and Applied Analysis 3 The nonlinear local fractional equation reads as L α u + N α u = 0, (19) where L α and N α are linear and nonlinear local fractional operators, respectively. Local fractional variational iteration algorithm can be written as [37] u n+1 (t) = u n (t) + t0 I t (α) {ξ α [L α u n (s) + N α u n (s)]} . (20) Here, we can construct a correction functional as follows [37]: u n+1 ...

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze a...

In this paper we describe a new multiscale model for char acterizing positive valued and long range dependent data The model uses the Haar wavelet transform and puts a con straint on the wavelet coe cients to guarantee positivity which results in a swift O N algorithm to synthesize N point data sets We elucidate our model s ability to capture the covariance structure of real data study its mult...

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a po...

The forecasting slope deformation potential is required to evaluate slope safety during open-pit mining, allowing us to formulate and promote effective emergency strategies in advance to prevent slope failure disasters. Although fractal models have been used to predict slope deformation, such limitations as low prediction accuracy, poor stability and the requirement for large amounts of data mu...

Cellular automata (CA) have been increasingly applied to ecohydraulics modelling owing to its advantages in simulating local behaviours and spatial patterns. However, methods for evaluating CA model performance, mostly comparing with RS observations, have yet to be established. A conventional way is to compute the overall error between model outputs and observations. This aggregated approach wi...

Fractures play an important role in steam production from geothermal reservoirs. It has been a challenge for a long time to characterize materials with a high density of fractures such as The Geysers rock. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of Berea sandstone. Methods to characterize the difference between the two have be...

This paper explores the temporal scaling behavior induced shear-branching structure in response to variant temperatures and strain rates during plastic deformation of Zr-based bulk metallic glass (BMG). The data analysis based on the compression tests suggests that there are two states of shear-branching structures: the fractal structure with a long-range order at an intermediate temperature of...