We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of three-dimensional plates to the folding of two-dimensional sheets and further to the packing of one-dimensional strings are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.

We point out that the chemical space of a totally disconnected Cantor dust K(n) [Symbol: see text E(n) is a compact metric space C(n) with the spectral dimension d(s) = d(ℓ) = n > D, where D and d(ℓ) = n are the fractal and chemical dimensions of K(n), respectively. Hence, we can define a random walk in the chemical space as a Markovian Gaussian process. The mapping of a random walk in C(n) into K(n) [Symbol: see text] E(n) defines the quenched Lévy flight on the Cantor dust with a single step duration independent of the step length. The equations, describing the superdiffusion and diffusion-reaction front propagation ruled by the local quenched Lévy flight on K(n) [Symbol: see text] E(n), are derived. The use of these equations to model superdiffusive phenomena, observed in some physical systems in which propagators decay faster than algebraically, is discussed.

We study the dynamics of the seismic activity in Mexico within a framework of dynamic scaling approach to time series fluctuations, recently suggested by Balankin (Phys. Rev. E, 76 (2007) 056120). We found that the relative seismic activity and the long-sampled fluctuations of seismic activity both display a self-affine invariance within a wide range of consecutive seismic evens. Furthermore, we found that the long-sampled fluctuations of seismic activity obey the dynamic scaling ansatz analogous to the Family-Vicsek dynamic scaling ansatz in the theory of kinetic roughening of moving interfaces. These findings imply that the records of recurrent seismic events possess hidden, long-term correlations associated with the scaling dynamics of seismic activity fluctuations.

We study the effects of ambient air humidity on the dynamics of imbibition in a paper. We observed that a quick increase of ambient air humidity leads to depinning and non-Washburn motion of wetting fronts. Specifically, we found that after depinning the wetting front moves with decreasing velocity v[proportionality](h(p)/h(D))(γ), where h(D) is the front elevation with respect to its pinned position at lower humidity h(p), while γ=/~1/3. The spatiotemporal maps of depinned front activity are established. The front motion is controlled by the dynamics of local avalanches directed at 30° to the balk flow direction. Although the roughness of the pinned wetting front is self-affine and the avalanche size distribution displays a power-law asymptotic, the roughness of the moving front becomes multiaffine a few minutes after depinning.

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper