KdV-Class Solitons -- Generalized KdV Equations. NLS and DNLS Equations -- Classic Two- and Three-Dimensional KP Models and Their Applications -- Generalized Two- and Three-Dimensional Models and Their Applications -- Appendices.This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced …
The Role of Mathematics in Physical Sciences — Interdisciplinary and Philosophical Aspects -- Mathematics and Physics: Reflecting on the Historical Role of Mathematics -- Oliver Heaviside’s “Dinner” -- Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity -- John von Neumann on Mathematical and Axiom…
Tutorial: Introductory Material -- Quantum Annealing: Basics and Applications -- Other Optimizations.Quantum annealing employs quantum fluctuations in frustrated systems or networks to anneal the system down to its ground state, or more generally to its so-called minimum cost state. Often this procedure turns out to be more effective, in multivariable optimization problems, than its classical c…
Equations with One Dependent Function -- Systems of Equations -- Method of the Degenerate Hodograph -- Method of Differential Constraints -- Invariant and Partially Invariant Solutions -- Symmetries of Equations with Nonlocal Operators -- Symbolic Computer Calculations.Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each so…
Neural Networks: An Overview -- Modeling with Neural Networks: Principles and Model Design Methodology -- Modeling Metholodgy: Dimension Reduction and Resampling Methods -- Neural Identification of Controlled Dynamical Systems and Recurrent Networks -- Closed-Loop Control Learning -- Discrimination -- Self-Organizing Maps and Unsupervised Classification -- Neural Networks without Training for O…
Dirac Monopole -- Magnetic Monopole in Classical Theory -- The Electron-Monopole System:Quantum-Mechanical Interaction -- Topological Roots of the Abelian Monopole -- Abelian Monopole: Relativistic Quantum Theory -- Monopole in Non-Abelian Gauge Theories -- ’t Hooft-Polyakov Monopole -- Multimonopole Configurations -- SU(2) Monopole in Quantum Theory -- Monopoles Beyond SU(2) Group -- Monopol…
Information and telecommunication systems for emergency management -- High Performance Computing in Engineering and Science -- Completely splitting method for the Navier-Stokes problem -- Methods of shock wave calculation -- Distributed and collaborative visualization of simulation results -- Safety problems of technical objects -- Direct numerical simulations of shock-boundary layer interactio…
Equations of State, Initial and Boundary Conditions -- Underwater Explosions, Shock Tubes, and Explosive Sound Sources -- Explosion of Cylindrical and Circular Charges -- Single Bubble, Cumulative Effects and Chemical Reactions -- Shock Waves in Bubbly Media -- Problems of Cavitative Destruction -- Jet Flows at Shallow Underwater Explosions -- Conclusion: Comments on the Models.Hydronamics of E…
Modeling and computer simulation of characteristics nanosystems -- Optical Properties of Small-Radius SWNTs within a Tight-Binding Model -- The Electronic Structure of Nanotubes and the Topological Arrangements of Carbon Atoms -- Irradiation Effect on the Electron Transport Properties of Single-Walled Carbon Nanotube -- Calculation of the Density Profile of Liquid Located in the Multi-Walled Ca…
Elementary Finite Elements -- Nonconforming Finite Elements -- Mixed Finite Elements -- Discontinuous Finite Elements -- Characteristic Finite Elements -- Adaptive Finite Elements -- Solid Mechanics -- Fluid Mechanics -- Fluid Flow in Porous Media -- Semiconductor Modeling.This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students …