bluuebunny/crossref_metadata_2025 huggingface dataset:
Paramagnetism
Authors: Dobbs E R
Published: November 2023

Early measurements of the magnetic properties of solid helium 3 were made over a range of pressures that included both the b.c.c. and h.c.p. phases (see Fig. 2.3), but were limited to temperatures above a few millikelvin.
The renormalization group at T ≠ T
c
Authors: Binney J J , Dowrick N J , Fisher A J , Newman M E J
Published: November 2023

To calculate the remaining critical exponents and to complete our understanding of the Landau-Ginzburg model in the critical regime, we have to calculate quantities in the limit m2 → 0, rather than at m2 = 0.
Thermometry
Authors: White Guy K , Meeson Philip J
Published: November 2023

The zeroth law of thermodynamics says that two bodies which are in thermal equilibrium with a third body are in thermal equilibrium with each other. Then no heat flows from one to the other and they are said to be at the same temperature. Changes in their temperature will usually produce changes in their physical properties, be it electrical resistance, dimensions, vapour pressure, etc. Such properties can therefore serve in instruments for measuring temperature or temperature change. A temperature scale can be defined in terms of any of a number of thermometric properties, and the scale and size of particular temperature intervals may be fixed by reference to common phenomena such as boiling or freezing points or other phase changes. So the thermal expansion of a liquid or gas, the electrical resistance of a metal or semiconductor or thermopower are all physical parameters which for the chosen substance could define a temperature scale with the scale chosen to be a linear or other function of the parameter.
Near neutrality and its implications for evolution
Authors: Ohta Tomoko
Published: November 2023

By the middle of the twentieth century, neo Darwinism was very popular among evolutionary scientists and random genetic drift was thought to be unimportant except in the context of Wright’s shifting balance theory. Then, in the 1960s, Kimura applied population genetics theory to biochemical data. He compared amino acid sequences of cytochrome ca and hemoglobin a among mammalian species available at that time, and found that the number of mutant substitutions in evolution was larger than expected according to Haldane’s prediction based on genetic load. In 1968, Kimura proposed the neutral theory of molecular evolution (Kimura 1968).
Rates and effects of deleterious mutations and their evolutionary consequences
Authors: Garca-Dorado Aurora , López-Fanjul Carlos , Caballero Armando
Published: November 2023

In a highly influential paper, Muller (1950) put forward the idea that deleterious mutations affecting the heterozygote appear at a high rate in populations, thus, imposing a reduction in fitness (mutational load) that could become unbearable. As shown by Haldane (1937), this load is mainly determined by the rate of deleterious mutations and is practically independent of their severity, although it is modulated by their degree of dominance. It took a long time until adequate experimental data for Drosophila viability were first obtained by Mukai (1964), who estimated a high genomic rate of mutations (haploid rate A > = 0.3, the number of deleterious mutations appearing per gamete and generation) showing very little dominance (average coefficient of dominance E(h) = 0.4, where h = 0, 0.5, and 1 denotes recessive, additive and dominant gene action of mutations, respectively) and mild average effects (average selection coefficient E(s) < 007E 0.03, the relative reduction in fitness of the homozygous mutant).
Cooperation and conflict during the unicellular–multicellular and prokaryotic–eukaryotic transitions
Authors: Michod Richard E , Nedelcu Aurora M
Published: November 2023

Individuals often associate in groups that, under certain conditions, may evolve into higher-level individuals. It is these conditions and this process of individuation of groups that we wish to understand. These groups may involve members of the same species or different species. For example, under certain conditions bacteria associate to form a fruiting body, amoebae associate to form a slug-like slime mold, solitary cells form a colonial group, normally solitary wasps breed cooperatively, birds associate to form a colony, and mammals form societies.
The New Kingdom
Authors: Brown Andrew
Published: November 2023

The Cavendish Laboratory in 1927 was passing through a quiet period. Patrick Blackett’s bright star was already shining in the firmament, but the other young men in Rutherford’s department were engaged in painstaking preparatory work – refining experimental techniques and building new equipment – not yet making fundamental discoveries of their own. Rutherford was steadfast in his intent to reveal the structure of the atomic nucleus, relying for the most part on the trusty a-particle as his major tool of interrogation. Unlike Bernal, Rutherford was sceptical of the new quantum theory, and did not disguise his mistrust – for example, thanking Heisenberg, who had just delivered an invited lecture to the Cavendish Physical Society in perfect English, for ‘a lot of interesting nonsense’.
Scientist At War
Authors: Brown Andrew
Published: November 2023

In the summer of 1939, Bernal returned to the United States for the first time since he had been taken there as a small boy by his mother. As before, California was his main destination, but now he was invited to give a series of lectures at Stanford University. These were part of the celebrations organized by the University to mark the centenary of the theory that all living things, plant and animal, are composed of cells. At the end of June, Bernal gave lectures on successive days to the Pacific Division of the American Academy of the Advancement of Science on the structure of proteins, and to the American Physical Society on the X-ray studies of plant virus particles. After the fourth-of-July holiday, he took part in a four-day meeting at Stanford on colloids.
Overlord
Authors: Brown Andrew
Published: November 2023

The headquarters of Combined Operations (COHQ) occupied what was formerly the town house of the Dukes of Buccleuch, in Richmond Terrace. One of the more volatile and cantankerous characters in residence during 1942–3 was Evelyn Waugh, the novelist. He was there as Liaison Officer representing the Special Service Brigade, until he was forced out by his senior officers for constantly causing trouble. He was often drunk. The week after Bernal returned from his travels, Waugh arrived for lunch with Mountbatten ‘rather tipsy’ and ‘found the house a nest of Communists’, suggesting that Sage was back at work. Habbakuk remained the highest priority for Bernal, although the Canadians were not pressing ahead with a large-scale model and there seemed no prospect of an operational berg ship until 1945. A meeting was held at COHQ to review the situation at the end of May; Bernal stated that he still believed a berg ship was feasible and that Pykrete was the best material to use. Perutz indicated that 1.7 million tons of Pykrete in block form would need to be produced during the next Canadian winter to construct one berg ship ready for use in 1945.
Lessons Of War
Authors: Brown Andrew
Published: November 2023

The complexities of South-East Asia Command (SEAC) were such that they would have overwhelmed a leader without Mountbatten’s ineffable selfconfidence. By 1943, most of South-East Asia was firmly under Japanese control, following the unstoppable advances they had made through thick jungles, which the British had long regarded as impenetrable. To the British soldier, the Japanese had taken on the aura of invincibility, and morale was further depressed by the debilitating tropical conditions that bred mosquitoes and malaria. Mountbatten’s approach to raising spirits was direct and simple. Relying on his royal pedigree, he cheerfully informed the troops that they were not the Forgotten Army: no one had ever heard of them, but this was all going to change under his leadership. His absurd optimism and ironic humour proved irresistible.
Evaluating the relative strengths of biotic versus abiotic controls on ecosystem processes
Authors: McBride M A Huston ,A C
Published: November 2023

There is no doubt that the rates of ecosystem processes and the resulting properties and structure of ecosystems are influenced both by biotic factors, including species properties and interactions among multiple species, and by abiotic factors, such as climate, geology, and soils. The critical issue (and the focus of the debate about diversity and ecosystem function) is the relative contribution of each of these general factors to any particular ecosystem process, under any particular conditions, and at any particular scale.
How can marine ecology contribute to the biodiversity-ecosystem functioning debate?
Authors: Emmerson M , Huxham M
Published: November 2023

Recent debate over the effects of species loss has been informed by experiments carried out largely in terrestrial ecosystems (McNaughton 1993; Tilman et al. 1996; Hooper and Vitousek 1997; Wardle et al. 1997a; Hector et al. 1999). A few studies have examined the effects of species loss on ecosystem processes such as biomass, density, decomposition and respiration in aquatic microbial (McGrady Steed et al. 1997; Naeem and Li 1997; Petchey et al. 1999) and invertebrate (Hulot et al. 2000; Norberg 2000) ecosystems. Fewer still have explicitly addressed the effects of species richness on eco system processes in the marine environment (Stachowizc et al. 1999; Duffy et al. 2001; Emmerson et al. 2001).
Biodiversity, ecosystem functioning and above-ground-below-ground linkages
Authors: Wardle D A , Putten W H van der
Published: November 2023

All terrestrial ecosystems consist of an explicit producer subsystem and a decomposer subsystem. While traditionally these components have usually been considered in isolation from one another, they are obligatory dependent upon each other. Producers provide the organic carbon sources that drive the decomposer community and decomposer activity is in turn responsible for mineralizing nutrients required for maintaining growth of the producers. Mutualists, herbivores, pathogens and parasites affect producer-decomposer interactions both by directing changes in the flow of energy and resources, and by imposing selective forces that lead to evolutionary changes in individual producer and decomposer populations. The direct and indirect interactions between above-ground and below ground communities therefore have the potential to operate as major drivers of population-, community- and ecosystem-level processes (Hooper et al. 2000; Van der Putten et al. 2001; Wardle 2002).
Biodiversity, ecosystem functioning and soil decomposer food webs
Authors: Mikola J , Bardgett R D , Hedlund K
Published: November 2023

Decomposer organisms are essential for the functioning of terrestrial ecosystems; they mineralize carbon and nutrients that are bound to dead organic matter and provide resources for primary production. However, linking soil decomposer diversity with ecosystem functioning is difficult as processes in soil are not controlled by a uniform group of organisms but an array of interacting bacteria, fungi and fauna (Beare et al. 1995; Ekschmitt and Griffiths 1998). Further, the considerable lack of knowledge about the roles of individual species (especially within bacteria, fungi, microfauna and mesofauna) hinders our ability to identify the unique functions that decomposer species might perform.
Meson-Exchange Currents
Authors: Castel B , Towner I S
Published: November 2023

To introduce the topic of meson-exchange currents it is necessary to review some elements of quantum electrodynamics. We have relegated most of this to Appendix A, which serves mainly as a way of introducing our notation. We will assume the reader has some familiarity with the topics of field theory, Lagrangians, Dirac equation, and Feynman diagrams; if not, there are many textbooks that can be consulted.
Quadrupole Moments and Collective Model Theories
Authors: Castel B , Towner I S
Published: November 2023

Large quadrupole moments and E2 transition rates, characteristic of deformed systems, are often well described using simple collective models. These models which were actually first devised for this purpose have also shown some success in describing vibrational excitations and in particular an harmonic excitations. We will examine them in this chapter in an evolution having a dual character, from the phenomenological to the microscopic and from the vibrational to the rotational. We thus first concentrate on collective excitations in spherical nuclei.
Introduction
Authors: Harakeh M N , van der Woude A
Published: November 2023

1.1 What is a giant resonance? A powerful method to study the properties of a system is to subject it to a weak external perturbation and to examine its response. For the atomic nucleus subjected to the absorption of a photon or to the scattering of a particle (electron, proton, etc.) the response is sketched in Fig. 1.1 as a function of the energy and linear momentum transferred to the system. The lower curve shows the response (cross section) for photon absorption in which case the momentum transfer is equal to the energy transfer, in natural units q = w, while the upper curve gives the response for the scattering of a particle with q = 2 fm-1 ≠ ω. Up to about 10 MeV the nucleus responds through the excitation of relatively simple states often involving only one or a few particles. In the energy range between 10 and 30 MeV the system response exhibits broad resonances. These are the giant resonances which are the subject of this book. The large, broad resonance located around an energy transfer of about 100 MeV in the upper curve corresponds to the quasi-elastic scattering of the projectile off an individual nucleon in the nucleus while the Δ33 resonance is due to nucleon excitation.
Decay of GRs
Authors: Harakeh M N , van der Woude A
Published: November 2023

Since most GRs are located above the particle-decay threshold, they will mainly decay by particle emission, i.e. neutrons and protons, and in light nuclei also by a-particles. GR decay is a very valuable tool to learn about the microscopic damping mechanisms of these collective modes. Therefore, it is not surprising that there exists an extensive literature on experimental and theoretical studies of GR decay. Several review papers give a good overview of this kind of research - see (BER83, WAM88, KNO91, BER94a, BOR98). In a heavy nucleus charged-particle decay is strongly suppressed because of the Coulomb barrier so that for these nuclei particle decay occurs mainly by neutrons. γ-decay, although much weaker, is also possible. In general, such studies involve coincidence experiments of the type (x, x’ c) where c can be any kind of particle or a photon. The study of the decay properties of GRs is interesting for several reasons.
Protein Serine-Threonine Kinases
Authors: Kennelly Peter J , Edelman Arthur M
Published: November 2023

In nature, a broad range of proteins become modified via the covalent bonding of phosphate to nucleophilic functional groups located on the side-chains of their constituent amino acids. Although numerous amino acids can be modified in this way, by far the most widespread and quantitatively significant phosphorylation events take place on the hydroxyl groups of serine and threonine (Hunter 1991). Protein phosphorylation is a truly ubiquitous phenomenon, both in terms of the range of proteins modified-a murine fibroblast contains several hundred phosphoproteins (Levenson and Blackshear 1989) and a Escherichia coli contains over a hundred (Cortay et al. 1991)-as well as the diversity of organisms in which it has been observed. Virtually all living cells, regardless of function, habitat, or phylogeny, are sites of protein phosphorylation.
Inhibitors of Viral DNA Polymerase
Authors: Foster Scott A , Cheng Yung-chi
Published: November 2023

Viral DNA polymerase offers an attractive target for the development of anti-viral agents. Many DNA viruses encode a DNA polymerase. Examples include adenoviruses (AdV) (Challberg and Kelly 1989), poxviruses such as vaccinia virus (Moss 1986), and herpes viruses such as herpes simplex virus types 1 and 2 (HSV-1 and HSV-2), human cytomegalovirus (CMV), varicella-zoster virus (VZV), and Epstein-Barr virus (EBY) (Roizman, and Batterson 1986). The DNA polymerase of these viruses is a key enzyme for their replication. Further, the viral DNA polymerases often differ enough from the host DNA polymerases to allow some degree of selective inhibition of the viral enzyme over the host DNA polymerases. In addition to the inherent differences between the viral and host DNA polymerases, specificity in inhibiting the viral DNA polymerase over the host enzymes can be achieved through the exploitation of other biochemical differences between infected and uninfected cells. Such differences could include membrane changes associated with the viral infection that allow anti-viral agents to penetrate infected cells more easily or metabolic changes that allow the selective activation of pro-drugs in infected cells.
Steroidogenesis Pathway Enzymes
Authors: Brodie Angel
Published: November 2023

The enzymes involved in the biosynthesis of cholesterol and steroid hormones are proving to be major targets for therapeutic intervention. Inhibitors of several of these enzymes have established clinical efficacy and are proving to be important in the treatment of disease. The most important of these enzymes and their inhibitors will be reviewed in the following sections. Figure 9A.1 of this chapter shows an abbreviated version of the biosynthetic sequence of cholesterol and steroid hormones from the three carbon units of mevalonate which are mediated by these enzymes.

Inhibitors of aromatase (oestrogen synthetase) and 5a-reductase have gained much attention in recent years in the treatment of steroid-hormone related disorders. Aromatase is an enzyme complex consisting of a cytochrome P450 haemoprotein and a ubiquitous electron-donating flavo protein, NADPH-cytochrome P450 reductase. The C19 androgen substrates androstenedione and testosterone bind to the P450 aromatase (P450 arom) which catalyses the aromatization of the androgen A ring and the loss of the C19 methyl group to yield oestrone and oestradiol (Cole and Robinson 1990).
DNA Topoisomerases
Authors: Foste! Jennifer , Shen Linus L
Published: November 2023

DNA topoisomerases are a class of enzymes that modulate the topo logical structure of DNA. Since the discovery of the first topoisomerase 20 years ago (Wang 1971), many of the properties of this class of enzymes have been elucidated and this progress has been the subject of many reviews (Cozzarelli 1980; Gellert 1981; Liu 1983; Drlica 1984; Wang 1985, 1987b; Maxwell and Gellert 1986; Yanagida and Wang 1987; Osheroff 1989a; Austin and Fisher 1990, Champoux 1990; Hsieh 1990;.Osheroff et al. 1991). In purified systems, topoisomerases relax supercoiled DNA, and can tie and untie DNA knots, and link and unlink catenated DNA circles. In eukaryotic cells, type I topoisomerases are associated with elongating transcription and replication forks, while type II topoisomerases are essential for segregating daughter chromosomes after DNA replication is complete (Yanagida and Wang 1987). Topoisomerases are also the target of a number of antineoplastic and antibacterial agents whose cytotoxic effects appear to arise from the stabilization of a complex between the topoisomerase and DNA (Ross 1985; Glisson and Ross 1987; Drlica and Franco 1988; Liu 1989; Smith 1990).
Inhibitors of Gastric H +, K+ -ATPase
Authors: Wallmark Bjorn , Keeling David , Lindberg Per
Published: November 2023

Acid-related diseases include reflux oesophagitis, duodenal ulcer, gastric ulcer, and the Zollinger-Ellison syndrome. These disorders are treated by a reduction of gastric acid secretion which can be achieved by surgery, antacids, or pharmacological agents. Several classes of antisecretory agent have been developed and introduced into clinical use. These include anti cholinergic compounds, such as pirenzipine, and the histamine H2-receptor antagonists (H2RAs), such as cimetidine (Black et al. 1972). The intro duction of cimetidine was followed later by other H2RAs, such as ranitidine and famotidine. In addition, stable prostaglandin analogues with antisecretory properties have been developed. However, these agents have been found to possess relatively weak ulcer healing properties (Nicholson 1985).
Fundamental Properties of the Neutron
Authors: Alexandrov Yu. A , Drozdova T F
Published: November 2023

The neutron is an elementary particle that has been extensively studied, both theoretically and experimentally. This book reviews and analyses the results of the mainly experimental research on the neutron and rationalizes what is known so far about its intrinsic properties. The book covers topics that have not previously been dealt with in detail, including the gravitational properties of the neutron, precise determination of its mass, beta-decay, and its electromagnetic properties. This translation is an updated version of the original Russian text and also covers the more recent advances made during the past 7-8 years, including the application of methods based on the storage of ultra-cold neutrons to the study of beta-decay, new precise measurement of the mass of the neutron, and confirmation of modern theories of the internal structure of the neutron.
Magnetic Moment of the Neutron
Authors: Alexandrov Yu. A , Drozdova T F
Published: November 2023

The neutron is a Dirac particle and according to the Dirac equation it must have a zero magnetic moment. However, at the beginning of the 1930s, as soon as the magnetic moments of the proton and deuteron had been determined, Esterman and Stern[168] showed that the obtained results led to a hypothesis of the neutron having a negative magnetic moment of about 2µN, where µN = eħ/2mp  c is the nuclear magneton and mP is the proton mass. Tamm and Altschuler[169] were able to make an analogous suggestion on analysing the nuclear magnetic moments data. In 1937 Frisch et al.[170] made one of the first attempts to determine the magnetic moment of the neutron µn by observing the reorientation of the moments in a beam of polarized neutrons using an alternating magnetic field in resonance with the Larmor frequency of precession of the neutrons in a superimposed uniform magnetic field. The result of the experiment was more qualitative than quantitative and confirmed that the neutron magnetic moment is negative and approximately equal to 2µN.
Magnetic dichroisrn
Authors: Lovesey S W , Collins S P
Published: November 2023

Dichroism is the polarization dependence of the absorption of light. In general, the response of an electron charge distribution to an electromagnetic disturbance is anisotropic, due for example to the directionality of chemical bonds, crystal fields, and molecular orientation. Depending on the local symmetries exhibited by a material, this can lead to linear- and/or circular-polarization-dependent attenuation coefficients. Undoubtedly, the most famous example of linear dichroism at optical wavelengths is Polaroid sheet, in which oriented long-chain molecules absorb only the component of light which is linearly polarized parallel to the chains. Dichroism has been observed in a wide range of materials, at wavelengths extending up to hard X-rays. In the X-ray region, though, the effect is usually only significant very close to absorption edge resonances, where the excited photoelectrons are most strongly influenced by the internal fields of the absorber.
Resonant diffraction from antiferromagnets
Authors: Lovesey S W , Collins S P
Published: November 2023

The extreme weakness of magnetic X-ray diffraction compared with non-magnetic scattering, outlined in Chapter 2, presents a considerable challenge to experiments. Indeed, a great deal of effort has been deployed towards the goal of increasing the magnetic sensitivity of X-ray scattering. To this end, a fecund discovery (Namikawa et al. 1985) was a small, yet crucially important, resonance enhancement to the magnetic scattering from ferromagnetic nickel at wavelengths very close to the K-shell absorption edge (§6.2.3). This and the following chapter address the volume of work reported subsequent to the discovery.
Electronic energy bands: semiconductors
Authors: Balkanski M , Wallis R F
Published: November 2023

Pure semiconductors without deviations from periodicity have the important characteristic that at the absolute zero of temperature all energy bands up to and including a certain band are completely full of electrons and bands of higher energy are completely empty. There is a gap between the top edge of the highest filled band and the bottom edge of the lowest empty band. This gap is called the fundamental gap. The electrons occupying the lowest filled bands are strongly localized about individual nuclei and are termed core electrons. The electrons in the higher filled bands are less localized than core electrons and participate in covalent bonds between atoms. These electrons are valence electrons, and the bands they occupy are valence bands. For reasons that will become clear later, the bands that are empty at OK are conduction bands.
Electronic effects of impurities
Authors: Balkanski M , Wallis R F
Published: November 2023

Impurities can have a drastic effect on the properties of semiconductors, particularly the electrical properties. They can provide additional current carriers, such as conduction electrons or valence holes, and scattering centers which perturb the motion of the carriers. Impurities are conveniently classified according to the column of the periodic table in which they occur.
Bipolar iunction transistor
Authors: Balkanski M , Wallis R F
Published: November 2023

In Chapter 12 the p-n junction and the metal-semiconductor junction were discussed. These devices are two-terminal devices which are useful as rectifiers, but cannot be used as amplifiers because they contain no mechanism for modulating the electric current in such a way as to produce gain. What is needed is a third terminal to provide the necessary modulation.
Phonons in superlattices
Authors: Balkanski M , Wallis R F
Published: November 2023

We have seen in Chapter 7 that in a three-dimensional homogeneous crystal there are three frequency ranges of importance for the normal modes of vibration of the atoms. The low-frequency range contains the acoustic branches. In crystals containing two atoms per unit cell, the acoustic branches lie below an intermediate frequency range corresponding to a forbidden gap. The high-frequency range lies above the gap and contains the optical branches. Under certain circumstances, there may be no for-bidden gap even though optical modes exist. If there are more than two atoms per unit cell, there may be several forbidden gaps and several frequency ranges containing optical modes.
Metal-semiconductor devices
Authors: Balkanski M , Wallis R F
Published: November 2023

Among the most common heterostructures found in device applications are the metal-oxide-semiconductor (MOS) structure and the metal-semiconductor (MS) structure. The former is used in the metal-oxide-semiconductor capacitor and the metal-oxide-semiconductor field effect transistor, while the latter is the basis for the metal-semiconductor diode. These devices are referred to as unipolar devices, because current is transported by carriers of a single polarity, typically electrons. They are to be contrasted with bipolar devices such as the BJT which involve carriers of both polarities.
Group Theory in Subnuclear Physics
Authors: Stancu Fl
Published: November 2023

This book is a useful and accessible introduction to symmetry principles in particle physics. New ideas are explained in a way that throws considerable light on difficult concepts, such as Lie groups and their representations. This book begins with introductions both to the types of symmetries known in physics and to group theory and representation theory. Successive chapters deal with the symmetric groups and their Young diagrams, braid groups, Lie groups and algebras, Cartan's classification of semi-simple groups, and the Lie groups most used in physics are treated in detail. Gauge groups are discussed, and applications to elementary particle physics and multiquark systems introduced throughout the book where appropriate. Many worked examples are also included. There is a growing interest in the quatk structure of hadrons and in theories of particle interactions based on the principle of gauge symmetries. In this book the concepts of group theory are clearly explained and their applications to sub-nuclear physics brought up-to-date.
Elements of Group Theory
Authors: Stancu Fl
Published: November 2023

The purpose of this chapter is to familiarize the reader with the principal concepts of group theory. In order to prevent the presentation from becoming too abstract, examples of very simple groups are given. In later chapters these concepts are used for a detailed study of a selection of groups currently used in physical applications. For important topics of group theory not covered in this book the reader is referred to other books or detailed articles (see references).
linear Representations of a Group
Authors: Stancu Fl
Published: November 2023

In quantum mechanics we are interested in the properties of eigenstates under various transformations (Chapter 1 ). Group theory offers a systematic way of finding these properties from the symmetries of the Hamiltonian. The eigenstates form linear vector spaces which in terms of group theory provide matrix representations of the group of transformationsG under consideration. Let us denote byD(g) such a representation where g is an element ofG.
The Orthogonal Group
Authors: Stancu Fl
Published: November 2023

In Section 5.6, the orthogonal group was introduced as the group of transformations which leave invariant the complex quadratic form Σ(xi)2, where xi are the components of a vector in an n-dimensional space.
Multiquark Systems
Authors: Stancu Fl
Published: November 2023

To date, quarks have not been observed as isolated particles. They are thought to exist only in bound states (confined). They carry a new degree of freedom, called colour, but the bound states they form are always colourless (i.e. SUc(3) singlets, cf. Exercise 10.2).
Basic concepts: Definitions and Axioms
Authors: Chandrasekhar S
Published: November 2023

Two lessons on Definitions and Axioms (or Laws of Motion) precede the formal opening of Book I: The motion of bodies of the Principia. In these two lessons, Newton formulates and elaborates the basic concepts and laws that are the underpinnings of his Natural Philosophy. The concepts are complex and are interrelated. And Newton’s Definitions and Axioms should be read in their totality and in their context keeping in mind that they ‘Shall be explained at large in the following treatise’ (for which end it was composed!). We shall quote rather more extensively than may be considered necessary; but they draw attention to issues that are commonly ignored; and Newton states his ideas with such clarity that it is a joy to learn them anew.
On the notion of limits and the ratios of evanescent quantities
Authors: Chandrasekhar S
Published: November 2023

In Section I, Book I of the Principia, Newton describes the elementary notions of differential calculus (without explicitly so stating) that are at the base of his entire treatment. And, as he explains in the Scholium at the end of the section, These Lemmas are premised to avoid the tediousness of deducing involved demonstrations ad absurdum, according to the method of the ancient geometers.
The law of areas and some relations which fallow
Authors: Chandrasekhar S
Published: November 2023

Since the equable description of areas indicates that there is a centre to which tends that force by which the body is most affected, and by which it is drawn back from its rectilinear motion, and retained in its orbit, why may we not be allowed, in the following discourse, to use the equable description of areas as an indication of a centre, about which all circular [circulatory]* motion is performed in free spaces? In this chapter we consider the propositions and lemmas in Section II, Book I of the Principia. These propositions and lemmas (as those of Section III) are, in the main, included in De Motu Corporum in Gyrum written in the summer of 1684 (cf. Chapter 1, §4) but not with the completeness or incisiveness as in the Principia.
A pause
Authors: Chandrasekhar S
Published: November 2023

By the end of Section IX, we again reach a watershed in the development of the Principia; and again, as at the end of Section III, we have a pause; but this time a shorter one addressed to ‘... “oscillating pendulous motions of bodies”‘. There is much of great interest in this section particularly in those parts dealing with cycloidal pendulums. But we shall pass them by as they are not in the mainstream of the development. But Propositions XLVI and XLVII are exceptions: Proposition XLVI provides an important generalization of Proposition XLII on the initial-value problem; and Proposition XLVII is a beautiful theorem which is at the base of another beautiful Proposition LXIV established in Section XI (see Chapter 12).
The three-body problem: the foundations of Newton’s lunar theory
Authors: Chandrasekhar S
Published: November 2023

In Propositions LXV-LXIX, Newton took the first steps in the study of the motions of three bodies under their mutual attractions. His main considerations are devoted to the changes in elements of a Kepler orbit effected by an external perturbation, in particular that of a distant third body. The considerations are clearly intended as a prelude to his lunar theory to be elaborated further, in Book III (Propositions XXVXXXIII; Chapter 22).
A digression into Opticks
Authors: Chandrasekhar S
Published: November 2023

These attractions bear a great resemblance to the reflections and refractions of light made in a given ratio of the secants, as was discovered by Snell; and consequently in a given ratio of the sines, as was exhibited by Descartes. Besides, it gave Newton the occasion to expand on his ‘query’ on the nature of light though he protests that in establishing Propositions XCIV-XCVI he was not at all considering the nature of the rays of light, or inquiring whether they are bodies or not; but only determining the curves of bodies which are extremely like the curves of the rays.
The figure of the Earth and of the planets
Authors: Chandrasekhar S
Published: November 2023

Newton’s consideration of the figure of the Earth and of the theory of the tides are towards this end: it is the gravitational attraction of the protuberant part of the Earth, caused by its own rotation or by the tidal action of the Sun and the Moon, that are the direct causes. And Newton’s absorption in the lunar theory derives in part from the same concern. The very nature of these problems requires a careful examination of the relevant data. Newton is conscientious in these matters. But in our account, we shall pass them by and restrict ourselves to the theoretical aspects and the basic theorems.
The lunar theory
Authors: Chandrasekhar S
Published: November 2023

he basic elements of the lunar theory have already been set out in the first seventeen corollaries of Proposition LXVI of Book I, albeit with only the barest indications of how they were established. In the fourteen Propositions, XVII, XXI-XXIII, and XXVI-XXXV in Book III (now to be considered), the theory is elaborated with derivations and applications to the perturbations of the orbit of the Moon about the Earth, caused by the tidal action of the Sun. Considering the wealth of information contained in these propositions, we shall first abstract their substance.
The precession of the equinoxes
Authors: Chandrasekhar S
Published: November 2023

Lemmas I, II, and III, culminating in Proposition XXXIX ‘to find the precession of the equinoxes’ is one of those sections, interspersed throughout the Principia, in which new ideas are formulated in the context of new problems that are constantly arising. In Lemmas I, II, and III, Newton introduces, for the first time, notions that are relevant to the dynamics of rigid bodies: the moment of inertia (which determines the ‘efficacy to wheel [a body] with circular motion about a centre’); the moment of momentum (which measures the ‘motions of the whole [body] about its axis of rotation’) and the torque-’the power to wheel about’--exerted by an external force on a non-spherical body; and, indeed, the principles underlying gyroscopic motion. All these notions are defined in the context of a dynamical theory of the precession of the equinoxes which derives from the oblateness of the Earth and the inclination of its axis of rotation to the plane of the ecliptic.
The solid of least resistance
Authors: Chandrasekhar S
Published: November 2023

In the Scholium to Proposition XXXIV, Newton formulates his problem of the solid of revolution which experiences the least resistance in moving through a ‘rare medium’ with a constant velocity in the direction of its axis. With hardly a hint of an explanation, Newton states an integral (which, as we shall presently verify, is a first integral of the appropriate Euler-Lagrange equations) and concludes with the assertion: ... the solid described by the revolution of this figure about its axis ... will be less than any other circular solid whatsoever, described of the same length and breadth.
The diffusion of momentum under various flow conditions
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

In the previous chapter, we have seen how heat-or miscible tracers-are transported by diffusion. The flux of heat, or of tracer, is then proportional to the gradient of the quantity being transported (temperature or tracer concentration) and directed along this gradient. the direction of the flux being such as to tend to attenuate the gradients. There exists another mechanism, often much more effective, of heat or tracer transport: convection through flow.
The dynamics of fluids: local equations
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

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

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

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.
Hydrodynamic instabilities
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

On repeated occasions, we have underscored the effectiveness of convective processes in the transport of physical quantities by the velocity field as opposed to diffusive processes.
Electronic Structure of Materials
Authors: Sutton Adrian P
Published: November 2023

This book describes the modern real-space approach to electronic structures and properties of crystalline and non-crystalline materials in a form readily accessible to undergraduates in materials science, physics, and chemistry.
Introduction
Authors: Sutton Adrian P
Published: November 2023

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

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

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

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

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

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

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

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.