Full Description
The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering. The practice of implementing these techniques and their value are largely realized by showing their application to problems of nonlinear wave phenomena in electronic transport in solid state materials, especially bulk semiconductors and semiconductor superlattices. The authors are recognized leaders in this field, with more than 30 combined years of contributions.
Contents
Preface. Acknowledgments. 1. Introduction. 1.1 Overview of Nonlinear Wave Phenomena. 1.2 Nonlinear Waves and Electronic Transport in Materials. 1.3 Structural Outline of the Book. 2. Dynamical Systems, Bifurcations, and the Chapman-Enskog Method. 2.1 Introduction. 2.2 Review of Dynamical Systems Concepts. 2.3 Analysis of the Hopf Biofurcation: An Introduction to the Chaman-Enskog Methods. 3. Excitable Media I: Continuum Systems. 3.1 Introduction. 3.2 Basic Excitability - the FitzHugh-Nagumo System. 3.3 Matched Asymptotics: Excitability and Oscillations. 3.4 The Scalar Bistable Equation: Wave Pulses as Heteroclinic Connections. 3.5 Traveling Waves of the FitzHugh-Nagumo System. 4. Excitable Media II: Discrete Systems. 4.1 Introduction. 4.2 The Spatially Discrete Nagumo Equation. 4.3 Asymptotic Construction of Pulses. 4.4 Numerically Calculated Pulses. 4.5 Propagation Failure. 4.6 Pulse Generation at a Boundary. 4.7 Concluding Remarks. 5. Electronic Transport in Condensed Matter: From Quantum Kinetics to Drift-diffusion Models. 5.1 Introduction. 5.2 Superlattices. 5.3 Concluding Remarks. 6. Electric Field Domains in Bulk Semiconductors I: the Gunn Effect. 6.1 Introduction. 6.2 N -shaped Current-Field Characteristics and Kroemer's Model. 6.3 Stationary Solutions and Their Linear Stability in the Limit L " 1. 6.4 Onset of the Gunn Effect. 6.5 Asymptotics of the Gunn Effect for Long Samples ad N-shaped Electron Velocity. 6.6 Asymptotics of the Gunn Effect for Long Samples and Saturating Electron Velocity. 6.7 References on the 1D Gunn Effect and Closing Remarks. 7. Electric Field Domains in Bulk Semiconductors II: Trap-mediated Instabilities. 7.1 Introduction. 7.2 Drift-Diffusion Transport Model for Trap-Mediated System. 7.3 Nondimensional Form and the Reduced Model. 7.4 Steady States, J-E Curves, and Steady Wave Solutions on the Infinite Line under Current Bias. 7.5 Nonlinear Wave Solutions in Finite Samples under Voltage Bias. 7.6 Multiple Shedding of Wavefronts in Extrinsic Material. 8. Nonlinear Dynamics in Semiconductor Superlattices. 8.1 Introduction. 8.2 Spatially Discrete Model for the Doped Weakly Coupled SL. 8.3 Nondimensionalization of the Discrete Drift-Diffusion Model. 8.4 Wave Fronts and Stationary States under Current Bias. 8.5 Static Field Domains in Voltage-Biased SLs. 8.6 Relocation of EFDs. 8.7 Self-Sustained Oscillations of the Current. 8.8 Spin Transport in Dilute magnetic Semiconductor Superlattices. 9. Nonlinear Wave Methods for Related Systems in the Physical World. 9.1 Introduction. 9.2 Superlattice Transport Model with Both Vertical and Lateral Dynamics. 9.3 Semi-Insulating GaAs. 9.4 Multidimensional Gunn Efect. 9.5 Fluctuations in Gunn Diodes. 9.6 Dynamics of Dislocations in Mechanical Systems: Nanoarrays. Index.
