caa a22 4500 528785532 20181217030312.0 cr unu---uuuuu 180924e20121019xx s 000 0 eng 10.3929/ethz-b-000058374 doi 10.1038/srep00751 doi (ETHRESEARCH)oai:www.research-collection.ethz.ch:20.500.11850/58374 Schrenk K. Julian How to share underground reservoirs [Elektronische Daten] [K. Julian Schrenk, Nuno A.M. Araújo, Hans J. Herrmann] Sci Rep Open access ethresearch Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fractal dimension 1.55 ± 0.03, the set of all lines has dimension 1.69 ± 0.02. The size distribution of the loops follows a power law and the evolution of the set of lines exhibits a tricritical point described by a crossover with a negative dimension at criticality. Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0 ethresearch Theoretical physics ethresearch Statistical physics, thermodynamics and nonlinear dynamics ethresearch Scaling laws ethresearch Chemical engineering ethresearch Araújo Nuno A.M. joint author Herrmann Hans J. joint author Scientific Reports London : Nature Publishing Group 2, p. 751 2045-2322 http://hdl.handle.net/20.500.11850/58374 text/html WWW-Backlink auf das Repository (Open access) 1 Journal Article ethresearch ETHRESEARCH 856 40 http://hdl.handle.net/20.500.11850/58374 text/html WWW-Backlink auf das Repository (Open access) ETHRESEARCH 100 1- Schrenk K. Julian ETHRESEARCH 700 1- Araújo Nuno A.M. joint author ETHRESEARCH 700 1- Herrmann Hans J. joint author ETHRESEARCH 773 0- Scientific Reports London : Nature Publishing Group 2, p. 751 2045-2322 BK010053 XK010053 XK010000 ETHRESEARCH ETHRESEARCH ETHRESEARCH Journal Article Open access