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Informationen zum Autor Dr. Su is Adjunct Professor at James Cook University, Australia and Guest Professor at Ningxia University, China. He was previously Guest Professor at several universities in China. He received a PhD at the Australian National University, MSc at the Institute of Soil and Water Conservation, the Chinese Academy of Sciences, and BSc at the College of Agricultural Science, Ningxia University. His research interests span several fields including hydrology, environmental modelling and applications of fractional calculus, which have evolved while working in Australia, China and New Zealand. Zusammenfassung This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications. Inhaltsverzeichnis Application of Fractional Calculus in Water Flow and Related Processes Overview Objectives of this book A brief description of key concepts Notation in the book Mathematical Preliminaries Introduction Integral transforms Asymptotic analysis Special Functions Fundamental solution, Green function, delta functions and generalized functions Fractional integration and fractional differentiation Summary Essential Properties of Soils and Aquifers as Porous Media Introduction: Soils and aquifers as porous media Descriptive concepts and definitions of soils and aquifers Fundamental equations of flow in soils and aquifers Applicability of Darcy’s law Traditional and new parameters for hydraulic properties Similarity, scales, models and measurements Other forces coupled with the flow of fluids in porous media Heterogeneities and isotropy Summary Transition from Classic Diffusion to Anomalous Diffusion– The evolution of concepts and ideas Introduction The inception of models based on fractional calculus in geoscience and related fields Theory, models and parameters for water flow and solute transport in porous media Relationships and differences between anomalous diffusion and scale-dependent and time-dependent transport processes Dimensions of the parameters in fPDEs Variable-order fractional derivatives and related fPDEs Summary Fractional Partial Differential Equations for Water Movement in Soils Introduction Integer calculus-based models for water flow in soils Fractional calculus-based models for water movement in soils Conservation of mass in the context of fPDEs fPDEs for coupled water movement, energy transfer, gas flow and solute transport in porous media Functional-order fractional partial differential equations Exchange of water between mobile and immobile zones Summary Applications of Fractional Partial Differential Equations to Infiltration and Water Movement in Soils Introduction Background and connections between different equations of infiltration Equations of infiltration derived from fractional calculus with the concentration boundary condition Infiltration into soils on hillslopes Infiltration equations derived from an fPDE with a given flux on the soil surface Water exchange between large and small pores Example of solutions for water movement in a soil of finite depth Summary Fractional Differential Equations for Solute Transport in Soils Introduction Solute transport in non-swelling soils Concurrent water flow and solute transport in swelling soils Fractional Partial Differential Equations for Anomalous Solute Transport in Soils Dimensions of the parameters in...
