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　　《物理及工程中的分數維微積分（第2捲）：應用（英文版）》適閤於對概率和統計、數學建模和數值模擬方麵感興趣的學生、工程師、物理學傢以及其他專傢和學者，以及任何不想錯過與這個越來越流行的數學方法接觸的讀者。

內容簡介

　　《物理及工程中的分數維微積分（第2捲）：應用（英文版）》的第1捲介紹分數維微積分的數學基礎和相應的理論，為這個現代分析學中的重要分支提供瞭詳細而又清晰的分析與介紹。第Ⅱ捲是應用篇，講述瞭分數維微積分在物理學中的實際的應用。在湍流與半導體、等離子與熱力學、力學與量子光學、納米物理學與天體物理學等學科應用方麵，《物理及工程中的分數維微積分（第2捲）：應用（英文版）》給讀者展示一個全新的處理方式和新銳的視角。

作者簡介

　　尤查金（Vladimir V.Uchaikin）教授為著名的俄羅斯科學傢，俄羅斯自然科學院院士。他在分數維領域研究瞭近40年，已發錶過300多篇論文並齣版10多部著作。

內頁插圖

目錄

Mechanics
7.1 Tautochrone problem
7.1.1 Non-relativistic case
7.1.2 Relativistic case
7.2 Inverse problems
7.2.1 Finding potential from a period-energy dependence
7.2.2 Finding potential from scattering data
7.2.3 Stellar systems
7.3 Motion through a viscous fluid
7.3.1 Entrainment of fluid by a moving wall
7.3.2 Newton's equation with fractional term
7.3.3 Solution by the Laplace transform method
7.3.4 Solution by the Green functions method
7.3.5 Fractionalized fall process
7.4 Fractional oscillations
7.4.1 Fractionalized harmonic oscillator
7.4.2 Linear chain of fractional oscillators
7.4.3 Fractionalized waves
7.4.4 Fractionalized Frenkel-Kontorova model
7.4.5 Oscillations of bodies in a viscous fluid
7.5 Dynamical control problems
7.5.1 PID controller and its fractional generalization
7.5.2 Fractional transfer functions
7.5.3 Fractional optimal control problem
7.6 Analytical fractional dynamics
7.6.1 Euler-Lagrange equation
7.6.2 Discrete system Hamiltonian
7.6.3 Potentials of non-concervative forces
7.6.4 Hamilton-Jacobi mechanics
7.6.5 Hamiltonian formalism for field theory

References
Continuum Mechanics
8.1 Classical hydrodynamics
8.1.1 A simple hydraulic problem
8.1.2 Liquid drop oscillations
8.1.3 Sound radiation
8.1.4 Deep water waves
8.2 Turbulent motion
8.2.1 Kolmogorov's model of turbulence
8.2.2 From Kolmogorov's hypothesis to the space-fractional equation
8.2.3 From Boltzmann's equation to the time-fractional telegraph one
8.2.4 Turbulent diffusion in a viscous fluid
8.2.5 Navier-Stokes equation
8.2.6 Reynolds' equation
8.2.7 Diffusion in lane flows
8.2.8 Subdiffusion in a random compressible flow
8.3 Fractional models of viscoelasticity
8.3.1 Two first models of fractional viscoelasticity
8.3.2 Fractionalized Maxwell model
8.3.3 Fractionalized Kelvin-Voigt model
8.3.4 Standard model and its generalization
8.3.5 Bagley-Torvik model
8.3.6 Hysteresis loop
8.3.7 Rabotnov's model
8.3.8 Compound mechanical models
8.3.9 The Rouse model of polymers
8.3.10 Hamiltonian dynamic approach
8.4 Viscoelastic fluids motion
8.4.1 Gerasimov's results
8.4.2 E1-Shahed-Salem solutions
8.4.3 Fractional Maxwell fluid： plain flow
8.4.4 Fractional Maxwell fluid： longitudinal flow in a cylinder
8.4.5 Magnetohydrodynamic flow
8.4.6 Burgers' equation
8.5 Solid bodies
8.5.1 Viscoelastic rods
8.5.2 Local fractional approach
8.5.3 Nonlocal approach

Reference
Porous Media
9.1 Diffusion
9.1.1 Main concepts of anomalous diffusion
9.1.2 Granular porosity
9.1.3 Fiber porosity
9.1.4 Filtration
9.1.5 MHD flow in porous media
9.1.6 Advection-diffusion model
9.1.7 Reaction-diffusion equations
9.2 Fractional acoustics
9.2.1 Lokshin-Suvorova equation
9.2.2 Schneider-Wyss equation
9.2.3 Matignon et al. equation
9.2.4 Viscoelastic loss operators
9.3 Geophysical applications
9.3.1 Water transport in unsaturated soils
9.3.2 Seepage flow
9.3.3 Foam Drainage Equation
9.3.4 Seismic waves
9.3.5 Multi-degree-of-freedom system of devices
9.3.6 Spatial-temporal distribution of aftershocks

References
10 Thermodynamics
10.1 Classical heat transfer theory
10.1.1 Heat flux through boundaries
10.1.2 Flux through a spherical surface
10.1.3 Splitting inhomogeneous equations
10.1.4 Heat transfer in porous media
10.1.5 Hyperbolic heat conduction equation
10.1.6 Inverse problems
10.2 Fractional heat transfer models
10.2.1 Fractional heat conduction laws
10.2.2 Fractional equations for heat transport
10.2.3 Application to thermoelasticity
10.2.4 Some irreversible processes
10.3 Phase transitions
10.3.1 Ornstein-Zernicke equation
10.3.2 Fractional Ginzburg-Landau equation
10.3.3 Classification of phase transitions
10.4 Around equilibrium
10.4.1 Relaxation to the thermal equilibrium
10.4.2 Fractionalization of the entropy

References
11 Electrodynamics
11.1 Electromagnetic field
11.1.1 Maxwell equations
11.1.2 Fractional multipoles
11.1.3 A link between two electrostatic images
11.1.4 "Intermediate" waves
11.2 Optics
11.2.1 Fractional differentiation method
11.2.2 Wave-diffusion model of image transfer
11.2.3 Superdiffusion transfer
11.2.4 Subdiffusion and combined （bifractional） diffusion

transfer models
11.3 Laser optics
11.3.1 Laser beam equation
11.3.2 Propagation of laser beam through fractal medium
11.3.3 Free electron lasers
11.4 Dielectrics
11.4.1 Phenomenology of relaxation
11.4.2 Cole-Cole process： macroscopic view
11.4.3 Microscopic view
11.4.4 Memory phenomenon
11.4.5 Cole-Davidson process
11.4.6 Havriliak-Negami process
11.5 Semiconductors
11.5.1 Diffusion in semiconductors
11.5.2 Dispersive transport： transient current curves
11.5.3 Stability as a consequence of self-similarity
11.5.4 Fractional equations as a consequence of stability
11.6 Conductors
11.6.1 Skin-effect in a good conductor
11.6.2 Electrochemistry
11.6.3 Rough surface impedance
11.6.4 Electrical line
11.6.5 Josephson effect

References
12 Quantum Mechanics
12.1 Atom optics
12.1.1 Atoms in an optical lattice
12.1.2 Laser cooling of atoms
12.1.3 Atomic force microscopy
12.2 Quantum particles
12.2.1 Kinetic-fractional Schodinger equation
12.2.2 Potential-fractional Schrodinger equation
12.2.3 Time-fractional Schrodinger equation
……
13 Plasma Dynamics
14 Cosmic Rays
15 Closing Chapter

Appendix A Some Special Functions
Appendix B Fractional Stable Densities
Appendix C Fractional Operators： Symbols and Formulas
Index
物理及工程中的分數維微積分（第2捲）：應用（英文版） [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application 下載 mobi epub pdf txt 電子書

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1870年，剋隆尼剋給齣瞭有限阿貝爾群的抽象定義；狄德金開始使用“體”的說法，並研究瞭代數體；1893年，韋伯定義瞭抽象的體；1910年，施坦尼茨展開瞭體的一般抽象理論；狄德金和剋隆尼剋創立瞭環論；1910年，施坦尼茨總結瞭包括群、代數、域等在內的代數體係的研究，開創瞭抽象代數學。

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