Energy Localisation And Transfer

This book provides an introduction to localised excitations in spatially discrete systems, from the experimental, numerical and mathematical points of view. Also known as discrete breathers, nonlinear lattice excitations and intrinsic localised modes, these are spatially localised time periodic motions in networks of dynamical units. Examples of such networks are molecular crystals, biomolecules, and arrays of Josephson superconducting junctions. The book also addresses the formation of discrete breathers and their potential role in energy transfer in such systems.

This book provides an introduction to localised excitations in spatially discrete systems, from the experimental, numerical and mathematical points of view. Also known as discrete breathers, nonlinear lattice excitations and intrinsic localised modes, these are spatially localised time periodic motions in networks of dynamical units. Examples of such networks are molecular crystals, biomolecules, and arrays of Josephson superconducting junctions. The book also addresses the formation of discrete breathers and their potential role in energy transfer in such systems. Contents:Computational Studies of Discrete BreathersVibrational Spectroscopy and Quantum LocalizationSlow ManifoldsLocalized Excitations in Josephson ArraysProtein Functional Dynamics: Computational ApproachesNonlinear Vibrational Spectroscopy: A Method to Study Vibrational Self-TrappingBreathers in Biomolecules?Statistical Physics of Localized VibrationsLocalization and Targeted Transfer of Atomic-Scale Nonlinear Excitations: Perspectives for Applications Readership: Advanced graduate students and postdoctoral researchers in nonlinear dynamics. Keywords:Energy Localisation;Transfer;Breathers;Quantum Localisation;Spectroscopy;Josephson Junctions;Protein Dynamics;Statistical Physics;Nonlinear Physics;Hamiltonian Dynamics

This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays). Contents:The Discrete Nonlinear Schrödinger Equation — 20 Years on (J C Eilbeck & M Johansson)Breathers and Conformational Transitions in Molecular Crystals (M Barthes)Some Exact Results for Quantum Lattice Problems (J C Eilbeck)Isochronous Potentials (S Bolotin & R S Mackay)Dynamics of Discrete Breathers in Flexible Chains (J M Sancho et al.)Interaction of Moving Breathers with an Impurity (J Cuevas et al.)Quantum Targeted Energy Transfer (P Maniadis et al.)Spontaneous Pattern Retrieval in a Neural Network (M-P Zorzano)Discrete Breathers in 2D Josephson Arrays (J J Mazo)Fluxon Ratchet Potentials (J J Mazo et al.)and other papers Readership: Researchers, academics and graduate students in the fields of new materials, analysis & differential equations, numerical & computational mathematics, stochastic theory, theoretical physics, statistical physics, semiconductors and mathematical biology. Keywords:Nonlinearity;Spatial Discreteness;Energy Transfer;Crystals;Biomolecules;Josephson Array;Localization

This book highlights the role that renewable energy can play in achieving sustainable development. It focuses on rural areas of developing countries, looking in particular at stand-alone solar home systems and grid-connected biomass cogeneration plant. It provides a summary of the main barriers to the successful transfer of renewable energy technology, illustrated by case studies drawn from Indonesia, the Philippines, Vietnam, Thailand, the South Pacific, Kenya and India. Options for overcoming the barriers and the role of key players are presented. The book also outlines the potential role of the Clean Development Mechanism of the Kyoto Protocol in facilitating renewable energy technology transfer in the context of climate change.The book will appeal to academics, consultants, technology manufacturers, international funding bodies, multilateral and bilateral aid agencies, policy-makers and planners in developing countries.

This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).

This monograph evolved over a period of nine years from a series of papers and presentations addressing the subject of passive vibration control of mechanical s- tems subjected to broadband, transient inputs. The unifying theme is Targeted - ergy Transfer – TET, which represents a new and unique approach to the passive control problem, in which a strongly nonlinear, fully passive, local attachment, the Nonlinear Energy Sink – NES, is employed to drastically alter the dynamics of the primary system to which it is attached. The intrinsic capacity of the properly - signed NES to promote rapid localization of externally applied (narrowband) - bration or (broadband) shock energy to itself, where it can be captured and dis- pated, provides a powerful strategy for vibration control and the opens the pos- bility for a wide range of applications of TET, such as, vibration and shock i- lation, passive energy harvesting, aeroelastic instability (?utter) suppression, se- mic mitigation, vortex shedding control, enhanced reliability designs (for ex- ple in power grids) and others. The monograph is intended to provide a thorough explanation of the analytical, computational and experimental methods needed to formulate and study TET in mechanical and structural systems. Several prac- cal engineering applications are examined in detail, and experimental veri?cation and validation of the theoretical predictions are provided as well. The authors also suggest a number of possible future applications where application of TET seems promising. The authors are indebted to a number of sponsoring agencies.

1. Nonholonomically constrained motions. 1.1. Newton's equations. 1.2. Constraints. 1.3. Lagrange-d'Alembert equations. 1.4. Lagrange derivative. 1.5. Hamilton-d'Alembert equations. 1.6. Distributional Hamiltonian formulation. 1.7. Almost Poisson brackets. 1.8. Momenta and momentum equation. 1.9. Projection principle. 1.10. Accessible sets. 1.11. Constants of motion. 1.12. Notes -- 2. Group actions and orbit spaces. 2.1. Group actions. 2.2. Orbit spaces. 2.3. Isotropy and orbit types. 2.4. Smooth structure on an orbit space. 2.5. Subcartesian spaces. 2.6. Stratification of the orbit space by orbit types. 2.7. Derivations and vector fields on a differential space. 2.8. Vector fields on a stratified differential space. 2.9. Vector fields on an orbit space. 2.10. Tangent objects to an orbit space. 2.11. Notes -- 3. Symmetry and reduction. 3.1. Dynamical systems with symmetry. 3.2. Nonholonomic singular reduction. 3.3. Nonholonomic regular reduction. 3.4. Chaplygin systems. 3.5. Orbit types and reduction. 3.6. Conservation laws. 3.7. Lifted actions and the momentum equation. 3.8. Notes -- 4. Reconstruction, relative equilibria and relative periodic orbits. 4.1. Reconstruction. 4.2. Relative equilibria. 4.3. Relative periodic orbits. 4.4. Notes -- 5. Carathéodory's sleigh. 5.1. Basic set up. 5.2. Equations of motion. 5.3. Reduction of the E(2) symmetry. 5.4. Motion on the E(2) reduced phase space. 5.5. Reconstruction. 5.6. Notes -- 6. Convex rolling rigid body. 6.1. Basic set up. 6.2. Unconstrained motion. 6.3. Constraint distribution. 6.4. Constrained equations of motion. 6.5. Reduction of the translational [symbol] symmetry. 6.6. Reduction of E(2) symmetry. 6.7. Body of revolution. 6.8. Notes -- 7. The rolling disk. 7.1. General set up. 7.2. Reduction of the E(2) x S[symbol] symmetry. 7.3. Reconstruction. 7.4. Relative equilibria. 7.5. A potential function on an interval. 7.6. Scaling. 7.7. Solutions of the rescaled Chaplygin equations. 7.8. Bifurcations of a vertical disk. 7.9. The global geometry of the degeneracy locus. 7.10. Falling flat. 7.11. Near falling flat. 7.12. The bifurcation diagram. 7.13. The integral map. 7.14. Constant energy slices. 7.15. The spatial rotational shift. 7.16. Notes.