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We investigate the problem of estimating geodesic tortuosity andconstrictivity as two structural characteristics of stationary random closedsets. They are of central importance for the analysis of effective transportproperties in porous or composite materials. Loosely speaking, geodesictortuosity measures the windedness of paths whereas the notion ofconstrictivity captures the appearance of bottlenecks resulting from narrowpassages within a given materials phase. We first provide mathematicallyprecise definitions of these quantities and introduce appropriate estimators.Then, we show strong consistency of these estimators for unboundedly growingsampling windows. In order to apply our estimators to real datasets, the extentof edge effects needs to be controlled. This is illustrated using a model for amulti-phase material that is incorporated in solid oxid fuel cells.

Estimation of geodesic tortuosity and constrictivity in stationary random closed sets