title: Percolation thresholds for discrete-continuous models with nonuniform probabilities of bond formation.
abstract: We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.
authors.affiliation: College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Żwirki i Wigury 93, 02-089 Warsaw, Poland.
authors.forename: Bartłomiej
authors.initials: B
authors.lastname: Szczygieł
authors.affiliation: Modern Technologies and Filtration, Przybyszewskiego 73/77 lok. 8, 01-824 Warsaw, Poland.
authors.forename: Marek
authors.initials: M
authors.lastname: Dudyński
authors.affiliation: Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland and Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Prosta 69, 00-838 Warsaw, Poland.
authors.forename: Kamil
authors.initials: K
authors.lastname: Kwiatkowski
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Barcelona, Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Campanys 23, 08010 Barcelona, Spain.
authors.forename: Maciej
authors.initials: M
authors.lastname: Lewenstein
authors.affiliation: Spanish National Research Council (IDAEA-CSIC), E-08034 Barcelona, Spain and ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Barcelona, Spain.
authors.forename: Gerald John
authors.initials: GJ
authors.lastname: Lapeyre
authors.affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA.
authors.forename: Jan
authors.initials: J
authors.lastname: Wehr