考研網 » 考試圖書 » 英文版 » Waves and structures in nonlinear nondispersive media:Genera.. » 全部考試圖書分類

圖書簡介

     本書結合數學模型介紹了非線性非分散介質中的波和結構的基礎理論。全書分成兩部分：第ⅰ部分給出了很多具體的例子，用于闡明一般的分析方法；第ⅱ部分主要介紹非線性聲學的應用，內容包括一些具體的非線性模型及其精確解，非線性的物理機理，鋸齒形波的傳播，自反應現象，非線性共振及在工程、醫學、非破壞性試驗、地球物理學等的應用。
     本書是碩士生和博士生學習具有各種物理性質的非線性波理論非常實用的教材，也是工程師和研究人員在研究工作中遇到需要考慮和處理非線性波因素時一本很好的參考書。

目錄

part i foundations of the theory of waves in nondispersive media
1 nonlinear equations of the first order
　1.1 simple wave equation
　　1.1.1 the canonical form of the equation
　　1.1.2 particle flow
　　1.1.3 discussion of the riemann solution
　　1.1.4 compressions and expansions of the particle flow
　　1.1.5 continuity equation
　　1.1.6 construction of the density field
　　1.1.7 momentum-conservation law
　　1.1.8 fourier transforms of density and velocity
　1.2 line-growth equation
　　1.2.1 forest-fire propagation
　　1.2.2 anisotropic surface growth
　　1.2.3 solution of the surface-growth equation
　1.3 one-dimensional laws of gravitation
　　1.3.1 lagrangian description of one-dimensional gravitation
　　1.3.2 eulerian description of one-dimensional gravitation
　　1.3.3 collapse of a one-dimensional universe
　1.4 problems to chapter 1
　　references
2 generalized solutions of nonlinear equations
　2.1 standard equations
　　2.1.1 particle-flow equations
　　2.1.2 line growth in the small angle approximation
　　2.1.3 nonlinear acoustics equation
　2.2 multistream solutions
　　2.2.1 interval of single-stream motion
　　2.2.2 appearance of multistreamness
　　2.2.3 gradient catastrophe
　2.3 sum of streams
　　2.3.1 total particle flow
　　2.3.2 summation of streams by inverse fourier transform
　　2.3.3 algebraic sum of the velocity field
　　2.3.4 density of a "warm" particle flow
　2.4 weak solutions of nonlinear equations of the first order
　　2.4.1 forest fire
　　2.4.2 the lax-oleinik absolute minimum principle
　　2.4.3 geometric construction of weak solutions
　　2.4.4 convex hull
　　2.4.5 maxwell's rule
　2.5 the e-rykov-sinai global principle
　　2.5.1 flow of inelasfically coalescing particles
　　2.5.2 inelastic collisions of particles
　　2.5.3 formulation of the global principle
　　2.5.4 mechanical meaning of the global principle
　　2.5.5 condition of physical realizability
　　2.5.6 geometry of the global principle
　　2.5.7 solutions of the continuity equation
　2.6 line-growth geometry
　　2.6.1 parametric equations of a line
　　2.6.2 contour in polar coordinates
　　2.6.3 contour envelopes
　2.7 problems to chapter 2
　　references
3 nonlinear equations of the second order
　3.1 regularization of nonlinear equations
　　3.1.1 the kardar-parisi-zhang equation
　　3.1.2 the burgers equation
　3.2 properties of the burgers equation
　　3.2.1 galilean invariance
　　3.2.2 reynolds number
　　3.2.3 hubble expansion
　　3.2.4 stationary wave
　　3.2.5 khokhlov's solution
　　3.2.6 rudenko's solution
　3.3 general solution of the burgers equation
　　3.3.1 the hopf-cole substitution
　　3.3.2 general solution of the burgers equation
　　3.3.3 averaged lagrangian coordinate
　　3.3.4 solution of the burgers equation with vanishing viscosity
　3.4 model equations of gas dynamics
　　3.4.1 one-dimensional model of a polytropic gas
　　3.4.2 discussion of physical properties of a model gas
　3.5 problems to chapter 3
　　references
4 field evolution within the framework of the burgers equation
　4.1 evolution of one-dimonsional signals
　　4.1.1 self-similar solution, once more
　　4.1.2 approach to the linear stage
　　4.1.3 n-wave and u-wave
　　4.1.4 sawtooth waves
　　4.1.5 periodic waves
　4.2 evolution of complex signals
　　4.2.1 quasiperiodic complex signals
　　4.2.2 evolution of fractal signals
　　4.2.3 evolution of multi-scale signals - a dynamic turbulence model
　4.3 problems to chapter 4
　　references
5 evolution of a noise field within the framework of the burgers equation
　5.1 burgers turbulence - acoustic turbulence
　5.2 the burgers turbulence at the initial stage of evolution
　　5.2.1 one-point probability density of a random eulerian velocity field
　　5.2.2 properties of the probability density of a random velocity field
　　5.2.3 spectra of a velocity field
　5.3 turbulence evolution at the stage of developed discontinuities
　　5.3.1 phenomenology of the burgers turbulence
　　5.3.2 evolution of the burgers turbulence: statistically homogeneous potential and velocity (n ] 1 and n [ -3)
　　5.3.3 exact self-similarity (n ] 2)
　　5.3.4 violation of self-similarity (1 [ n [ 2)
　　5.3.5 evolution of turbulence: statistically inhomogeneous potential (-3 [ n [ 1)
　　5.3.6 statistically homogeneous velocity and inhomogeneous potential (-1 [ n [ 1)
　　5.3.7 statistically inhomogeneous velocity and in_homogeneous potential (-3 [ n [ -1)
　　5.3.8 evolution of intense acoustic noise
　　references
6 multidimensional nonlinear equations
　6.1 nonlinear equations of the first order
　　6.1.1 main equations of three-dimensional flows
　　6.1.2 lagrangian and eulerian description of a three-dimentional low
　　6.1.3 jacobian matrix for the transformation from lagrangian to eulerian coordinates
　　6.1.4 density of a multidimensional flow
　　6.1.5 weak solution of the surface-growth equation
　　6.1.6 flows of locally interacting particles and a singular density field
　6.2 multidimensional nonlinear equations of the second order
　　6.2.1 the two-dimensional kpz equation
　　6.2.2 the three-dimensional burgers equation
　　6.2.3 model density field
　　6.2.4 concentration field
　6.3 evolution of the main perturbation types in the kpz equation and
　　in the multidimensional burgers equation
　　6.3.1 asymptotic solutions of the multidimensional burgers equation and local self-similarity
　　6.3.2 evolution of simple localized perturbations
　　6.3.3 evolution of periodic structures under infinite reynolds numbers
　　6.3.4 evolution of the anisotropic burgers turbulence
　　6.3.5 evolution of perturbations with complex internal structure
　　6.3.6 asymptotic long-time behavior of a localized perturbation
　　6.3.7 appendix to section 6.3. statistical properties of maxima of inhomogeneous random gaussian fields
　6.4 model description of evolution of the large-scale structure of the universe
　　6.4.1 gravitational instability in an expanding universe
　　6.4.2 from the vlasov~poisson equation to the zeldovich approximation and adhesion model
　　references
　　part ii mathematical models and physical phenomena in nonlinear acoustics
7 model equations and methods of finding their exact solutions
　7.1 introduction
　　7.1.1 facts from the linear theory
　　7.1.2 how to add nonlinear terms to simplified equations
　　7.1.3 more general evolution equations
　　7.1.4 two types of evolution equations
　7.2 lie groups and some exact solutions
　　7.2.1 exact solutions of the burgers equation
　　7.2.2 finding exact solutions of the burgers equation by using the group-theory methods
　　7.2.3 some methods of finding exact solutions
　7.3 the a priori symmetry method
　　references
8 types of acoustic nonlinearities and methods of nonlinear acoustic diagnostics
　8.1 introduction
　　8.1.1 physical and geometric nonlinearities
　8.2 classification of types of acoustic nonlinearity
　　8.2.1 boundary nonlinearities
　8.3 some mechanisms of bulk structural nonlinearity
　　8.3.1 nonlinearity of media with strongly compressible inclusions
　　8.3.2 nonlinearity of solid structurally inhomogeneous media
　8.4 nonlinear diagnostics
　　8.4.1 inverse problems of nonlinear diagnostics
　　8.4.2 peculiarities of nonlinear diagnostics problems
　8.5 applications of nonlinear diagnostics methods
　　8.5.1 detection of bubbles in a liquid and cracks in a solid
　　8.5.2 measurements based on the use of radiation pressure
　　8.5.3 nonlinear acoustic diagnostics in construction industry
　8.6 non-typical nonlinear phenomena in structurally inhomogeneous media
　　references
9 nonlinear sawtooth waves
　9.1 sawtooth waves
　9.2 field and spectral approaches in the theory of nonlinear waves
　　9.2.1 general remarks
　　9.2.2 generation of harmonics
　　9.2.3 degenerate parametric interaction
　9.3 diffracting beams of sawtooth waves
　9.4 waves in inhomogeneous media and nonlinear geometric acoustics
　9.5 the focusing of discontinuous waves
　9.6 nonlinear absorption and saturation
　9.7 kinetics of sawtooth waves
　9.8 interaction of waves containing shock fronts
　　references
10 self-action of spatially bounded waves containing shock fronts
　10.1 introduction
　10.2 self-action of sawtooth ultrasonic wave beams due to the heating of a medium and acoustic wind formation
　10.3 self-refraction of weak shock waves in a quardatically nonlinear medium
　10.4 non-inertial self-action in a cubically nonlinear medium
　10.5 symmetries and conservation laws for an evolution equation describing beam propagation in a nonlinear medium
　10.6 conclusions
　　references
11 nonlinear standing waves, resonance phenomena and frequency characteristics of distributed systems
　11.1 introduction
　11.2 methods of evaluation of the characteristics of nonlinear resonators
　11.3 standing waves and the q-factor of a resonator filled with a dissipating medium
　11.4 frequency responses of a quadratically nonlinear resonator
　11.5 q-factor increase under introduction of losses
　11.6 geometric nonlinearity due to boundary motion
　11.7 resonator filled with a cubically nonlinear medium
　　references
　　appendix fundamental properties of generalized functions
　a.1 definition of generalized functions
　a.2 fundamental sequences
　a.3 derivatives of generalized functions
　a.4 the leibniz formula
　a.5 derivatives of discontinuous functions
　a.6 generalized functions of a composite argument
　a.7 multidimensional generalized functions
　a.8 continuity equation
　a.8.1 singular solution
　a.8.2 green's function
　a.8.3 lagrangian and eulerian coordinates
　a.9 method of characteristics inde

同類熱銷圖書

書名	作者	出版社	價格	購買
愛的教育（典藏英文原版）——英語學習者必讀！200年來最..	艾德蒙多·..	延邊人民出版社	￥25.00 ￥15.00	詳情
美國語文(英文原版)(精裝版)(套裝共6冊）	威廉•..	天津人民出版社	￥158.00 ￥109.00	詳情
飄（英文版）	（美）米切..	外文出版社	￥36.00 ￥27.90	詳情
傲慢與偏見-世界經典讀本（英文原版）	（英）奧斯..	中央編譯出版社	￥28.00 ￥17.10	詳情
小婦人（典藏英文原版）——英語學習者課外必讀！打動萬千..	（美）奧爾..	延邊人民出版社	￥47.00 ￥26.00	詳情
英文經典－傲慢與偏見(英文版)	〔英國〕簡..	譯林出版社	￥32.00 ￥22.10	詳情
呼嘯山莊（典藏英文原版）——唯一未經刪減與修改的版本，..	（英）勃朗..	延邊人民出版社	￥16.80 ￥13.50	詳情
紅樓夢（全三卷）	（清）曹雪..	外文出版社	￥198.00 ￥151.40	詳情
當幸福來敲門（英文版）——新東方英語培訓必看電影	（美）加德..	清華大學出版社	￥45.80 ￥33.10	詳情
京華煙云(林語堂英文作品集)(月亮石)——林語堂先生最自豪..	林語堂 著	外語教學與研究出..	￥49.90 ￥40.80	詳情
Reader's Choice讀者的選擇（第4版）	馬克·A·..	世界圖書出版公司	￥49.00 ￥36.80	詳情
霧都孤兒（典藏英文原版）——英語學習者課外必讀！完美再..	查爾斯·狄..	延邊人民出版社	￥45.00 ￥25.00	詳情
狼圖騰（英文版）	姜戎 著，..	長江文藝出版社	￥96.00 ￥72.00	詳情
英漢對照:每天讀點英文經典短篇小說全集（典藏英文全集 36..	馬鐘元 ..	中國宇航出版社	￥39.80 ￥29.90	詳情
丁曉鐘-英美外刊超精讀	丁曉鐘　主..	哈爾濱工程大學出..	￥52.00 ￥37.80	詳情
影響你一生的47部電影(附MP3)（賞好片，學英語，一書在手..	《新東方英..	西安交通大學出版..	￥29.80 ￥22.00	詳情
飄-世界經典讀本（1.2）（英文原版）	（美）米切..	中央編譯出版社	￥68.00 ￥48.90	詳情
一地雞毛(中國故事)	劉震云 著	外語教學與研究出..	￥45.00 ￥36.00	詳情
吾國與吾民(林語堂英文作品集)(月亮石)——林語堂英文原版..	林語堂 著	外語教學與研究出..	￥24.90 ￥20.30	詳情
安徒生童話全集（插圖·中文導讀英文版）	（丹）安徒..	清華大學出版社	￥139.00 ￥113.50	詳情
福爾摩斯經典系列全集（上海世圖--名著典藏 英文全本 英..	（英）柯南..	世界圖書出版公司	￥58.00 ￥38.90	詳情
圣經的故事（英文原版ⅠⅡ）	（美）赫爾..	中央編譯出版社	￥69.00 ￥52.90	詳情
飄（上海世圖--名著典藏 英文全本 美國小說卷，總銷售冊..		世界圖書出版公司	￥35.80 ￥26.90	詳情
魯濱遜漂流記（典藏英文原版）——英語學習者課外必讀！影..	丹尼爾·笛..	延邊人民出版社	￥28.00 ￥16.00	詳情
世界文學名著全英文版·英國篇第一輯--原版原味!（含《德..	（英）哈代..	中國對外翻譯出版..	￥90.80 ￥59.00	詳情