Topological properties of two-dimensional number systems

Universal topological properties of two-dimensional trivalent cellular patterns.

Universal topological properties of two-dimensional trivalent cellular patterns are found from shell analysis of soap froth and computer-generated Voronoi diagrams. We introduce a cluster analysis based on the shell model and find the universal relation ln(a/mu(2)) = A+Bln(mu(2)), with the generalized Aboav parameter a and second moment of the number of cell edge distribution mu(2). For the sec...

Two{dimensional Topological Dynamics

Generic properties for two-dimensional dynamic systems

This paper studies the concept of genericity for two dimensional dynamic systems. The basic model is the differential model, proposed by S. Smale, of constructing generic properties for diffeomorphisms defined on compact varieties . The generic property concept for dynamic systems defined on an open set G, is proposed. The aim of the construction is to test the conditions for which, in two-dime...

Computational design of two- dimensional topological materials

The progress in science and technology is largely boosted by the continuous discovery of new materials. In recent years, the state-of-art first-principles computational approach has emerged as a vital tool to enable materials discovery by designing a priori unknown materials as well as unknown properties of existing materials that are subsequently confirmed by experiments. One notable example i...

Equilibrium properties and phase diagram of two-dimensional Yukawa systems.

Properties of two-dimensional strongly coupled Yukawa systems are explored through molecular dynamics simulations. An effective coupling coefficient gamma* for the liquid phase is introduced on the basis of the constancy of the first peak amplitude of the pair-correlation functions. Thermodynamic quantities are calculated from the pair-correlation function. The solid-liquid transition of the sy...