We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent α ≈ 1.1 for intermediate and with exponent γ ≈ 0.6 for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a ...

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D t u(t, x) = Bu + u · Ẇ , where D t is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R and Ẇ a time homogeneous fractional ...

We consider the role of finite size effects on the value of the effective Hurst exponent H . This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer’s identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = 1/2) i...

An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture ...

The results of kinetic Monte Carlo simulations of epitaxial growth on fcc~100! and bcc~100! surfaces in which the correct crystal geometry is taken into account are reported. The existence of downward funneling to fourfold hollow sites leads to a downward current for large angles and to angle selection as observed in a variety of experiments. We have used our model to simulate Fe/Fe~100! deposi...

A network model of porous media is used to assess the effects of pore structure and matrix wettability on the resistivity of partially saturated rocks. Our focus is the magnitude of the saturation exponent n from Archie’s law and the hysteresis in resistivity between drainage and imbibition cycles. Wettability is found to have the dominant effect on resistivity. The network model is used to inv...

Abstract A saturation–capillary pressure relationship is proposed that applicable for all wettabilities, including mixed-wet and oil-wet or hydrophobic media. This formulation more flexible than existing correlations only match water-wet data, while also allowing saturation to be written as a closed-form function of capillary pressure: we can determine explicitly from saturation, vice versa. We...

Loynes’ distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley’s recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but does not know their probabilistic properties, what are the statistical limits of estimating the tail exponent of Loynes’ distribution? We conjecture that in b...