We review and discuss recent progress in modelling non-linear and non-local transport
processes in heterogeneous media. The non-locality that we consider is caused by long …

Over the past two decades percolation theory has been used to explain and model a wide
variety of phenomena that are of industrial and scientific importance. Examples include …

This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity
are isolated and framed in terms of a special class of matroids, which are a natural …

We use a new algorithm to find the stress-carrying backbone of" generic" site-diluted
triangular lattices of up to 10 6 sites. Generic lattices can be made by randomly displacing …

Using a recently developed algorithm for generic rigidity of two-dimensional graphs, we
analyze rigidity and connectivity percolation transitions in two dimensions on lattices of …

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The starting point of the theory of matroids goes back to the 1930s when BL van der
Waerden ([93,150]) considered not only linear dependence but the algebraic dependence …

The infinitesimal rigidity (or briefly rigidity) of a bar-and-joint framework (in any dimension)
can be formulated as a rank condition of the so-called rigidity matrix. If there are n joints in …

A rectangle in the plane can be continuously deformed preserving its edge lengths, but
adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized …

1 CONNECTIVITY FOR RIGIDITY 1. Introduction Frameworks consist of rigid rods and rotatable
joints. Consider the framework with w Page 1 Studies of the University of Zilina Mathematical …