Percolation in networks with long-range connections

✍ Scribed by Cristian F. Moukarzel

• Book ID: 104078300
• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 188 KB
• Volume: 372
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2006.08.049

✦ Synopsis

Two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to PðrÞ$r Àa . By changing the decay exponent a one can go from d-dimensional short-range networks to 1-dimensional networks topologically similar to random graphs. Percolation on these networks is numerically studied for systems of up to 10 7 sites. The shortest-path, fractal and chemical dimensions are determined at the critical threshold, as a function of the decay exponent a.