bluuebunny/crossref_metadata_2025_split huggingface dataset:
Surface patches
Authors: Marciniak Krzysztof 
Published: November 2023

Abstract
We restrict ourselves to the linear methods of surface patch definition. The important property of linearity is that the surface can be represented by a mapping R(u) = R(u1, u2) of the form where a; are coefficients and b1(u) = b1(u1,u2) are scalar bivariate functions, termed basis functions. They usually form a basis of the linear space.
Contouring on 2CL milling machines
Authors: Marciniak Krzysztof 
Published: November 2023

Abstract
On NC milling machines with a control unit of type 2CL a tool moves in such a way that the direction of the rotation axis is constant. This kinematic constraint means that a tool movement may be uniquely defined by the movement of an arbitrarily chosen point on its axis of rotation. In addition, on 2CL milling machines movements are restricted to flat trajectories in mutually parallel planes (Fig. 10.1). Rapid movements do not conform to this restriction and may be used to move a cutter to the next parallel plane. The contouring trajectory consists of machining movements in mutually parallel planes and rapid changes of machining planes. The tool trajectory is then similar to the contours on maps.
Plane stress and plane strain
Authors: Mohr G A 
Published: November 2023

Abstract
The basic constitutive relationships of Chapter 2, the energy-based displacement method of Chapter 3, and some of the interpolation functions of Chapter 5 are used to develop several finite elements for the analysis of plane stress and plane strain. In the first two sections explicit formulations are obtained using Cartesian polynomial interpolations. These provide a useful introduction to two-dimensional finite elements but for higher-order elements interpolation functions expressed in terms of dimensionless coordinates and numerical integration are used in the remainder of the text.
Boundary solution techniques
Authors: Mohr G A 
Published: November 2023

Abstract
The boundary element method is based upon the use of integral equations. To obtain an integral equation solution to the problem of determining the distribution of a function y = y(s) in a domain one begins by expressing the solution in the form and integration by parts is used to force the solution to the boundary. In practice F(x, s) consists of two parts: a forcing function b(x) describing the variation in intensity of some ‘loading’ effect, and a response or influence function G(x, s) which gives the response at s resulting from a point loading at x.
Generalization of constraint techniques and optimization programs
Authors: Mohr G A 
Published: November 2023

Abstract
We have seen the application of constraints to finite element formulations at many points in preceding chapters. Of particular note are the penalty factor, Lagrange multiplier, and basis transformation techniques introduced in Chapter 4 and frequently used subsequently. The present chapter begins by examining the relationships between these methods, giving particular attention to conversion of Lagrange multiplier formulations to obtain equivalent penalty formulations. Application of the latter to integral constraints is then discussed in relation to both variational and weighted residual formulations. Finally, the chapter closes with several programs for the optimization of finite element models of problems in both solids and fluids.
Constraint Methods Applied in Contact Problems with Small Displacements
Authors: Zhong Zhi-Hua 
Published: November 2023

Abstract
Contact problems are characterized by contact constraints which must be imposed on contacting boundaries. To impose the contact constraints, two basic methods are available. These two basic methods are the Lagrange multiplier method and the penalty method (Kikuchi and Oden 1988). Other constraint methods based on the basic methods have also been proposed and applied. For example, a perturbed Lagrangian method is discussed in Simo et al. (1985). In this chapter, alternative constraint methods are introduced and applied in contact problems with small displacements. Basic features of the alternative constraint methods in different applications will be identified. It must be pointed out, however, that the discussions on constraint methods are not exclusive to this chapter. The performance of alternative constraint methods will also be examined in subsequent chapters, for example in Chapters 7 and 9.
Dynamics Of Charged Particles
Authors: Woods L C 
Published: November 2023

Abstract
A plasma is a mixture of positive ions, electrons and neutral particles, electrically neutral over macroscopic volumes, and usually permeated by macroscopic electrical and magnetic fields. In addition to these ‘smoothed’ or averaged electromagnetic fields, which with laboratory plasmas are often imposed from outside the plasma volume, there are the microfields due to the individual particles. The trajectories of the charged particles are thus continuously modified by a range of electromagnetic forces, the average fields acting like body forces and the microfields like collisional forces. The microfields are responsible for the transmission of pressure and viscous forces, for the conduction of particle energy, and for the friction forces between diffusing components of the plasma. Some care is needed in dividing the continuum of electromagnetic forces into their macroscopic and microscopic components, but once this has been achieved, there is little formal distinction between the kinetic theory of neutral gases and the kinetic theory of magnetoplasmas. The most important practical distinction is that in strong magnetic fields, for cross-field transport, the terms second-order in the Knudsen number E dominate the first-order terms. This occurs because the 0(∈) terms are much more strongly suppressed by the magnetic fields than are the O(∈) terms.
Design, Assembly, And Testing Of A Prototype Ultrasonic Motor
Authors: Sashida Toshiiku , Kenjo Takashi 
Published: November 2023

Abstract
We have so far discussed the theoretical aspect of the ultrasonic motor. In this chapter, our subject is the actual assembly and testing of a prototype ultrasonic motor. In Section 3.9 we examined various limiting conditions as factors affecting motor design in general. Here we show some calculation examples and make comparisons with theory based more or less on a complete motor. Design experience with ultrasonic motors, unlike that with electro- magnetic motors, has been very limited and there still remain many unresolved questions about its characteristics. Thus the authors feel that it is unrealistic to present a design theory for the ultrasonic motor in a final and orderly manner, and it is their wish that the material presented in this chapter may serve as a starting point for further research.
Periodic Laminar Regime
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The steady, elongated and closed near-wake becomes unstable whenRe&gt; Reosc, where the subscriptosc stands for oscillation. The transverse oscillation starts at the end of the near-wake and initiates a wave along the trail as shown in Fig. 1.6(a). It has been pointed out in Chapter 2 that the maximum adverse pressure gradient also occurs around the confluence point at the near-wake end. The coincidence of the location of the instability and the adverse pressure gradient indicates their interrelationship.
Transition In Boundary Layers
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The advance of transition to turbulence in free ‘shear layers towards the separation line is impeded in the TrSL3 regime because the separated shear layers are squeezed beyond the separation by the accelerated free stream. This stabilizing effect begins to diminish with risingRe at the beginning of the TrBL state of flow. The perturbed boundary layers adhere longer to the surface and the separation is gradually displaced further downstream. The separated free shear layers become more and more aligned with the adjacent free stream and the aforementioned stabilizing effect is gradually weakened until eventually the transition to turbulence reaches the displaced separation line.
Fully Turbulent State
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The least explored and known is the turbulent or T state of flow. It is eventually reached when all three disturbed flow regions - wake, shear and boundary layers - are ‘fully’ turbulent. The transition in boundary layers moves upstream towards the stagnation region asRe rises in the TrBL4 regime. The advance is fast in the region of the adverse pressure gradient and becomes more and more retarded in the region of the favourable pressure gradient.
Solutions Of The N-S Equations
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The equations of motion of viscous fluid, expressed in a differential form, are a statement of equilibrium of all forces acting on the fluid and the rate of change of momentum. The surface forces are expressed through the stress tensor with pressure and friction forces acting normally and tangentially to the surface, respectively. The relationship between the stress and rate of strain for a Newtonian fluid is linear.
Vortex Models And Stability
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The simplest vortex model is the Helmholtz point-vortex in an irrotational and two-dimensional flow and its counterpart the Biot-Savartline-vortex in an irrotational and three-dimensional flow. The flow around the pointvortex is described in a polar coordinate system by the following velocity potential,w, radial,u, and tangential,v, velocity components
Free Stream Turbulence
Authors: Zdravkovich M M 
Published: November 2023

Abstract
The free stream is usually turbulent in most practical applications. Most research, however, has been carried out in wind/water tunnels with low-level turbulence. A particularly strong effect of very low free stream turbulence is observed in three transition states of flow past cylinders. This means that the experimental data obtained in smooth flows cannot be used for practical flows without correction.
Electromagnetic Waveguides and Transmission Lines
Authors: Olyslager Frank 
Published: November 2023

Abstract
This monograph deals with the theoretical aspects of the circuit modelling of high-frequency electromagnetic structures using the Lorentz reciprocity theorem. This is the first book to cover the generalization from closed structures to open-boundary waveguides and circuit structures. The author has developed a new way to represent a general waveguide by transmission lines: and was awarded the Microwave Prize of the IEEE for this work. The first part of the book discusses the construction of transmission line models for waveguide structures. Then the incidence of external electromagnetic waves on high-frequency structures is studied, and finally the concepts derived in the earlier parts of the book are generalized to reciprocal and non-reciprocal anisotropic, bi-isotropic, and bianisotropic materials.
Transmission Lines For Full-Wave Fields
Authors: Olyslager Frank 
Published: November 2023

Abstract
In the previous chapter it was shown that at low frequencies Maxwell’s equations in electric waveguides can be reduced to transmission line equations. The aim of this chapter is to extend these transmission line equations to all types of isotropic waveguides and to arbitrary frequencies. Before being able to construct these models, it will be instructive to study some properties of general isotropic waveguides.
Rapidly oscillating periodic functions
Authors: Donato Patrizia 
Published: November 2023

Abstract
In this chapter we study a relevant class of periodic oscillating functions, which plays an essential role in homogenization theory. We turn our attention, in particular, to functions of the form where a is a periodic function and where, from now on, ε &gt; 0 takes its values in a sequence which tends to zero. Let us point out that if a is Y-periodic (see Definition 2.1 below), then a ε is εY-periodic. Moreover, as can be seen in the examples below, the smaller ε is, the more rapid are the oscillations.
Some variational elliptic problems
Authors: Donato Patrizia 
Published: November 2023

Abstract
We study in this chapter some classical elliptic partial differential equations in the framework of weak solutions. The problems we deal with are linear elliptic partial differential equations with different boundary conditions: Dirichlet, Neumann, Robin and periodic conditions. In all these cases, the existence and uniqueness of the solution are obtained by applying the Lax–Milgram theorem. This important theorem is proved in Section 4.2 below.
Tartar’s method of oscillating test functions
Authors: Donato Patrizia 
Published: November 2023

Abstract
We begin this chapter with the proof of Theorem 6.1. This is done by using the method introduced by Tartar (1977a, 1978). In Section 8.2 we prove the convergence of the energy associated to problem (6.1). This convergence allows us to show in Section 8.3 a corrector result. Sections 8.4 and 8.5 contain some further convergence properties of the solution u ε of the model problem (6.1).
The two-scale convergence method
Authors: Donato Patrizia 
Published: November 2023

Abstract
In the first two sections of this chapter, we present the two-scale convergence method and we use it in Section 9.3 to prove again Theorem 6.1. As the multiplescale method, it also takes into account the fact that we have a ‘macroscopic’ scale x and a ‘microscopic’ one x/ε.
Homogenization in linearized elasticity
Authors: Donato Patrizia 
Published: November 2023

Abstract
In this chapter we are interested in the asymptotic behaviour as ε → 0 of the solution of the linearized elasticity system introduced in Section 5.2. We refer to Duvaut (1978), Sanchez-Palencia (1980), Bakhvalov and Panasenko (1989), Oleinik, Shamaev, and Yosifian (1992), Sanchez-Hubert and Sanchez-Palencia (1992) for this subject and to references herein.
Homogenization of the wave equation
Authors: Donato Patrizia 
Published: November 2023

Abstract
In this chapter we are concerned with the asymptotic behaviour as ε → 0 of the solution u ε = u ε (x, t) of the wave equation introduced in Section 5.2 (Example 5.3), namely, where as in the previous chapter, the operators div and ▽ are taken with respect to the space variable x ∈ Ω and ‘ denotes the derivative with respect to the time variable l ∈]0, T[ with T &gt; 0.
N
Authors: Perrot Pierre 
Published: November 2023

Abstract
At equilibrium, if T &gt; 0, the entropy increases with internal energy, whereas if T &lt; 0, it varies inversely. Consider for instance an assembly of moment-carriers in a magnetic field. If every moment is oriented in the reverse direction to the field, the energy of the system is a maximum and its entropy a minimum. This state corresponds to the temperature T = - 0 K. If all the moments are oriented in the direction of the field, the energy of the system is then a minimum and its entropy is also a minimum. This state corresponds to a temperature T = +0 K. Between these two states, the entropy of the system goes through a maximum (directions of moments haphazard), a state corresponding to an infinite temperature.
V
Authors: Perrot Pierre 
Published: November 2023

Abstract
Vacancy—The name given to an unoccupied crystal site. Vacancies are point defects which are thermodynamically stable. In fact, the formation of a vacancy at a site, an endothermic phenomenon (ArH &gt; 0), correspondingly introduces disorder (Ar S &gt; 0). As a consequence, there is an equilibrium vacancy concentration which is calculated by seeking the minimum of the function G =H -TS.
W
Authors: Perrot Pierre 
Published: November 2023

Abstract
Waage, Peter (1833-1900) —Norwegian chemist who, together with Cato Guldberg, expressed the mass action law in a mathematical form in 1864. Wagner, Carl (1901-1977) —German physical chemist and metallurgist, who made an important contribution to the study of defects in crystals and in dilute solutions. He introduced interaction parameters.
Legendre Polynomials and Related Functions
Authors: Andrews Larry C 
Published: November 2023

Abstract
The Legendre polyrwmials are closely associated with physical phen omena for which spherical geometry is important. In particular, these polynomials first arose in the problem of expressing the newtonian potential of a conservative force field in an infinite series involving the distance variables of two points and their included central angle (see Sec. 4.2). Other similar problems dealing with either gravita tional potentials or electrostatic potentials also lead to Legendre polynomials, as do certain steady-state heat conduction problems in spherical solids, and so forth.
Likelihood Calculation in Molecular Phylogenetics
Authors: Bryant David , Galtier Nicolas , Poursat Marie-Anne 
Published: November 2023

Abstract
Likelihood estimation is central to many areas of the natural and physical sciences and has had a major impact on molecular phylogenetics. In this chapter we provide a concise review of some of the theoretical and computational aspects of likelihood-based phylogenetic inference. We outline the basic probabilistic model and likelihood computation algorithm, as well as extensions to more realistic models and strategics of likelihood optimization. We survey several of the theoretical underpinnings of the likelihood framework, reviewing research on consistency, identifiability, and the effect of model mis-specification, as well as advantages, and limitations, of likelihood ratio tests.
Reconstructing the Duplication History of Tandemly Repeated Sequences
Authors: Gascuel Olivier , Bertrand, Denis , Elernento Olivier 
Published: November 2023

Abstract
Tandemly repeated sequences can be found in all genomes that have been sequenced so far. However, their evolution is only beginning to be understood. In this chapter, we present state-of-the-art mathematical concepts and approaches for studying tandemly repeated sequences, from an evolutionary perspective. We describe a tandem duplication model for representing the evolution of these sequences, and shows that it has strong biological support. Then, we provide extensive mathematical and combin-atorial characterization of tandem duplication trees and describe several algorithms for inferring tandem duplication trees from aligned and ordered sequences. We finally compare these algorithms using computer simulations and discuss directions for further research.
The Inversion Distance Problem
Authors: Bergeron Anne , Mixtacki, .Iulia , Stoye Jens 
Published: November 2023

Abstract
Among the many genome rearrangement operations, signed inversions stand out for many biological and computational reasons. Inversions, also known as reversals, are widely identified as one of the common rearrangement operations on chromosomes, they are basic to the understanding of more complex operations such as translocations, and they offer many com-putational challenges. From the first formulation of the inversion distance problem, ca. 1992, to its first polynomial solution in 1995, to the several simplifications of the solution in recent years, there is not yet a simple, complete, and elementary treatment of the subject. ‘l’his is the goal of this chapter.
Scale and island ecological theory: towards a new synthesis
Authors: Whittaker Robert J , Fernández-Palacios José María 
Published: November 2023

Abstract
In the previous two chapters we have reviewed island ecological theories from both macroecological and ecological-biogeographical perspectives, tracing the development of ideas following the appearance of the seminal work of MacArthur and Wilson (1963, 1967). We return again to their equilibrium theory at the outset of this chapter. The exploration of these ideas by ecologists has produced many insights, sometimes consistent with the original models, sometimes inconsistent. Departures from predicted behaviours are in many respects of greatest interest, as they show how the models need to be modified. As a research programme, this body of work is characterized by a general assumption that the systems can be characterized as dynamic and equilibrial: indeed we might consider this paradigmatic. Yet, as we know, this assumption may not be supported in all cases. Accordingly, we will consider the alternatives in the present chapter. In so doing we hope to reconcile the apparently conflicting lessons from 40 years of research and to suggest where island ecological theory might be heading.
Anthropogenic losses and threats to island ecosystems
Authors: Whittaker Robert J , Fernández-Palacios José María 
Published: November 2023

Abstract
Throughout our discussions of island ecology and evolution, we have mostly set to one side the significance of humans as shapers of island biogeography. As this chapter will show, this is a questionable practice, as human societies have had a profound influence on island biodiversity in both recent historical and prehistorical time (Morgan and Woods 1986; Johnson and Stattersfield 1990; Groombridge 1992; Pimm et al. 1995). This influence has been manifested in many ways, but the most profound must surely be the extinction of numerous island races and species. Of all the species that have ever lived on the Earth, only a small fraction are alive today. Natural catastrophes, such as volcanic eruptions, meteorite impacts, climate changes, marine transgressions and regressions, in combination with biotic forcing, have been key agents of species extinction in the past. Extinction rates have varied through time, with five phases recognized as particularly intense and widespread events in the fossil record, the so
The brain—gambler and logician
Authors: Berthoz Alain 
Published: November 2023

Abstract
Is the brain a calculator that uses probability theory to make decisions [1] ?The basic principles of probability theory were first hammered out in an exchange of letters between Blaise Pascal and Pierre de Fermat on the subject of gambling. Pascal suggested that when in doubt, one should bet that God exists because that way there is everything to gain—life everlasting—and nothing to lose. After all, if God does not exist, neither does anything else. But the modern concept of probability is the brainchild of Jakob Bernoulli, who in 1713 set forth in Ars conjectandi a general theory for making rational decisions in uncertain circumstances.
Walking and balance
Authors: Berthoz Alain 
Published: November 2023

Abstract
If, on a beautiful summer afternoon, it pleases you to take a leisurely stroll through the Luxembourg Gardens, reading the poems of Verlaine, it is unlikely you will be making many strategic cognitive decisions. Still, watch out for the child who suddenly comes looking for his ball between your dreamer’s legs and trips you! But if you play for a French football, rugby, or basketball team, if you are a mountain hiker, a police officer chasing a thief, a roofer on the top of a five-storey building, it’s a completely different matter. You can choose to go quickly or slowly, to walk or run, to jump from one foot to the other, or with both feet together.