bluuebunny/crossref_metadata_2025_split huggingface dataset:
The dynamics of fluids: local equations
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D 
Published: November 2023

Abstract
Having introduced in the previous chapter the concept of the rate of strain of a flowing fluid, we discuss here the manner in which such deformations can be produced by application of a stress (external force, pressure, and so on). In the mechanics of solids, there exists a proportionality between the strain (or relative deformation) and the stresses, as long as the stresses are not too strong.
The conservation laws
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D 
Published: November 2023

Abstract
This chapter deals with various conservation laws for a moving fluid: conservation of mass, of momentum, and of energy. The question of the conservation of mass, already derived in Chapter 3, is only briefly restated here (Section 5.1), while the conservation of circulation (angular momentum) is treated in detail in Chapter 7.
Vorticity: dynamics of vortices
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D 
Published: November 2023

Abstract
In the discussion (Section 3.2) of deformations of an element of fluid, we have seen the appearance of a term involving the local rotation-the antisymmetric part of the velocity gradient tensor. The corresponding local rotation vector equals half the vorticity vector, defined as the curl of the velocity field. Thus, vorticity is the tool that enables us to characterize the local rotation within a fluid. In some cases, it can be localized in space, as in vortices; in others, it is continuously distributed, as in a fluid in uniform rotation.
Introduction
Authors: Sutton Adrian P 
Published: November 2023

Abstract
This book was written in order to replace two second-year undergraduate courses that used to be taught in the Department of Materials at Oxford University on free electron theory and band theory. Those courses considered the electronic structure of perfect crystals and exploited the translational symmetry of perfect crystals to set the problem up in reciprocal space. It was recognized that they did not serve the needs of a modern degree in materials science. Modern materials science is at least as concerned with defects in crystals and noncrystalline materials as it is with the properties of perfect crystals. (In a phrase often attributed to F. C Frank ‘crystals are like people-it is the defects in them that make them interesting’.) Band theory and free electron theory have very little to say about such things, because they rely on perfect translational symmetry and Bloch’s theorem.
Into two and three dimensions
Authors: Sutton Adrian P 
Published: November 2023

Abstract
In the last chapter we saw that an infinite chain of interacting atoms may simply be regarded as a one-dimensional molecule. If the chain does not consist of a periodic sequence of atoms the task of determining the eigenstates of the infinite system is impossible because it involves finding the eigenvalues and eigenvectors of a matrix of infinite dimensions. But if periodicity is present then Bloch’s theorem enables us to write down the eigenstates of the infinite system almost at a stroke as Bloch functions. In this chapter we shall show how these ideas are readily applied to two- and three-dimensional infinite perfect crystals. In this way we shall develop the standard machinery of the band theory of solids. However, we shall certainly not abandon our real space picture of solids in terms of local densities of states, the moments theorem, and bond orders. The relationships between the real and reciprocal space pictures that we developed in the last chapter for one-dimensional systems will be shown to be just as valid in two and three dimensions. Thus, we can use Bloch’s theorem to analyse the eigenstates of an infinite periodic system and we can use the local densities of states and bond orders to analyse the chemical bonding.
Band gaps: origins and consequences
Authors: Sutton Adrian P 
Published: November 2023

Abstract
Our discussion of the formation of energy bands in Chapters 3 and 4 was based on a simple s-band model. We associated ones state with each atom and we found just one band of states. Of course, the s-band model is a gross simplification because an atom is associated with more than just one s state. Depending on the value of the principal quantum number there may be s, p, d, ... states within each shell of the atom. At higher energies there is a continuum of free electron energy states, which far from the atom are represented by plane waves. We are concerned only with the valence electron states of the atom because the core states are too strongly bound to the atom for significant tunnelling to occur to neighbouring atoms. In the solid state, under normal pressures, core states remain bound to the core and therefore they do not give rise to energy bands. In this chapter we shall find that there is one band for each valence state in a unit cell of the crystal.
The transition metals
Authors: Sutton Adrian P 
Published: November 2023

Abstract
The transition metals are not simple metals. Their densities of states are characterized by a partially filled narrow d band, superimposed on a broad free electron-like s-p band, as shown schematically in Fig. 9.1. As we move across the series the d band is gradually being filled, until at the noble metals Cu, Ag, and Au it is filled. We shall see in this chapter that most of the properties of the transition metals are characterized by the filling of the d band, and that for many purposes we may neglect the sp electrons as a first approximation. This was first recognized by Friedel in his simple d-band model which we describe in the next section.
Where band theory breaks down
Authors: Sutton Adrian P 
Published: November 2023

Abstract
In this book we have tried to keep a balance between a real space, chemical picture, and a reciprocal space band theory picture of the electronic structure of a solid. In an amorphous solid the reciprocal space approach breaks down completely. There is no translational symmetry with which to define a reciprocal lattice or Brillouin zone and we are forced to think in terms of chemical bonds. One could argue that this remark applies to a crystalline solid containing a defect but that is not entirely fair because it is possible to think of the defect as a perturbation to the crystal and to solve for its electronic structure using perturbation theory. But in an amorphous material that is not possible because the whole specimen is ‘perturbed’ in the sense that there is no crystalline material anywhere.
Diluted Magnetic Semiconductors
Authors: Miura Noboru 
Published: November 2023

Abstract
When semiconductor crystals are doped with magnetic impurity ions, the crystals possess both semiconducting and magnetic properties. Thus many possibilities for application to useful devices are opened up. A number of early attempts to clarify the properties of magnetic impurities in semiconductors were made in order to study the electron spin resonance in magnetic ions. In the early 1970s, a Warsaw-based group developed a new class of diluted magnetic semiconductors, II-VI semiconductors doped with transition metal ions such as Mn2+ or Fe2+ [494–496]. The magnetic ions are substituted for the cations of the mother crystals isoelectrically, and act as randomly distributed paramagnetic ions.
Electromagnetic radiation—observed and imagined
Authors: Duke Philip John 
Published: November 2023

Abstract
In Chapter 2 it was shown that electromagnetic fields can be propagated through space at the speed of light and that the field in this dynamic form is known as electromagnetic radiation. The identification of electromagnetic radiation with light, combined with the direct observation of radio waves and the measurement of the velocity of these waves by Hertz (Heinrich Rudolf Hertz, 1857–94), generated some serious conceptual problems. The speed at which the light was moving would be expected to depend on the relative movement of the source and the observer.
Behaviour of the electron beam in a synchrotron radiation storage ring. Betatron oscillations
Authors: Duke Philip John 
Published: November 2023

Abstract
In Chapter 10 we obtained the equation of motion of a particle in the magnetic fields of a storage ring and we showed how the motion of an individual particle could be traced throughout the storage ring using the transformation matrices. In order to proceed further, we must now describe the individual behaviour of a particle as it travels around the storage ring and relate this motion to the concept of the phase space ellipse which we developed in the last chapter.
Behaviour of the electron beam in a synchrotron radiation storage ring. Energy oscillations
Authors: Duke Philip John 
Published: November 2023

Abstract
Just as deviations form the ideal orbit lead to betatron oscillations, so also deviations from the ideal energy lead to energy oscillations which are sometimes called synchrotron oscillations. These oscillations contribute to the size of the electron beam in the horizontal plane because energy deviations lead to deviations in position and direction of the electrons through the dispersion function fsee eqn ( 11.9)]. Because the dispersion function depends on the value of the s-coordinate around the ring, the contribution of the energy oscillations to beam size also depends on D(s). Furthermore, because the dispersion function tends to follow the contour of the beta function [see eqn ( I 1.11)], the effects of the betatron and synchrotron oscillations tend to combine to increase the beam size instead of cancelling each other out. If the energy distribution of the electrons follows a Gaussian function with standard deviation σ(E), then from eqn (11.9) the contribution of the energy oscillations to the total beam width is (σ (E)/ Eo) × D(s). In any practical storage ring, Q is a long way from resonance so we can assume that the two types of oscillations are uncorrelated and add the contributions from the betatron [eqn ( 10.29)] and synchrotron oscillation in quadrature.
Transverse Beam Dynamics In Circular Particle Accelerators For High Energy Physics
Authors: Asner Fred M 
Published: November 2023

Abstract
Classical and superconducting magnets and conventional and superconductive high frequency cavities are the basic elements in any circular accelerator and collider. The magnets determine the particle or beam behaviour in the transverse plane, the cavities in the longitudinal. Specific beam oscillations, related to the interplay of both transverse and longitudinal phenomena, will not be considered. Since we are mainly interested in the quality and requirements on superconducting accelerator magnets, a short introduction to transverse beam dynamics and beam optics will be given. The success of any accelerator or collider for high energy physics will, among others, depend on a close harmonization and mutual matching between transverse beam dynamics requirements and the superconducting magnet performances from the design stage to the completion and operation of the accelerator.
Perturbation Theory and the WKB Approximation
Authors: Kashiwa T , Ohnuki Y , Suzuki M 
Published: November 2023

Abstract
Path integral formulae for the (p, q) system and (a†, a) of the Bose and Fermi systems can only be calculated exactly in the harmonic oscillator case. Other physical situations require some approximation schemes. In this chapter we try to make explicit calculations for the harmonic oscillator and discuss a perturbation technique and the WKB approximation that is considered to be most suited to the path integral formalism. As an illustrative example, a detailed computation is performed for the case where non-trivial solutions, called instantons, exist in the classical equation of motion.
Problems in Solid State Physics
Authors: Kashiwa T , Ohnuki Y , Suzuki M 
Published: November 2023

Abstract
In the present chapter, we explain some basic applications of the path integral method in condensed matter physics without going into details of calculations, with a great emphasis on the conceptual parts of it. The first example is a theory of stochastic processes in which the path integral is explained physically. Using this, a fundamental mechanism of order formation in an unstable system is discussed. The second topic is to treat a chemical reaction quantum mechanically from the viewpoint of molecular collisions, using the path integral formulation. The third topic is macrscopic tunnelling and its frictional effect.
Properties of an isolated polymer molecule
Authors: Doi M , See H 
Published: November 2023

Abstract
A polymer is a large molecule made up of many small, simple chemical units, joined together by chemical reaction. For example, polyethylene As with most other substances, in order to understand the properties of polymeric materials we must consider a large assembly of molecules. However, in the case of polymers, the molecules themselves are very large, and we need to use statistical mechanics to calculate the characteristics of even an isolated polymer. One way to investigate the properties of a single polymer is to place it in a very dilute solution, so that interactions between the polymers can be neglected. Experimentally, such dilute polymer solutions are used to determine the size and molecular weight of the molecule. In this chapter, we will theoretically investigate the properties of an isolated, single polymer chain in solution.
Concentrated solutions and melts
Authors: Doi M , See H 
Published: November 2023

Abstract
As the concentration in a polymer solution is increased, the molecules start to overlap and begin to entangle with each other as shown in Fig. 2.1. The critical concentration at which this commences is called the overlap concentration. Let us write c* for the number of segments per unit volume at this concentration, so that the number of polymers per unit volume is c* / N.Since the volume of one polymer is of the order R/, we must have Notice that the overlap starts at very low concentration if N is large. (For example, polystyrenes of molecular weight 10 start to overlap at 0.5 % weight concentration.) Therefore, polymers with large molecular weight are almost always in the entangled state, and are strongly interacting with each other.
Quantum Theory
Authors: Araki Huzihiro 
Published: November 2023

Abstract
In this chapter we explain how we can describe quantum theory within the general framework given in Chapter 1. We do not discuss various theories concerning the question of how quantum theory can (or cannot) be deduced from experimental facts or from a verifiable axiomatic system. Instead we start by introducing the assumptions of quantum theory. The main content is the algebraic viewpoint of quantum theory based on the theory of operator algebras, the GNS construction which supplies the fundamental relation between the description of the states by Hilbert space vectors and the description of the states in this general framework, the Wigner theorem which is basic for the mathematical description of quantum mechanical symmetries, and its generalizations. The basic definitions and theorems about Hilbert spaces and operator algebras are collected in the appendix.
Magnetism Of Ferrimagnetic Oxides
Authors: Chikazumi Sōshin , Graham, Jr C D 
Published: November 2023

Abstract
Most oxides are electrically insulating. Therefore magnetic oxides such as ferrites exhibit very low losses when magnetized in high-frequency fields. This characteristic has been very useful in magnetic materials for communication and information devices. In Section 9.1 we note the general features of oxide crystals, then discuss magnetic and crystalline properties of spinel ferrites in Section 9.2, garnet ferrites in Section 9.3, hexagonal ferrites in Section 9.4, and finally other oxides in Section 9.5.
Magnetism Of Amorphous Materials
Authors: Chikazumi Sōshin , Graham, Jr C D 
Published: November 2023

Abstract
In Chapters 8−10, we treated metals, oxides and compounds, all in crystalline form with atoms arranged on regular lattices. There is another group of materials,amorphous materials,in which the atoms are distributed in an irregular manner. Ordinary glass is a representative example of an amorphous material. When a beam of monochromatic X-rays is scattered by such an amorphous material, there is no well-defined diffraction pattern, as in the case for crystalline materials. Instead there are only diffuse halos, from which we can deduce the statistical distribution of atoms.
Spin Distribution And Domain Walls
Authors: Chikazumi Sōshin , Graham, Jr C D 
Published: November 2023

Abstract
Micromagnetics is the name coined by Brown1,2 for the procedure by which the distribution of spins in a ferromagnet of finite size is solved from first principles. In an infinitely long, thin ferromagnet, the spontaneous magnetization is aligned parallel to the long axis, thus forming a single domain. In a ferromagnet of finite size, such a single domain produces surface free poles which give rise tomagnetostatic energy,Umag In order to reduce Umag, the spin distribution must be altered, which modifies the complete parallel spin alignment. As a result,exchange energy, Uex, magnetoc,ystalline energy, Ua,or Ua magnetoelastic energy, Uλare increased. The stable spin distribution is determined by minimizing the total energy
Fundamental Constants And Energy Conversion Factors
Authors: Taylor Barry N , Cohen E Richard 
Published: November 2023

Abstract
This chapter gives the values of the basic fundamental physical constants and energy conversion factors of physics and chemistry currently recommended for international use by CODATA*. These values, the most up-to-date, self consistent set presently available, are a direct result of the 1986 CODATA least-squares adjustment of the fundamental constants carried out by the authors under the auspices of the CODATA Task Group on Fundamental Constants. The 1986 CODATA set of recommended values replaced the 1973 set, its immediate predecessor, which resulted from the 1973 CODATA least-squares adjustment.3’4 That adjustment was also carried out by the authors under the auspices of the Task Group.
Tables Of Alpha-Particle Emitters: Energies And Emission Probabilities
Authors: Nichols A L 
Published: November 2023

Abstract
A large majority of the alpha-particle-emitting radionuclides are identified with the heavier elements, which are generally more unstable with respect to 4He emissions than the other decay modes. It should be noted that the result¬ing tabulations are not comprehensive; they do not include all known alpha particle-emitting radionuclides nor all of the alpha-particle emissions identified with each individual radionuclide. Only the major alpha-particle emissions are listed (i.e. generally emission probabilities greater than 0.01), along with indications of the commonly used energy and emission probability standards.
Table of Nuclides*
Authors: Tuli† Jagdish K 
Published: November 2023

Abstract
This table presents half-life, abundance, decay modes, spin, parity, and mass excess for all known nuclides and some of their isomeric states. The data given here are from the adopted properties of the various nuclides as given in the Evaluated Nuclear Structure Data File (ENSDF)1. The data in ENSDF are based on experimental results as reported in Nuclear Data Sheets for A=45 to 266 and in Nuclear Physicsfor A&lt;45. For those nuclides for which either there are no data in ENSDF or more recent data are available, the half-life and decay modes are taken from the Chart of the Nuclides, 14th Edition.
Resume of bulk semiconductor physics
Authors: Kelly M J 
Published: November 2023

Abstract
In this chapter, we collect some of the key basic facts about the bulk properties of the semiconductors silicon, gallium arsenide, and aluminium arsenide that form the background material for the rest of this book. The material is selected solely on the basis of its use in subsequent chapters. If this were a book on solid state physics, such as those written by Kittel (1986), Ashcroft and Mermin (1976), or Madelung (1978), or on bulk semiconductors, such as those by Smith (1978), Seeger (1991), or Harrison (1980), much greater detail would be appropriate. We refer readers to these texts in the search of that greater detail. In particular, the terms in italics in this chapter have precise definitions which can be obtained from these texts.
III-V Semiconductor Homojunctions And Heterojunctions
Authors: Kelly M J 
Published: November 2023

Abstract
In the Introduction, we referred to the hundredfold reduction in the lateral feature size of transistors in integrated circuits over the period from the late 1960s to the present day. This reduction has been accompanied by a similar scaling down of vertical dimensions of the devices, i.e. in the thicknesses of the individual layers (see Dennard et al. (1974) and Chapter 21 below). Indeed, if one takes the p-n-p bipolar transistor from its earliest fabrication to the present day, new technologies that have allowed the ever sharper internal interfaces of devices to be achieved have appeared at intervals of approximately 10 years. The original transistors were made in the 1950s by alloying in the species to make a p-type layer in a host n-type material, and then overalloying to produce a new n-type layer near the surface. This technique is exceptionally crude by today’s standards. The interface between then- and p-type material is uncontrolled over thicknesses of micrometres. Furthermore, the interface follows the melt front of the alloying species.
Fabrication Technologies For Semiconductor Microstructu Res
Authors: Kelly M J 
Published: November 2023

Abstract
The last chapter began with a reference to the hundredfold decrease in the key feature sizes of the transistors that appear in memory chips from small fractions of a millimetre in the 1960s to fractions of a micrometre today. In Fig. 3.1, we show a section of part of a Si circuit and a high magnification photograph of the surface. In general, such diagrams and photographs do not do justice to the very tight tolerances that must be achieved before the devices work to full specification, but we should bear them in mind as we proceed. It is not sufficient to produce a small structure as the key part of a device, unless that structure can be repeated millions of times with a spread in properties that is a smaller fraction again of the structure of interest, for example 0.1 µm length gates with rather less than 10 per cent variation in that length. The purpose of this chapter is to describe the technologies used in the fabrication of semiconductor microstructures for physics and device studies. The techniques described here as used for research purposes are recognizable extrapolations of the technologies as used in the manufacture of today’s integrated circuits (whether in Si or GaAs). These state-of-the-art fabrication techniques are available precisely because they are foreseen as essential in one or other strategy for the fabrication of future devices. The physics investigation of these microstructures, quite apart from its intrinsic interest, is meant to shed light on the various choices of technology that might be applied in the year 2000 and beyond.