We obtain numerically the thermal conductivity of a quasi-one-dimensional classical chain of hard sphere particles as a function of the length of the chain, introducing a fresh model for this problem. The conductivity scales as a power law of the length over two decades, with an exponent very close to the analytical prediction of 1/3.

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switch...

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent tau{a}=1.5. We derive a scaling relation tau{a}=2tau-1 between the local cluster exponent tau{a} and the global avalanche exponen...

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponen...

Explicit formulae for Weber-Schafheitlin type integrals with exponent 1 are derived. The results of these integrals are distributions on R+. Received 07 April 2008; Revised 30 June 2008

In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, whose solution admits a smooth density with respect to Lebesgue’s measure. The result is obtained through the use of an explicit representation of the solution when the vector fields of the equation are nilpotent, plus a Norris type lemma in the roug...

in this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. it is proved that an abelian group of finite exponent is strongly coatomic.