点击选择搜索分类
首页 - 医学文献- 正文
☆☆☆☆☆
||
[俄罗斯] 尤查金(Vladimir V.Uchaikin) 著
出版社: 高等教育出版社 ISBN:9787040307344 版次:1 商品编码:11123493 包装:精装 丛书名: 非线性物理科学 外文名称:Fractional Derivatives for Physicists and Engineers Volume Ⅱ Applications 开本:16开 出版时间:2013-01-01 用
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
物理及工程中的分数维微积分(第2卷):应用(英文版) [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application 电子书 下载 mobi epub pdf txt
物理及工程中的分数维微积分(第2卷):应用(英文版) [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application-so88
物理及工程中的分数维微积分(第2卷):应用(英文版) [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[俄罗斯] 尤查金(Vladimir V.Uchaikin) 著
出版社: 高等教育出版社 ISBN:9787040307344 版次:1 商品编码:11123493 包装:精装 丛书名: 非线性物理科学 外文名称:Fractional Derivatives for Physicists and Engineers Volume Ⅱ Applications 开本:16开 出版时间:2013-01-01 用
编辑推荐
《物理及工程中的分数维微积分(第2卷):应用(英文版)》适合于对概率和统计、数学建模和数值模拟方面感兴趣的学生、工程师、物理学家以及其他专家和学者,以及任何不想错过与这个越来越流行的数学方法接触的读者。内容简介
《物理及工程中的分数维微积分(第2卷):应用(英文版)》的第1卷介绍分数维微积分的数学基础和相应的理论,为这个现代分析学中的重要分支提供了详细而又清晰的分析与介绍。第Ⅱ卷是应用篇,讲述了分数维微积分在物理学中的实际的应用。在湍流与半导体、等离子与热力学、力学与量子光学、纳米物理学与天体物理学等学科应用方面,《物理及工程中的分数维微积分(第2卷):应用(英文版)》给读者展示一个全新的处理方式和新锐的视角。作者简介
尤查金(Vladimir V.Uchaikin)教授为著名的俄罗斯科学家,俄罗斯自然科学院院士。他在分数维领域研究了近40年,已发表过300多篇论文并出版10多部著作。内页插图
目录
Mechanics7.1 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
物理及工程中的分数维微积分(第2卷):应用(英文版) [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 贪玩的人类——那些将我们带进科学的人 9787030271341 李建荣(老多)-RT
- 【精装彩印礼盒装】正版现货陆俨少画集礼盒装彩印16开共2卷中国现代名家画集山水画刍议书籍国画全集书法
- 缤纷的生命 [美]爱德华·威尔逊 金恒镳
- 绘画快速入门教程--素描头像+石膏头像 全两册 素描(石膏几何体石膏人像静物人物头像) 李家友主编
- 解读地球密码 中生代霸主:恐龙
- 无所事事的夏天 治愈系的水彩画入门 飞乐鸟工作室 水利水电出版社
- 带领孩子走向何方-中国文化下的教育
- 政府绩效管理:理论与实践的双重变奏
- 发明总动员 李正明
- 中国政党制度发展史论 [The History of China Political Party System]
- 品尝的科学:从地球生命的口:到饮食科学研究前沿 9787550299931
- 美人绘色铅笔人物画入门 彩色铅笔人物绘 彩铅入门基础教程书籍
- 探秘世界之最(学生版)/探索天下
- 二战风云 二战绝密档案 第二次世界大战史 历史军事战争系列 二战全史 二战解密回忆录世界通史
- 让我们运动吧!-听爸爸讲科普-(低幼版)