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物理科学中的奇异摄动（影印版）
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物理科学中的奇异摄动（影印版）
样章
作者：
John C. Neu
定价：
135.00元
ISBN：
978-7-04-063249-1
版面字数：
550.00千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2025-02-14
物料号：
63249-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
计算数学
购买：
样章阅读
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图书目录
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前辅文
Acknowledgments
Introduction
Chapter 1. What is a singular perturbation?
Prototypical examples
Singularly perturbed polynomial equations
Radiation reaction
Problem 1.1: Bad truncations
Problem 1.2: Harmonic oscillator with memory, and even worse truncations
Convection-diffusion boundary layer
Problem 1.3: A simple boundary layer
Problem 1.4: Pileup near x = 0
Modulated oscillations
Problem 1.5: Secular terms
Problem 1.6: Approach to limit cycle
Problem 1.7: Adiabatic invariant for particle in a box
Guide to bibliography
Chapter 2. Asymptotic expansions
Problem 2.1: Uniqueness
A divergent but asymptotic series
Problem 2.2: Divergent outer expansion
Problem 2.3: Another outrageous example
Asymptotic expansions of integrals — the usual suspects
Problem 2.4: Simple endpoint examples
Problem 2.5: Stirling approximation to n!
Problem 2.6: Endpoint and minimum both contribute
Problem 2.7: Central limit theorem
Steepest descent method
Chasing the waves with velocity v >0
No waves for v <0
Problem 2.8: Steepest descent asymptotics
A primer on linear waves
Problem 2.9: Amplitude transport
Problem 2.10: How far was that meteor?
Problem 2.11: Wave asymptotics in non-uniform medium
A hard logarithmic expansion
Problem 2.12: Logarithmic expansion
Guide to bibliography
Chapter 3. Matched asymptotic expansions
Problem 3.1: Physical scaling analysis of boundary layer thickness
Problem 3.2: Higher-order matching
Problem 3.3: Absorbing boundary condition
Matched asymptotic expansions in practice
Problem 3.4: Derivative layer
Corner layers and internal layers
Problem 3.5: Phase diagram
Problem 3.6: Internal derivative layer
Problem 3.7: Where does the kink go?
Guide to bibliography
Chapter 4. Matched asymptotic expansions in PDE’s
Moving internal layers
Chapman–Enskog asymptotics
Problem 4.1: Relaxation of kink position
Problem 4.2: Hamilton–Jacobi equation from front motion
Problem 4.3: Chapman–Enskog asymptotics
Projected Lagrangian
Problem 4.4: Circular fronts in nonlinear wave equation
Problem 4.5: Solitary wave dynamics in two dimensions
Problem 4.6: Solitary wave diffraction
Singularly perturbed eigenvalue problem
Homogenization of swiss cheese
Problem 4.7: Neumann boundary conditions and effective dipoles
Problem 4.8: Two dimensions
Guide to bibliography
Chapter 5. Prandtl boundary layer theory
Stream function and vorticity
Preliminary non-dimensionalization
Outer expansion and “dry water”
Inner expansion
Problem 5.1: Vector calculus of boundary layer coordinates
Leading order matching and a first integral
Problem 5.2: The body surface is a source of vorticity
Problem 5.3: Downstream evolution
Displacement thickness
Solutions based on scaling symmetry
Blasius flow over flat plate
Nonzero wedge angles (m≠0)
Precursor of boundary layer separation
Problem 5.4: Wedge flows with source
Problem 5.5: Mixing by vortex
Guide to bibliography
Chapter 6. Modulated oscillations
Physical flavors of modulated oscillations
Problem 6.1: Beats
Problem 6.2: The beat goes on
Problem 6.3: Wave packets as beats in spacetime
Problem 6.4: Adiabatic invariant of harmonic oscillator
Problem 6.5: Passage through resonance for harmonic oscillator
Problem 6.6: Internal resonance between waves on a ring
Method of two scales
Problem 6.7: Nonlinear parametric resonance
Problem 6.8: Forced van der Pol ODE
Problem 6.9: Inverted pendulum
Strongly nonlinear oscillations and action
Problem 6.10: Energy, action and frequency
Problem 6.11: Hamiltonian analysis of the adiabatic invariant
Problem 6.12: Poincar´e analysis of nonlinear oscillations
A primer on nonlinear waves
Modulation Lagrangian
Problem 6.13: Nonlinear geometric attenuation
Problem 6.14: Modulational instability
A primer on homogenization theory
Problem 6.15: Direct homogenization
Guide to bibliography
Chapter 7. Modulation theory by transforming variables
Transformations in classical mechanics
Problem 7.1: Geometry of action-angle variables
Problem 7.2: Stokes expansion for quadratically nonlinear oscillator
Problem 7.3: Frequency-action relation
Problem 7.4: Follow the bouncing ball
Near-identity transformations
Problem 7.5: van der Pol ODE by near-identity transformations
Problem 7.6: Subtle balance between positive and negative damping
Problem 7.7: Adiabatic invariants again
Dissipative perturbations of the Kepler problem
Modulation theory of damped orbits
Guide to bibliography
Chapter 8. Nonlinear resonance
Problem 8.1: Modulation theory of resonance
A prototype example
What resonance looks like
Problem 8.2: Resonance of the bouncing ball
Problem 8.3: Resonance by rebounds off a vibrating wall
Generalized resonance
Energy beats
Modulation theory of generalized resonance
Problem 8.4: Modulation theory for generalized resonance
Thickness of the resonance annulus
Asymptotic isolation of resonances
Guide to bibliography
Bibliography
Index
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