Intro; Preface; Contents; Part I Charge and Spin Transport in Low-Dimensional Structures; Nonlinear Quantum Mechanics; 1 Introduction; 2 The Local Density Approximation; 3 Homogeneous Quantum Wells; 4 The Hartree Iteration; 5 Intersubband Absorption; 6 Time-Dependent Local Density Approximation; 7 Nonlinear Phenomena in Asymmetric Quantum Wells; 8 Experimental Search by Morris and Sherwin (2011); 9 The Anticipated Results: The Quantum Oscillator; 10 Semiconductor Superlattices; 11 Model; 11.1 Noise; 11.2 Disorder; 12 Numerical Methods; 13 Results; 13.1 N=10; 13.2 N > 10; 13.3 Noise

13.4 Disorder14 Discussion; 15 Conclusions; References; Chaotic Current Self-oscillations in Doped, Weakly Coupled Semiconductor Superlattices for True Random Number Generation; 1 Introduction; 2 Electric-Field Domain Formation and Chaos in Semiconductor Superlattices; 2.1 Electric-Field Domains; 2.2 Spontaneous Current Self-oscillations and Chaos; 2.3 Spontaneous Current Self-oscillations at Room Temperature; 3 True Random Number Generator Based on GaAs/A0.45Ga0.55As Superlattices; 4 Chaos Synchronization in Networks of GaAs/A0.45Ga0.55As Superlattices; 5 Summary and Conclusions

5 Deformation Potential Coupling and Deformation Hamiltonian6 Discussions; References; Part II Modeling Biological Phenomena from Nano- to Macro-scales; Stochastic Models of Tumor Induced Angiogenesis; 1 Introduction; 2 Langevin Tip Cell Models; 3 Deterministic Description; 4 Soliton and Collective Coordinates; 5 Random Walk Tip Cell Models; 6 Cellular Potts Models; 7 Blood Flow and Vascular Network; 8 Conclusions; References; Biofilm Mechanics and Patterns; 1 Biofilm Shapes; 2 Filamentary Structures in Flows; 2.1 Helical Biofilms; 2.2 Discrete Rod Framework