This book provides theoretical concepts and applications of
fractals and multifractals to a broad range of audiences from
various scientific communities, such as petroleum, chemical, civil
and environmental engineering, atmospheric research, and hydrology.
In the first chapter, we introduce fractals and multifractals from
physics and math viewpoints. We then discuss theory and practical
applications in detail. In what follows, in chapter 2,
fragmentation process is modeled using fractals. Fragmentation is
the breaking of aggregates into smaller pieces or fragments, a
typical phenomenon in nature. In chapter 3, the advantages and
disadvantages of two- and three-phase fractal models are discussed
in detail. These two kinds of approach have been widely applied in
the literature to model different characteristics of natural
phenomena. In chapter 4, two- and three-phase fractal techniques
are used to develop capillary pressure curve models, which
characterize pore-size distribution of porous media. Percolation
theory provides a theoretical framework to model flow and transport
in disordered networks and systems. Therefore, following chapter 4,
in chapter 5 the fractal basis of percolation theory and its
applications in surface and subsurface hydrology are discussed. In
chapter 6, fracture networks are shown to be modeled using fractal
approaches. Chapter 7 provides different applications of fractals
and multifractals to petrophysics and relevant area in petroleum
engineering. In chapter 8, we introduce the practical advantages of
fractals and multifractals in geostatistics at large scales, which
have broad applications in stochastic hydrology and hydrogeology.
Multifractals have been also widely applied to model atmospheric
characteristics, such as precipitation, temperature, and cloud
shape. In chapter 9, these kinds of properties are addressed using
multifractals. At watershed scales, river networks have been shown
to follow fractal behavior. Therefore, the applications of fractals
are addressed in chapter 10. Time series analysis has been under
investigations for several decades in physics, hydrology,
atmospheric research, civil engineering, and water resources. In
chapter 11, we therefore, provide fractal, multifractal,
multifractal detrended fluctuation analyses, which can be used to
study temporal characterization of a phenomenon, such as flow
discharge at a specific location of a river. Chapter 12 addresses
signals and again time series using a novel fractal Fourier
analysis. In chapter 13, we discuss constructal theory, which has a
perspective opposite to fractal theories, and is based on
optimizationof diffusive exchange. In the case of river drainages,
for example, the constructal approach begins at the divide and
generates headwater streams first, rather than starting from the
fundamental drainage pattern.
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