bluuebunny/crossref_metadata_2025_split huggingface dataset:
Three-Dimensional State Space and Chaos
Authors: Hilborn Robert C. 
Published: January 2010

Abstract
This chapter extends state space descriptions to systems with three (or more) dimensions. For systems described by differential equations, higher state space dimensions allow for more complex behaviour including quasi-periodic behaviour and chaotic behaviour. Chaotic behaviour is characterized by strange attractors in state space. Intermittency and crises as new types of bifurcations are described. Stable manifolds, unstable manifolds, and homoclinic and heteroclinic orbits are used to describe three-dimensional state space behaviour. These ideas are used to understand some of the dynamics of the famous Lorenz model and the Smale horseshoe map. Lyapunov exponents provide a quantitative measure of the degree of chaos.
Quasi-Periodicity and Chaos
Authors: Hilborn Robert C. 
Published: January 2010

Abstract
This chapter explores the quasi-periodicity route to chaos in which the behaviour is characterized by two (or more) incommensurate frequencies. Poincare sections, frequency-locking, winding numbers, Arnold tongues, and the devil's staircase help describe and quantify quasi-periodic behaviour. Frequency-locking is a common phenomenon whenever two or more nonlinear oscillating systems interact. The circle map provides a simple model in which these effects occur. The surprising utility of number theory, including continued fractions, Fibonacci sequences, and the Farey Tree, in explaining the transition to chaos is developed in a simple context.
Hamiltonian Systems
Authors: Hilborn Robert C. 
Published: January 2010

Abstract
When a system involves no dissipative mechanisms such as friction, we say that the system is conservative because its total energy is conserved and the behaviour is described by a time-independent Hamiltonian function. In that case, the notion of attractor no longer applies. Different initial conditions (starting points in state space) can lead to dramatically different behaviour and there is no convergence to an attractor. Nevertheless, the state space is still highly organized. The famous Kolmogorov–Arnold–Moser (KAM) Theorem describes how the state space structure changes as the system behaviour changes from integrable to non-integrable. The Henon–Heiles model is used to illustrate many of these features. Area-preserving iterated map systems, such as the Chirikov Standard Map and the Arnold Cat Map, share many of the features of Hamiltonian systems and these are explored through a series of numerically generated diagrams. Applications of Hamiltonian dynamics in astronomy, particle accelerator dynamics, superconductivity and optics are described briefly.
Quantum Chaos, The Theory of Complexity, and Other Topics
Authors: Hilborn Robert C. 
Published: January 2010

Abstract
This chapter explores the connection between quantum mechanics, the theory of particle behaviour at the atomic scale, and classical chaos. The essential issue is the behaviour of quantum systems when their classical counterparts exhibit chaotic behaviour. Even though the Schrödinger equation for the quantum wave function is a linear equation, classical chaos has several intriguing quantum counterparts. Other topics discussed are the connection between chaotic behaviour and algorithm complexity, time-delay models, stochastic resonance, the control of chaotic systems, and the synchronization of chaotic systems. A collection of references to simple experiments on systems exhibiting chaotic behaviour is also provided.
Nuclear Structure from a Simple Perspective
Authors: Casten Richard F. 
Published: January 2010

Abstract
This textbook on nuclear structure takes a unique and complementary approach compared to existing texts on the topic. Avoiding complicated calculations and complex mathematical formalism, it explains nuclear structure by building on a few elementary physical ideas. Even such apparently intricate topics as shell model residual interactions, the Nilsson model, and the random phase approximation analysis of collective vibrations are explained in a simple, intuitive way so that predictions can usually be made without calculations, essentially by inspection. Frequent comparison with data allows the relevance of theoretical approaches to be immediately evident. This edition includes new chapters on exotic nuclei and radioactive beams, and on correlations of collective observables. Completely new discussions are given of isospin, the shell model, nature of collective vibrations, multi-phonon states, superdeformation, bandmixing, geometric collective model, Fermi gas model, basic properties of simple nuclear potentials, the deuteron, and low energy nuclear structure, as well as other topics.
Phonon drag thermopower of low-dimensional systems
Authors: Fletcher R. , Zaremba E. , Zeitler U. 
Published: January 2010

Abstract
This chapter reviews the experimental and theoretical literature on phonon drag thermopower in reduced dimensionality conductors, particularly in the two-dimensional (2-D) case. It emphasizes the relationship between the mobility of electrons due to electron-phonon scattering and phonon drag, which is valid in the case when the electron mobility is dominated by elastic impurity scattering. This relationship applies at low magnetic fields, and also for composite Fermions at even denominator fractional filling factors where the effective magnetic field can be taken to be weak. The chapter also surveys weak and strong electron localization effects, and results in the integer and fractional quantum Hall regimes.
Differential geometry, topology and fibre bundles
Authors: Bertlmann Reinhold A. 
Published: January 2010

AbstractThis chapter introduces all necessary mathematical concepts. Section 2.1 briefly summarizes some topological definitions. Section 2.2 explains the homotopy of maps and the homotopy of groups. Section 2.3 introduces the concept of differentiable manifolds while Section 2.4 presents the differential forms together with their Hodge duals, along with the differentiation and integration. Section 2.5 discusses homology and de Rham cohomology. Section 2.6 explains important concepts such as pullback of a differential form the Lie derivative, the Lie group, and the Lie algebra. Finally, Section 2.7 constructs fibre bundles including connection and curvature, which turn out to be a suitable mathematical concept to describe the physics of gauge theories.
Gravitation
Authors: Bertlmann Reinhold A. 
Published: January 2010

AbstractThis chapter focuses on gravitation. It first reviews some basic concepts of the Riemannian geometry and establishes notation. It then discusses the gravitational action, specifically the fermionic action. It introduces Einstein-, Lorentz-, and Weyl anomalies by violating the corresponding Einstein-, Lorentz-, and Weyl symmetries, and establishes consistency conditions. The equivalence of the Einstein- and Lorentz anomaly is demonstrated, and the covariant anomaly is discussed. Finally, the chapter treats gravitation on a BRS level, deriving the SZ chain of descent equations. Index theorems are use to carry out explicit anomaly examples.
Transverse motion
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
This chapter deals with the motion of particles as they travel around a circular accelerator or storage ring, guided by dipole magnets and focussed by quadrupoles. The parameters magnetic rigidity and the momentum of the particle determine the radius of the path and this is calculated for a relativistic particle. A diagram shows the path of particles passing through a dipole magnet. It describes the effect of a quadrupole magnet, focusing in one of two orthogonal transverse planes and defocusing in the other. It derives the bending angle of the dipole and the focal length of the quadrupole from the normalised strength and gradient of their magnetic fields. The principle of alternating gradient focusing is explained. Trajectories of focused particles are shown as they pass through the quadrupoles. The ellipse, which is the locus of the motion in a phase space plot of divergence versus displacement, is defined.
Longitudinal dynamics
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
The radio frequency cavities that accelerate a beam provide focusing in the longitudinal direction along the path of the beam. Particles oscillate about a stable phase on the rising accelerating voltage wave. Their circulation time depends upon two competing factors—their speed and the circumference of their orbit—which both depend on their momentum with respect to the ideal particle. As they approach the velocity of light, the effect of orbit length dominates and stability is found on the falling edge of the wave. The effects balance at transition energy. This chapter defines the central or closed orbit of the beam, and the dispersion function that determines its momentum dependence. The equation of synchrotron motion embodies these concepts and its solutions define a limited stable area of motion—the bucket—in the energy-time phase-space for the motion. The motion is analogous to the large amplitude oscillations of a rigid pendulum.
Non-linearities and resonances
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
This chapter shows how multipole magnets generate field shapes corresponding to the terms of a Taylor Series expansion about the centre line of the magnet. Sextupoles produce a parabolic field shape in the median plane, octupoles a cubic, etc. Each term in the expansion drives dangerous lines in the working diagram. An example is the four, third order, resonance lines that converge on points in the working diagram at one third integer values of Q. The effects of these resonances are derived with the help of the circle diagram introduced in Chapter 6. The effect of an n-th order resonance is to produce n islands in phase space, and beyond these, an unstable non-linear growth in amplitude that causes the beam to be lost. Multipoles can however be used to positive effect by introducing a Q that depends on amplitude, contributing to Landau damping of beam instabilities.
Colliders
Authors: Wilson E. J. N. 
Published: January 2010

Abstract
The first colliders were built at Stanford and at Novosibirsk. Electrons circulated in two rings colliding where they touched. Single ring colliders circulated electrons and positrons in opposite directions—a configuration later used for protons and antiprotons in CERN's SPS and at Fermilab's Tevatron. The historical pattern seems first to collide protons in high-energy machines followed by cleaner lower energy studies with lepton rings. The Intersecting Storage Rings at CERN, for protons, were followed by the Large Electron-Positron machine at CERN. The concept of luminosity is introduced. The factors that govern it are beam size at collision, beam intensity, and the beam-beam tune shift. The superconducting Large Hadron Collider reverts to a two-ring proton configuration and uses superconducting magnets to reach seven TeV per beam. Lepton colliders for the next step will have to be linear machines. Future colliders include opposing lepton linacs and, perhaps later, circulating muon rings.
Testing an interatomic force model
Authors: Finnis Mike 
Published: January 2010

AbstractThis chapter gives some practical advice on how to test the quality and transferability of an interatomic force model. The calculation of crystal structure, lattice parameters, and elastic constants is described, including a new and detailed derivation of the structural energy difference theorem and its meaning. The Cauchy relationship between elastic constants is discussed, since it is a measure of how non-central the forces are. An introduction to lattice dynamics in the harmonic approximation follows, including a description of how to calculate force constants. Finally, there is a discussion of the calculation of point defect formation energies, especially the vacancy formation energy.
Tight Binding
Authors: Finnis Mike 
Published: January 2010

Abstract
This chapter derives tight-binding models from the Hohenberg–Kohn–Sham density functional theory of total energy. The approach taken is to expose the successive approximations that can be invoked, starting with the neglect of three-centre integrals, and ending with the second moment approximation to the density of states, each leading to a slightly simpler tight-binding model. A rich variety of models can be derived on the way with applications to transition metals, semiconductors or even insulators. Attention is given to the role of self-consistency. The first comprehensive and self-contained description of bond-order potentials is given.
1 Introduction
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
This chapter introduces the basic idea of quasielastic neutron scattering as a probe for diffusion processes in condensed matter. Neutron scattering and solid state diffusion have in common that they both can be separated into two problems: the single event (scattering on a single nucleus or single diffusive jump, respectively) and the cooperative combination (in space and time) of those events in solids. The history of neutron scattering is outlined with the development of neutron sources and neutron scattering instruments. All large scale neutron scattering facilities, based on research reactors or on neutron spallation sources, are nowadays operated as user facilities with the consequence that neutron scattering is not ‘big science’ like high energy particle physics, but the practise of neutron scattering is characterized by a large variety of small groups working on many different scientific problems. A brief summary of the remainder of the book covers the fundamentals of quasielastic neutron scattering and its application to different material systems.
2 The neutron
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
The first part of the chapter introduces the relevant physical properties of the neutron and their relationship with kinetic properties. It explains neutron detection via the ionizing products of appropriate nuclear reactions. The second part deals with neutron sources. It explains the principle of research reactors (nuclear splitting) and the safety features (active, passive, inherent), and outlines the relationship between thermal flux, luminosity, and neutron current density. The low incident energy neutrons needed for QENS originate from so-called cold sources, mostly liquid deuterium. Alternatives to the research reactors are the neutron spallation sources, where high energy protons hit on nuclei of heavy elements and induce the ‘evaporation’ of neutrons. Pulsed spallation sources and continuous spallation sources are in operation nowadays, with certain advantages and disadvantages. From the cold source neutrons are led to the neutron scattering instruments in so-called neutron guides, where the principle of total reflection of the neutrons on the guide walls is utilized. Here, the use of super mirrors (multi-layer gradient coatings) has increased the available incident neutron intensity considerably.
5 Incoherent quasielastic neutron scattering
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
In the case of spatially limited jump diffusion, the incoherent scattering function consists of an elastic and a quasielastic part, and the fraction of elastic intensity is called the incoherent structure factor, EISF. This chapter evaluates different scenarios and the corresponding EISFs. Long range translational diffusion gives rise to quasielastic scattering consisting of a single Lorentzian with a linewidth proportional to Q2. The Chudley–Elliott model for lattice gases describes translational jump diffusion in Bravais lattices. QENS from translational jump diffusion on lattices with all sites equivalent consists of a set of Lorentzians. Even more complex is QENS from diffusion over energetically different sites. The system of rate equation is expressed in terms of a jump matrix, but this matrix is not hermitean. The resulting eigenvalues are the linewidths of the Lorentzians, whereas from the eigenvectors the intensity of the Lorentzians can be calculated. This full power of QENS can only be realized on the basis of direction-dependent measurements on single-crystalline samples. A completely different approach is the so-called two-state model which applies for disordered systems and which is also derived in full detail.
8 Hydrogen in metals
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
This chapter focuses on special classes of materials. For QENS studies metal/hydrogen systems are particularly suited due to the huge incoherent scattering cross section of H, low concentrated systems and thus single particle behaviour can be studied, the mobility is large and thus well-pronounced line broadening are obtained, and if H is replaced by D, additionally coherent QENS can be performed. Long range diffusion studies are presented for intermetallic hydrides which allow statements about the rate limiting step in the hydrogen absorption kinetics. For NbDx, an extensive study of the collective diffusion is presented; the separation of coherent and incoherent scattering is done both by software (skillful data evaluation) and by hardware (polarization analysis). Then the diffusion mechanisms in metal/hydrogen systems of increasing complexity are discussed, where QENS exhibits its full power because of single-crystalline samples: H in fcc metals, H in bcc metals, hexagonal closed packed α-phase hydrides, β-V2H as an example of an ordered metal hydride, and LaNi5Hα as an example of an intermetallic hydride. Another scientific problem is the nature of the single diffusion step: hydrogen tunnelling in Nb doped with O, N, C, and in α-ScHx. Tunnelling is even more pronounced for the positive muon, an exotic isotope of the proton; muon diffusion studies in Al and Cu are presented for comparison. Finally, examples of hydrogen diffusion in disordered systems (crystalline metals with trapping impurities or even amorphous metals) are discussed.
12 Solid ionic conductors
Authors: Hempelmann Rolf 
Published: January 2010

Abstract
This chapter presents incoherent QENS studies performed on Li+, Na+, H-, and Cl- ions. Purely coherent QENS concerns F- and O2- conductors, whereas for Ag+ a mixture of coherent and incoherent QENS prohibits quantitative data evaluation. On the other hand, AgI is one of the best solid ionic conductors, and QENS studies are performed and combined with impedance spectroscopy at high frequencies. For this system, the well-known jump relaxation model is derived. Na+ motion in β-Al2O3 is investigated by QENS in detail. Much effort has been spent on Li+ diffusion motivated by applications of Li in batteries. For anionic conductors, the system best investigated by means of QENS is Cl- diffusion in SrCl2.
Quantum Dot Lasers
Authors: Ustinov Victor M. , Zhukov Alexey E. , Egorov Anton Yu. , Maleev Nikolai A. 
Published: January 2010

AbstractThis book is devoted to the physics and technology of diode lasers based on self-organized quantum dots (QD). It addresses the fundamental and technology aspects of QD edge-emitting and vertical-cavity surface-emitting lasers, reviewing their current status and future prospects. The theoretically predicted advantages of an ideal QD array for laser applications are discussed and the basic principles of QD formation using self-organization phenomena are reviewed. Structural and optical properties of self-organized QDs are considered with a number of examples in different material systems. The book includes recent achievements in controlling the QD properties such as the effect of vertical stacking, changing the matrix bandgap and the surface density of QDs. The book is also focused on the use of self-organized quantum dots in laser structures, fabrication and characterization of edge- and surface-emitting diode lasers, their properties and optimization. Special attention is paid to the relationship between structural and electronic properties of QDs and laser characteristics. The threshold and power characteristics of the state-of-the-art QD lasers are also demonstrated. Issues related to the long-wavelength (1.3-um) lasers on a GaAs substrate are also addressed and recent results on InGaAsN-based diode lasers presented for the purpose of comparison.
Intensities of plane waves in the transmission geometry
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter is concerned with the transmission, or Laue, geometry, and an incident plane wave. Two cases are considered, Laue–Laue and Laue–Bragg. After describing the boundary conditions at the exit surface, the reflectivity is calculated for absorbing crystals and the properties of the properties of the rocking curves are discussed. Finally, the integrated intensity is determined.
10 Spherical-wave dynamical theory: I. Kato’s theory
Authors: AUTHIER ANDRÉ 
Published: January 2010

Abstract
This chapter is the first of two dealing with the dynamical diffraction of incident spherical waves. It makes use of Kato's theory, which is based on a Fourier expansion of the spherical wave. The transmission and reflection geometries are handled separately. Two methods of integration are given — direct integration and integration by the stationary phase method. The amplitude and intensity distributions of the reflected and refracted waves on the exit surface are calculated. It is shown that equal-intensity fringes are formed within the Borrmann triangle (Pendellösung fringes) that can be interpreted as due to interferences between the waves associated with the two branches of the dispersion surface. The integrated intensity is calculated and the influence of the polarization of the incident wave discussed. The last section describes the diffraction of ultra-short pulses of plane-wave X-rays such as those emitted by a free-electron laser and which can be handled by considering their Fourier expansion in frequency space.
The Allan variance and the rms time error
Authors: Matthys Robert James 
Published: January 2010

Abstract
The traditional plot of a clock's time error versus time is far superior to the Allan variance for showing a pendulum clock's time performance. The Allan variance is admittedly a universal and statistically more accurate measure of a clock or oscillator's random frequency and time variations (that is, variance), because it is averaged over multiples of each time interval. However, it is a whole curve on a graph instead of being just a single memorable number, and its value is drastically reduced by the short time span it is able to cover. The variance, however, can be used to generate an oscillator's ‘root mean square (rms) time error versus time’ curve, a curve that is much easier to understand. But the rms time error's equally short time span also drastically limits its value to the clockmaker.
Transient temperature effects in a pendulum
Authors: Matthys Robert James 
Published: January 2010

Abstract
This chapter describes some transient temperature measurements made on a pendulum with a quartz pendulum rod. Time offset error occurs because different parts of the pendulum change temperature at different rates. Before and after a temperature change, the pendulum is the right length (hopefully) and runs at the right rate. But during the temperature change, the pendulum is the wrong length, due to its different parts changing temperature at different rates, and it runs at the wrong rate during the temperature change interval. Experiments were carried out to measure the pendulum temperatures using small thermistors. The pyrex sleeve provides about one-third of the temperature compensation, while two thin-walled pyrex tubes located on opposite sides of the quartz pendulum rod provide the other two-third. The temperature data provide an interesting look into the thermodynamics of a pendulum. The suspension spring assembly changes temperature relatively slowly, whereas the bob, with its large thermal mass, changes temperature the slowest of any part of the pendulum.