in degree: they are three $1$-parameter families of pentagonal subdivisions of the Platonic solids, with…
We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second,…
We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through…
We propose the use of entropy, measured from the spatial and flux distribution of pixels in the residual image, as a potential diagnostic and stopping metric for the CLEAN algorithm. Despite its broad success as the standard deconvolution…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a…
We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the…
Square-triangle-rhombus ($\mathcal{STR}$) tilings are encountered in various self-organized multi-component systems. They exhibit a rich structural diversity, encompassing both periodic tilings and long-range ordered quasicrystals,…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
Motivated by a question of Erd\"{o}s and inquiries by Beeson and Laczkovich, we explore the possible $N$ for which a triangle $T$ can tile into $N$ congruent copies of a triangle $R$. The \emph{reptile} cases (where $T$ is similar to $R$)…
The four major asymptotic level density laws of random matrix theory may all be showcased though their Jacobi parameter representation as having a bordered Toeplitz form. We compare and contrast these laws, completing and exploring their…
Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or…
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…
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry…
Conformal field theories in curved backgrounds have been used to describe inhomogeneous one-dimensional systems, such as quantum gases in trapping potentials and non-equilibrium spin chains. This approach provided, in a elegant and simple…