Deterministic Small-World Networks

Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two nodes). These networks have been characterized as small-world networks and modeled by the addition of randomness to regular structures. We show that small-world networks can be constructed in a deterministic way. This exact approach permits a direct calculation of relevant network parameters allowing their immediate contrast with real-world networks and avoiding complex computer simulations.Comment: 6 pages, 1 figur

Small-World Networks in Geophysics

Many geophysical processes can be modelled by using interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we try to use and modify the small-world theory to model geophysical processes such as diffusion and transport in disordered porous rocks. We develop an analytical approach as well as numerical simulations to try to characterize the pollutant transport and percolation properties of small-world networks. The analytical expression of system saturation time and fractal dimension of small-world networks are given and thus compared with numerical simulations

Us in a Small World

Us in a Small World is an event of environmentalist performance art at Wild Goose Creative, co-produced by Livable Futures, a project of the Global Arts and Humanities Discovery Theme, and The Ohio State University Honors & Scholars Center. It was scheduled for March 29th, 2020, at 4 & 6 pm. However, due to the spread of COVID-19, this performance was canceled. The show design featured personal and solicited choreography, dance film, and music that deals with environmentalist themes. My personal choreographic project is an approximately fifteen-minute work built from five duets, each made with a different co-creator and drawing inspiration from a different animal. The overarching research question is how a piece of art can remind the audience and participants that they are a part of and connected to the natural world. The main objective of the work is to call for environmentally conscious action.Livable Futures, a project of the Global Arts and Humanities Discovery ThemeThe Ohio State University Honors & Scholars CenterNo embargoAcademic Major: Danc

Ising model in small-world networks

The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the thermodynamic limit, the phase transition has a mean-field character for any finite value of the rewiring probability p, which measures the disorder strength of a given network. For small values of p, both the transition temperature and critical energy change with p as a power law. In the limit p -> 0, the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure

Relaxation Properties of Small-World Networks

Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure