We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffu...

Abstract The statistics of nonlinear processes in avalanching systems, based on the self-organized criticality (SOC) concept Bak et al. (1988), predicts power-law-like size (or occurrence frequency) distribution functions. Following up previous work, we define a standard SOC model terms six assumptions: (i) area fractality, (ii) volume (iii) flux–volume proportionality, (iv) classical diffusion...

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...

The present study attempted deriving and solving the falling- cylinder governing equations for power law model non-Newtonian fluids. Based on this theoretical study, a novel falling- cylinder rheometer (FCR) was designed and constructed to measure the Theological properties of non-Newtonian fluids. Different falling cylinders with predesigned densities were used to determine the apparent viscos...

We perform simulations of model proteins to study folding on rugged energy landscapes. We construct "first-passage" networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to basins and transitions between them in the energy landscape. We find power-law relations between the folding time and the number of nodes and bonds. We show that ...

We present analysis of spatial patterns of generic disease spread simulated by a stochastic long-range correlation SIR model, where individuals can be infected at long distance in a power law distribution. We integrated various tools, namely perimeter, circularity, fractal dimension, and aggregation index to characterize and investigate spatial pattern formations. Our primary goal was to unders...

We explore the behavior of the fractal-shot-noise driven doubly stochastic Poisson point process or FSNDP, for which the associated impulse response functions assume a decaying power-law form. For a variety of parameters of the process, we obtain expressions for the count number distribution and moments, Fano factor, normalized coincidence rate, power spectral density, and time probability dens...

In contrast to the conventional wisdom that scale-free networks are prone to epidemic propagation, in the paper we present that disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, “large-world” behavior, ...

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated tha...

the ardabil geothermal area is located in the northwest of iran, which hosts several hot springs. it is situated mostly around the sabalan mountain. the sabalan geothermal area is now under investigation for the geothermal electric power generation. it is characterized by its high thermal gradient and high heat flow. in this study, our aim is to determine the fractal parameter and top and botto...