We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and mass fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough...

Recent studies by mathematicians and physicists have identified a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. It is now recognised that Cantorian fractal space-time fluctuations characterise dynamical systems of all space-time scales ranging from the microscopic su...

one of the important aspects of soil is, knowing the relationships between spatial features of soil and quantity in statistical model. the goal of this research is to estimate saturated hydraulic conductivity by regression and co-active neuro-fuzzy inference system (anfis) with using the parameters of bulk density, real density, porosity, fractal dimension of particle size, and clay percent, si...

We study the behaviour of the power spectrum (PS) in the case of fractal structures. We show that in this case the main observational features of the PS, the large scale flattening and the scaling of the amplitude with sample depth, are related to finite size effects, due to the fractal nature of galaxy distribution in the sample. Comparing with the recent results of the PS for the CfA2 we conc...

A quantitative understanding of complex urban growth patterns and processes is crucial to sustainable land management and urban development planning in cities. The spatial organization of urban patterns can be treated as fractals and can be characterized with fractal dimension. However, the calculation of fractal dimension of urban form is often constrained by imperfect and incomplete higher te...

A new method is proposed to establish the statistical fractal model for liver diseases classification. Firstly, the fractal theory is used to construct the high-order tensor, and then Generalized N-dimensional Principal Component Analysis (GND-PCA) is used to establish the statistical fractal model and select the feature from the region of liver; at the same time different features have differe...

Large-range dependence (LRD) is essential phenomena both in LAN and WAN data traffic. Modeling such traffic traces is significant to understand the nature of the original traffic and to synthesize simulation traffic traces. Existing work such as multi-fractal wavelet model (MWM) was proposed to model IP traces and has reached much exactness. However, the nature of IP traffic exploits burst that...

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration ord...

We have characterized soot particles measured in situ a laminar co-flow ethylene-air diffusion flame using small-angle X-ray scattering (SAXS). The analysis includes temperature measurements made with coherent anti-Stokes Raman spectroscopy (CARS) and complements volume-fraction maturity laser-induced incandescence (LII). compared the results of fits to SAXS unified model fractal core-shell mod...