Fractional Calculus for Hydrology, Soil Science and Geomechanics
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portes grátis
Fractional Calculus for Hydrology, Soil Science and Geomechanics
An Introduction to Applications
Su, Ninghu
Taylor & Francis Ltd
11/2020
358
Dura
Inglês
9781138491663
15 a 20 dias
725
Descrição não disponível.
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 multi-term fPDEs
Functional-order fPDEs
The fPDE and its solution for solute exchange between mobile and immobile zones
Fractional flux-residential solute concentration relationships during anomalous transport
Applications of fPDEs for coupled solute transport in swelling and non-swelling soils
Summary
Hydraulics of Anomalous Flow on Hillslopes, in Catchment Networks and Irrigated Fields
Introduction
Rainfall-infiltration-runoff relations on a planar hillslope
Rainfall-infiltration-runoff relations on convergent and divergent hillslopes
Solute transport by runoff on hillslopes
Related topics
Streamflow through catchment networks
Anomalous flow during irrigation
Summary
Fractional Partial Differential Equations for Groundwater Flow
Introduction
Governing equations for isothermal groundwater flow in confined aquifers
Governing equation for groundwater flow in unconfined aquifers
Unified concepts and equations for groundwater flow in confined and unconfined aquifers
Radial flow and hydraulics of wells in confined and unconfined aquifers
Earth tides and barometric effects on groundwater
Other factors related to model construction for groundwater flow
fPDEs for isothermal groundwater flow in unconfined aquifers
fPDEs for isothermal groundwater flow in confined aquifers
Distributed-order fPDEs in Cartesian coordinates
fPDEs for hydraulics of anomalous radial flow in wells on a horizontal base
Exchange of water between mobile and immobile zones
Example: Solutions of fPDEs for groundwater flow in aquifers subject to boundary conditions of the first kind
Groundwater flow as a multiphase flow
Summary
Fractional Partial Differential Equations for Solute Transport in Groundwater
Introduction
fPDE-based models for solute transport in different dimensions
Fractional conservation of mass
Symmetrical fADE for solute transport
fPDEs for reactive solute transport with sink and source terms
fPDEs of distributed order for solute transport in aquifers
Solute transfer between mobile and immobile zones
fPDEs for flux and residential solute relationships
fPDEs of distributed order and their asymptotic solutions
Radial anomalous solute transport in groundwater
Functional-order fPDEs
Multi-dimensional symmetrical fPDEs with variable and functional orders
Tempered anomalous solute transport
Summary
Fractional Partial Differential Equations, Poroviscoelastic Media and Geomechanics
Introduction
Basic concepts regarding poroviscoelastic materials, and relationships between them
Approaches to viscoelastic materials with linear elasticity
Fractional calculus-based models for linear viscoelasticity and poroviscoelasticity
Summary
Bibliography
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 multi-term fPDEs
Functional-order fPDEs
The fPDE and its solution for solute exchange between mobile and immobile zones
Fractional flux-residential solute concentration relationships during anomalous transport
Applications of fPDEs for coupled solute transport in swelling and non-swelling soils
Summary
Hydraulics of Anomalous Flow on Hillslopes, in Catchment Networks and Irrigated Fields
Introduction
Rainfall-infiltration-runoff relations on a planar hillslope
Rainfall-infiltration-runoff relations on convergent and divergent hillslopes
Solute transport by runoff on hillslopes
Related topics
Streamflow through catchment networks
Anomalous flow during irrigation
Summary
Fractional Partial Differential Equations for Groundwater Flow
Introduction
Governing equations for isothermal groundwater flow in confined aquifers
Governing equation for groundwater flow in unconfined aquifers
Unified concepts and equations for groundwater flow in confined and unconfined aquifers
Radial flow and hydraulics of wells in confined and unconfined aquifers
Earth tides and barometric effects on groundwater
Other factors related to model construction for groundwater flow
fPDEs for isothermal groundwater flow in unconfined aquifers
fPDEs for isothermal groundwater flow in confined aquifers
Distributed-order fPDEs in Cartesian coordinates
fPDEs for hydraulics of anomalous radial flow in wells on a horizontal base
Exchange of water between mobile and immobile zones
Example: Solutions of fPDEs for groundwater flow in aquifers subject to boundary conditions of the first kind
Groundwater flow as a multiphase flow
Summary
Fractional Partial Differential Equations for Solute Transport in Groundwater
Introduction
fPDE-based models for solute transport in different dimensions
Fractional conservation of mass
Symmetrical fADE for solute transport
fPDEs for reactive solute transport with sink and source terms
fPDEs of distributed order for solute transport in aquifers
Solute transfer between mobile and immobile zones
fPDEs for flux and residential solute relationships
fPDEs of distributed order and their asymptotic solutions
Radial anomalous solute transport in groundwater
Functional-order fPDEs
Multi-dimensional symmetrical fPDEs with variable and functional orders
Tempered anomalous solute transport
Summary
Fractional Partial Differential Equations, Poroviscoelastic Media and Geomechanics
Introduction
Basic concepts regarding poroviscoelastic materials, and relationships between them
Approaches to viscoelastic materials with linear elasticity
Fractional calculus-based models for linear viscoelasticity and poroviscoelasticity
Summary
Bibliography
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Fractional Derivatives;Fractional Partial Differential Equations;water infiltration and movement in soils and aquifers;Soil Science;heat transfer in soils and aquifers;Immobile Zones;movement of nutrients, solutes and contaminants in soils and aquifers;Fractional Calculus;analytical solutions and numerical methods for fractional partial differential equations;Moisture Content;mechanics of fluid flow and material transport in swelling and viscoelastic media;Non-swelling Soils;hydrology;Porous Media;Time Fractional Diffusion Equation;geomechanics;Swelling Soils;Fractional PDEs;Residential Solute Concentrations;Confined Aquifers;Unconfined Aquifers;Solute Transport;Laplace Transform;Cumulative Infiltration;Functional Order;Hydraulic Conductivity;Mittag Leffler Function;Fractional Diffusion Wave Equation;Space Fractional Derivative;Asymptotic Solution;Hydraulic Head;Final Infiltration Rate
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 multi-term fPDEs
Functional-order fPDEs
The fPDE and its solution for solute exchange between mobile and immobile zones
Fractional flux-residential solute concentration relationships during anomalous transport
Applications of fPDEs for coupled solute transport in swelling and non-swelling soils
Summary
Hydraulics of Anomalous Flow on Hillslopes, in Catchment Networks and Irrigated Fields
Introduction
Rainfall-infiltration-runoff relations on a planar hillslope
Rainfall-infiltration-runoff relations on convergent and divergent hillslopes
Solute transport by runoff on hillslopes
Related topics
Streamflow through catchment networks
Anomalous flow during irrigation
Summary
Fractional Partial Differential Equations for Groundwater Flow
Introduction
Governing equations for isothermal groundwater flow in confined aquifers
Governing equation for groundwater flow in unconfined aquifers
Unified concepts and equations for groundwater flow in confined and unconfined aquifers
Radial flow and hydraulics of wells in confined and unconfined aquifers
Earth tides and barometric effects on groundwater
Other factors related to model construction for groundwater flow
fPDEs for isothermal groundwater flow in unconfined aquifers
fPDEs for isothermal groundwater flow in confined aquifers
Distributed-order fPDEs in Cartesian coordinates
fPDEs for hydraulics of anomalous radial flow in wells on a horizontal base
Exchange of water between mobile and immobile zones
Example: Solutions of fPDEs for groundwater flow in aquifers subject to boundary conditions of the first kind
Groundwater flow as a multiphase flow
Summary
Fractional Partial Differential Equations for Solute Transport in Groundwater
Introduction
fPDE-based models for solute transport in different dimensions
Fractional conservation of mass
Symmetrical fADE for solute transport
fPDEs for reactive solute transport with sink and source terms
fPDEs of distributed order for solute transport in aquifers
Solute transfer between mobile and immobile zones
fPDEs for flux and residential solute relationships
fPDEs of distributed order and their asymptotic solutions
Radial anomalous solute transport in groundwater
Functional-order fPDEs
Multi-dimensional symmetrical fPDEs with variable and functional orders
Tempered anomalous solute transport
Summary
Fractional Partial Differential Equations, Poroviscoelastic Media and Geomechanics
Introduction
Basic concepts regarding poroviscoelastic materials, and relationships between them
Approaches to viscoelastic materials with linear elasticity
Fractional calculus-based models for linear viscoelasticity and poroviscoelasticity
Summary
Bibliography
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 multi-term fPDEs
Functional-order fPDEs
The fPDE and its solution for solute exchange between mobile and immobile zones
Fractional flux-residential solute concentration relationships during anomalous transport
Applications of fPDEs for coupled solute transport in swelling and non-swelling soils
Summary
Hydraulics of Anomalous Flow on Hillslopes, in Catchment Networks and Irrigated Fields
Introduction
Rainfall-infiltration-runoff relations on a planar hillslope
Rainfall-infiltration-runoff relations on convergent and divergent hillslopes
Solute transport by runoff on hillslopes
Related topics
Streamflow through catchment networks
Anomalous flow during irrigation
Summary
Fractional Partial Differential Equations for Groundwater Flow
Introduction
Governing equations for isothermal groundwater flow in confined aquifers
Governing equation for groundwater flow in unconfined aquifers
Unified concepts and equations for groundwater flow in confined and unconfined aquifers
Radial flow and hydraulics of wells in confined and unconfined aquifers
Earth tides and barometric effects on groundwater
Other factors related to model construction for groundwater flow
fPDEs for isothermal groundwater flow in unconfined aquifers
fPDEs for isothermal groundwater flow in confined aquifers
Distributed-order fPDEs in Cartesian coordinates
fPDEs for hydraulics of anomalous radial flow in wells on a horizontal base
Exchange of water between mobile and immobile zones
Example: Solutions of fPDEs for groundwater flow in aquifers subject to boundary conditions of the first kind
Groundwater flow as a multiphase flow
Summary
Fractional Partial Differential Equations for Solute Transport in Groundwater
Introduction
fPDE-based models for solute transport in different dimensions
Fractional conservation of mass
Symmetrical fADE for solute transport
fPDEs for reactive solute transport with sink and source terms
fPDEs of distributed order for solute transport in aquifers
Solute transfer between mobile and immobile zones
fPDEs for flux and residential solute relationships
fPDEs of distributed order and their asymptotic solutions
Radial anomalous solute transport in groundwater
Functional-order fPDEs
Multi-dimensional symmetrical fPDEs with variable and functional orders
Tempered anomalous solute transport
Summary
Fractional Partial Differential Equations, Poroviscoelastic Media and Geomechanics
Introduction
Basic concepts regarding poroviscoelastic materials, and relationships between them
Approaches to viscoelastic materials with linear elasticity
Fractional calculus-based models for linear viscoelasticity and poroviscoelasticity
Summary
Bibliography
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Fractional Derivatives;Fractional Partial Differential Equations;water infiltration and movement in soils and aquifers;Soil Science;heat transfer in soils and aquifers;Immobile Zones;movement of nutrients, solutes and contaminants in soils and aquifers;Fractional Calculus;analytical solutions and numerical methods for fractional partial differential equations;Moisture Content;mechanics of fluid flow and material transport in swelling and viscoelastic media;Non-swelling Soils;hydrology;Porous Media;Time Fractional Diffusion Equation;geomechanics;Swelling Soils;Fractional PDEs;Residential Solute Concentrations;Confined Aquifers;Unconfined Aquifers;Solute Transport;Laplace Transform;Cumulative Infiltration;Functional Order;Hydraulic Conductivity;Mittag Leffler Function;Fractional Diffusion Wave Equation;Space Fractional Derivative;Asymptotic Solution;Hydraulic Head;Final Infiltration Rate
