Sandpiles subjected to sinusoidal drive.

This paper considers a sandpile model subjected to a sinusoidal external drive with the period T. We develop a theoretical model for the Green's function in a large T limit, which predicts that the avalanches are anisotropic and elongated in the oscillation direction. We track the problem numerically and show that the system additionally shows a regime where the avalanches are elongated in the perpendicular direction with respect to the oscillations.

Self-similar but not conformally invariant traces obtained by modified Loewner forces.

The two-dimensional Loewner exploration process is generalized to the case where the random force is self-similar with positively correlated increments. We model this random force by a fractional Brownian motion with Hurst exponent H≥1/2≡H_{BM}, where H_{BM} stands for the one-dimensional Brownian motion. By manipulating the deterministic force, we design a scale-invariant equation describing self-similar traces which lack conformal invariance.

Invasion percolation in short-range and long-range disorder background.

In the original invasion percolation model, a random number quantifies the role of necks, or generally the quality of pores, ignoring the structure of pores and impermeable regions (to which the invader cannot enter). In this paper, we investigate invasion percolation (IP), taking into account the impermeable regions, the configuration of which is modeled by ordinary and Ising-correlated site percolation (with short-range interactions, SRI), on top of which the IP dynamics is defined. We model the long-ranged correlations of pores by a random Coulomb potential (RCP).

Self-organized criticality in cumulus clouds.

The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, in addition to turbulence, they are driven by self-organized criticality. Our observations yield exponents that support the fact the clouds, when projected to two dimensions, exhibit conformal symmetry compatible with c=-2 conformal field theory.

Superstatistical two-temperature Ising model.

The previous approach of the nonequilibrium Ising model was based on the local temperature in which each site or part of the system has its own specific temperature. We introduce an approach of the two-temperature Ising model as a prototype of the superstatistic critical phenomena. The model is described by two temperatures (T_{1},T_{2}) in a zero magnetic field.