Related papers: Structural Complexity and Correlated Disorder in M…
We discuss the behavior of a crystalline surface with a disordered substrate. We focus on the possible existence of a {\em super-rough} glassy phase, with height-height correlation functions which vary as the square logarithm of the…
Photonic crystals are extremely sensitive to structural disorder even to the point of completely losing their functionalities. While on one side this can be detrimental for applications in traditional optical devices, on the other side, it…
Metal oxides such as VO$_2$ undergo structural transitions to low-symmetry phases characterized by intricate crystalline order, accompanied by rich electronic behavior. We derive a minimal ionic Hamiltonian based on symmetry and local…
We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…
Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along…
Compositional disorder induces myriad captivating phenomena in perovskites. Target-driven discovery of perovskite solid solutions has been a great challenge due to the analytical complexity introduced by disorder. Here, we demonstrate that…
Diffuse scattering is usually associated with some disorder in the analyzed material. Different kinds of disorder may produce different diffuse scattering -- or not. In this letter, we demonstrate some aspects of the variety of diffuse…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given…
In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single…
There is a widespread assumption that the universe in general, and the Earth's biosphere in particular, is becoming more complex over time. This paper formulates this assumption as a macroscopic law, the law of increasing complexity, for a…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
Supercooled liquids are sometimes described as being composed of a mosaic of patches that may be listed in a `library', each one having some form of non-periodic order. Looking closer, one finds this construction elusive. In attempting to…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
The global availability of communication services makes it possible to interconnect independently developed systems, called constituent systems, to provide new synergistic services and more efficient economic processes. The characteristics…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
This paper deals with the arrow of complexification of engineering. We claim that the complexification of engineering consists in (a) that shift throughout which engineering becomes a science; thus it ceases to be a (mere) praxis or…
Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one…