CONTENTS -- Preface -- Symmetry Reduction for an Inhomogeneous Nonlinear Diffusion Equation -- 1 Introduction -- 2 Nonclassical symmetries -- 3 Some exact solutions -- Applying a New Algorithm to Derive Nonclassical Symmetries -- 1 Introduction -- 2 Nonclassical symmetries -- 3 Some examples -- 4 Conclusions -- Turbulence and Surface Gravity Waves on the Sun -- 1 Introduction -- 2 The model -- 3 The perturbation equations -- 4 The dispersion relation -- 5 Asymptotic results -- 6 Numerical results -- 7 Discussion -- The Linear Stability of Interfacial Solitary Waves in a Two-Layer Fluid -- 1 Introduction -- 2 Basic equations -- 3 Asymptotic analysis -- 4 Criterion for the stability -- 5 Stability of specific solitary waves -- 6 Concluding remarks -- On the Transition to Diffusion Chaos in the Kuramoto-Tsuzuki Equation -- 1. Introduction -- 2. Scenario of transition to chaos in the few-mode approximations -- 3. Scenario of transition to chaos in the phase space of the Kuramoto-Tsuzuki equation -- 4. Conclusion -- Fractional Calculus for Transport in Disordered Semiconductors -- 1 Introduction -- 2 CTRW model -- 3 The normal transport process -- 4 Where fractional derivatives come from -- 5 How fractional derivatives come into equations -- 6 Solutions in terms of a+-densities -- 7 Application to some transport problems -- 8 Concluding remark -- Resonant Influence of Spatial Oscillations of a Perturbation on Motion of a Nonlinear Oscillator -- 1 Introduction -- 2 Theoretical analysis -- 3 Numerical simulation -- 4 Summary -- Chaotic Transport and Fractals in a Geophysical Jet Current -- 1 Introduction -- 2 Model flow -- 3 Chaotic mixing and transport -- 4 Fractal geometry of mixing -- Experiments on Pattern Formation in Reacting Systems with Chaotic Advection -- I Introduction.

II. Pattern formation in a blinking vortex flow -- III. Front propagation and mode-locking -- IV. Synchronization of a continuous network of oscillators -- V. Continuing work -- Properties of Chaotic Advection in a 2-Layer Model of Vortex Flow -- 1 Introduction -- 2 Model -- 3 Chaotic transport -- 4 Conclusions and discussion -- Monte Carlo Simulation of Atomic Transport in a Laser Field -- 1 Introduction -- 2 Hamilton-Schrodinger equations of motion with quantum jumps -- 3 Numerical simulation of light-induced mechanical effects -- 4 Correlations between internal and external degrees of freedom of an atom -- 5 Conclusion -- A Fuzzy Blue Sky Catastrophe -- 1 Introduction -- 2 The FGCM Method -- 3 A Blue Sky Catastrophe -- 4 Concluding Remarks -- Efficient and Reliable Stability Analysis of Solutions of Delay Differential Equations -- 1 Introduction -- 2 Computation of the rightmost characteristic roots by an LMS method -- 3 Steplength heuristics for the LMS method -- 4 Examples -- 5 Conclusions -- Grazing Phenomena in a Harmonically Excited Oscillator with Dry-Friction on a Sinusoidally Time-Varying Traveling Surface -- 1. Introduction -- 2. Mechanical Model -- 3. Grazing Mechanism -- 4. Grazing Conditions -- 5. Illustrations -- 6. Numerical Simulations -- 7. Conclusion -- Complex Dynamics in the Trajectory Control of Redundant Manipulators -- 1. Introduction -- 2. Generalized Inverses -- 3. Kinematics of redundant manipulators -- 4. Robot trajectory control -- 5. Analyzing the chaotic-like responses of the pseudoinverse algorithm -- 6. Conclusions -- Under-Damped Oscillator with Cross-Correlated Colored Noises Input Modulated by Periodic Signal -- 1. Introduction -- 2. Under-damped linear model -- 3. Discussions and conclusions.

A 3D Turning Model for the Interpretation of Machining Stability and Chatter -- 1. Introduction -- 2. Model Description -- 3. SDOF Model With Uncoupled EQM For The Tool -- 4. Numerical Results and Discussion -- 5. Conclusion -- Nonlinear Dynamics and Optimization of Spur Gears -- Introduction -- Analytical Model -- Comparison with literature -- Optimization -- Conclusion -- Global Bifurcation and Chaotic Behavior Research of a Truncated Conical Shallow Shell Rotating Around a Single Axle -- 1. Introduction -- 2. Base equations -- 3. Homoclinic orbit bifurcation -- 4. Subharmonic bifurcation of resonance periodic orbit -- 5. Numerical simulation of chaotic motion -- 6. Conclusive remarks -- Technology of Magnetic Flux Leakage Signal Detection Based on Scale Transformation Stochastic Resonance -- 1. Introduction -- 2. Theory of stochastic resonance (SR) -- 3. Scale transformation stochastic resonance (STSR) -- 4. Magnetic flux leakage (MFL) signals detection based on STSR -- 5. Conclusions -- Periodic Motions and Bifurcations of Vibro-Impact Systems Near a Strong Resonance Point -- 1. Introduction -- 2. Mechanical models and Poincare map -- 3. Center manifold and normal form map associated with 1:4 resonance case -- 4. Numerical analyses of Neimark-Sacker and tangent bifurcations -- 5.1:4 strong resonance bifurcations of the vibratory system with symmetrical rigid stops -- 6. Conclusions -- On the Nonlinear Dynamic Characteristics of Truck Rear Full-Floating Axle -- 1. Introduction -- 2. Problem Statement -- 3. Axle's Dynamic Behavior -- 4. Discussions -- 5. Conclusion -- Nonlinear Vibration Analysis of an Unbalanced Rotor on Rolling Element Bearings Due to Cage Run-Out -- 1. Introduction -- 2. Modeling of the System -- 3. Results & Discussion -- 4. Conclusion.

Perturbation Analysis of Nip Contact Delay System -- 1. Introduction -- 2. Mathematic Modelling of Nip Contact -- 3. Perturbation Analysis -- 4. Numerical Results and Discussions -- 5. Conclusions -- Vibration Signal Analysis and Feature Extraction Based on Wavelet Energy Spectrum -- 1. Introduction -- 2 Discrete wavelet transform -- 3 Discrete wavelet energy spectrum -- 4 Numerical experiment -- 5. Experimental data analysis -- 6. Conclusions -- Experimental Analysis of Cumulants Scaling Properties in Fully Developed Intermittent Turbulence -- 1 Introduction -- 2 Cumulants and analycity of the cumulant generating function -- 3 Experimental analysis -- 4 Conclusion -- Exact Solutions of Second Grade Fluid in a Porous Medium -- 1. Introduction -- 2. Basic Equations -- 3. Problem Formulation -- 4. Steady Flow Solutions -- 5. Unsteady Flow Solutions (Type A) -- Approximate Analytic Solutions of Stagnation-Point Flows in a Porous Medium -- 1. Introduction -- 2. Governing equations -- 3. Numerical solutions -- 4. Series solutions -- 5. Results and discussion -- 6. Conclusions -- Lump Solutions of 2D Generalized Gardner Equation -- 1. Introduction -- 2. Modification of the Petviashvili numerical method -- 3.Results of numerical calculations -- 4. Conclusion -- Wood Fracture Behavior Simulation Using Stochastic FEM -- 1. Introduction -- 2. Power-law nonlinear stochastic finite element method -- 3. Wood fracture parameter and its ratio -- 4. Fracture parameter ratio calculated by SFEM and difference check -- 5. Stochastic analysis example of fracture -- 6. Wood fracture strength factor and its variation ratio -- 7. Conclusions -- A Novel Numerical Computation Based on FEM for Wood Temperature Distribution Field -- 1. Introduction -- 2. Basic theory of wood steady heat conduction analysis -- 3. Numerical computation.

4. Experimental tests and analysis -- 5. Conclusions -- Elastic Wave Field in a Porous Medium Fully Saturated with a Newtonian Viscous Fluid -- 1. Introduction -- 2. Mathematical model establishment -- 3. Consideration of multi-energy sources -- 4. Numerical Simulation -- 5. Conclusion -- Ball Bearing Remnant Life Prediction of Induction Motor - Impact Inspection Approach -- 1. Introduction -- 2. The hitch inspection method and the simple principles -- 3. The sample data -- 4. Data analysis and mathematical modeling -- 5. The application of two predicting models -- 6. Concluding remarks -- Nonlinear Airway Smooth Muscle Stiffness Changes Using Artificial Neural Network -- 1. Introduction -- 2. Neural Network Model -- 3. Neutral Network training -- 4. Results -- 5 Conclusions -- In-Plane Free Vibrations of Compound High Speed Rotating Disks -- 1. Introduction -- 2. Nomenclature -- 3. Governing equation of motion -- 4. Modal displacements and stresses for each part -- 5. Modal Displacements and Stresses For Compound Disks -- 6. Numerical Results -- 7. Conclusion -- 8. References -- Self-Excited Vibration and Stability Analyses for Axially Traveling Strings under Steady Wind Loadings -- 1. Introduction -- 2. Modeling and Approximation -- 3. Equilibrium Configuration and Its Stability -- 4. Periodic Motions and Stability Analysis -- 5. Conclusions -- Nonlinear Dynamical Analysis of Micro Self-Acting Gas Journal Bearing -- 1. Introduction -- 2. Dynamic Model -- 3. Dynamical simulation and disturbance response -- 4. Conclusion -- Parametric Modelling of Microresonators Dynamics with Considering Thermal Effects -- 1. Introduction -- 2. Mathematical Modeling -- 3. Conclusion -- Design and Analysis of General and Travelling Wave Dielectrophoresis -- 1. Introduction -- 2. Theoretical Background -- 3. Numerical Integration.

4. Results and Discussion.