Picture map of Europe with pins indicating European capital cities

Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

Explore research outputs by the European Policies Research Centre...

Statistical mechanics of two-dimensional tilings

Kaatz, F.H. and Estrada, Ernesto and Bultheel, A. and Sharrock, N. (2012) Statistical mechanics of two-dimensional tilings. Physica A: Statistical Mechanics and its Applications, 391 (10). pp. 2957-2963. ISSN 0378-4371

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.