Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.

Fundamental Problems in Viscoplasticity

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The Discrete Nonlinear Schrödinger Equation

The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyse some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g. the linear or the nonlinear limit or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.

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Nonlinear waves in Bose-Einstein condensates: physical relevance and mathematical techniques

Mechanics of Solids, Bela I. Sandor Introduction Statics Dynamics Vibrations Mechanics of Materials Structural Integrity and Durability Comprehensive Example of Using Mechanics of Solids Methods Engineering Thermodynamics, Michael J. Moran Fundamentals Control Volume Applications Property Relations and Data Combustion Exergy Analysis Vapor and Gas Power Cycles Guidelines for Improving Thermodynamic Effectiveness Fluid Mechanics, Frank Kreith Fluid Statics Equations of Motion and Potential Flow Similitude: Dimensionless Analysis and Data Correlation Hydraulics of Pipe Systems Open Channel Flow External Incompressible Flows Compressible Flow Multi-Phase Flow Non-Newtonian Flow Tribology, Lubrication, and Bearing Design Pumps and Fans Liquid Atomization and Spraying Flow Measurement Micro/Nanotribology Heat and Mass Transfer, Frank Kreith Conduction Heat Transfer Convection Heat Transfer Radiation Phase-Change Heat Exchangers Temperature and Heat Transfer Measurements Mass Transfer Applications Non-Newtonian Fluids - Heat Transfer Electrical Engineering, Giorgio Rizzoni Introduction Fundamentals of Electric Circuits Resistive Network Analysis AC Network Analysis AC Power Frequency Response, Filters, and Transient Analysis Electronics Power Electronics Operational Amplifiers Digital Circuits Measurements and Instrumentation Electromechanical Systems Mechanical System Controls, Jan F. Kreider Human-Machine Interaction The Need for Control of Mechanical Systems Control System Analysis Control System Design and Application Advanced Control Topics Energy Resources, D. Yogi Goswami Introduction Types of Derived Energy Fossil Fuels Biomass Energy Nuclear Resources Solar Energy Resources Wind Energy Resources Geothermal Energy Energy Conversion, D. Yogi Goswami Steam Power Plant Gas Turbines Internal Combustion Engines Hydraulic Turbines Stirling Engines Advanced Fossil Fuel Power Systems Energy Storage Nuclear Power Nuclear Fusion Solar Thermal Energy Conversion Wind Energy Conversion Energy Conversion of the Geothermal Resource Direct Energy Conversion Ocean Energy Technology Combined Cycle Power Plants EMERGY Evaluation and Transformity Air Conditioning and Refrigeration, Shan K. Wang Introduction Psychrometrics Air Conditioning Processes and Cycles Refrigerants and Refrigeration Cycles Outdoor Design Conditions and Indoor Design Criteria Load Calculations Air Handling Units and Packaged Units Refrigeration Components and Evaporative Coolers Water Systems Heating Systems Refrigeration Systems Thermal Storage Systems Air Systems Absorption Systems Air Conditioning Systems and Selection Desiccant Dehumidification and Air Conditioning Transportation, Frank Kreith Transportation Planning Design of Transportation Facilities Operations and Environmental Impact Transportation Systems Alternative Fuels for Motor Vehicles Electric Vehicles Intelligent Transportation Systems Engineering Design, Leonard D. Albano and Nam P. Suh Introduction Elements of the Design Process Concept of Domains The Axiomatic Approach to Design Algorithmic Approaches to Design Strategies for Product Design Design of Manufacturing Systems and Processes Precision Machine Design Robotics Computer-Based Tools for Design Optimization Materials, Richard L. Lehman and Malcolm G. McLaren Metals Polymers Adhesives Wood Portland Cement Concrete Composites Ceramics and Glass Modern Manufacturing, Jay Lee and Robert Schafrik Introduction Unit Manufacturing Processes and Assembly Processes Essential Elements in Manufacturing Processes and Equipment Modern Design and Analysis Tools for Manufacturing Rapid Prototyping Underlying Paradigms in Manufacturing Systems and Enterprise Management for the 21st Century Robotics, Frank L. Lewis Introduction Commercial Robot Manipulators Robot Configurations End Effectors and Tooling Sensors and Actuators Robot Programming Languages Robot Dynamics and Control Planning and Intelligent Control Design of Robotic Systems Robot Manufacturing Applications Industrial Material Handling and Process Applications of Robots Mobile, Flexible-Link, and Parallel-Link Robots Computer-Aided Engineering, Kyran Mish Introduction Computer Programming and Computer Architecture Computational Mechanics Computer Intelligence Computer-Aided Design (CAD) Environmental Engineering, Jan F. Kreider Introduction Benchmarks and Reference Conditions Sources of Pollution and Regulations Regulations and Emission Standards Mitigation of Water and Air Pollution Environmental Modeling Global Climate Change Engineering Economics and Project Management, Chan S. Park and Donald D. Tippet Engineering Economic Decisions Establishing Economic Equivalence Measures of Project Worth Cash Flow Projections Sensitivity and Risk Analysis Design Economics Project Management Communications and Information Systems, Lloyd W. Taylor Introduction Network Components and Systems Communications and Information Theory Applications Mathematics, William F. Ames and George Cain Tables Linear Algebra and Matrices Vector Algebra and Calculus Difference Equations Differential Equations Integral Equations Approximation Methods Integral Transforms Calculus of Variations Approximation Optimization Methods Engineering and Statistics Numerical Methods Experimental Uncertainty Analysis Chaos Fuzzy Sets and Logic Patent Law and Miscellaneous Topics, Frank Kreith Patents and Other Intellectual Property Product Liability and Safety Bioengineering Mechanical Engineering Codes and Standards Optics Water Desalination Noise Control Lighting Technology Appendices, Paul Norton Properties of Gases and Vapors Properties of Liquids Properties of Solids SI Units Miscellaneous Index

The CRC handbook of mechanical engineering

I Dimensions and Components.- General Introduction and Derivation of the DNLS Equation.- The One-Dimensional Case.- The Two-Dimensional Case.- The Three-Dimensional Case.- The Defocusing Case.- Extended Solutions and Modulational Instability.- MultiComponent DNLS Equations.- II Special Topics.- Experimental Results Related to DNLS Equations.- Numerical Methods for DNLS.- The Dynamics of Unstable Waves.- A Map Approach to Stationary Solutions of the DNLS Equation.- Formation of Localized Modes in DNLS.- Few-Lattice-Site Systems of Discrete Self-Trapping Equations.- Surface Waves and Boundary Effects in DNLS Equations.- Discrete Nonlinear Schr#x00F6 dinger Equations with Time-Dependent Coefficients ( of Lattice Solitons).- Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws.- Solitary Wave Collisions.- Related Models.- DNLS with Impurities.- Statistical Mechanics of DNLS.- Traveling Solitary Waves in DNLS Equations.- Decay and Strichartz Estimates for DNLS.

The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives

Finite Difference Equations

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Finite Difference Equations