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Waves and structures in nonlinear nondispersive media:General theory and applica

作者：
GRS
定价：
0.00 元
版面字数：
580千字
开本：
暂无
装帧形式：
暂无
版次：
暂无
最新版次
印刷时间：
1899年
ISBN：
978-7-04-031695-7
物料号：
31695-A0
出版时间：
2011-08-30
读者对象：
学术著作
一级分类：
自然科学
二级分类：
交叉学科

《非线性非分散介质中的波与结构：非线性声学的一般理论及应用》全面介绍非线性波的结构和动力学行为例如振动、波阵面、锯齿形波、三维细胞结构的第一本专 著，描述了天体物理学、声学、机械、地球物理学、海洋资源研究中已经观测到的非线性现象，包括数学模型、一般理论、例子及工程应用叙述清晰、易学易懂，关 键词：非线性结构，锯齿形波，发展方程，生物医学工程，非线性检验，非线性物理学。

  • 目录
    • 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
                                                                                                                                                                                                                                                                                                                                                                                                                            • index

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