Sharif Digital Repository

Several investigators worked on various aspects of tensile behavior of concrete because of its wide usage in structural design. One of the observable phenomena during tensile failure of concrete is strain softening, i.e. a negative slope in the stress-deformation diagrams. There are many kinds of experiment-based softening curves for concrete. In current research, use of newly introduced concept of fractal geometry and a failure model yields to a new softening curve for concrete. This new curve is denominated "Quasi-fractal" softening curve, which is a theorybased softening model. Comparison of Quasi-fractal softening curve with a set of proposed experimental softening curves has been... 

Using the Fractal Geometry in Signal processing has been extended nowadays [1]. They have found several applications in signal detection and recognitions. They use the chaotic feature of the noise and clutter and try to distinguish between the noise, clutter and the desired target [2] [3]. Recent works show that lots of clutters like sea and ground clutters have fractal behavior so this kind of approach to the signal detection has been extended these days[3][4]. In this paper we have used the Box-Counts of a signal rather than the Fractal dimension of a signal as will be defined later in the text. By applying the new defined concept we have developed different methods of signal detection. We... 

Many of heterogeneous structural materials, like concrete, have different behavior under tensile stresses in comparison to their behavior under compressive stresses. The aim of this paper is to interpret behavior of such materials subjected to tensile stresses, by using newly introduced concept of fractal geometry. In the first part of this paper, tensile behavior of granular composites has been studied by using fractal geometry. It is shown that the fractality of the cross section in this kind of composites can be used to interpret the size effect on tensile strength. In fact, this work is a modification with innovations on the previous studies on fractal based size effect. This hypothesis... 

We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p≥pc, in two and three dimensions. We find that the fractal dimensions of LERWp are close to normal LERW in a Euclidean lattice, for all p>pc. However, our results reveal that LERW on critical incipient percolation clusters is fractal with df=1.217±0.002 for d=2 and 1.43±0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERWp crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to... 

A wavelet transform focuses on localised signal structures with a zooming procedure that progressively reduces the scale parameter. On the other hand, fractal geometry has recently been applied to the analysis of high range resolution radar sea clutters. Using both concepts in designing a new detector, reveals considerable improvement in performance of target detection within sea clutter. In support of this argument, simulation results using real radar data samples are presented  

Concrete is a heterogeneous material with a wide variety of usage in structural design. Concrete under tension exhibits strain softening, i.e., a negative slope in the stress-deformation diagrams. Different softening curves have been proposed in the literature to interpret this phenomenon. In current research, a new softening curve for concrete has been proposed by using the newly introduced concept of fractal geometry. This new softening curve is denominated a 'Quasi-fractal' softening curve and consists of two parts, a linear portion at the beginning and an exponential portion in the rest of the curve. A comparison of a "Quasi-fractal" softening curve with a set of proposed experimental... 

Accurate modeling of sea clutter and detection of low observable targets within sea clutter are the major goals of radar signal processing applications. Recently, fractal geometry has been applied to the analysis of high range resolution radar sea clutters. The box-counting method is widely used to estimate fractal dimension but it has some drawbacks. We explain the drawbacks and propose a new fractal dimension based detector to increase detection performance in comparison with traditional detectors. Both statistically generated and real data samples are used to compare detector performance  

Reservoir heterogeneity has a major effect on the characterization of reservoir properties and consequently reservoir forecast. In reality, heterogeneity is observed in a wide range of scales from microns to kilometers. A reasonable approach to study this multi-scale variations is through fractals. Fractal statistics provide a simple way of relating variations on larger scales to those on smaller scales and vice versa. Simple statistical fractal models (fBm and fGn) can be useful to understand the model construction and help the reservoir structure characterization. In this paper, the fractal methods (fGn and fBm) have been applied to characterize and to estimate of reservoir properties.... 

Sea clutter refers to the radar returns from the sea surface. Accurate modelling of sea clutter and detection of low observable targets within sea clutter are major problems in remote sensing and radar signal processing applications. Recently fractal geometry is applied to the analysis of high range resolution radar sea clutters. The box-counting method is widely used to estimate fractal dimension but it has some drawbacks rarely considered in literature. We explain the problem of box size range and present a novel method to select an appropriate range  

This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's (2003 Eng. Fract. Mech. 70 1659-74) embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack. These results are then used in conjunction with the final stretch criterion to study the quasi-static stable crack extension, which in ductile materials precedes the global failure. The material...