We discuss the concept of discrete-scale invariance and how it leads to complex critical
exponents (or dimensions), ie to the log-periodic corrections to scaling. After their initial …

This introductory article presents the special Discussion and Debate volume “From black
swans to dragon-kings, is there life beyond power laws?” We summarize and put in …

Disorder and long-range interactions are two of the key components that make material
failure an interesting playfield for the application of statistical mechanics. The cornerstone in …

We test the concept that seismicity prior to a large earthquake can be understood in terms of
the statistical physics of a critical phase transition. In this model, the cumulative seismic …

The electrical conductivity of carbon black–polymer composites was found to depend on the
structure of the carbon black particles and to deviate from the expectations of classical …

We propose that catastrophic events are “outliers” with statistically different properties than
the rest of the population and result from mechanisms involving amplifying critical cascades …

Classical percolation theory is concerned with the onset of geometrical connectivity and the
accompanied onset of electrical connectivity in disordered systems. It was found, however …

Under extreme conditions the mechanical or electrical properties of solids tend to
destabilize, leading to failure or breakdown. These instabilities often nucleate or spread from …

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 …

The electrical resistivity of carbon black filled high density polyethylene increases
significantly when the composite is heated to the melting temperature of the matrix. The …