bluuebunny/crossref_metadata_2025 huggingface dataset:
Crystal shapes and defects
Authors: Dobbs E R
Published: November 2023

Many of the structural properties of solid helium are similar for He and He, although there have been many more structural studies of solid He than of solid He. In this chapter, recent developments in the growth of He crystals and in their defects are discussed, while references to comparable studies on He crystals are given for background reading.
Models
Authors: Binney J J , Dowrick N J , Fisher A J , Newman M E J
Published: November 2023

In this chapter we introduce a number of models that have played important rô les in the development of the theory of phase transitions. To avoid disappointment later it should be emphasized here that these are all toy models designed to be tractable rather than realistic. In fact some are frankly unphysical and are of interest mainly for the light they throw on other, more realistic models. But among the systems we shall play with are ones that seem to capture the essence of what happens when a real system undergoes a continuous phase transition.
Numerical simulations
Authors: Binney J J , Dowrick N J , Fisher A J , Newman M E J
Published: November 2023

We have now seen how powerful the tools of statistical mechanics can be in the study of complex systems in thermal equilibrium and how they can be used to determine exactly the behaviour of some simplified, but nevertheless interesting, models of phase transitions. However, these exact solutions are sometimes lengthy and difficult and there is no guarantee that any particular model will yield exact results. For example, we were able to solve the two-dimensional, but not the three-dimensional, Ising model, and that only in zero magnetic field. So, it is natural to consider whether we can use a computer to simulate these systems. In this chapter we shall see that this is indeed possible; a great deal of our understanding of critical phenomena is based wholly or partly on the results of such numerical work. However, as we shall also see, such simulations are not entirely straightforward and a number of tricks are needed to obtain accurate results. This is partly a consequence of the very physics that makes the phase transitions interesting to start with. One should probably think of numerical simulation as a whole subject, almost an art, of its own; we shall have time only to scratch at the surface and discuss a few of the most important ideas.
Diagrammatic perturbation theory
Authors: Binney J J , Dowrick N J , Fisher A J , Newman M E J
Published: November 2023

In the last chapter we introduced the Landau-Ginzburg model and calculated its partition function in a crude approximation known as Landau theory. In this chapter we develop a systematic method for calculating the Landau-Ginzburg partition function, the associated correlation functions, and the Helmholtz and Gibbs free energies. In subsequent chapters we shall use the techniques developed here to find the critical exponents for the Landau-Ginzburg model.
The calculation of critical exponents for T ≤ T
c
Authors: Binney J J , Dowrick N J , Fisher A J , Newman M E J
Published: November 2023

Before we dive into the calculation of the first of our critical exponents, it will be helpful for us to consider a little more closely some of the problems that arise from the perturbation expansion we have developed for our correlation functions. This expansion is an expansion in powers of the coupling constant A, whose coefficients are integrals given by the Feynman rules. In §9.4, we were concerned with the behaviour of some of these integrals as we let the wavevector cutoff A tend to infinity.
Production of temperatures to 1 K
Authors: White Guy K , Meeson Philip J
Published: November 2023

In Chapter 2 we look more closely at the methods of cooling down to ˜1 K which are currently in general use, concentrating on the techniques and problems encountered on the laboratory scale rather than in industrial installations which deal with hundreds of tonnes of LNG (liquefied natural gas), liquid oxygen or liquid hydrogen. Further details of many of these methods may be found in Collins and Cannaday (1958), Croft (1971) and Walker and Bingham (1994). We described in Chapter 1 how cooling takes place through a process of isothermal compression and adiabatic decompression, literally when the working substance is a gas such as nitrogen or helium and more conceptually in the case of, for instance, magnetic cooling. In order for the refrigerator to operate continuously the cooling needs to become cyclic, that is, the compression-decompression cooling process needs to be repeated indefinitely. We describe below the various schemes that have emerged for achieving this.
Hard disks and spheres
Authors: Krauth Werner
Published: November 2023

In the first chapter of this book, we considered simple problems in statistics: pebbles on the beach, needles falling but never rolling, and people strolling on heliports by night. We now move on to study model systems in physics-particles with positions, velocities, and interactions-that obey classical equations of motion. To understand how physical systems can be treated with the tools of statistics and simulated with Monte Carlo methods, we shall consider the hard-sphere model, which lies at the heart of statistical mechanics. Hard spheres, which are idealizations of billiard balls, in free space or in a box, behave as free particles when ever they are not in contact with other particles or with walls, and obey simple reflection rules on contact.
Density matrices and path integrals
Authors: Krauth Werner
Published: November 2023

In this chapter, we continue our parallel exploration of statistical and computational physics, but now move to the field of quantum mechanics, where the density matrix generalizes the classical Boltzmann distribution. The density matrix constructs the quantum statistical probabilities from their two origins: the quantum mechanical wave functions and the Boltzmann probabilities of the energy levels. The density matrix can thus be defined in terms of the complete solution of the quantum problem (wave functions, energies), but all this information is available only in simple examples, such as the free particle or the harmonic oscillator. A simple general expression exists for the density matrix only at high temperature.
Gene duplication and evolution
Authors: Lynch Michael
Published: November 2023

Motivated in part by Ohno’s (1970) influential book, substantial attention has been given to the idea that gene duplication is a major mechanism for the origin of new gene functions. A theoretical population genetic framework for understanding the evolutionary mechanisms responsible for the success versus demise of gene duplicates has begun to emerge. Substantial evidence now exists that many of the key evolutionary lineages of multicellular eukaryotes have experienced one or more complete genome doublings (polyploidization) sometime in the distant past (Wolfe 2001), and the newly unveiled genomic sequences of diverse species clearly indicate that gene duplication is an ongoing process in all organisms.
Genomics and evolution: the path ahead
Authors: González-Candelas Fernando , Ho Julie C , Casa Alexandra M , Kresovich Stephen
Published: November 2023

The draft of the human genome sequence published by two separate groups in February 2001 (International Human Genome Sequencing Con sortium 2001; Venter et al. 2001) marks the beginning of a new era for biology and promises applications that should benefit humankind for centuries to come. Thousands of researchers from different countries have mobilized towards a common goal and now share multimillion-dollar budgets. Although initially criticized by organismal and environmental specialists for its concentration of resources and research efforts, this initiative is now widely acknowledged for its far-reaching, positive impact on all areas of biology, including evolutionary biology.
From ecosystems to molecules: cascading effects of habitat persistence on dispersal strategies and the genetic structure of populations
Authors: Denno Robert F , Peterson Merrill A
Published: November 2023

Knowledge of the evolutionary links between ecosystem-level properties and variation at the genetic level predates even the discovery of the molecular basis of genes. Much of the research in this arena has been motivated by observations that organisms possess attributes that enhance their performance in their local ecosystems. Early experiments provided convincing evidence such presumed adaptations to the environment often have a genetic basis, by demonstrating heritable ecotypic variation among populations (e.g. Clausen et al. 1940). More recent studies have shown that variation at the level of specific genes or gene products is clearly the result of adaptation to ecosystem properties (e.g. Koehn and Hilbish 1987).
Using molecules to understand the distribution of animal and plant diversity
Authors: Hewitt Godfrey M
Published: November 2023

Many questions in ecology can now be addressed through the use of molecular markers, making molecular ecology a thriving multichanneled interface. Using recently available DNA sequence information, a wide spectrum of ecological topics is being investigated. These range from paternity analysis, through population structure, to speciation and systematics; they include all living kingdoms in all realms of the globe, and have application from pest control and animal breeding to conservation and sociobiology. The field is growing rapidly, as witnessed by the number of papers and journals reporting on it.
Cambridge Undergraduate
Authors: Brown Andrew
Published: November 2023

The Great War changed Cambridge from a vibrant university town to a dark, cheerless place, where army divisions camped and drilled before going to fight in the trenches. Their officers spent a last few civilized weeks living in the colleges. Tens of thousands of soldiers returned to Cambridge from the front after being blinded, maimed or gassed, for treatment at the First Eastern General Hospital (a medical campground spread over the gardens and backs behind King’s and Clare Colleges). About sixteen thousand Cambridge undergraduates and recent graduates went to war, of whom a third were either killed or seriously wounded. Teaching did not stop altogether, but the undergraduate numbers for the last three years of the conflict averaged about one fifth of the pre-war level. At Emmanuel College, the photograph of the 1916 freshmen contained just five, solemn, young men – three of oriental appearance. At the end of a war that had lasted a year longer than the usual degree course, the new Master of Trinity College, Sir J.J. Thomson, was concerned that the hiatus might result in a permanent loss of traditional ways and customs. He soon realized that his worries were groundless.
Science Fantasy
Authors: Brown Andrew
Published: November 2023

While at the Royal Institution, Bernal began to write his memoir. He might perhaps have chosen the title, A Portrait of the Scientist as a Young Man, as a nod to his countryman James Joyce (a writer whom he admired), but instead settled on the duller but less pretentious, Microcosm. Although clearly intended for publication, Microcosm was never finished and survives only as a collection of mostly undated manuscripts (some typed) and notebooks. The writings begin with the following statement: ‘At the age of twenty-five I have set myself the task of writing down the results of my life, the sum of all the influences that have borne on me, and what my mind makes of these in its knowledge and action.’ Realizing that such an undertaking at his tender age might be regarded as impertinent, Bernal quickly acknowledged that he did not ‘despise the wisdom of age or prefer that of youth’ but thought that ‘they are different wisdoms’.
The Entertainment Of The Scientist
Authors: Brown Andrew
Published: November 2023

Dorothy Crowfoot spent the summer of 1934 in Cambridge taking more X-ray photographs of pepsin, but then returned to Oxford to take up a fellowship at Somerville College. At the same time, Bernal lost his other PhD researcher, Helen Megaw, who went to Vienna to spend a year working as a post-doctoral student with Hermann Mark, now professor of physical chemistry there. The loss of these two hard-working and talented young women resulted in a temporary drying-up of the stream of new data from Bernal’s laboratory. His growing involvement with the Association of Scientific Workers, FIL and the Cambridge Scientists Anti-War Group precluded him from spending the long hours necessary to generate and interpret X-ray photographs, and he could no longer summon the solitariness of purpose necessary to undertake such demanding work himself. He spent almost as much time in London as he did in Cambridge and was often out of the country. At the end of 1934, he spent two months in the USSR with Margaret Gardiner, coming home via Vienna.
Marxist Envoy
Authors: Brown Andrew
Published: November 2023

Soon after the war, Sage wrote that ‘the day of the wandering scholar is over’. He then spent much of the next twenty years attempting to revive the tradition. In addition to the triennial International Union of Crystallography meetings, invitations to speak at foreign universities, and his globe-trotting for the World Peace Council and the World Federation of Scientific Workers, he took several lengthy trips to nations that interested him. These visits were usually at the invitation of the national science academy of the country in question, and the ostensible reason for the visit would be a one-man review of their leading centres of science and technology. For emerging countries with limited resources, Sage represented expertise in physics, chemistry, crystallography, materials science and metallurgy, the building industry and agriculture. He was indefatigable and cheap. As a scientist, he regarded himself as a world citizen and was determined to do all he could to bring the benefits of pure and applied science to developing lands. If the places were not established communist states like China and the USSR, they were often ex-colonial nations that appeared ripe for conversion to some form of socialism, when, of course, the planning of science would become a central edict.
Do species interactions buffer environmental variation (in theory)?
Authors: Hughes J B , Ives A R , Norberg J
Published: November 2023

The interconnectedness of species within ecosystems underlies the popular notion that biodiversity contributes to a balance of nature. Species interactions are also fundamental to ecologists’ formulations of how biodiversity and the stability of ecosystem functioning are related. Many have reviewed how the intricacies of stability definitions affect these relationships (e.g. McCann 2000; Pimm 1984). Fewer have examined how the varied aspects of species interactions, such as strength and number, affect diversity-stability relationships in models (e.g. Benedetti-Cecchi 2000; May 1973) and experiments (e.g. Aoki and Mizushima 2001; Mulder et al. 2001).
Biodiversity and stability in soil ecosystems: patterns, processes and the effects of disturbance
Authors: Ruiter P C de , Griffiths B , Moore J C
Published: November 2023

Soil harbours a large part of the world’s biodiversity and governs processes that are regarded as globally important components in the cycling of materials, energy and nutrients (Wolters 1997; Griffiths et al. 2000). The taxonomy of soil organ isms is however relatively poorly known and possibly the majority of the species is still to be identified (Mikola et al., Chapter 15). Precise taxonomical descriptions of the soil biodiversity are hampered by technical difficulties in extracting and identifying the soil organisms and by the large variation in species richness among soil ecosystems (Lawton et al. 1996; Wall and Virginia 1999; Mikola et al., Chapter 15).
Slippin’ and slidin’ between the scales: the scaling components of biodiversity-ecosystem functioning relations
Authors: Bengtsson J , Engelhardt K , Giller P , Hobbie S , Lawrence D , Levine J , Vila M , Wolters V
Published: November 2023

Whilst the problems of scale are well-known to most ecologists, many subdisciplines of ecology are still struggling with its central concepts-how the dimensions of space and time, and levels of organization, influence ecological patterns and processes (e.g. Peterson and Parker 1998; O’Neill and King 1998; Petersen and Hastings 2001; Schneider 2001). Individual ecologists may, at their own peril, ignore the problem and focus on one scale and one level of organization only. However, the synthesis of many individual studies con ducted at different scales requires a better under standing of the influence of scale on ecological processes. This is particularly evident in the study of biodiversity and ecosystem functioning. Although studying at least two levels-community and ecosystem-most research has been performed at small spatial and short temporal scales (Loreau et al. 2001; Naeem 2001), and it is not clear if such studies can be used to inform the public and policymakers about the large-scale consequences of biodiversity loss.
Effect of biodiversity on ecosystem functioning in managed ecosystems
Authors: Vandermeer J , Lawrence D , Symstad A , Hobbie S
Published: November 2023

Depending on definition, as much as 90% of the terrestrial surface of the earth is estimated to be maintained in some sort of managed state, usually forestry or agriculture (Western and Pearl 1989). This very abundance should be sufficient to place managed ecosystems at the centre of the analysis of biodiversity and ecosystem function, and indeed a large literature has emerged on this topic in agricultural and forestry ecosystems (Pimentel et al. 1992; Paoletti et al. 1993; Collins and Qualset 1999). In this chapter, we first cast the major questions about biodiversity and ecosystem functioning in the context of managed systems, introducing the ideas of planned versus associated biodiversity and the intensification gradient, concepts that are unique to managed systems.
Experimental Methods Used in GR Studies
Authors: Harakeh M N , van der Woude A
Published: November 2023

In this chapter we present an overview of experimental techniques used to excite GRs built on the ground state. GRs can be excited through the strong (nuclear) and electromagnetic interactions. In principle, it should also be possible to excite them through the weak interaction but because of the small cross sections involved these interactions have never been used to study GRs. As is already clear from the discussion in Chapter 1, there are many different types of resonances: the major excitation modes have been illustrated in Fig. 1.3. Since the strength distributions of many of these modes overlap in excitation energy one should use a probe which is as much as possible selective for the mode one wants to study. In the inelastic scattering of charged hadrons, i.e. protons, a-particles and heavy ions, both nuclear and electromagnetic interactions contribute, but for the lighter projectiles the nuclear interaction dominates.
Properties of Isoscalar Electric GRs
Authors: Harakeh M N , van der Woude A
Published: November 2023

In this chapter we will present an overview of the characteristic properties of isoscalar electric (non-spin-flip) GRs. These properties are: • Excitation energy Ex; this parameter is relatively easy to determine from the experimental data, as is clear from the examples shown in Chapter 3. For a specific resonance it should smoothly depend on the size of the nucleus, i.e. on the atomic number A. • Sum-rule strength Sexp; as discussed in Chapter 2, for each type of resonance the theoretical energy-weighted sum rule (EWSR) Sth depends under certain general valid assumptions only on ground-state parameters. Usually Sexp is expressed as a fraction S of Sth. A resonance is giant if, say, S is >50%. The experimental determination of Sexp from the excitation cross section can be difficult since the various resonances often overlap and are on top of a large continuum. If so, the uncertainty in S is usually ∼20%. • Width Γ: for the same reasons as for S this parameter also is sometimes difficult to determine. It is an important parameter since it reflects the damping mechanisms of the GRs.
Spin-Flip Transitions in Charge-Exchange Reactions
Authors: Harakeh M N , van der Woude A
Published: November 2023

In this chapter collective excitations involving particle-hole excitations induced by a residual nucleon-nucleon (NN) interaction of the type: In the liquid-drop model these modes correspond to oscillations involving the spin degree of freedom. In the isoscalar mode nucleons with spin up oscillate against nucleons with spin down; the protons and neutrons move in phase. In the isovector spin mode neutrons with spin up oscillate against protons with spin down and neutrons with spin down oscillate against protons with spin up. Microscopically, these collective excitations give information on the spin and isospin effective interactions in the nuclear medium.
Spin-Flip Strength from Inelastic Scattering
Authors: Harakeh M N , van der Woude A
Published: November 2023

Spin-flip transitions excited in inelastic scattering of protons, electrons and photons (magnetic resonances) have been studied both experimentally and theoretically for many decades with ever improving means. The work up to 1980 has been reviewed, for instance, by Hanna (HAN80). An extensive review of the work up to 1990 on these giant magnetic resonances can be found in reference (RAM91). Spin-flip modes can be excited by hadronic and electromagnetic probes and also, in principle, by weak probes. All these probes strongly favour excitation of the isovector spin-flip transitions over the isoscalar spin-flip ones.
Multiphonons
Authors: Harakeh M N , van der Woude A
Published: November 2023

In the previous chapters we discussed the properties of GRs of different multipolarities and carrying different spin-isospin quantum numbers built on the ground state of a nucleus. But according to the Brink-Axel hypothesis (BRI55,AXE62), a GR can also be built on an excited state. Its basic features such as its energy and strength, which in a mean-field approximation are determined by the nuclear force, should be unaffected by the pre-excitation of the nucleus. Thus, the energy of the resonance, with respect to the state on which it is built, and its sum-rule strength do not depend on the excitation energy and structure of that state. This feature is extensively used to study the properties of IVGDRs in hot nuclei as will be discussed in the next chapter. In this chapter we restrict ourselves to a special case, namely where the excited state itself is a GR. Although in such a double GR excitation each GR can have a different set of quantum numbers, most experimental and theoretical work refers to the case where they are identical. Only in pion charge-exchange reactions have states corresponding to the simultaneous excitation of two different GRs been observed - see Section 9.2. In principle, states which consist of more than two GRs are also possible, but such excitations have not yet been observed.
The Giant Dipole Resonance in Hot Nuclei
Authors: Harakeh M N , van der Woude A
Published: November 2023

A common way of getting a deeper understanding of the structure of a physical system is to submit it to extreme conditions of, for instance, temperature, pressure or stress. This applies also to nuclear systems which have been and still are studied at conditions very different from the ground state of stable nuclei. Here, we are focusing on nuclei at high excitation energies produced, for example, in nuclear fusion reactions or in inelastic scattering. These systems are unstable and decay by emission of particles (nucleons, a-particles, etc.) and heavier fragments. Various properties such as the temperature of the emitting system can be derived from measuring the spectra of the emitted particles.
HMG-CoA Reductase Inhibitors
Authors: Ashton M J , Fenton G
Published: November 2023

Numerous clinical studies evaluating the effects of diet and/ or cholesterol lowering drugs on reducing morbidity and mortality from coronary heart disease (CHD) have been performed in the previous decades. The out come of many of these trials has been reviewed by Havel (1988). These results, combined with studies of experimentally induced atherosclerosis in animals and observations from patients genetically predisposed to CHD, has led to a wide acceptance that elevated plasma cholesterol, associated with raised concentrations of low density lipoprotein (LDL), is linked to an increased risk of morbidity in CHD but not conclusively to mortality.
β Decay of the Free Neutron
Authors: Alexandrov Yu. A , Drozdova T F
Published: November 2023

The Free Neutron Decays According to the Scheme where is the electron antineutrino. This process is allowed since the total mass of the particles in the right-hand side of the scheme is smaller than the neutron mass.
Resonant magnetic diffraction from ferromagnets
Authors: Lovesey S W , Collins S P
Published: November 2023

In ferromagnetic crystals, the reciprocal lattices describing chemical and magnetic structures can overlap, bringing into play a host of interference phenomena between magnetic and charge scattering amplitudes. Of particular relevance are interference terms which are of odd order (usually linear) in the magnetic orientation, since these can be isolated in a sensitive field difference experiment. Chapter 3 was devoted to an important class of experiments, which measure the interference between non-resonant magnetic and charge scattering. In centrosymmetric crystals, such scattering is only possible when the primary beam is elliptically polarized, otherwise the charge and magnetic amplitudes are 90° out of phase and add in quadrature, with no possibility of interference.
Semiconductor Physics and Applications
Authors: Balkanski M , Wallis R F
Published: November 2023

This textbook combines a thorough theoretical treatment of the basic physics of semiconductors with applications to practical devices by putting special emphasis on the physical principles upon which these devices operate. Topics treated are the detailed band structure of semiconductors, the effect of impurities on electronic states, and semiconductor statistics. Also discussed are lattice dynamical, transport, and surface properties as well as optical, magneto-optical, and electro-optical properties. The applied part of the book treats p-n junctions, bipolar junction transistors, semiconductor lasers and photodevices, after which the subject of heterostructures and superlattices is taken up with coverage of electronic, lattice dynamical, optical, and transport properties. The book concludes with treatments of metal-semiconductor devices such as MOSFETs and devices based on heterostructures. Graduate students and lecturers in semiconductor physics, condensed matter physics, electromagnetic theory, and quantum mechanics will find this a useful textbook and reference work.
Charge Carrier Scattering And Transport Properties
Authors: Balkanski M , Wallis R F
Published: November 2023

Transport properties such as electrical conductivity play a crucial role in the application of semiconductors to electronic devices. In this chapter we shall be concerned with the flow of a quantity such as electric charge in response to an externally applied force such as that due to an electric field. The carriers of electric charge of interest in semiconductors are primarily conduction electrons and holes.
Optical properties of semiconductors
Authors: Balkanski M , Wallis R F
Published: November 2023

The optical properties of matter, whether in the form of a solid, a liquid, or a gas, are associated with the absorption, dispersion, and scattering of electromagnetic radiation. These processes arise as a result of the perturbation of the material system by the electromagnetic field. The perturbation can involve the electronic states or the vibrational states or both and leads to transitions between states. From calculations of the transition rate one can evaluate the parameters that characterize the optical property under consideration.
Permutation Group Sn
Authors: Stancu Fl
Published: November 2023

In Chapter 2 the symmetric group Sn was introduced together with its basic properties. Its role in quantum mechanics was also specified. In this chapter we shall analyse the irreducible representations of Sn. by using Young diagrams (Young 1928). These diagrams play a very important role in group theory because they relate the symmetric group to some continuous groups which are also important in physics. The relation is such that one can use Young diagrams to describe representations of the symmetric group as well as of most Lie groups. The use of Young diagrams for Lie groups was initiated by Herman Weylin 1931 (see Weyl 1946). The method works particularly well for SU(l + 1) groups. For further discussion see Chapter 5.
Lie Groups
Authors: Stancu Fl
Published: November 2023

Continuous groups were briefly introduced in Chapter 2 as another category of groups used in physical applications. They consist of an infinite number of elements, in contrast to finite groups, and have numerous applications in quantum mechanics and field theories. Although they have some analogies with finite groups (especially the continuous compact groups) they require a distinct treatment of their own. The most familiar example of a continuous group is the rotation group (Chapter 6). Other groups currently used in physics are the special unitary groups SU(n) (Chapter 8) and the Lorentz and Poincare groups (Chapter 7).
The Poincaré Group and the Lorentz Group
Authors: Stancu Fl
Published: November 2023

These transformations could be rotations (proper and improper), Lorentz transformations or translations in Minkowski space-time, or any combination of them. When translations are excluded the group is called the complete homogeneous Lorentz group L.
Newton’s Principia for the Common Reader
Authors: Chandrasekhar S
Published: November 2023

Representing a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.
The problem of the brachistochrone
Authors: Chandrasekhar S
Published: November 2023

The problem of the brachistochrone is the following: let A and B be given points, A higher than B; and suppose they are joined by a smooth wire in the vertical plane through AB. A particle starts from rest at A and slides down the wire to B under the action of gravity. The problem is to find the curve which minimizes the time of descent. As we have stated already (p. 538), this problem* was issued by Johann Bernoulli on New Year’s Day 1697, as a challenge to ‘the sharpest mathematicians in the whole world’. Bernoulli’s principal object(?) in issuing the challenge was to demonstrate to the ‘whole world’ the superiority of the German-Swiss mathematicians.
Physical Hydrodynamics
Authors: Guyon Etienne , Hulin Jean-Pierre , Petit Luc , Mitescu Catalin D
Published: November 2023

In the course of the last twenty years, teaching and research in fluid mechanics has expanded considerably into the physics and chemistry communities, who in their turn developed new approaches to the teaching of this topic. These approaches are mainly oriented towards the comprehension of fluids of different hierarchies, the development of various experimental tools, and explanations in terms of elementary physical mechanics. Physical Hydrodynamics presents this original approach for the first time. The elementary microscopic basics of the statistical theory of fluids is discussed, as are the classical aspects of deformation and pressure and the laws of conservation. The problem of Low-Reynolds-Number Flows will be addressed, its applications to suspensions and porous media explained. A discussion of the aspects of boundary layers, high-velocity flows and instabilities conclude this presentation of incompressible fluid hydrodynamics. The present book provides a thorough introduction into the topic from a primarily physical point of view and will be a useful textbook and reference work for graduate students, lecturers and researchers.
Free electron theory
Authors: Sutton Adrian P
Published: November 2023

Metals have quite different properties from insulators. Apart from their much greater electrical conductivity, metals also have a greater thermal conductivity, their surfaces, when clean, are lustrous and, on the whole, metals are much more ductile. Understanding these fundamental differences was the first challenge to be addressed by solid state theorists around the turn of the century, and indeed it can be said that these questions brought solid state physics into being. The first theory was put forward by Drude and although it was entirely classical in nature it enjoyed some immediate and dramatic successes. Acccording to this theory the electrons in the outermost shell become completely detached and are free to wander through the crystal, forming an electron gas.
Introduction
Authors: Miura Noboru
Published: November 2023

Magnetic fields quantize the energy states of the conduction bands and the valence bands in semiconductors. In high magnetic fields, the quantization of energy states in semiconductors becomes very prominent and the radius of the cyclotron motion of conduction electrons or the electron wave-function extension is much reduced. The quantization of the electronic states and the modification of the electronic wave function cause many new quantum phenomena in high magnetic fields. Electrons in most semiconductors possess high mobility or long relaxation time between scattering. Today, electron mobility of the best GaAs crystals reaches higher than 107 cm2/Vs at low temperatures, which corresponds to a mean free path of mm. Moreover, in most cases, the effective masses of electrons and holes are smaller than the free electron mass. These features are most favorable for observing the effects of quantization.
Cyclotron Resonance and Far-Infrared Spectroscopy
Authors: Miura Noboru
Published: November 2023

Cyclotron resonance is a powerful tool to determine the effective mass of carriers, and to study energy band structure, electronic states, electron interactions with other elementary excitations, and electron-electron excitations. There are two ways to observe cyclotron resonance. One is by fixing the magnetic field constant and varying the wavelengh of the incident eletromagnetic radiation. The other method is to sweep the magnetic field at a constant wavelength. The latter is particularly suitable for pulsed high magnetic fields, since the magnetic field is automatically swept and hits the resonance when a monochromatic light is incident on a sample. High magnetic fields are advantageous in many ways for cyclotron resonance.
Synchrotron Radiation Production and Properties
Authors: Duke Philip John
Published: November 2023

This book introduces in a thorough and self-contained way the production of electromagnetic radiation by high energy electron storage rings. This radiation, which is called synchroton radiation, has become a research tool of wide application. Physicists, chemists, biologists, geologists, engineers, material scientists, and other scientific disciplines use it as a structural probe for the study of surfaces, bulk material, crystals, and viruses. Solids, liquids and gases can be spectroscopically analysed by using synchroton radiation. This book brings together for the first time the properties as well as the means of production of synchroton radiation and presents them in a coherent and clear way. It will be an indispensable reference for all those involved in modern synchroton radiation experiments.
Synchrotron radiation from dipole magnets
Authors: Duke Philip John
Published: November 2023

The simplest situation in which synchrotron radiation is produced is when an electron (or a positron, which is a positively charged electron) is forced to move in a circular path by the action of a magnetic field which is uniform (has the same value) along the entire path of the electron. Let us first establish some elementary properties of circular motion. Figure 5.1 shows a right-handed coordinate system in which a small object with position vector R is moving with velocity v whose magnitude is constant and equal to ds/dt, where ds is a small distance along the trajectory (see Fig. 5.2).
High Field Superconducting Magnets
Authors: Asner Fred M
Published: November 2023

Superconducting devices, which can carry huge currents and generate strong magnetic fields without losing energy, are improving at a tremendous pace. This book provides a modern, up-to-date reference on both the physics and the technology of superconducting magnets. It is unique in combining the theoretical aspects of superconductivity, electromagnetic field theory, and the thermodynamics of helium cooling with the technological details of producing and engineering high performance superconducting materials. The book provides the reliable, expert advice for designing, manufacturing, and testing complex high field superconducting magnets of predictable performance, and it places particular emphasis on beam transport and accelerator magnets in high energy particle physics.
Manufacturing And Application Of Advanced Technical Superconductors
Authors: Asner Fred M
Published: November 2023

Among the hard Type II superconductors described in Chapters 2 and 3 only fine filamentary NbTi and Nb3Sn conductors are in worldwide use today as technical superconductors, where NbTi is used in 80—90% of all superconducting devices. Their manufacturing techniques and applications shall be presented with sufficient detail to help the reader in choosing a suitable superconductor for a specific application. Other cryogenic or low temperature superconductors which seem promising for future applications will be mentioned at the end of the chapter. High temperature superconductors—HTS—will not be extensively considered, notably because of their low overall current densities and the difficulty of manufacturing them in the form of long wires. However, their evolution should not be excluded, as some of them may in the future exhibit interesting properties at liquid helium temperatures. Their application to high field magnets in the more or less distant future should not be prejudiced or excluded.
Cooling Of Superconducting High Field Magnets
Authors: Asner Fred M
Published: November 2023

Efficient cooling of superconducting high field magnets is one of the pillars of any successful magnet design. Heat losses are inherent to superconductive magnet windings; they have a considerable impact on the magnet design and its ultimate performance. With respect to their duration one can subdivide the heat losses into steady state and short, transient losses. Steady state losses include the heat input to the coolant by thermal conduction and radiation between parts of the magnet at ambient (or intermediate) temperature and those at liquid helium temperature, heat deposited in the windings due to beam losses, osmic losses generated in the conductor or cable joints, ac losses due to ripples in the excitation current, and the magnetization and eddy current losses which also appear in de operated magnets during excitation and de-excitation. These losses can be calculated with reasonable accuracy and cooling systems designed for their safe elimination.
Path Integral Methods
Authors: Kashiwa T , Ohnuki Y , Suzuki M
Published: November 2023

The last two decades have seen a consistent growth in the significance of path integrals. They are useful in quantum as well as statistical mechanics, providing more intuitive and easier methods of handling equations than more commonly-known treatments. However, the method is still greeted with skepticism. Where has the operator ordering problem gone? Do polar coordinates work in PI, despite the fact that they cannot exist in the canonical operator formalism? Is it possible to obtain a quantum mechanics on the sphere by inserting a delta function into the unconstrained formula? This book addresses and solves these fundamental issues, and covers more recent topics, such as the lattice fermion problem in quantum theory and the Monte Carlo method in statistical mechanics.
Application to Field Theory
Authors: Kashiwa T , Ohnuki Y , Suzuki M
Published: November 2023

In this chapter we apply the path integral technique to field theory. First we introduce a lattice in order to describe field variables, defined as in- finitely many degrees of freedom, unambiguously. Using a scalar field as an example, we discuss the method of effective potential, which may show the validity of the Euclidean technique. Contrary to the case of the scalar field, fermions on the lattice suffer from a peculiar difficulty: they cannot preserve the chiral symmetry that was a guiding principle for building a unified model of the weak and electromagnetic interaction. Finally the auxiliary field method, which is considerably useful in various aspects, will be presented.
Algebraic Generalization
Authors: Kashiwa T , Ohnuki Y , Suzuki M
Published: November 2023

The path integral method discussed up to the preceding section is based on Trotter’s formula (1.10) and its accuracy is of the order of Δt for the time slice Δt. This is sufficient for discussing quantum systems qualitatively. Higher accuracy of the Quantum Monte method is required for studying quantum systems numerically. In the present chapter, we explain the algebraic generalization of the path integral method. By applying the integral representations given in chapters 1−4 to such generalized product formulae, some new kinds of path integral of higher accuracy can be obtained. This is crucial when the essence of a phenomenon can be found only by increasing the accuracy of calculations. It should be emphasized that such higher order decomposition formulae to be explained in the present chapter can also be applied not only to the path integral method but to many other problems such as non-linear dynamics in Hamiltonian systems.
Introduction to Polymer Physics
Authors: Doi M , See H
Published: November 2023

A polymer is a very large molecule consisting of many atoms covalently bonded like a chain. Polymers take a random coil conformation in solution and entangle each other when the polymer concentration is high. The unique structure gives unique physical properties to polymer solutions. This book is an introduction to the modern theory of polymer physics. It describes basic concepts and methods to discuss the statistical properties of the assembly of chain-like molecules. This involves scaling theory, concentration fluctuation, gels and reptation.
Molecular motion of polymers in dilute solution
Authors: Doi M , See H
Published: November 2023

A flexible polymer molecule in solution has an extremely large number of degrees of freedom, and its shape is incessantly changing. This perpetual molecular motion can be analysed through light scattering experiments on the solution, and recently it has become possible to observe directly the motion of very large molecules such as DNA using fluorescence microscopy (see Fig. 4.1). The understanding of molecular motion in polymer solutions enables us to explain many non-equilibrium phenomena, such as diffusion, dielectric relaxation, birefringence, etc.
Molecular motion in entangled polymer systems
Authors: Doi M , See H
Published: November 2023

If the concentration in a polymer solution exceeds c*, the polymer molecules will begin to overlap. In this state, excluded volume interactions, hydrodynamic interactions, and entanglement interactions all strongly affect the molecular motion, and the calculations become extremely complicated. A rigorous treatment of the entanglement interactions is particularly difficult, and an analysis from first principles is almost impossible. For these reasons, present theories of the dynamics of concentrated polymer systems are based on very rough models, which manage to capture some features of the motion very well, but cannot describe all aspects of the dynamics. Present theories of the dynamics of entangled polymer systems are based on two theories that have met with reasonable success.
States and Observables
Authors: Araki Huzihiro
Published: November 2023

The states and the observables are basic concepts in the description of a physical system and their description has undergone a drastic fundamental change in the transition from the classical theory to the quantum theory.
The Relativistic Symmetry
Authors: Araki Huzihiro
Published: November 2023

In this chapter we discuss the theory of special relativity as a quantum mechanical symmetry. A particle is understood as an irreducible unitary representation of the inhomogeneous Lorentz group.
Sector Theory
Authors: Araki Huzihiro
Published: November 2023

In the previous sections we treated the irreducible representation space associated with the vacuum state. In this chapter we treat other representation spaces necessary to describe particle systems with the vacuum as a background. Such representation spaces are characterized as transportable localized excitations on the vacuum background. If we assume Haag’s duality of the vacuum representation, such a localized excitation is described by a localized endomorphism of the observables and its equivalence classes correspond to different representations called sectors(eigensubspaces of the superselection rules in each of which unrestricted superposition principle holds). From the discussion about composition and conjugation of localized endomorphisms, we define the statistics (of a sector) which represents the behaviour of more than two equivalent localized excitations under permutation, and we derive the connection of spin and statistics. We also introduce the lattice of local field algebras as operators intertwining different sectors, and the gauge group acting on them. Then the local observable algebras are the gauge invariant part of the local field algebras and sectors are inequivalent representations of the gauge group. The local field algebras can be chosen to satisfy the standard commutation or anticommutation relations between space-like separated regions and we can derive the connection of spin and statistics of sectors. In this way we obtain a deep understanding of the reason why Fermi fields in spatially separated regions anticommute.
Atomic Magnetic Moments
Authors: Chikazumi Sōshin , Graham, Jr C D
Published: November 2023

In the classical Bohr model of the atom, Z electrons are circulating about the atomic nucleus which carries an electric charge Ze (C), where Z is the atomic number, and e(C) is the elementary electric charge. One of the origins of the atomic magnetic moment is this orbital motion of electrons. Suppose that an electron moves in a circular orbit of radiusr(m) at an angular velocity ω(s−1) (Fig. 3.1). Since the electron makes ω/21rturns per second, its motion constitutes a current of−eω/2π(A), where -eis the electric charge of a single electron. The magnetic moment of a closed circuit of electric currentiwhose included area isS(m) is known from electromagnetic theory to beμ0iS(Wb m).