ArticleEntropy (Basel, Switzerland)2026
Percolation with Distance-Dependent Site Occupational Probabilities.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
We introduce a new method for preparing a percolation system by employing an inverse percolation model. Unlike standard percolation, where the site occupancy is uniform, the new model imposes a distance-dependent probability of site removal, where sites closer to the lattice center have a higher probability of being removed and are more prone to damage as compared to those at the periphery of the system. The variation in this removal probability is a function of the distance (d) from the central point. Thus, the central point plays a key role. This is reflected in our effort to model the role of a tumor cell and its surroundings (the tumor microenvironment). The tumor causes a decrease in the concentration of key elements, such as O2 (resulting in hypoxia) and Ca, in the region close to it, which in turn is an impediment to the efficiency of radiotherapy and chemotherapy. This decrease is the largest in sites adjacent to the tumor and smaller away from the tumor. Such change in the concentrations of these elements is vital in the mechanism of cancer therapies. Starting from a fully occupied lattice, we introduce a distance-dependent removal probability q(d). The value of q(d) is 1 at and next to the tumor (center) and decreases linearly away from it to a limiting value qp, which is the value of
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