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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 epub pdf  mobi txt 下载

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 epub pdf mobi txt 下载

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 epub pdf mobi txt 下载



[俄罗斯] 尤查金(Vladimir V.Uchaikin) 著

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发表于2020-01-23

商品介绍



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

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 epub pdf mobi txt 下载



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  《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

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

物理及工程中的分数维微积分(第2卷):应用(英文版) [Fractional Derivatives for Physicists and Engineers Volume Ⅱ Application epub pdf mobi txt 下载

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 下载 epub mobi pdf txt

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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 mobi pdf epub txt 下载

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 epub pdf mobi txt 下载

读者评价

评分

评分

  到现在为止,数学家们已经研究过200多种这样的代数结构,其中最主要德若当代数和李代数是不服从结合律的代数的例子。这些工作的绝大部分属于20世纪,它们使一般化和抽象化的思想在现代数学中得到了充分的反映。

评分

书不错,应该会很有用。下次把第一卷也买下来

评分

内容专业,适合专业人士使用

评分

评分

1870年,克隆尼克给出了有限阿贝尔群的抽象定义;狄德金开始使用“体”的说法,并研究了代数体;1893年,韦伯定义了抽象的体;1910年,施坦尼茨展开了体的一般抽象理论;狄德金和克隆尼克创立了环论;1910年,施坦尼茨总结了包括群、代数、域等在内的代数体系的研究,开创了抽象代数学。

评分

跟比自己大几岁的高中朋友聊了几句,他得出一个结论:“高中生懂的东西太简单了。”在15岁那年,他“心安理得”地走进了复旦大学的课堂。

评分

正版,送货快

评分

不得不说张首晟在某种意义上是一个“天才”——初中还没毕业,就赶上恢复高考,父亲拿给他一套数理化自学丛书,读了一个暑假,“试了一下”,他就考上了。

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 epub pdf mobi txt 下载

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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 epub pdf mobi txt 下载



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