bluuebunny/crossref_metadata_2025 huggingface dataset:
The Finite Element Method and its Reliability
Authors: Babuška Ivo , Strouboulis Theofanis
Published: November 2023

The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand more and more at the forefront of engineering and theoretical interests. The present book presents the mathematical theory of the finite element method and focuses on the question of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.
m-dissipative operators
Authors: Cazenave Thierry , Haraux Alain , Martel Yvan
Published: November 2023

Throughout this chapter, X is a Banach space, endowed with the norm II 11-Remark 2.1.2. Note that a linear unbounded operator can be either bounded or not bounded. This somewhat strange terminology is in general use and should not lead to misunderstanding in our applications. Remark 2.1.5. In this chapter, a linear unbounded operator is just called an operator where there is no risk of confusion. As usual, we denote the pair (D, A) by A with D(A) = D, meaning the domain of A is D. Note, however, that when one defines an operator, it is absolutely necessary to define its domain.
Inhomogeneous Equations and abstract semilinear problems
Authors: Cazenave Thierry , Haraux Alain , Martel Yvan
Published: November 2023

Throughout this chapter, we assume that X is a Banach space and that A is an m-dissipative operator with dense domain. We denote by (T(t))to the contraction semigroup generated by A.
The Schrödinger equation
Authors: Cazenave Thierry , Haraux Alain , Martel Yvan
Published: November 2023

Property (iv) above is a regularity result. As well as being interesting in its own right, this result will be indirectly useful in §7.6 (blow-up in finite time) and §7.7 (behaviour at infinity) to establish the fundamental identity (7.58).
Reduction of algebraic curves
Authors: Liu Qing , Erné Reinie
Published: November 2023

For a long time, we have known that the arithmetic of an algebraic variety V defined over a number field K is only well understood if we take into account its behavior modulo the finite and infinite places of K. The theory of reduction of varieties is concerned with the finite places. Crudely speaking, we extend V to a scheme V over the ring of integers OK of K, while trying to preserve as many good properties of Vas possible.
Revealed Preferences: Understanding the Theory of Epistemic Entrenchment
Authors: Rott Hans
Published: November 2023

The notion of the epistemic entrenchment has attracted quite some attention of philosophers, logicians and researchers in knowledge representation and reasoning.335 It was introduced, first under the name ‘epistemic importance’, by Peter Giirdenfors (1984, 1988). He specified two possible ‘origins’ of epistemic entrenchment: an information-theoretic approach and a paradigm approach. However, neither of these approaches squares well with the logical constraints which are placed on entrenchment relations in the later and more mature 1988 work of Giirdenfors and Makinson (1988). Although it has since then become well-known how epistemic entrenchment can be put to work technically, the problem of providing a systematic justification of the postulates for entrenchment relations is still in need of a systematic clarification. The present chapter offers a reconstructive solution to this problem which is faithful to the literal meaning of the term ‘entrenchment’. It is worth emphasizing that for most of the present chapter we shall reconstruct epistemic entrenchment from belief change or choice behaviour rather than use epistemic entrenchment for constructing belief changes. A ‘complementary’, more constructive approach has been the background of several proposals to extract entrenchment relations from other information structures336 which are surveyed in Rott (2000a).
Bright Birds
Authors: Hamilton W D
Published: November 2023

A lot of the students attending my graduate-level course in the Museum of Zoology in Ann Arhor were interested in birds. The Bird Division of the museum \Vas we Unknown to university in the USA and Canada and the Michigan Graduate School consequently drew bird oriented people from all North America. Peter and Rosemary my colleagues in Biological Sciences who had joined the University of Michigan about a year I did, studied birds exclusively and were busy every year in the Northern Summer with their now-famous study of evolutionary ecology-the actual year-by-year evolution-of the finches of the Galapagos Islands .
Wind in the Baobabs
Authors: Hamilton W D
Published: November 2023

The Zoology and Psychology departments in Oxford are housed in one concrete block consisting of two wide tower buildings connected at ground level and then by two bridges on the third floor. From the air the two must look like rather rectangular ciliate protozoans in syzygy. This beautiful word, which was among the more mystical factors attracting me to biology when I was at school, has a meaning that is properly a secret amongst us biologists and no one who hasn’t suffered a three-year degree course is supposed either to understand or use it. I break the rules of secrecy briefly here, however, to tell you that it refers simply to a state of symmetrical copulation—each individual acting as donor and recipient at once (an enviable hedonic situation one would think, although our textbooks don’t emphasize this). Usually tubes are formed through which the partners exchange hereditary material.
Time Like a Dripping Tap
Authors: Hamilton W D
Published: November 2023

Manuscripts stacked and waiting, tired editors, slow contributors to multiauthor volumes, finally, and not least, obtuse and sometimes malicious referees—all these combine to confuse the sequence of a scientist’s ideas as they proceed, via pencil or keyboard, to their printed form. The paper of this chapter is another example that is out of order not only in my sequence of thinking but also of writing. It was started after several versions of the chapter that follows it in this volume had been completed and had been rejected by more than one journal. It expresses some of the estrangement I was feeling through such unsuccess.
The Concept of Geometry
Authors: Semple J G , Kneebone G T
Published: November 2023

OUR main purpose in this book is to construct and develop a systematic theory of projective geometry, and in order to make the system both rigorous and easily comprehensible we have chosen to build it on a purely algebraic foundation. In adopting such a course, however, we may run the risk of appearing to reduce our subject to an ingenious manipulation of symbols in accordance with certain arbitrarily prescribed rules. Although the axiomatic form is the proper one in which to present a mathematical theory, we must not lose sight of the fact that an abstract system can only be fully appreciated when seen in relation to a more concrete background; and this is the reason why we have prefaced the formal development of projective geometry with two introductory chapters of a more informal character. The present chapter is devoted to a rather general consideration of the nature of mathematics and, more specifically, of geometry, while Chapter II contains an outline of the intuitive treatment of projective geometry from which the axiomatic theory has gradually been disentangled by progressive abstraction.
Further Properties of Conics
Authors: Semple J G , Kneebone G T
Published: November 2023

IN Chapter V we laid the foundations for a systematic treatment of the projective geometry of the conic, and showed also how the affine and euelidean properties of conics find a natural place in the scheme. In this chapter we shall develop the theory in greater detail, and it will be part of our purpose to prove a number of well-known geometrical properties of conics, such as, for example, Pascal’s Theorem. The reader should by this time be fully conversant with the relationship between the different geometries of the projective hierarchy, and he should be able from time to time to change his point of view without losing sight of the logical structure of the system as a whole. Our principal object of study, he will understand, is projective geometry over the complex field; but by considering only real points as actual and properly complex points as ideal, and by suitably restricting the class of allowable coordinate representations, we can treat affine or euelidean space as a specialization of complex projective space. Up to the present we have been careful to maintain a clear separation between the different kinds of space, but from now on we shall allow ourselves greater freedom, dealing for the most part with projective space, but permitting digressions into more special spaces whenever these seem appropriate or illuminating.
Linear Systems of Conics
Authors: Semple J G , Kneebone G T
Published: November 2023

If, now, we consider conics instead of lines, the situation is somewhat different. The totality of all conics in the plane is an 005 linear system, and it contains proper ∞r linear subsystems for every value of r from 1 to 4. We shall discuss in some detail the ∞ system or pencil of conics, and then we shall refer more briefly to the ∞ system or net.
Projective Geometry of Three Dimensions
Authors: Semple J G , Kneebone G T
Published: November 2023

IF we given the value 3 in the general definition at the beginning of Chapter III, we obtain formal definitions of three-dimensional projective space S3 and projective geometry of three dimensions. The projective properties of S3 can then all be deduced from the fundamental definition of a three-dimensional projective domain, for the most part by methods of linear algebra, but in the present chapter we do not propose to go into all the details of this development. Many of the subsidiary definitions and the enunciations and proofs of theorems are strictly analogous to those already given for S2 in Chapter IV, and the reader can easily supply them for himself. We shall accordingly pass quickly over this part of the theory, merely’ calling attention to certain features that arise for the first time when the number of dimensions attains the value 3.
The Quadric
Authors: Semple J G , Kneebone G T
Published: November 2023

IN the projective plane the simplest locus that we can consider, apart from the straight line, is the conic locus, and we have already seen how to establish its projective properties. In three-dimensional projective space, on the other hand, where a point has three degrees of freedom, there are two essentially different kinds of locus to be considered; and we have two particular loci, each of which is in its way a proper space-analogue of the conic, namely the quadric surface and the twisted cubic curve.
Line Geometry
Authors: Semple J G , Kneebone G T
Published: November 2023

Our main purpose in the present chapter is to introduce the reader to the systematic study of those subsystems of the full system of ℛ4 lines of S3 which are of geometrical interest; but before doing so we need to look more closely at the way in which lines are represented by the Pij
Estimation Problems
Authors: Jeffreys Harold
Published: November 2023

In the problems of the last chapter we were considering the probabilities that various observable events would occur, given certain laws and the values of all parameters included in these laws. The usual use of these results is that they provide the likelihood for different values of the parameters; then, taking the observed results as given, and using the principle of inverse probability, we can assess the relative probabilities of the different values of the parameters. A problem of estimation is one where we are given the form of the law, in which certain parameters can be treated as unknown, no special consideration needing to be given to any particular values, and we want the probability distributions of these parameters, given the observations.
Approximate Methods and Simplifications
Authors: Jeffreys Harold
Published: November 2023

Maximum likelihood. If a law containing parameters α, β, γ, … and a set of observations θ lead to the likelihood function L (α, β, γ, … ), and if the prior probability is (4.1)P(dαdβdγ…|H)∝f(α,β,γ…)dαdβdγ…,(1).
Significance Tests: One New Parameter
Authors: Jeffreys Harold
Published: November 2023

General discussion. In the problems of the last two chapters we were concerned with the estimation of the parameters in a law, the form of the law itself being given. We are now concerned with the more difficult question: in what circumstances do observations support a change of the form of the law itself? This question is really logically prior to the estimation of the parameters, since the estimation problem presupposes that the parameters arc relevant. On the other hand, many problems that arise in practice are genuinely estimation problems. For instance, the latitude and longitude of the epicentre and the time of occurrence are obviously relevant to the times of arrival of a pulse sent out by an earthquake.
Significance Tests: Various Complications
Authors: Jeffreys Harold
Published: November 2023

Combination of tests. The problems discussed in the last chapter are all similar in a set of respects. There is a clearly stated hypothesis q under discussion, and also an alternative q’ involving one additional adjustable parameter, the possible range of whose values is restricted by the values of quantities that have a meaning even if the new parameter is not introduced. We are in the position at the outset of having no evidence to indicate whether the new parameter is needed, beyond the bare fact that it has been suggested as worth investigating; but the mere fact that we are seriously considering the possibility that it is zero may be associated with a presumption that if it is not zero it is probably small. Subject to these conditions we have shown how, with enough relevant evidence, high probabilities may be attached on the evidence, in some cases to the proposition that the new parameter is needed, in others to the proposition that it is not. Now at the start of a particular investigation one or more of these conditions may not be satisfied, and we have to consider what corrections are needed if they are not.
Frequency Definitions and Direct Methods
Authors: Jeffreys Harold
Published: November 2023

Most of current statistical theory, as it is stated, is made to appear to depend on one or other of various definitions of probability that claim to avoid the notion of degrees of reasonable belief. Their object is to reduce the number of postulates, a very laudable aim; if this notion could be avoided our first axiom would be unnecessary. My contention is that this axiom is necessary, and that in practice no statistician ever uses a frequency definition, but that all use the notion of degree of reasonable belief, usually without even noticing that they are using it and that by using it they arc contradicting the principles they have laid down at the outset. I do not offer this as a criticism of their results. Their practice, when they come to specific applications, is mostly very good; the fault is in the precepts.
Magnetic force and magnetic induction.
Authors: Maxwell James Clerk
Published: November 2023

We have already (art. 385) determined the magnetic potential at a given point due to a magnet, the magnetization of which is given at every point of 1ts substance, and we have shewn that the mathematical result may be expressed either in terms of the actual magnetization of every element of the magnet, or in terms of an imaginary distribution of ‘ magnetic matter,’ partly condensed on the surface of the magnet and partly diffused throughout its substance.
Exploration of the field by means of the secondary circuit.
Authors: Maxwell James Clerk
Published: November 2023

We have proved in arts. 582, 583, 584 that the electromagnetic action between the primary and the secondary circuit depends on the quantity denoted by m, which is a function of the form and relative position of the two circuits.
Comparison of coils
Authors: Maxwell James Clerk
Published: November 2023

We have seen in art. 717 that in a sensitive galvanometer the coils should be of small radius, and should contain many windings of the wire. It would be extremely difficult to determine the electrical constants of such a coil by direct measurement of its form and dimensions, even if we could obtain access to every winding of the wire in order to measure it. But in fact the greater number of the windings are not only completely hidden by the outer windings, but we are uncertain whether the pressure of the outer windings may not have altered the form of the inner ones after the coiling of the wire.
Fibring Logics
Authors: Gabbay Dov M
Published: November 2023

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.
An overview of fibred semantics and the combination of logics
Authors: Gabbay Dov M
Published: November 2023

The purpose of this chapter is to present an intuitive explanation of the author ‘s fibred semantics methodology for combining logics and systems, and to give a brief overview of the main results, ideas and open problems in the book.
Introducing self-fibring
Authors: Gabbay Dov M
Published: November 2023

The purpose of this chapter is to introduce a coherent semantics for the following self-fibring problem.
Fibring semantic tableaux
Authors: Gabbay Dov M
Published: November 2023

In this chapter we extend the fibring approach to calculi for logical systems: we describe how to uniformly construct a sound and complete tableau calculus for the combined logic from calculi for the component logics.
Conclusion and discussion
Authors: Gabbay Dov M
Published: November 2023

We saw that the idea of fibred semantics is basically very simple. If we encounter a symbol of a foreign language while evaluating an expression in our own language, then we regard this symbol as atomic (in our language) and turn to the semantics of the foreign language to get a value for it.
Prologue
Authors: Schilthuizen Menno
Published: November 2023

Archirrhinos haeckelii from the Pacific Hi-lay islands is a remarkable creature. To the casual observer, it might appear to be a sort of shrew with an exceptionally large nose. When seen in pursuit of prey, however, its uniqueness becomes apparent. Having caught a cockroach, the animal will quickly dive forwards on to its fleshy snout. The snout then spreads out to support the entire body, leaving all legs free for handling and crushing the prey.
Wham, Bam, Brand New Species
Authors: Schilthuizen Menno
Published: November 2023

In a corner of the Botanical Gardens of the University of Amsterdam stands the bust of a bearded man. Around the pedestal, tall yellow flowers grow. The mossy statue portrays the Dutch botanist Hugo de Vries; the flowers at his feet are evening primroses, the plants that made him famous.
A Chronic Case of Rhagoletis
Authors: Schilthuizen Menno
Published: November 2023

The Natural History Museum in London is one of the most impressive museums in the world. Its huge crenellated building, occupying the sunny side of Cromwell Road, houses an estimated 90 million specimens. In the public exhibits, not much of the vast collection is visible. Most of it is hidden behind oaken doors marked ‘STAFF ONLY’ or ‘NO ACCESS’. But the visitor who is fortunate enough to be allowed beyond those doors, leaving behind the noise of shouting <lino-crazed schoolchildren and the hissing and puffing of pneumatic grasshoppers, enters the serene world of handwritten labels, formalin, and patient cataloguing.
Analysis of Hamiltonian PDEs
Authors: Kuksin Sergei B
Published: November 2023

For the last 20–30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and will be an invaluable source of information for postgraduate mathematics and physics students and researchers.
Linearized Lax-integrable equations
Authors: Kuksin Sergei B
Published: November 2023

If (5.1) is a Lax-integrable equation, then its £, A pair can be used to construct solutions of the linearized equation (5.2) as quadratic expressions of eigenfunctions of the £-operator and its adjoint. Below we present the construction, mostly following Krichever (1991).
First-order linear differential equations on the n-torus
Authors: Kuksin Sergei B
Published: November 2023

The ‘right’ estimate for the solution x turns out to be independent of B and E. This is stated by the following theorem.
Flows At Moderate Reynolds Number
Authors: Succi Sauro
Published: November 2023

In this chapter we present the application of LBE to the problem of transitional flows at moderate Reynolds numbers. This is an important area of theoretical and applied fluid mechanics, one that relates mainly with the onset of nonlinear instabilities and their effects on the transport properties of the unsteady flow configuration. The regime of Reynolds numbers at which these instabilities take place is usually not too high, of the order of thousands, and consequently basically within reach of present day computer capabilities. Nonetheless, following the entire evolution of these highly dynamic transitional flows requires very long integrations with short time-steps which demand conspicuous computational power. Which is why, again, efficient numerical methods are in great demand. As we shall see, LBE has good credentials to meet this demand. 7.1 Moderate Reynolds flows in simple geometry Let us consider a rectangular channel of length L and height H . The fluid enters the channel from the left side (inlet) and flows steadily down the channel under the effect of a constant pressure drop ΔP = P i P o between the inlet and outlet section. At the top and bottom boundaries the flow speed vanishes (noslip boundary condition) as a result of the drag exerted by the rigid walls. This is how dissipation balances the momentum input from the pressure gradient. If the Reynolds number is small enough, typically below 2000 in a real pipe, occasional fluctuations are unable to break the one-dimensional symmetry of the flow so that the nonlinear terms of the Navier–Stokes equations, (∂buaub ), vanish identically and have no effect on the evolution of the flow.
Estimating the age of mutations using variation at linked markers
Authors: Reich David E , Goldstein David B
Published: November 2023

We present a general method for estimating the dates of mutations using variation at linked microsatellite markers. Risch et al. ( 1995) take a similar approach to estimating the age of the mutation causing idiopathic torsion dystonia among Ashkenazic Jews, but they do not describe how to produce a confidence interval for the date. Here, we not only obtain a confidence interval for the date by assessing the degree of correlation among samples, but also describe how to use a Markov transition matrix approach to take full account of the complexities of the recombination process. Finally, we show how the method has been applied to a specific example: estimation of a date for a mutation that confers resistance to HIV-1 infection (Stephens et al. 1998).
Genes and personality
Authors: Little Peter
Published: November 2023

I deliberately created a future history for Jean Battler and Jeanne Dream that does not tell us much about their personalities because I wanted to concentrate on other aspects of their lives but, of course, each would have had a distinct personality because possession of a personality is an inextricable feature of being a human—it would be as impossible to conceive of a human without a personality as it would be to think of two humans with absolutely identical personalities.
Pearson Type II Errors-in-Variables Models
Authors: Bolfarine Heleno , Gasco Loretta , Iglesias Pilar
Published: November 2023

In this paper, invariant error-in-variables models (EIVM) are studied. We show that considering special invariance assumptions about the observable variables is equivalent to replace the usual normal EIVM by special Pearson type II EIVM. The proximity between these two formulations is studied in the context of de Finetti type representation theorems, following results established in Diaconis et al. (1992) in conection with multivariate Pearson type II distributions.
Fixed-Lag Smoothing using Sequential Importance Sampling
Authors: Clapp Tim C , Godsill Simon J
Published: November 2023

In this paper we present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) for state space models with unknown parameters. Sequential processing using Monte Carlo simulation is an area of growing interest for many engineering and statistical applications where data arrive point by point rather than in a batch. The methods presented here are related to the particle filtering ideas seen in Gordon et al. (1993), Liu and Chen (1995), Berzuini et al. (1997), Pitt and Shephard (1999) and Doucet (1998). Techniques for fixed-lag simulation using either the filtering density or the smoothing density are developed. In addition we describe methods for regenerating parameters of the state-space model by sampling. We are concerned in particular with problems in Digital Communication systems where off-line or batch-based methods, such as Markov chain Monte Carlo (MCMC), are not well suited. The new techniques are demonstrated by application to a standard digital communications model and the performance of the various methods is compared.
On the Different Structures of Posterior Distributions with Respect to the Prior Distribution
Authors: Macci Claudio
Published: November 2023

The aim of this paper is to understand which samples-give rise to each one the above cases without deriving a family of posterior distributions and to compute the probabilities to have these theree cases.
Simplifying Complex Designs: Bayes Linear Experimental Design for Grouped Multivariate Exchangeable Systems
Authors: Shaw Simon C , Goldstein Michael
Published: November 2023

We adopt a Bayes linear approach to tackle design problems with many variables cross-classified in many ways. We investigate designs where we wish to sample individuals belonging to different groups, exploiting the powerful properties of the adjustment of second-order exchangeable vectors. The types of information we gain by sampling are identified with the orthogonal canonical directions. We show how we may express these directions in terms of the different factors of the model. This allows us to solve a series of lower dimensional problems, through which we may identify the different aspects of our adjusted beliefs with the different aspects of the choice of design, leading both to qualitative insights and quantitative guidance for the optimal choice of design.
Amygdala: role in modulation of memory storage
Authors: McGaugh James L , Ferry Barbara , Vazdarjanova Almira , Roozendaal Benno
Published: November 2023

This chapter reviews evidence from studies investigating the involvement of the amygdala in modulating the consolidation of long-term explicit/declarative memory. Extensive findings from animal experiments indicate that drugs of several classes, as well as the adrenal stress hormones adrenaline and corticosterone, modulate memory storage when administered post-training and that such effects critically involve activation of the basolateral amygdala (BLA). Lesions of the BLA block such modulatory influences on memory storage. Further, memory storage is modulated by post-training infusions of adrenergic and glucocorticoid agonists and antagonists administered selectively into the BLA. The memory-modulatory influences involve activation of [3-adrenoceptors within the BLA and subsequent activation of other brain regions through projections mediated, primarily if not exclusively, by the stria terminalis. As lesions of the BLA do not prevent the learning or retention of the tasks used in these experiments, it is clear that this brain region is not essential for the learning and is not a likely neural locus of the explicit/declarative memory of the training experiences. Rather, our findings suggest that the BLA modulates the consolidation of explicit/declarative memory in other brain regions and that such modulation serves to ensure that the significance of experiences influences their remembrance.
Modulation of long-term memory storage in humans by emotional arousal: adrenergic activation and the amygdala
Authors: Cahill Larry
Published: November 2023

Anchored in an extensive literature involving infra-human subjects, a rapidly growing number of studies involving human subjects confirms the theory that the sympathetic nervous system and the amygdala are crucial for the modulation of long-term memory storage for emotionally arousing events. Several studies indicate adrenergic participation in memory for emotional events in humans. Amygdala participation is indicated by converging evidence from neuropsychological and brain imaging studies. Substantial evidence from both infra-human and human subject studies suggests that the degree of emotional arousal involved in a learning situation, rather than its pleasant/unpleasant nature, determines the degree of amygdala engagement in learning. Although evidence for amygdala participation in long-term memory storage for emotionally arousing events in humans is strong, evidence for its participation in memory retrieval, or for its participation in the production of emotion per se, currently is less clear. The chapter closes with a novel, testable proposal regarding a mechanism by which this system may modulate long-term memory storage.
Neurophysiology and functions of the primate amygdala, and the neural basis of emotion
Authors: Rolls Edmund T
Published: November 2023

Four main groups of neurons in the primate amygdala are described. One group responds to stimuli which are primary (unlearned) reinforcers, such as taste. Both rewarding and aversive tastes are represented neuronally in macaques and, correspondingly, functional magnetic resonance imaging (fMRI) investigations in humans show that the amygdala can be activated by both pleasant and unpleasant tastes.
Regulation
Authors: Sellers James R
Published: November 2023

The MgATPase activity of most myosins that have been studied is regulated. A notable exception to this is the myosin from vertebrate striated muscle and possibly some invertebrate striated muscles, such as that from the fast muscle of lobster ([1968), but see [1969)). In general, regulation of myosin is accomplished by either phosphorylation or, in the case of molluscan muscles, direct calcium binding to myosin. Phosphorylation might occur on regulatory light chains or on the heavy chain or both depending on the myosin. In some cases, these phosphorylations are regulatory in that they profoundly affect the actin-activated MgATPase activity of the myosin, in others they are modulatory and have only a small effect on the activity. In quite a few cases, the phosphorylations have no apparent effects on any biochemical process. Below, we will discuss the details of both the covalent regulation by phosphorylation and the noncovalent regulation by calcium binding. At the same time, we will discuss other known phosphorylations even if they have not been linked to a change in function.
On the current state of finite element methods — solids and structures with full coupling to fluid flows
Authors: Bathe Klaus-Jurgen , Rugonyi Sandra , De Suvranu
Published: November 2023

Finite clement methods are med abundantly in today’s engineering practice. Various general-purpose commercial computer programs and many special pm pose programs written for specific applications are in wide use. Finite element methods are employed to an increasing extent to study physical phenomena, to help identify good designs, and to improve designs with respect to performance and cost [2].
Macroscopic models of superconductivity
Authors: Chapman S J
Published: November 2023

One of the interesting aspects of superconductivity is the variety of models available to describe the phenomenon at different lengthscales, ranging from the microscopic theory of Bardeen, Cooper & Schreiffer through the mesoscopic theories of London and Ginzburg & Landau, to the macroscopic Critical State theories such as the Bean model. Through a series of appropriate asymptotic limits we will derive a hierarchy of models connecting the Ginzburg-Landau model to the London model with isolated superconducting vortices as line singularities, to vortex-density models, and finally to macroscopic critical-state models. The basic building block in deriving this hierarchy is the superconducting vortex, which is a thin core of nonsuperconducting material circled by a superconducting electric current. Similar line singularities are found in other systems, for example, line vortices in an inviscid fluid, or Volterra dislocations in an elastic crystal. This raises the interesting question of whether analogous hierarchies of models exist in each of these other systems, and whether similar connections can be established between them.
Future research avenues in computational engineering and design
Authors: Jameson A , Alonso J J
Published: November 2023

The objective of this paper is to present a coherent view of future avenues of research in computational engineering and science based on recent accomplishments in accurate and robust algorithm development, and on techniques for the automatic design of systems governed by partial differential equations. In light of these developments, we propose our view of a computational engineering environment for the design of multidisciplinary aerospace systems based on high-fidelity methods.
Whizzkids: two exercises in computational discrete optimization
Authors: Aarts Emile
Published: November 2023

The number of students in the exact sciences in the Netherlands has sharply de creased over the past years. In 1986 over 500 students in mathematics entered the universities, in 1999 fewer than 180. In addition to demographic developments, there may be several reasons for this: the infantilization of the mathematics pro gram in high schools, which turns off the bright students; the risk-averse behavior of some students, which directs them towards easier and financially more reward ing subjects; sociological developments, which cause others to prefer life sciences and humanities; and the elitist attitude of mathematicians, which does not help in creating an attractive career perspective.
Study of Flow Stability Using Direct Numerical Simulation of the Disturbance Equations
Authors: Spentzos A , Drikakis D
Published: November 2023

The present study deals with the flow stability in suddenly-expanded channels. The stability analysis is performed by numerically solving the linearised disturbance equations rather than the full set of the Navier Stokes equations (see for example in [l]). The kinetic energy of the disturbances is employed as stability criterion for calculating the eigenvalue corresponding to the least stable mode and, subsequently, detecting the stability regimes. The computations reveal that for Reynolds numbers in the stability regime, an initial random flow perturbation is quickly attenuated. On the contrary, in the case of unstable flows the perturbations continue to exist as the time progresses, and concentrate in the regions of the flow field where instabilities appear. Incompressible flows in suddenly-expanded channels are encountered in various physiological flows for example, flows through prosthetic devices and aortic stenoses. At certain Reynolds numbers these flows present instabilities which may lead to bifurcation, unsteadiness, and chaos. Study of such flows can improve our understanding of hydrodynamic stability and the mechanism of laminar-to-turbulent flow transition. Past experimental studies of low Reynolds number flows in symmetric suddenly-expanded channels have been performed by Chedron et al. [2] and Fearn et al. [3]. Those studies revealed a flow instability beyond a certain Reynolds number, which was appeared in the form of asymmetric separation be tween the upper and lower channel’s walls.
Platelet Deposition in Stagnation Point Flow: An Analytical Study and Computational Simulation
Authors: David T , Thomas S , Walker P G
Published: November 2023

A mathematical and numerical model is developed for the adhesion of platelets in steady stagnation point flow. The model provides for a correct representation of the axi-symmetric flow and explicitly uses shear rate to characterise not only the convective transport but also the simple reaction mechanism used to model platelet adhesion at the wall surface. Excellent agreement exists between the analytical solution and that obtained by the numerical integration of the full Navier-Stokes equations and decoupled conservation of species equations. It has been shown that for a constant wall reaction rate modelling platelet adhesion the maximum platelet flux occurs at the stagnation point streamline. This is in direct contrast to that found in experiment where the maximum platelet deposition occurs at some distance downstream of the stagnation point. However, if the wall reaction rate is chosen to be linearly dependent on the wall shear stress then the results show that the maximum platelet flux occurs downstream of the stagnation point, providing a more realistic model of experimental evidence. The first stage of thrombogenesis is platelet adhesion. This may then be followed by platelet aggregation and the formation of mural thrombi [2] and [3]. Although the formation of thrombi in stasis is fairly well understood the influence of blood flow characteristics has yet to be fully investigated. Fluid dynamic studies of blood flow, in models of arteries, suggests a set of fluid dynamic conditions which appear to predispose thrombus formation, principally at arterial bifurcations [7], T-junctions and curved sections, in particular, Schoepheoster and Dewanjee [15] found that areas of flow stagnation or recirculation are shown to promote thrombus formation.
The Application of Computational Fluid Dynamics and Solid Mechanics to Haemodynamics in Arterial Organs and to Related Problems
Authors: Zhao S Z , Collins* M W , Long Q , Xu X Y
Published: November 2023

Cardiovascular haemodynamics forms an important current class of medical research. Over the last ten years, as the current generation of Computational Fluid Dynamics (CFD) codes have been developed, so they have been applied to arterial problems and have been demonstrated to be a valuable and reliable tool in this area. This paper will discuss a range of topics in our efforts to correlate haemodynamics to risk factors underlying the genesis and progression of cardiovascular disease. In the course of discussion, the state of art of CFD is described and its application in blood flows demonstrated. Furthermore, our approach has been extended to incorporate solid mechanics into haemodynamic studies so as to address the problems in a. more realistic and comprehensive manner. To obtain predictions which can reflect the real situations in the human body, image and data processing software has been developed to take raw clinical data from Magnetic Resonance Imaging and interface it with the CFD code. As the vessels become smaller in size, so wall effects increase in complexity, and we give relevant data from a major study of nanoscale fluid problems in human biology. Cardiovascular diseases such as atherosclerosis are known to be influenced by blood flows in terms of their genesis and progression (1, 2]. In order to in vestigate what is a complex mechanism a broad knowledge of detailed arterial flow phenomena is necessary. Modern techniques such as ultrasound and Magnetic Resonance Imaging enable measurements of pulsatile blood velocities to be undertaken. However, accurate assessment of wall shear stress, which is of considerable physiological interest, is quite difficult.
The Convergence Technique in Numerical Solutions of Coupled Fluid-Wall Problems
Authors: Hughes A D , Thom S A
Published: November 2023

A comprehensive coupled fluid-wall interaction dynamics model was developed for the simulation of blood flow in arteries. Blood flow was treated as pulsatile, laminar, Newtonian and incompressible. The structural model accounted for both material and geometric nonlinearities. A multiblock body fitted grid was used to subdivide the flow domain into computational finite volume cells. Shell elements were used to discretize the arterial wall. A finite volume computational fluid dynamics code and a finite element structural dynamics code were used to solve the flow and structure equations, respectively. This paper discusses some important is sues related to the coupled model, particularly numerical convergence. In addition to convergence considerations within each code, convergence be tween the two codes must also be dealt with. And a relaxation technique has been introduced to improve and accelerate the convergence performance. Fluid-wall interaction problems exist in the cardiovascular system where blood interacts dynamically with its surroundings. In order to understand both the haemodynamics and vessel wall mechanics in a real artery, computer simulation of this complex system has become more and more demanding [1, 2]. In the present paper, a numerical solution procedure for solving general fluid-wall interactions is developed. In this approach, the time-dependent Navier-Stokes equations of the fluid are not explicitly assembled with the dynamics equilibrium equations of the wall, but instead an iterative procedure is used to obtain the solution. Combining two established commercial codes, CFX for fluid flow and ABAQUS for wall motion [3, 4], this iterative algorithm preserves the nature of software modularity and offers a distinct advantage in that the most efficient codes for fluid flow and structural analysis can be used to deal with complex problems.
Choice Sequences and Spreads
Authors: Dummett Michael
Published: November 2023

In intuitionistic mathematics, all infinity is potential infinity: there is no completed infinite. Since the distinction between the potential and the actual infinite arises within classical mathematics in a perfectly reasonable way, this dictum may at first appear as the expression of a groundless prejudice.
Enemy Alien
Authors: Perutz Max F
Published: November 2023

It was a cloudless Sunday morning in May of 1940. The policeman who came to arrest me said that I would be gone for only a few days, but I packed for a long journey. I said goodbye to my parents. From Cambridge, they took me and more than a hundred other people to Bury St. Edmunds, a small garrison town twenty-five miles to the east, and there they locked us up in a school. We were herded into a huge empty shed cast into gloom by blacked-out skylights thirty feet above us. A fellow-prisoner kept staring at a blank piece of white paper, and I wondered why until he showed me that a tiny pinhole in the blackout paint projected a sharp image of the sun’s disc, on which one could observe the outlines of sunspots. He also taught me how to work out the distances of planets and stars from their parallaxes and the distances of nebulas from the red shifts of their spectra. He was a warmhearted and gentle German Roman Catholic who had found refuge from the Nazis at the Observatory of Cambridge University.
How the Secret of Life Was Discovered*
Authors: Perutz Max F
Published: November 2023

In 1936, I left my hometown of Vienna, Austria, for Cambridge, England, to seek the Great Sage. I asked him, “How can I solve the secret of life?” He replied, “The secret of life lies in the structure of proteins, and X-ray crystallography is the only way to solve it.” The “Sage” was John Desmond Bernal, a flamboyant Irishman who headed the Crystallographic Department of the Cavendish Laboratory and who had been the first to discover that protein crystals give detailed X-ray diffraction patterns extending to spacings of the order of interatomic distances.2 We really called him Sage, because he knew everything. During a discourse at the Royal Institution in London in 1939, Bernal said:
Darwin Was Right
Authors: Perutz Max F
Published: November 2023

Three hundred years ago Isaac Newton claimed that scientists work from the particular to the general, first observing phenomena and only later drawing generalisations from them. In his Principia, he stated that “In experimental philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction.” Karl Popper has disputed this, arguing that imagination comes first: scientists begin by formulating hypotheses and then proceed to test them by observation. Only hypotheses that can be falsified experimentally are scientific. If the hypothesis turns out to be inadequate, scientists formulate a new and improved one that can be again subjected to experimental tests. In this way, science has evolved by an interplay of imaginative conjections and experimental refutation.
A Passion for Crystals
Authors: Perutz Max F
Published: November 2023

In October 1964, the Daily Mail carried a headline “Grandmother wins N bel Prize.” Dorothy Hodgkin won it “for her determination by Xray techniques of the structures of biologically important molecules:’ She used a physical method first developed by W.L. Bragg, X-ray crystallography, to find the arrangements of the atoms in simple salts and minerals. She had the courage, skill, and sheer willpower to extend the method to compounds that were far more complex than anything attempted before. The most important of these were cholesterol, vitamin D, penicillin, and vitamin B12 Later, she was most famous for her work on insulin, but this reached its climax only five years after she had won the prize.
The Right to Choose*
Authors: Perutz Max F
Published: November 2023

The world population now increases by 1.7 percent (90 million) per year, while production of cereals is increasing by only 0.9 percent per year. During the past twenty years there have been about 200 million hunger-related deaths; the growing food deficit may raise that number fivefold in the next twenty years.
How WL Bragg Invented X-ray Analysis
Authors: Perutz Max F
Published: November 2023

I first met Bragg in Cambridge in the autumn of 1938 when he had just been appointed Rutherford’s successor as Cavendish Professor of Experimental Physics. One day I burst into his room announcing proudly, “I have received an honour that you can’t match, I have had a glacier named after me.” “I have one that you can’t match” retorted Bragg, “I have had a cuttlefish named after me.” He then told me that as a boy in Adelaide he had been a keen collector and found a new species which his seniors promptly named Sepia Braggi.