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S Galam

Publications and source records attributed to S Galam.

10 recordsLinked to original sources
PubMed2005

Possible crossover of a nonuniversal quantity at the upper critical dimension.

We report on a possible crossover of a nonuniversal quantity at the upper critical dimensionality in the field of percolation. Plotting recent estimates for site percolation thresholds of hypercubes in dimension 6 < or =d < or =13 against corresponding predictions from the Galam-Mauger (GM) formula p(c) = p(0) [(d-1) (q-1)](-a) d(b) for percolation thresholds, a significant departure of p(c) is observed for d > or =6 . This result is reminiscent of the crossover undergone by universal quantities in critical phenomena. For bond percolation, evidence of such a crossover of dimensionality would require an improvement of the GM formula to reach a relative error of typically 0.2%, while it is currently at 0.9% for hypercubes.

Journal Article↗
PubMed2001

Cancerous tumor: the high frequency of a rare event.

A simple model for cancer growth is presented using cellular automata. Cells diffuse randomly on a two-dimensional square lattice. Individual cells can turn cancerous at a very low rate. During each diffusive step, local fights may occur between healthy and cancerous cells. Associated outcomes depend on some biased local rules, which are independent of the overall cancerous cell density. The models unique ingredients are the frequency of local fights and the bias amplitude. While each isolated cancerous cell is eventually destroyed, an initial two-cell tumor cluster is found to have a nonzero probabilty to spread over the whole system. The associated phase diagram for survival or death is obtained as a function of both the rate of fight and the bias distribution. Within the model, although the occurrence of a killing cluster is a very rare event, it turns out to happen almost systematically over long periods of time, e.g., on the order of an adults life span. Thus, after some age, survival from tumorous cancer becomes random.

Animals↗