Modeling of Extreme Waves in Technology and Nature is a two-volume set, comprising Evolution of Extreme Waves and Resonances (Volume I) and Extreme Waves and Shock-Excited Processes in Structures and Space Objects (Volume II).

The theory of waves is generalized on cases of extreme waves. The formation and propagation of extreme waves of various physical and mechanical nature (surface, elastoplastic, fracture, thermal, evaporation) in liquid and solid media, and in structural elements contacting with bubbly and cryogenic liquids are considered analytically and numerically. The occurrence of tsunamis, giant ocean waves, turbulence, and different particle-waves is described as resonant natural phenomena.

Nonstationary and periodic waves are considered using models of continuum. The change in the state of matter is taken into account using wide-range determining equations.

The desire for the simplest and at the same time general description of extreme wave phenomena that takes the reader to the latest achievements of science is the main thing that characterizes this book and is revolutionary for wave theory. A description of a huge number of observations, experimental data, and calculations is also given.

The theory of waves is generalized on cases of extreme waves. The formation and propagation of extreme waves of various physical and mechanical nature (surface, elastoplastic, fracture, thermal, evaporation) in liquid and solid media, and in structural elements contacting with bubbly and cryogenic liquids are considered analytically and numerically. The occurrence of tsunamis, giant ocean waves, turbulence, and different particle-waves is described as resonant natural phenomena.

Nonstationary and periodic waves are considered using models of continuum. The change in the state of matter is taken into account using wide-range determining equations.

The desire for the simplest and at the same time general description of extreme wave phenomena that takes the reader to the latest achievements of science is the main thing that characterizes this book and is revolutionary for wave theory. A description of a huge number of observations, experimental data, and calculations is also given.

Chapter 1. Models of continuum 1.1. The system of equations of mechanics continuous medium 1.2. State (constitutive) equations for elastic and elastic-plastic bodies 1.3. The equations of motion and the wide range equations of state of an inviscid fluid 1.4. Simplest example of fracture of media within rarefaction zones 1.4.1. The state equation for bubbly liquid 1.4.2. Fracture (cold boiling) of water during seaquakes 1.4.3. Model of fracture (cold boiling) of bubbly liquid 1.5. Models of moment and momentless shells 1.5.1. Shallow shells and the Kirchhoff - Love hypotheses 1.5.2. The Timoshenko theory of thin shells and momentless shells Chapter 2. The dynamic destruction of some materials in tension waves 2.1. Models of dynamic failure of solid media 2.1.1. Phenomenological approach 2.1.2. Microstructural approach 2.2. Models of interacting voids (bubbles, pores) 2.3. Pores on porous materials 2.4. Mathematical model of materials containing pores Chapter 3. Models of dynamic failure of weakly-cohesived media (WCM) 3.1. Introduction 3.1.1. Examples of gassy material properties 3.1.2. Behavior of weakly-cohesive geomaterials within of extreme waves 3.2. Modelling of gassy media 3.2.1. State equation for mixture of condensed matter/gas 3.2.2. Strongly nonlinear model of the state equation for gassy media 3.2.3. The Tait-like form of the state equation 3.2.4. Wave equations for gassy materials 3.3. Effects of bubble oscillations on the one-dimensional governing equations 3.3.1. Differential form of the state equation 3.3.2. The strongly nonlinear wave equation for bubbly media 3.4. Linear acoustics of bubbly media 3.4.1. Three speed wave equations 3.4.2. Two speed wave equations 3.4.3. One-speed wave equations 3.4.4. Influence of viscous properties on the sound speed of magma-like media 3.5. Examples of observable extreme waves of WCM 3.5.1. Mount St Helens eruption 3.5.2. The volcano Santiaguito eruptions 3.6. Nonlinear acoustic of bubble media 3.6.1. Low frequency waves: Boussinesq and long wave equations 3.6.2. High frequency waves: Klein-Gordon and Schroedinger equations 3.7. Strongly nonlinear Airy-type equations and remarks to the Chapters 1-3 Chapter 4. Lagrangian description of surface water waves 4.1. The Lagrangian form of the hydrodynamics equations: the balance equations, boundary conditions, and a strongly nonlinear basic equation 4.1.1. Balance and state equations 4.1.2. Boundary conditions 4.1.3. A basic expression for the pressure and a basic strongly nonlinear wave equation 4.2. 2D strongly nonlinear wave equations for a viscous liquid 4.2.1. The vertical displacement assumption 4.2.2. The 2D Airy-type wave equation 4.2.3. The generation of the Green-Naghdi-type equation 4.3. A basic depth-averaged 1D model using a power approximation 4.3.1. The strongly nonlinear wave equation 4.3.2. Three-speed variants of the strongly nonlinear wave equation 4.3.3. Resonant interaction of the gravity and capillary effects in a surface wave 4.3.4. Effects of the dispersion 4.3.5. Examples of nonlinear wave equations 4.4. Nonlinear equations for gravity waves over the finite-depth ocean 4.4.1. Moderate depth 4.4.2. The gravity waves over the deep ocean 4. 5. Models and basic equations for long waves 4.6. Bottom friction and governing equations for long extreme waves 4. 7. Airy- type equations for capillary waves and remarks to the Chapter 4 Chapter 5. Euler's figures and extreme waves: examples, equations and unified solutions 5.1. Example of Euler's elastica figures 5.2. Examples of fundamental nonlinear wave equations 5.3. The nonlinear Klein-Gordon equation and wide spectre of its solutions 5.3.1 The one dimensional version and one hand travelling waves 5.3.2. Exact solutions of the nonlinear Klein-Gordon equation 5.3.3. The sine-Gordon equation: approximate and exact elastica-like wave solutions 5.4. Cubic nonlinear equations describing elastica-like waves 5.5. Elastica-like waves: singularities, unstabilities, resonant generation 5. 5. 1. Singularities as fields of the Euler's elastic figures generation 5. 5. 2. Instabilities and generation of the Euler's elastica figures 5. 5. 3. 'Dangerous' dividers and self-excitation of the transresonant waves 5. 6. Simple methods for a description of elastica-like waves 5. 6. 1. Modelling of unidirectional elasica-like waves 5. 6. 2. The model equation for Faraday waves and Euler's figures 5.7. Nonlinear effects on transresonant evolution of Euler figures into particle-waves References PART II. Waves in finite resonators Chapter 6. Generalisation of the d'Alembert's solution for nonlinear long waves 6.1. Resonance of travelling surface waves (site resonance) 6.2. Extreme waves in finite resonators 6. 2. 1. Resonance waves in a gas filling closed tube 6. 2. 2. Resonant amplification of seismic waves in natural resonators 6. 2. 3. Topographic effect: extreme dynamics of Tarzana hill 6. 3. The d' Alembert- type nonlinear resonant solutions: deformable coordinates 6.3.1. The singular solution of the nonlinear wave equation 6.3.2. The solutions of the wave equation without the singularity with time 6.3.3. Some particular cases of the general solution (6.22) 6.4. The d' Alembert- type nonlinear resonant solutions: undeformable coordinates 6.4.1. The singular solution of the nonlinear wave equations 6. 4. 2. Resonant (unsingular in time) solutions of the wave equation 6. 4. 3. Special cases of the resonant (unsingular with time ) solution 6. 4. 4. Illustration to the theory: the site resonance of waves in a long channel 6. 5. Theory of free oscillations of nonlinear wave in resonators 6. 5. 1. Theory of free strongly nonlinear wave in resonators 6. 5. 2. Comparison of theoretical results 6. 6. Conclusion on this Chapter Chapter 7. Extreme resonant waves: a quadratic nonlinear theory 7.1. An example of a boundary problem and the equation determining resonant plane waves 7.1.1. Very small effects of nonlinearity, viscosity and dispersion 7.1.2. The dispersion effect on linear oscillations 7.1.3. Fully linear analysis 7.2. Linear resonance 7. 2. 1. Effect of the nonlinearity 7. 2. 2. Waves excited very near band boundaries of resonant band 7. 2. 3. Effect of viscosity 7. 3. Solutions within and near the shock structure 7.4. Resonant wave structure: effect of dispersion 7. 5. Quadratic resonances 7. 5. 1. Results of calculations and discussion 7.6. Forced vibrations of a nonlinear elastic layer Chapter 8. Extreme resonant waves: a cubic nonlinear theory 8. 1. Cubically nonlinear effect for closed resonators 8. 1. 1. Results of calculations: pure cubic nonlinear effect 8. 1. 2. Results of calculations: joint cubic and quadratic nonlinear effect 8. 1. 3. Instant collapse of waves near resonant band end 8. 1. 4. Linear and cubic-nonlinear standing waves in resonators 8. 1. 5. Resonant particles, drops, jets, surface craters and bubbles 8. 2. A half-open resonator 8. 2.1. Basic relations 8. 2.2. Governing equation 8.3 Scenarios of transresonant evolution and comparisons with experiments 8. 4. Effects of cavitation in liquid on its oscillations in resonators Chapter 9. Spherical resonant waves 9.1. Examples and effects of extreme amplification of spherical waves 9. 2. Nonlinear spherical waves in solids 9.2.1. Nonlinear acoustics of the homogeneous viscoelastic solid body 9. 2.2. Approximate general solution 9. 2.3. Boundary problem, basic relations and extreme resonant waves 9.2.4. Analogy with the plane wave, results of calculations and discussion 9.3. Extreme waves in spherical resonators filling gas or liquid 9.3.1. Governing equation and its general solution 9.3.2. Boundary conditions and basic equation for gas sphere 9. 3.3. Structure and trans-resonant evolution of oscillating waves 9.3.3.1. First scenario (C -B) 9.3.3.2. Second scenario (C = -B) 9.3.4. Discussion 9. 4. Localisation of resonant spherical waves in spherical layer hapter 10. Extreme Faraday waves 10. 1. Extreme vertical dynamics of weakly-cohesive materials 10. 1.1. Loosening of surface layers due to strongly-nonlinear wave phenomena 10.2 . Main ideas of the research 10. 3. Modelling experiments as standing waves 10.4. Modelling of counterintuitive waves as travelling waves 10. 4. 1. Modeling of the Kolesnichenko's experiments 10. 4. 2. Modelling of experiments of Bredmose et al. 10. 5. Strongly nonlinear waves and ripples 10.5. 1. Experiments of Lei Jiang et al. and discussion of them 10. 5. 2. Deep water model 10. 6. Solitons, oscillons and formation of surface patterns 10.7. Theory and patterns of nonlinear Faraday waves 10. 7.1 Basic equations and relations 10. 7.2. Modeling of certain experimental data 10.7.3. Two-dimensional patterns 10. 7.4 Historical comments and key result References PART III. Extreme ocean waves, resonances and phenomena Chapter 11. Long waves, Green's law and topographical resonance 11.1. Surface ocean waves and vessels 11.2. Observations of the extreme waves 11.3. Long solitary waves 11. 4. KdV-type, Burgers-type, Gardner-type and Camassa-Holm-type equations for the case of the slowly-variable depth 11. 5. Model solutions and the Green law for solitary wave 11. 6. Examples of coastal evolution of the solitary wave 11. 7. Generalizations of the Green's law 11. 8. Tests for generalisated Green's law 11. 8. 1. The evolution of harmonical waves above topographies 11. 8. 2. The evolution of a solitary wave over trapezium topographies 11. 8. 3. Waves in the channel with a semicircular topographies 11. 9. Topographic resonances and the Euler's elastica Chapter 12. Modelling of the tsunami described by Charles Darwin and coastal waves 12.1. Darwin's description of tsunamis generated by coastal earthquakes 12.2. Coastal evolution of tsunami 12.2.1. Effect of the bottom slope 12. 2. 2. The ocean ebb in front of a tsunami 12. 2. 3. Effect of the bottom friction 12 .3. Theory of tsunami: basic relations 12.4. Scenarios of the coastal evolution of tsunami 12.4.1. Cubic nonlinear scenarios 12.4.2. Quadratic nonlinear scenario 12. 5. Cubic nonlinear effects: overturning and breaking of waves Chapter 13. Theory of extreme (rogue, catastrophic) ocean waves 13. 1. Oceanic heterogeneities and the occurrence of extreme waves 13. 2. Model of shallow waves 13. 2. 1. Simulation of a hole in the sea met by the tanker Taganrogsky Zaliv 13. 2. 2. Simulation of typical extreme ocean waves as shallow waves 13.3. Solitary ocean waves 13. 4. Nonlinear dispersive relation and extreme waves 13. 4.1. The weakly nonlinear interaction of many small amplitude ocean waves 13. 4.2. The cubic nonlinear interaction of ocean waves and extreme waves formation 13. 5. Resonant nature of extreme harmonic wave Chapter 14. Wind -induced waves and wind-wave resonance 14.1. Effects of wind and current 14.2. Modeling the effect of wind on the waves 14. 3. Relationships and equations for wind waves in shallow and deep water 14. 4. Wave equations for unidirectional wind waves 14.5. The transresonance evolution of coastal wind waves Chapter 15. Transresonant evolution of Euler's figures into vortices 15.1. Vortices in the resonant tubes 15.2. Resonance vortex generation 15.3. Simulation of the Richtmyer-Meshkov instability results 15.4. Cubic nonlinearity and evolution of waves into vortices 15.5. Remarks to extreme water waves (Parts I-II) References Part IV. Counterintuitive behaviour CIB of structural elements after impact loads Chapter 16. Experimental data 16. 1. Introduction and method of impact loading 16. 2. CIB of circular plates: results and discussion 16. 3. CIB of rectangular plates and shallow caps 16.3.1. Discussion of CIB of shallow caps 16.3.2. Cap/ permeable membrane system 16.3.3. CIB of panels Chapter 17. CIB of plates and shallow shells: theory and calculations 17. 1. Distinctive features of CIB of plates and shallow shells 17.1. 1. Investigation techniques 17. 1.2. Results and discussion: plates , spherical caps and cylindrical panels 17. 2. Influences of atmosphere and cavitation on CIB 17. 2. 1. Theoretical models 17. 2. 2. Calculation details 17. 2. 3. Results and discussion References PART V. Extreme waves and structural elements Chapter 18. Extreme effects and waves in impact loaded hydrodeformable systerms 18.1. Introduction 18.2. Underwater explosions and the cavitation wave: experiments 18. 3. Experimental studies of formation and propagation of the cavitation waves 18. 3.1. Elastic plate/underwater wave interaction 18. 3.2. Elastoplastic plate/underwater wave interaction 18.4. Extreme underwater wave and plate interaction 18. 4. 1. Effects of deformability 18. 4. 2. Effects of cavitation on the plate surface 18. 4. 3. Effects of cavitation in the liquid volume on the plate-liquid interaction 18. 4. 4. Effects of plasticity 18. 5. Modelling of extreme wave cavitation and cool boiling in tanks 18. 5. 1. Impact loading of tank 18. 5. 2. Impact loading of liquid in tank Chapter 19. Shells and cavitation (cool boiling) waves 19. 1. Interaction of a cylindrical shell with shock wave in liquid 19. 2. Extreme waves in cylindrical elastic container 19. 2. 1. Effects of cavitation and cool boiling on the interation of shells 19. 2. 2. Features of bubble dynamics and their effect on shells 19. 3. Extreme wave phenomena in the hydro - gas-elastic system 19. 4. Effects of boiling of liquids within rarefaction waves on the transient deformation of hydroelastic systems 19. 5. A method of solving transient three-dimensional problems of hydroelasticity for cavitating and boiling liquids 19.5.1. Governing equations 19.5.2. Numerical method 19.5.3. Results and discussion Chapter 20. Interaction of extreme underwater waves with structures 20.1. Fracture and cavitation waves in thin plate/underwater explosion system 20.2. Fracture and cavitation waves in plate/underwater explosion system 20.3. Generation of cavitation waves after tank bottom buckling 20. 4. Transient interaction of a stiffened spherical dome with underwater shock waves 20. 4. 1. The problem and method of solution 20. 4. 2. Numeric method of problem solution 20. 4. 3. Results of calculations 20. 5. Extreme amplification of waves at vicinity of the stiffening rib References PART VI. Extreme waves excited by impact of heat, radiation or mass Chapter 21. Formation and amplification of heat waves 21.1. Linear analysis. Influence of hyperbolicity 21.2. Forming and amplifing of nonlinear heat waves 21.3. Strongly nonlinearity of thermodynamic function as a cause of formation of cooling shock wave Chapter 22. Extreme waves excited by radiation 22.1. Impulsive deformation and destruction of bodies at temperatures below the melting point 22.1.1. Thermoelastic waves excited by long-wave radiation 22.1.2. Thermo-elastic waves excited by short-wave radiation 22.1.3. Stress and fracture waves in metals during rapid bulk heating 22.1.4. Optimization of the outer laser-induced spalling 22.2. Effects of melting of material under impulse loading 22.2.1. Mathematical model of fracture under thermal force loading 22.2.2. Algorithm and results 22.3. Modelling of fracture, melting, vaporization and phase transition 22. 3.1. Calculations: effects of temperature 22.3.2. Calculations: effects of vaporization 22.3.3. Calculations: effect of vaporization on spalling 22.4. Two dimensional fracture and evaporation 22.5. Fracture of solid by radiation pulses as a method of ensuring safety in space 22.5. 1. Introduction 22.5. 2. Mathematical formulation of the problem 22.5. 3. Calculation results and comparison with experiments 22.5. 4. Special features of fracture by spalling 22.5. 5. Efficiency of laser fracture 22.5.6. Discussion and conclusion Chapter. 23. The melting waves in front of a massive perforator 23.1. Experimental investigation 23. 2. Numerical modeling. 23. 3. Results of the calculation and discussion References Part VII. Modelling of particle-wave, slit experiments and the origin of the Universe Chapter 24. Resonances, Euler figures and particle-waves 24.1. Scalar fields and Euler figures 24.1.1 Own nonlinear oscillations of a scalar field in a resonator 24.1.2. The simplest model of the evolution of Euler's figures into periodical particle-wave 24.2. Some data of exciting experiments with layers of liqud 24. 3. Stable oscillations of particle-wave configurations 24.4. Schroedinger and Klein-Gordon equations 24.5. Strongly localised nonlinear sphere-like waves and wave packets 24.6. Wave trajectories, wave packets and discussion Chapter 25. Nonlinear quantum waves in the light of recent slit experiments 25.1. Introduction 25. 2. Experiments using different kind of slits and the beginning of the discussion 25.3. Explanations and discussion of the experimental results 25.4. Casimir's effect 25.5. Thin metal layer and plasmons as the synchronizators 25.6. Testing of thought experiments 25.7. Main thought experiment 25. 8. Resonant dynamics of particle-wave, vacuum and Universe Chapter 26. Resonant models of origin of particles and the Universe due to quantum perturbations of scalar fields 26.1. Basic equation and relations 26.2. Basic solutions. Dynamic and quantum effects 26.3. Two-dimensional maps of landscapes of the field 26.4. Description of quantum perturbations 26.4.1. Quantum perturbations and free nonlinear oscillations in the potential well 26.4.2. Oscilations of scalar field, granular layer and the Bose-Einstein condensate 26.4.3. Simple model of the origin of the particles: mathematics and imaginations 26.5. Modelling of quantum actions: theory 26.6. Modelling of quantum actions: calculations References

Shamil U. Galiev obtained his Ph.D. degree in Mathematics and Physics from Leningrad University in 1971, and, later, a full doctorate (ScD) in Engineering Mechanics from the Academy of Science of Ukraine (1978). He worked in the Academy of Science of former Soviet Union as a researcher, senior researcher and department chair from 1965 to 1995. From 1984 to 1989 he served as a Professor of Theoretical Mechanics in the Kiev Technical University, Ukraine. Since 1996 he has served as Professor, Honorary Academic of the University of Auckland, New Zealand. Dr. Galiev has published approximately 90 scientific publications, and is the author of seven books devoted to different complex wave phenomena. From 1965-2014 he has studied different engineering problems connected with dynamics and strength of submarines, rocket systems, and target/projectile (laser beam) systems. Some of these results were published in books and papers. During 1998-2017 he did extensive research and publication in the area of strongly nonlinear effects connected with catastrophic earthquakes, giant ocean waves and waves in nonlinear scalar fields. Overall, Dr. Galiev's research has covered many areas of engineering, mechanics, physics and mathematics.