Fractional Dispersive Models And Applications

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

This book highlights original research and high-quality technical briefs on electromagnetic wave propagation, radiation, and scattering, and their applications in industry and biomedical engineering. It also presents recent research achievements in the theoretical, computational, and experimental aspects of electromagnetic wave propagation, radiation, and scattering. The book is divided into three sections. Section 1 consists of chapters with general mathematical methods and approaches to the forward and inverse problems of wave propagation. Section 2 presents the problems of wave propagation in superconducting materials and porous media. Finally, Section 3 discusses various industry and biomedical applications of electromagnetic wave propagation, radiation, and scattering.

Mankind has manipulated the quantity and quality of soil water for millennia. Food production was massively increased through fertilization, irrigation and drainage. But malpractice also caused degradation of immense areas of once fertile land, rendering it totally unproductive for many generations. In populated areas, the pollutant load ever more often exceeds the soil’s capacity for buffering and retention, and large volumes of potable groundwater have been polluted or are threatened to be polluted in the foreseeable future. In the past decades, the role of soil water in climate patterns has been recognized but not yet fully understood. The soil-science community responded to this diversity of issues by developing numerical models to simulate the behavior of water and solutes in soils. These models helped improve our understanding of unsaturated-zone processes and develop sustainable land-management practices. Aimed at professional soil scientists, soil-water modelers, irrigation engineers etc., this book discusses our progress in soil-water modeling. Top scientists present case studies, overviews and analyses of strengths, weaknesses, opportunities and threats related to soil-water modeling. The contributions cover a wide range of spatial scales, and discuss fundamental aspects of unsaturated-zone modeling as well as issues related to the application of models to real-world problems.

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.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.