bluuebunny/crossref_metadata_2025 huggingface dataset:
Liquid Crystals
Authors: Warner M , Terentjev E M
Published: November 2023

Liquid crystalline rubbery solids are polymer networks with nematic or smectic order. They display most of the complexities of conventional liquid crystals: directional but not translation long range order, optical birefringence and phase transitions. In fact they are liquid crystals with the exception that they cannot flow. Liquid crystal networks have many properties in addition to simple nematics and smectics, but to start understanding them, one must review conventional liquid crystals. Our review will be very selective since we require only the basics of what is a large and subtle subject. Moreover, excel lent monographs exist, such as (de Gennes and Prost, 1994) and (Chandrasekhar, 1977). More specialist reviews explain corners of the field, for instance Landau theory. Readers familiar with liquid crystals can skip the earlier sections of this chapter-these provide and set up the style of discussion and the notation essential for the rest of this book. In Sect. 2.8 major differences between conventional nematics and liquid crystal elastomers emerge.
Nematic Elastomers
Authors: Warner M , Terentjev E M
Published: November 2023

In this chapter we discuss for the first time examples of nematic elastomers which could be formed by crosslinking either or both main chain and side chain nematic polymers. Average molecular shape of long polymer chains, and its resistance to change, is at the heart of rubber elasticity. One then suspects that crosslinking liquid crystalline poly-mers, themselves capable of spontaneously changing shape already in the melt, will yield elastic solids displaying complex effects of coupling between the mechanical state of the sample and the state of its nematic order. Further, the high liquid-like molecular mobility in elastomers will allow the director to easily achieve gross changes in orienta-tion. Since the molecular elongation of polymer chains relates to this direction, nematic rotation will be mirrored by equally gross, macroscopic shape changes at relatively low energy that we shall term 'soft elasticity'. At the outset, when envisaging nematic poly-mers, de Gennes (1975) saw that networks would represent the most fertile outlet for the coupling of orientational order to average molecular shape in nematic polymers. As we shall see, this promise has been fulfilled both experimentally and theoretically.
Continuum Theory of Nematic Elastomers
Authors: Warner M , Terentjev E M
Published: November 2023

With the molecular theory of nematic networks, developed in the preceding chapters, many details of structure and properties of these materials have a clear explanation. The main success of this neo-classical theory of liquid crystalline rubber elasticity is in its ability to grasp a broad range of effects without much knowledge about the specific microscopic parameters. Therefore, many effects apparently have a truly universal nature-much sought after in physics in general. In spite of this seemingly fortunate situation, many partially explained phenomena depend of detailed molecular models, for instance the effects of molecular chirality on physical properties, random disorder introduced by quenched network crosslinks and its effect on macroscopic elastic response, additional constraints on polymer conformation in smectic phases of liquid crystalline elastomers and gels, and the practically important influence of crosslinking history and chemical composition of liquid crystalline networks. This specificity of behaviour is in contrast with the universality of the neo-classical theory of uniform nematic elastomers. While awaiting for such models to be developed and reconciled with each other, one is tempted to look at liquid crystalline elastomers and gels at a level of even greater universality, based on symmetry of the phases and corresponding degrees of freedom.
Health Effects Assessment
Authors: Baker Dean
Published: November 2023

All organs and systems of the body can be affected adversely by exposures to environ- mental hazards. Adverse effects range from subtle physiological and biochemical changes that may be asymptomatic, to individual perceptions or symptoms of illness, to clinically diagnosed disease, and finally, to death (see Figure 2.1 in Chapter 2). In general, toxic agents have specific molecular and cellular components which they target, so many toxic agents cause specific effects in particular target organs while other agents impact on multiple tissues and organs of the body.
The epidemiology of chemical incidents and natural disasters
Authors: Cullinan Paul , Hansell Anna
Published: November 2023

Disasters—of human or natural origin—share much in their epidemiological investigation and management. To illustrate some of the principles involved, this chapter focuses on chemical incidents related to industrial accidents and natural disasters arising from volcanoes. Other disasters generated by humans such as complex emergencies (war, civil strife, political conflict), technological disasters, transportation disasters, dam breaks, energy supply interruption and those due to other natural forces are covered elsewhere (e.g., see [1]).
Optical orientation of atoms and nuclei
Authors: Letokhov Vladilen
Published: November 2023

A century ago Einstein introduced the notion of the linear momentum of a photon, h  k, and analyzed its transfer to an atom (and back) in the establishment of thermodynamic equilibrium between black-body radiation and matter. In addition to a linear momentum, the photon also possesses an angular momentum, ħ, directed parallel (or antiparallel) to its propagation direction (the OZ axis in Fig. 4.1), depending on its polarization direction (left- or right-handed). This angular momentum is due to the spin of the photon, equal to 1. Half a century later, Kastler (1950) considered the use of the transfer of the angular momentum of a polarized photon to the angular momentum of an atom as a method of optical orientation of atoms. In essence, this was the first method to control atomic motion by means of low-intensity light, developed even before the advent of the laser; it which found widespread application in investigating and then using spin polarization effects in atomic physics. But even after lasers had made their appearance, the method of optical orientation of atoms (or pumping of certain magnetic sublevels in atoms) proved very important, specifically in the laser cooling of atoms (Chapter 5).
Laser cooling of atoms
Authors: Letokhov Vladilen
Published: November 2023

One of the most remarkable achievements of laser control is the manipulation of atomic particles, their velocities, positions, etc., which is referred to as laser cooling and laser trapping . These two effects are interrelated and usually prove effective when used jointly. That this is so one can see by considering as an example the laser cooling of trapped ions and the laser trapping of laser-cooled neutral atoms (Fig. 5.1). The sequences of processes in these two situations are directly opposite. Ions can easily be trapped in an electromagnetic trap of large depth (Paul 1990) and then be cooled for a long time by laser radiation (sideband cooling) (Wineland and Dehmelt 1975; Dehmelt 1990). Neutral atoms are first slowed down and cooled by laser radiation down to millikelvin temperatures, and only then confined in an optical trap. Trapped atoms can further be cooled to microkelvin temperatures. The present chapter and Chapter 6 consider the cooling and trapping of neutral atoms, the present chapter concentrating on their cooling, and Chapter 6 on trapping. But it would be reasonable first to familiarize the reader with the history of the early ideas in this field that eventually led to the advent of a new domain of physics—the physics of ultracold atoms and molecules (Chapters 7 and 8).
Introduction
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

The act of measurement is an essential component of scientific research, whether in the natural, social, or health sciences. Until recently, however, discussion regarding issues of measurement was noticeably absent in the deliberations of clinical researchers. Certainly, measurement played as essential a role in research in the health sciences as in other scientific disciplines.
Item response theory
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

Classical test theory (CTT) has been the underpinning for most test construction and theory for nearly a century. One reason for its popularity is that the assumptions that CTT makes about the items and the test are relatively ‘weak’ ones (e.g. that the error is independent of the true score), meaning that the theory is appropriate in most situations (Hambleton and Swaminathan 1985). However, there are a number of limitations to CTT (Shea et al. 1988). The primary one, as we have pointed out in the chapters on reliability and validity, is that the item and scale statistics apply only to the specific group of subjects who took the test.
Teleological and Referential Understanding of Action in Infancy
Authors: Csibra Gergely
Published: November 2023

There are two fundamentally different ways to attribute intentional mental states to others upon observing their actions. Actions can be interpreted as goal-directed, which warrants ascribing intentions, desires and beliefs appropriate to the observed actions, to the agents. Recent studies suggest that young infants also tend to interpret certain actions in terms of goals, and their reasoning about these actions is based on a sophisticated teleological representation. Several theorists proposed that infants rely on motion cues, such as self-initiated movement, in selecting goal-directed agents. Our experiments revealed that, although infants are more likely to attribute goals to self-propelled than to non-self-propelled agents, they do not need direct evidence about the source of motion for interpreting actions in teleological terms. The second mode of action-based mental state attribution interprets actions as referential, and allows ascription of attentional states, referential intents, communicative messages, etc., to the agents.
Action generation and action perception in imitation: an instance of the ideomotor principle
Authors: Wohlschläger Andreas , Gattis Merideth , Bekkering Harold
Published: November 2023

We review a series of behavioural experiments on imitation in children and adults that test the predictions of a new theory of imitation. Most of the recent theories of imitation assume a direct visual-to-motor mapping between perceived and imitated movements. Based on our findings of systematic errors in imitation, the new theory of goal-directed imitation (GOADI) instead assumes that imitation is guided by cognitively specified goals. According to GOADI, the imitator does not imitate the observed movement as a whole, but rather decomposes it into its separate aspects. These aspects are hierarchically ordered, the highest aspect becomes the imitator’s main goal. Other aspects become sub-goals.
Imitation as behaviour parsing
Authors: Byrne R W
Published: November 2023

Non-human great apes appear to be able to acquire elaborate skills partly by imitation, raising the possibility of the transfer of skill by imitation in animals that have only rudimentary mentalizing capacities: in contrast to the frequent assumption that imitation depends on prior understanding of others’ intentions. Attempts to understand the apes’ behaviour have led to the development of a purely mechanistic model of imitation, the ‘behaviour parsing’ model, in which the statistical regularities that are inevitable in planned behaviour are used to decipher the organization of another agent’s behaviour, thence to imitate parts of it. Behaviour can thereby be understood statistically in terms of its correlations (circumstances of use, effects on the environment) without under-standing of intentions or the everyday physics of cause-and-effect.
Models of dyadic social interaction
Authors: Griffin Dale , Gonzalez Richard
Published: November 2023

We discuss the logic of research designs for dyadic interaction and present statistical models with parameters that are tied to psychologically relevant constructs. Building on Karl Pearson’s classic nineteenth-century statistical analysis of within-organism similarity, we describe several approaches to indexing dyadic interdependence and provide graphical methods for visualizing dyadic data. We also describe several statistical and conceptual solutions to the ‘levels of analysis’ problem in analysing dyadic data. These analytic strategies allow the researcher to examine and measure psychological questions of interdependence and social influence. We provide illustrative data from casually interacting and romantic dyads.
Handbook of Single Molecule Fluorescence Spectroscopy
Authors: Gell Chris , Brockwell David , Smith Alastair
Published: November 2023

Analytical measurements at the single molecule level under ambient conditions have become almost routine in the past few years. The application of this technology to fundamental studies of heterogeneity in biomolecular structure and dynamics, chemical and biological reaction kinetics and photophysics provides a rich playground for molecular scientists. The potential use of single molecule detection for nanotechnology and quantum information processing is a new and almost unexplored area. This handbook is intended for those interested in a practical introduction to single molecule investigations using fluorescence techniques and places special emphasis on the practicalities of achieving single molecule resolution, analysing the resulting data and exploration of the applications in biophysics. It is ideal for graduate research students and others embarking on work in this exciting field.
Single molecule fluorescence techniques
Authors: Gell Chris , Brockwell David , Smith Alastair
Published: November 2023

The information that can be obtained from single molecule fluorescence data depends on the sophistication and reliability of the analysis employed. In order to understand what information single molecule fluorescence experiments can provide, we will take the approach of first understanding the methods of data analysis. For this purpose we will define two classes of single molecule fluorescence experiment; those involving freely diffusing molecules in solution and those in which molecules are immobilized at a surface.
Preparation of samples for single molecule fluorescence spectroscopy
Authors: Gell Chris , Brockwell David , Smith Alastair
Published: November 2023

We have seen in Chapters 2 and 3 that the measurement and analysis of the intensity of fluorescence emission from single molecules can readily be achieved. The missing component of the discussion so far is the production of biological molecules or their complexes that are labelled in such a manner as to report on the process of interest. Consequently, before any single molecule measurements are undertaken it is necessary to consider what dye, or dye pair, should be used together with the location and method of their conjugation to the biomolecule of interest.
Fluorescence spectroscopy of freely diffusing single molecules: examples
Authors: Gell Chris , Brockwell David , Smith Alastair
Published: November 2023

Perhaps the greatest advantage of studying single molecules that are freely diffusing in solution is the simplicity of the approach. Immobilization of molecules and complexes whilst maintaining their integrity and function is not straightforward and a higher level of rigour must be adopted in such experiments to ensure that artefacts due to the immobilization protocol or interactions with the surface are not encountered. In experiments in which the molecules are freely diffusing, burst analysis or correlation techniques can be used to extract both equilibrium and kinetic parameters of interest.
How to take matters further
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

Like most other resources, the resources required to undertake economic evaluations are scarce. Therefore, it is important to ensure that these resources are used efficiently (from the individual evaluator’s point of view it is also important to avoid wasting one’s time when this could be better spent on other activities). In this short chapter we present a list of questions the economic evaluators should ask themselves, or another party requesting an evaluation, when embarking on a new study.
Proxemics, Kinesics Gaze
Authors: Harrigan Jinni A
Published: November 2023

This chapter focuses on the methodologies for coding behaviors in proxemics, kinesics (i.e. body and head movements), and gaze. Working definitions for these three domains are: Proxemics is the study of our perception and structuring of interpersonal and environmental space.
Nonverbal beh av ior and psychopathology
Authors: Kring Ann M , Stuart Barbara K
Published: November 2023

The study of nonverbal behavior has captured the imagination and interest of re- searchers across a number of disciplines, including psychology, sociology, anthropology, ethology, and linguistics to name but a few. At least since Darwin’s 1872 publication of The Expression of Emotion in Man and Animals (see also Ekman 1998), the study of nonverbal behavior has been particularly central to researchers interested in emotion.
Strong Solutions For Steady Navier–Stokes Equations Of Compressible Barotropic Flow And Small Data
Authors: Novotný A , Straškraba I
Published: November 2023

In this chapter we investigate strong solutions near equilibria of steady barotropic Navier–Stokes equations in bounded and exterior domains (all results can be relatively easily extended to a general viscous compressible heat-conducting gas). The functional framework and main results are formulated in Section 5.1. The main ideas of the proofs via the Helmholtz decomposition are explained in Section 5.2. In Section 5.3, we investigate several auxiliary problems resulting from the decomposition, i.e. we deal with the Dirichlet and Neumann problems for the Laplacian, with the Stokes problem, with the transport equation in a bounded or in an exterior domains and with the Oseen problem in an exterior domain.
Introduction
Authors: Jean Yves
Published: November 2023

This book starts from the most elementary ideas of molecular orbital theory, and it leads the reader progressively towards an understanding of the electronic structure, of the molecular geometry and, in some cases, the reactivity of transition metal complexes.
π-type interactions
Authors: Jean Yves
Published: November 2023

In the preceding chapter, we derived the structure of the d block for several different MLn complexes in which the ligands were assumed to use only a single orbital to form the metal–ligand bond. This orbital was either nonbonding or essentially so, and oriented towards the metal centre. Since the overlap between this ligand orbital and a dorbital on the metal is of the axialtype, their interaction leads to the formation of a molecular orbital (MO) which characterizes a σ bond. As we have already seen in Chapter 1 (§ 1.5.2), some ligands have another orbital (or even two) that can in principle contribute to the bonding with the metal. The orientation of this orbital is usually perpendicular to the axis defined by the σ bond, so the resulting overlap with a d orbital on the metal is lateral, and the interaction of π type.
Elements of group theory and applications
Authors: Jean Yves
Published: November 2023

Examination of the geometries of isolated molecules shows that there are four types of symmetry elements: reflection planes, axes of rotation, inversion centres, and improper axes of rotation. A symmetry operationmoves a molecule from an initial configuration to another, equivalent configuration, either by leaving the position of the atoms unchanged, or by exchanging equivalent atoms. The ideas of symmetry element and symmetry operation are of course very closely linked, since a symmetry operation is defined with respect to a given element of symmetry, and, conversely, the presence of a symmetry element is established by the presence of one or more symmetry operations that are associated with that element.
In the Beginning
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

On a clear, moonless night, in a field far from city lights, the sky might be the cabinet of some celestial jeweller, displaying glittering points of light on a field of black velvet. A faint, irregular band meanders overhead, like a river of cosmic milk. On any particular night, noticeably bright stars might stand out among the others; on subsequent evenings, an observant watcher would find that these wandering lights had shifted their positions against the backdrop of stars. As the seasons change, so does the sky; some groups of stars visible in summer disappear during the winter, whereas others remain above the horizon all year.
Cosmology Becomes a Science
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

For thousands of years, the universe that occupied human minds was small, limited by human senses and abilities. The world seemed to end at the horizon, and few travelled far from the towns of their births. The heavens were the realm of gods, beyond the understanding of mortals. From such a narrow perspective, it is not surprising that the universe appeared to be dominated by the Earth. The stars were held to be eternally fixed in their positions on the celestial sphere.
The Special Theory of Relativity
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

In some faraway galaxy, an advanced civilization has mastered space travel. The crew of one of their starships discovers an asteroid on a collision course with one of their world’s space outposts, which would surely be destroyed if the asteroid collides with it. The asteroid is at a distance of 3,000,000 km, as measured by the sensors on the starship. The starship is flying toward the asteroid at nearly the speed of light as seen from the space station.
Black Holes
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

The death of supermassive stars must result in collapse; no known force can resist gravity in such stars once their nuclear fires have died. The result of this inevitable collapse is known as a black hole. The term black hole is nowadays bandied about so much, in science-fiction novels and movies, as well as in the occasional general-science articles of newspapers and magazines, that it would be difficult for any reasonably literate person to be unaware of the expression. Yet few understand why black holes exist, or what their properties really are.
The Expanding Universe
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

For at least as long as written history has existed, humanity has set its sights upon understanding the shape, scope, and history of the universe. To this task we bring our senses, our experience, and our reason. This was as true for ancient cosmologists as it is for modern scientists. Today, however, our senses are augmented by powerful tools, we benefit from the accumulated and recorded experience of many generations, and we have developed mathematical languages that provide an efficient means to systematize our reasoning.
Dark Matter and Large-Scale Structure
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

So far we have modeled the universe by treating it as mostly smooth and homogeneous, in keeping with the cosmological principle. In reality, the universe is not perfectly smooth; it contains stars, galaxies, clusters of galaxies, and even super clusters of galaxies. On the grandest scales, those appropriate to cosmological models, these local density enhancements can be averaged into a smooth background. Eventually, however, cosmologists must tackle the problem of the origin and evolution of structure in the universe.
The Edge of Time
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

In our journey through the universe, we have encountered many wonders. Once we leave behind the bounds of our Earthly velocities and distances, we realize that our cozy intuition is often wrong, our common sense does not apply. Special relativity seemed so strange at its introduction that even some of the most distinguished scientists of the day refused to accept it. General relativity had an easier time, but quickly gained such a formidable reputation that most people became convinced that none but the brightest genius could hope to grasp its concepts.
Lattice rules for nonperiodic integrands
Authors: Sloan I H , Joe S
Published: November 2023

So far we have assumed that the integral to be evaluated is where f has a continuous (and preferably smooth) one-periodic extension with respect to each component of x. Because such a periodic property does not often arise naturally, in Section 2.12 we showed how to force periodization.
Comparisons with other methods
Authors: Sloan I H , Joe S
Published: November 2023

In Chapter 6 we saw theoretical evidence (based on the criterion P0:) that maximal rank lattice rules obtained by copying rank-I lattice rules are at least comparable in accuracy with rank-I rules of similar order. Also, we saw that such maximal rank lattice rules have two practical advantages. Firstly, computer searches to find good rules are computationally less demanding than searches for good rank-I rules, with this advantage increasing as the dimension s increases and being very substantial when s is large.
Introduction to Surface Physics
Authors: Prutton M
Published: November 2023

This text, aimed at final-year undergraduate students and new postgraduates in physics, provides a broad introduction to surface physics, covering key areas of surface studies. Techniques are described that are used to determine which atoms are present on a surface and in what quantities, and to determine their relative arrangement. New results and theoretical advances are included, which provide fresh insights into the phenomena that occur at surfaces. Selected case studies are presented with particular reference to the (lll) surface of elemental silicon to illustrate the application of relevant techniques to the electronic, vibrational, and adsoption properties of surfaces.
Surface structure
Authors: Prutton M
Published: November 2023

Having determined what types of atoms are present upon a surface, the next important problem is to discover their arrangements with respect to each other and with respect to the underlying atoms of the solid. There are two parts to this problem-the determination of the symmetry of the surface atomic arrangement and the determination of details of the atomic positions. In bulk investigations, the former is normally carried out by using simple observations of the diffraction pattern obtained when a beam of X-rays, neutrons, or electrons is scattered from a single crystal of the sample. These observations yield information about the symmetry of the repeating unit of the structure, the unit cell, and the size and shape of this cell. The latter involves measurements of the intensity of diffracted beams and the comparison of these intensities with those predicted from postulated models of the structure. If successful, the result is a complete description of where each kind of atom is situated within the unit cell.
Geometric Structures and Loop Variables in (2+l)-dimensional Gravity
Authors: Carlip Steven
Published: November 2023

In this chapter, I review the relationship between the metric formulation of (2+l)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the classical geometry, via the theory of geometric structures, from the values of the loop variables. I close with a brief discussion of implications for quantization, particularly for covariant canonical approaches to quantum gravity.
Rates of convergence in the central limit theorem
Authors: Petrov Valentin V
Published: November 2023

Let F(x) and G(x) be arbitrary distribution functions, and let f(t) and g(t) be the corresponding characteristic functions. If f(t) and g(t) are identically equal, then F;(x) and G(x) are identically equal. If, however, we know only that f(t) and g(t) are close to each other in some sense, then we may expect a certain nearness of F(x) and G(x). There are many results which elucidate this point. The following theorem of Esseen is one of the most useful of these.
Strong limit theorems: the law of the iterated logarithm
Authors: Petrov Valentin V
Published: November 2023

Theorem 7.1 is in some sense as sharp as possible. Namely, if we replace o by O in the condition (7.1), the assertion of the theorem may fail. Using the arguments that we employed in the proof of Theorem 7.1, we can prove the following proposition on the connection between an estimate of the remainder term in the central limit theorem and the law of the iterated logarithm, i.e. the relation (7.3).
Introduction
Authors: Karlsson Erik b.
Published: November 2023

All physical measurements must be based on some kind of interaction between the system to be studied and the measuring instrument via direct physical contact, via a force acting at a distance, or by some kind of radiation acting as a messenger. Therefore each measuring method in physics has its own specific limitations and possibilities, not only regarding accuracy and range of the parameters observed, but also because it observes the system from its own particular point of view.
Magnetism
Authors: Karlsson Erik b.
Published: November 2023

In this chapter, and in subsequent chapters up to Chapter 10, contributions to solid state physics using the DPAC, DPAD, and μ.SR methods are presented in the form of examples. In an attempt to put these case studies into perspective they are preceded by short general discussions of the specific physical problems to be investigated and to what extent such problems can be studied by other more conventional methods. As far as magnetism is concerned, these methods include macroscopic measurements (which can now be performed on samples of very limited size or thickness using superconducting quantum interference devices (SQUIDs)), scattering measurements using neutrons, laser light, or synchrotron radiation, and microscopic measurements using NMR and ESR to observe the magnetism of individual atoms in solids. It will be shown that PAC and μSR methods, which both belong to the last of those categories mentioned above, can sometimes make an essential contribution to the information obtained. One of the main reasons is their high sensitivity, which means that signals can be observed even from probe spins present in very high dilution, another is their time windows which allow certain important dynamical processes to be followed, and a third is their ability to record magnetic phenomena without applying any magnetic fields that might perturb the systems to be investigated.
Hydrogen on Metallic Surfaces and in Metallic Superlattices
Authors: Karlsson Erik b.
Published: November 2023

As indicated in the previous chapter, the absorption and desorption of hydrogen in metallic materials is strongly influenced by surface and interface conditions. In absorption from the gas phase the first step is a dissociation of H molecules which is followed by diffusion on the surface and into the bulk material. The probability for dissociation of an impinging H molecule depends strongly on the electronic properties of the surface layers. It is represented by a dissociation barrier, which may be very low for certain metals like Pd and Pt. For single crystals, it also means that the geometry of the external face exposed to the hydrogen is an essential parameter. It is also strongly dependent on the presence of impurity atoms on the surface.
The Formal Theory Of Potential Scattering
Authors: Fröbrich P , Lipperheide R
Published: November 2023

Since potential scattering describes solely elastic scattering it covers only a small, although important, aspect of nuclear collisions. For the treatment of general nuclear reactions like inelastic scattering or transfer of particles, a more general formalism is required. This formalism, formal theory of reactions, will now be developed.
The Coupled-Channel Description Of Direct Reactions
Authors: Fröbrich P , Lipperheide R
Published: November 2023

In the single-step approximation introduced in Section 5.4 and discussed in detail in Chapter 7, one assumes the reaction to proceed directly from the initial to the final state, and thus ignores the existence of any other than the entrance and exit channels. It was shown formally in Section 5.5 how the coupled-channel description allows one to go beyond this approximation. We shall now turn to the practical implementation of the coupled-channel method.
Compound-Nucleus Reactions
Authors: Fröbrich P , Lipperheide R
Published: November 2023

Compound-nucleus reactions occur whenever the reaction mechanism involves many degrees of freedom in the combined projectile-target system at close contact. This is not the case if the collision partners are both light nuclei. But when a light, low-energy projectile combines with a nucleus which is heavy, a large number of different transitory configurations may be formed, as discussed in Section 9.2.1. They give rise to narrow isolated resonances in the reaction cross section as a function of the incident energy. When energy and mass of the projectile increase, the number of these transitory states increases as well, their structure becomes more complicated, and the resonances begin to overlap. Eventually, and this is generally the case in collisions where both partners are heavy ions, the complexity of the compound nucleus becomes so high that the latter can no longer be described in terms of individual compound states but must be treated by statistical methods. This leads us to the statistical picture of the compound nucleus introduced by Niels Bohr (1936), which has already been invoked in the previous chapter.
Analysis Of Deep-Inelastic Collisions, Fusion, And Heavy-Ion Induced Fission
Authors: Fröbrich P , Lipperheide R
Published: November 2023

In Chapter 11 we introduced friction and fluctuations in order to describe the dissipative processes occuring in deep-inelastic collisions. For the calculation of these effects we derived the Langevin and Fokker-Planck equations. We studied these equations for several simple examples and discussed general methods of solving them.
Introduction
Authors: Malinowski Grzegorz
Published: November 2023

The vital part of the studies of logic seeks to determine structural criteria for propositional validity and deals with formal inference relations. A suitable starting point for any analysis of these problems consists in the selection of a set of propositions from among all grammatically well-formed sentences, the members of which satisfy some specified syntactical and semantical conditions. The assumption stating that to every proposition it may be ascribed exactly one of the two logical values, truth or falsity, called the principle of bivalence, constitutes the basis of classical logic. It determines both the subject matter and the scope of applicability of the logic, the main systems of which are the classical propositional calculus (CPC) and the (first-order) predicate calculus (quantifier calculus). CPC is a theory of all truth-functional propositional connectives, i.e. sentence-argument propositional functions having the property that the logical value of any complex sentence formed with their use is determined uniquely by the logical values of its components. The predicate calculus is formed by introducing to the language system, with its semantics adequately extended, the symbols of name-argument propositional functions representing the names of properties and relations and name quantifiers. It renders possible the profound analysis of propositions within the principle of bivalence paradigm.
Many-valuedness
Authors: Malinowski Grzegorz
Published: November 2023

The application of specialized tools of the methodology of propositional calculi (see Wójcicki (1988)) affords possibilities for a profound investigation of many-valued constructions. The present chapter aims to present some important methods of that methodology, especially those revealing the complexity of the problem connected with a general characterization of logical many-valuedness.
Classical characterization of many-valued logics
Authors: Malinowski Grzegorz
Published: November 2023

Even the most radical authors of many-valued constructions devoted much attention to the classical logic. The matrix method inspired by truth-tables embodies a distinct shadow of two-valuedness in the division of the matrix universe into two subsets of designated and undesignated elements. Besides, it turned out that, by making use of some special, so-called standard, connectives, it is possible to map this division into the language as well as to describe consequence relations (operations) of some many-valued logics through appropriate sets of formulae and the consequence of the classical logic (see Chapter 8). In the 1970s the investigations of logical formalizations bore several descriptions of many-valued constructions in terms of zero-one valuations. Effectively, the interpretations associated with these descriptions shed new light on the problem of logical many-valuedness.
Intuitionism and the modal logics of Lewis
Authors: Malinowski Grzegorz
Published: November 2023

lntuitionistic logic and the modal logics of Lewis are the most important and best motivated non-classical logical constructions rendered axiomatically. Their creators were not guided by the idea of introducing supplementary logical values. However, it occurred that these logics can be characterized exclusively by means of infinite-valued matrices. On the other hand, non-matrix semantics formed to describe intuitionistic and modal logics became an important tool for interpreting and describing of all the non-classical logical constructions.
Resource Logics
Authors: Gabbay Dov M
Published: November 2023

This chapter will illustrate the use of the Metabox to define some known logics and a new class of logics called Resource Logics. We understand the term to cover all logics where it is important to know exactly from which assumptions and using which inference rules and at what order a conclusion is drawn. In this case the labels function as names to the assumptions (data) and the deductive process propagates the labels to the conclusion through an agreed labelling discipline.
Translation of an LDS into Classical Logic
Authors: Gabbay Dov M
Published: November 2023

In Chapter 1 we claimed that in LDS, the metalevel features are done by the labels while the object level features are done by the formulas of the logic. The meaning of the above statement, as well as notions of metalevel have to be clarified and formalised. This is the task of this Chapter.
Abduction in Labelled Deductive Systems
Authors: Gabbay Dov M
Published: November 2023

This section will introduce our intuitive theory of abduction within the framework of Labelled Deductive Systems, and give some simple examples.
Collisions, Quenching, and Particle Diffusion
Authors: Molisch Andreas F , Oehry Bernhard P
Published: November 2023

In this chapter, we deal with non-radiative processes that can create or destroy excited atoms.5 The theory of collisional excitation and de-excitation is extremely complicated. A thorough review of the work up to 1970 can be found in the five-volume book by Massey and Burhop (1968-1975). The work done after that time would probably fill another ten volumes. We will take here a mostly phenomenological point of view. The processes are described by effective cross-sections, and no investigation of the actual physical processes is done.
Formulation of the Classical Problem
Authors: Molisch Andreas F , Oehry Bernhard P
Published: November 2023

There are three principal mathematical approaches to describing trapping: the Holstein equation, the method of combining the equation of radiative transfer with the rate equation for the excited state atoms, and the multiple-scattering representation. Ultimately, these three descriptions are equivalent-as they should be, since they describe the same physical process. Their different formulations stem from different views of the trapping problem. Each method has its specific advantages and disadvantages for the evaluation, hence it is very helpful to fully understand all three formulations.
Landau theory
Authors: Bellac Michel Le , Barton G
Published: November 2023

The mean-field approximation studied in the last chapter is not always very reliable, and one would like to be able to calculate the effects of fluctuations, which the approximation neglects.
Macroirreversibility and microreversibility reconciled: the second law
Authors: Garrett A J M
Published: November 2023

There is a single consistent resolution of the reversible microdynamicsirreversible macrodynamics problem, stemming from better understanding of the role of probability in physics: the Bayesian viewpoint. The second law of thermodynamics arises on demanding that experiments on thermodynamic variables be reproducible though atomic microvariables differ from run to run. A general formulation for non-equilibrium statistical mechanics is outlined, based on Jaynes’ principle of maximum entropy, and the meaning of entropy is clarified using information theory. The conundrum facing the pioneers of kinetic theory in the late 19th century was to reconcile the reversible character of Hamiltonian atomic dynamics with the irreversibility of systems of atoms viewed on the large scale.
The Mathematical Formalism Of Quantum Mechanics
Authors: De Lange O L , Raab R E
Published: November 2023

Quantum mechanics was created mainly to account for microscopic phenomena that occur on a scale of order IO−10 m. It has turned out to be an astonishingly successful theory which applies on a scale down to at least 10−18 m. Quantum theory has become established as part of the essential core of physics. The purpose of this introductory chapter is twofold. Firstly, in Sections 1.1–1.7 we review the formalism of elementary nonrelativistic quantum mechanics. In this review we attempt to give enough of the terminology and basics of the subject so that a reader who is not already familiar with quantum mechanics will be able to follow the applications considered later in the book. For the reader who finds our discussion too brief, the literature on quantum mechanics is vast and we recommend in particular Refs 1–5. The second purpose of this chapter is to present the basic tools of operator methods as they are used in this book: thus in Sections 1.8–1.11 we discuss commutation relations, shift operators, and the virial, hypervirial, and Hellmann Feynman theorems.
Spherically Symmetric Potentials
Authors: De Lange O L , Raab R E
Published: November 2023

A number of quantum-mechanical problems involve a potential that is spherically symmetric, at least to a first approximation. For such potentials one can consider a ‘onedimensional’ problem, namely the eigenvalue equation for the radial Hamiltonian (see (5.26)), and in this chapter we use operator methods to treat certain important cases for which exact solutions are possible.
The Isotropic Harmonic Oscillator In An Angular Momentum Basis
Authors: De Lange O L , Raab R E
Published: November 2023

In Chapter 4 we considered a ‘twodimensional’ problem in which L2 and Lz constitute a c.s.c.o. and we derived shift operators for the angular momentum quantum numbers l and m in the eigenkets |lm> of these observables. In Chapter 5 we discussed a ‘one-dimensional’ problem, namely the eigenvalue equation for the radial Hamiltonian (eqn (5.25)). Here we use results from Chapters 4 and 5 to construct shift operators for the eigenkets of the three dimensional problem (5.11)–(5.13).
Relativistic Spherically Symmetric Problems
Authors: De Lange O L , Raab R E
Published: November 2023

In Section 12.1 we discuss some elementary properties of the Klein Gordon and Dirac equations with a spherically symmetric electrostatic potential. In Section 12.2 a simple similarity transformation is applied to the Dirac equation. The main result of this section is (12.70), which applies to the Schrodinger, Klein-Gordon, and (transformed) Dirac equations with a Coulomb potential. Shift operators for energy in the eigenkets of (12.70) are derived (Section 12.3) and they are used to obtain energy eigenvalues (Section 12.4). Expectation values and coordinate space wave functions for the Klein Gordon and Dirac Coulomb problems are calculated in Sections 12.5 and 12.6. A relativistic (Dirac) oscillator is discussed in Sections 12.8-12.10.
The multidimensional importance of time domain magnetic resonance
Authors: Ernst R R
Published: November 2023

It is sometimes claimed that the expansive development that led to the present importance of magnetic resonance in chemistry, biology, and medicine occurred after the introduction of Fourier transform spectroscopy in the late 1960s. It should, however, be recalled that all the basic principles had been known and investigated in detail before, many of them by Professor Erwin L. Hahn. These early investigations may be categorized in three classes: molecular beam magnetic resonance, continuous wave (c.w.) magnetic resonance, and time domain magnetic resonance. Surprisingly, molecular beam magnetic resonance has been the first successful method of observing resonance properties of nuclear spins [1-4], although it presents one of the most demanding approaches. Many important concepts have first been applied in these studies, such as continuous wave absorption, refocusing in inhomogeneous magnetic fields, and pulsed radiofrequency (r.f.) fields. In some sense, molecular beam studies have to be classified as frequency selective time domain experiments, as the particles rapidly move through the fields and the time-scale is provided by the beam velocity. The spectrum is recorded point by point by varying the frequency of the r.f. perturbation.
On the possibility of nuclear self-spin-locking in ferromagnets
Authors: Redfield A G
Published: November 2023

Nuclear spin systems in ferromagnets and antiferromagnets can bend the electronic magnetization, via their hyperfine interaction, so as to produce an apparent magnetic field that is proportional to the transverse nuclear spin magnetization and parallel to it. A nuclear spin system in any solid can also be ‘spin-locked’ by application of a resonant r.f. field along a transverse nuclear magnetization, and transverse spin relaxation is then prevented by the r.f. field. In this Article we combine these ideas and conclude that nuclear spin systems in (anti)ferromagnets might be placed in a transient self-locked state. The plausibility criterion for observation of self-locking is shown to be that the apparent field produced by the maximum nuclear magnetism be larger than the ordinary NMR linewidth. A simple treatment of the coupled electron-nuclear resonance frequency shift is given for the case of small or large tilt of the nuclear magnetization, and we show that if the small-tilt shift is greater than the NMR linewidth, self-locking might be attainable. There is an analogy between the self-locked state, and the random-phase representation of the BCS superconductor provided by Anderson. The self-locked state might be observed by looking for a longT2decay after a suitably chosen preparation.