We present exact results on the low-temperature behavior of the square lattice ±J Ising model, with a concentration c of ferromagnetic bonds and a concentration 1−c of antiferromagnetic bonds. We find that for T below a characteristic temperature T0, the system is “frozen” in the sense...

This talk will summarize the present status of an ongoing research program designed to answer the question posed in the title. Since a snapshot of liquid water with a subpicosecond shutter speed reveals that this system (a hydrogen-bonded liquid) is above its percolation threshold, it is...

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children...

We study the optimal distance ℓopt in random networks in the presence of disorder implemented by assigning random weights to the links. The optimal distance between two nodes is the length of the path for which the sum of weights along the path (“cost”) is a minimum. We study the case of...

We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability...

We determine the backbone mass distributions for bond percolation between two lines of arbitrary orientations in three dimensions. All simulations were performed at the percolation threshold pc. The slope of the power law regime of the backbone mass distribution is dependent upon the angle...

We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a “phase transition” in the MF spectrum for...

One plus one dimensional growth of an Eden model with acceleration sites is investigated by simulations, where the acceleration sites which are distributed at random before the process starts become immediately Eden cells if the surface of Eden cluster touches them. The critical concentration of...

An analysis of diffusion in a supercooled liquid based solely in the density of diffusive directions and the value of energy barriers shows how the potential energy landscape (PEL) approach is capable of explaining the α and β relaxations and the fragility of a glassy system. We find that the...

We discuss a family of clusters C corresponding to the region whose boundary is formed by a fractional Brownian path y(i) and by the moving average function yn(i)≡1n∑k=0n−1y(i−k). Our model generates fractal directed patterns showing spatio-temporal complexity, and we demonstrate that...