Morphisms, Symbolic Sequences, and Their Standard Forms

Morphisms are homomorphisms under the concatenation operation of the set of words over a finite alphabet. Changing the elements of the finite alphabet does not change the morphism in an essential way. We propose a method to select a unique representative from all these morphisms. This has applications to the classification of the shift dynamical...

Detection of contaminant plumes released from landfills: Numerical versus analytical solutions

Contaminant leaks released from landfills are a threat to groundwater quality. The groundwater monitoring systems installed in the vicinity of such facilities are vital. In this study the detection probability of a contaminant plume released from a landfill has been investigated by means of both a simulation and an analytical model for both...

The algebraic difference of two random Cantor sets: The Larsson family

In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor...

Correlated fractal percolation and the palis conjecture

Let F1 and F2 be independent copies of one-dimensional correlated fractal percolation, with almost sure Hausdorff dimensions dimH(F1) and dimH(F2). Consider the following question: does dimH(F1) + dimH(F2) > 1 imply that their algebraic difference F1 ? F2 will contain an interval? The well known Palis conjecture states that ‘generically’ this...

Subsurface Characterization Using a Cellular Automaton Approach

In this paper, a random Cellular Automaton model is developed to characterise heterogeneity of geological formations. The CA-model is multilateral and can be easily applied in both two and three dimensions. We demonstrate that conditioning on well data is possible and the method is numerically efficient. To construct the model, the subsurface is...