The operation of switching a finite graph was introduced by Seidel, in the study of strongly regular graphs. We may conveniently regard a graph as being a 2-colouring of a complete graph; then the extension to switching of an m-coloured complete graph is easy to define. However, the situation is very different. For m > 2, all m-coloured graphs lie in the same switching class. However, there are...

We investigate the behavior of turbulent systems in geometries with one compactified dimension. A novel phenomenological scenario dominated by the splitting of the turbulent cascade emerges both from the theoretical analysis of passive scalar turbulence and from direct numerical simulations of Navier-Stokes turbulence.

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...