Related papers: Detecting self-similarity in surface microstructur…
We introduce on any smooth oriented minimal surface in Euclidean $3$-space a meromorphic quadratic differential, $P$, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of…
Surfaces of multilayer semiconductors typically have regions of atomically flat terraces separated by atom-high steps. Here we investigate the properties of the low-energy states appearing at the surface atomic steps in \snte. We identify…
We study the class of self-similar probability density functions with finite mean and variance which maximize R\'{e}nyi's entropy. The investigation is restricted in the Schwartz space $S(\mathbb{R}^d)$ and in the space of…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
The electronic structure of the superconducting surface sheath in a type-II superconductor in magnetic fields $H_{c2}<H<H_{c3}$ is calculated self-consistently using the Bogoliubov-de Gennes equations. We find that the pair potential…
We prove that every quasisymmetric self-homeomorphism of the standard 1/3-Sierpi\'nski carpet $S_3$ is a Euclidean isometry. For carpets in a more general family, the standard $1/p$-Sierpi\'nski carpets $S_p$, $p\ge 3$ odd, we show that the…
Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern…
The interaction between two chemically identical charge-regulated surfaces is studied using the classical density functional theory. In contrast to common expectations and assumptions, under certain realistic conditions we find a…
We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. The method relies on the equilibrium statistics of the overlap between pairs of configurations measured in…
The microcanonical partition function for self-gravitational system in three dimensional case has been found. Used approach from the field theory of statistical description of the system was tailored to gravitational interacting particles…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Symmetry is one of the most beautiful yet mysterious concepts in science. In chemical systems, presence of local symmetries at specific fragments often serve as driving forces behind many physicochemical properties, including stability,…
The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or…
Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…
For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space,…