bluuebunny/crossref_metadata_2025_split huggingface dataset:
Regularized Theory for Smooth Unstable Energies; Dependence of Interfacial Energy
Authors: Gurtin Morton E 
Published: November 2023

Abstract
Unstable interfacial energies lead to backward-parabolic evolution equations for the interface. In this section we regularize the evolution equations by allowing for a curvature-dependent interfacial energy, a dependence that requires the introduction of capillary moments in conjunction with a more general balance law for moments. (a) Balance of forces and moments; power Consider an evolving interface 𝓈 with r a corresponding parametrization. The micromechanics of the interface is described by four interfacial fields: the capillary force C(s, t), the interactive force B(s, t), and the interactive moment m(s, t), discussed in Section 4.1, and an additional field, the capillary moment M(s, t), which represents the moment within the interface exerted across s.
Node-cell mappings for the cell vertex method
Authors: Morton K W 
Published: November 2023

Abstract
In the cell centre finite volume method, as in the Galerkin finite element method, there is no problem in identifying each discrete equation with a corresponding unknown. Hence it is a straight-forward matter to set up an iteration procedure to solve the equations, based for example on Runge-Kutta time-stepping schemes. The difficulties arise in establishing the stability of the equations and ensuring the convergence of the iteration at a reasonable rate.
Mesh adaption for compressible flows
Authors: Palmerio Bernadette 
Published: November 2023

Abstract
One of the principles of numerical analysis is to compute the solution of approximate problems, instead of the solution of continuous ones. The accordance between the discrete solution and the continuous one results from various, often antagonist, options such as choosing a fine mesh or saving computer cost. In most cases, the discrete solution is constructed in two phases: firstly a mesh is generated from the point of view of taking into account geometrical data, and then the solution is computed on the mesh, from the physical data, by solving a differential system.
The construction and behaviour of some unstructured grid algorithms for compressible flows
Authors: Peraire J , Vahdati M , Peiró J 
Published: November 2023

Abstract
The methods currently available for the solution of the equations of compressible flow have traditionally been classified as being of either centered or upwind type. Centered schemes are generally developed from the use of central difference type approximations to derivative operators [1], [2], [3], [4], [5]. Current upwind schemes, on the other hand, employ the solution of a one dimensional Riemann problem in the construction of the discrete form of the governing equations and are computationally more expensive [6], [7], [8], [9], [10]. Frequently, centered schemes rely on the explicit addition of artificial viscosity and this requires the empirical determination of the corresponding free parameters. Upwind methods are generally regarded as being parameter free.
A dynamically adaptive Godunov scheme for reservoir simulation on large aspect ratio grids
Authors: Edwards Michael G 
Published: November 2023

Abstract
1 Introduction
Large aspect ratio grids are commonly used in the simulation of a vertical cross section of a reservoir, where height is much smaller than length. Unit aspect ratio grids are typical for areal simulations.
The combination of a higher order Godunov scheme with dynamic grid adaptivity applied to reservoir simulation is significantly faster than the standard simulator scheme (first order upwind on a uniform grid) while producing far superior results for areal problems (Edwards 1992).
The results obtained from applying the adaptive higher order Godunov scheme to a vertical cross section using a grid with cells of large aspect ratio show a deterioration in accuracy as the aspect ratio is increased. Large local errors appear in the solution at grid interfaces which separate cells of different levels.
Shock capturing using auto-adaptive finite elements
Authors: Richter R , Leyland P 
Published: November 2023

Abstract
Shock capturing properties via numerical or artificial dissipation is highly linked to the underlying grid structure, and can be improved by using local refinement on adapted grids. Grid alignment is even necessary when one dimensional solvers are adapted to multidimensional problems, as is the case of many modern TVD methods. Also, complex flow calculations for solving secondary shock formation in shock-shock interactions are particularly difficult to simulate accurately. By the use of mesh adaptivity, these effects can be more accurately illustrated within the numerical simulation. Here, combining the relative grid dependency of the numerical scheme and auto-adaptive grids using refinement-derefinement algorithms on unstructured meshes provides a robust tool for capturing such shock formations, and a generic remeshing strategy for unsteady flows. Combining such techniques with directional scaling and stretching, using an elliptic spring analogy, further increases the shock precision, and leads to solutions of almost “shock fitted” quality. Unstructured meshes allow more freedom for these kinds of adaptivity algorithms than structured grids; the latter requiring complicated embedding techniques to achieve similar results.
A cartesian grid scheme for gas dynamic flows that involve complex geometries
Authors: Quirk James J 
Published: November 2023

Abstract
The desire to simulate flows around geometrically complex bodies has led many members of the shock capturing community to abandon schemes which employ body-fitted grids in favour of schemes which employ unstructured meshes. Now such is the success of unstructured grids, there is a danger that they will become de rigueur. Given the ever increasing reliance placed on computational results, such a state of affairs would give cause for some concern. If nothing else, the exercise of using several computer codes to cross check numerical results becomes ill-founded if all codes follow the same methodology. In this paper we outline an alternative approach for dealing with complex two-dimensional geometries, the so-called cartesian boundary method; solid bodies blank out areas of a background cartesian mesh and the cut cells which arise along solid boundaries are singled out for special treatment during the integration of the discretized flow solution.
A new implicit second order scheme based on a kinetic interpretation for solving the Euler Equations
Authors: Vuyst Florian De 
Published: November 2023

Abstract
Over the last decade, several numerical schemes for solving the compressible Euler equations have been built by the way of the kinetic interpretation of these equations. Variants of these Boltzmann-type schemes have been studied by Deshpande, Kaniel and others, using a physical repartition of the particle velocity: the Maxwellian distribution exp(-lvl2 /2). But the main drawback of these methods is their important numerical diffusion. In Perthame (1990) a new class of Boltzmann type schemes was introduced by considering compactly supported velocity distribution functions. Techniques for achieving second order accuracy have been elaborated in Perthame & Qiu (1991), guaranteeing the preservation of the positivity of density and pressure in one or two space variables. The underlying kinetic interpretation also allows the construction of fully multidimensional schemes taking into account the corner effects, and the treatment of wall boundary conditions by the way of specular reflection. In this paper, we present a classical two-dimensional finite volume method which uses the numerical fluxes coming from the one-dimensional scheme. Second order accuracy is performed by a generalized Van Leer’s MUSCL method, applicable to structured or unstructured meshes. We also extend these schemes to the simulation of high speed flows, where the nonequilibrium effects have to be dealt with.
A comparison of several implicit smoothing methods
Authors: Blazek J , Krollm N , Rossow C C 
Published: November 2023

Abstract
In recent years, several different numerical methods for the solution of Euler and Navier-Stokes equations were introduced in the literature. Due to their simplicity the explicit multistage time stepping schemes originated by Jameson et al (1981) quickly gained popularity and today they are in wide-spread use. In combination with various convergence acceleration techniques, such as local time stepping, residual smoothing and in particular multigrid, the multistage schemes proved to be very efficient for the calculation of both inviscid and viscous steady flow fields (Radespiel et al 1990 and Radespiel et al 1991). The use of implicit residual smoothing (IRS) extends the stability region of the basic explicit time stepping scheme and increases thereby the maximum allowable Courant number. Theoretically no restrictions on the time step are imposed provided that a large enough smoothing coefficient is used. In addition the residual smoothing strongly effects the damping properties of the scheme and the particular technique used may lead to a considerably improved damping of the high frequency variations of the residuals. This is essential for the design of fast and robust multigrid schemes. The drawback of the commonly used centrally weighted IRS is the restriction of the smoothing coefficient to only small values in practical computations. In this way only a moderate raise of the CFL number is possible. Recently, upwind biased IRS operators have been developed by the authors (Blazek et al. 1991) which for one-dimensional flows allow considerably higher CFL numbers.
Implementation of non-reflecting boundary conditions in an unsteady flow simulation system
Authors: Engel K , Faden M , Pokorny S 
Published: November 2023

Abstract
An interactive flow simulation system is under development by the authors to study and analyze the unsteady flow phenomena in turbomachines. Special emphasis is put on the unsteady effects of the flow through the blades of counter-rotating ducted fan rotors. The whole system has been setup on a parallel computer which provides the necessary computational power together with the required interactive access.
Valuation Systems and Consequence Relations
Authors: Ryan Mark , Sadler Martin 
Published: November 2023

Abstract
This chapter is an introduction to some of the basic concepts and machinery of logic, concentrating on the contemporary uses of logic in computer science. It is not comprehensive, since many topics (such as equational reasoning, algebras, categories and computability) are introduced in other chapters. In particular, we concentrate on the applications of logics as reasoning systems about computing rather than on the foundational aspects of computer science which logic addresses. This is not a standard introduction to classical first order logic and its model theory, such treatments being widely available elsewhere [Hamilton, 1978; Hodges, 1983; Makowsky, ]. Rather, we attempt to bring together some topics from the logics currently used for reasoning about programs and about computer systems, and see them within a unifying framework at an appropriate level of abstraction.
Uncertainty Logics
Authors: Kyburg Henry E 
Published: November 2023

Abstract
The formalization of ordinary deductive inference is not uncontroversial. There are questions of modality, many-valued truth functions, and the like. But there is a solid core of agreement underlying the variations. This is not true of uncertain inference. Much, if not most, of our ordinary reasoning is forced to take account of uncertainty. That is, in ordinary reasoning and argument, either our premises are less than incorrigibly certain, or the rule of inference that we follow is less than valid in the classical sense—it may be possible for our premises to be true and our conclusion false. But there is very little agreement, as yet, on the ways in which uncertainty should be represented, or on the forms that inference involving uncertainty should take, or on the logic characterizing uncertain inference.
Temporal logic and automata
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
This chapter1 covers certain automata, their expressive power, non-deterministic versus deterministic automata, and their relation to games. We apply these results to prove the decidability of certain related monadic second-order logics (‘SIS’ and ‘S2S’). These logics are equivalent to some temporal logics, and also very useful in proving decidability of a host of other temporal logics, as we saw in Chapter 15 of Volume 1 of the current work.
Intervals and planning
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
As described in [van Benthem, 1995], there are many and various motivations for using an interval temporal logic, which include philosophical considerations of time and events, natural language, processes in computations and planning problems. In this chapter we will motivate the study of interval temporal logics by glancing at philosophical arguments, seeing some of the interesting mathematics which underlies questions of expressiveness, decidability and axiomatic completeness for such logics and considering their application to planning problems. We will also see reasons why interval temporal logics have not become very popular: these include undecidability and a lack of expressive completeness.
The Declarative Past And Imperative Future
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
We propose a new paradigm in executable logic: that of the declarative past and imperative future. A future statement of temporal logic can be understood in two ways: the declarative way, that of describing the future as a temporal extension; and the imperative way, that of making sure that the future will happen the way we want. Since the future has not yet happened, we have a language which can be both declarative and imperative. We regard our theme as a natural meeting between the imperative and declarative paradigms.
Calendar Logic
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In this chapter we link temporal logic to real-time calendar systems. Instead of the very general operators like ‘sometime in the future’ or ‘always in the future’, we introduce relativized operators of the kind ‘sometime next week’ or ‘always in office hours’. Calendar logic is developed in three stages. We start with a system for specifying everyday temporal notions like ‘hours’, ‘weeks’, ‘weekend’, ‘office hour’, ‘holiday’ within a given calendar system. In this system one can check whether a given point in time lies within an interval specified by a time term, or whether a subsumption relation holds between two time terms.
Temporal logics presented in the predicate calculus: language—metalanguage
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark 
Published: November 2023

Abstract
Given a system of databases {Δt ⊢t), t ∈ T, we say in chapter 1 that there are two ways of describing the logical connections between the theories (Δt, ⊢t). One is to talk about the system declaratively from the outside, using a metalanguage M, and the other is to enrich the language of the theories At, add connectives and formulae to theory Δt, enabling it to express the way in which it is related to other theories.
Expressive completeness of Since and Until over integer and real time
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark 
Published: November 2023

Abstract
In this chapter we will show how the separation theorem — theorem 9.3.1 — can be used to prove the expressive completeness of the language with Until and Since over some very important flows of time. To do this we need to show the separation of the language over the flows. First, in section 10.2, we examine the discrete Dedekind complete flows of time, concentrating on the integers. This serves as a simple introduction to the techniques which we then use in section 10.3 to show separation of this language over any class of Dedekind complete flows of time. The separation procedure is performed in two stages: first some basic equivalences, called eliminations, are shown; then we show how to put eliminations together in the right order to achieve separation. In this section we prove that the language with the connectives S and U has the separation property over the flow of time of the integers. This proof appeared in [Gabbay, 1989a]. It can be seen that the proof will also work for the natural numbers.
From Logics to Classes of Logics
Authors: Chagrov Alexander , Zakharyaschev Michael 
Published: November 2023

Abstract
We have already met with sufficiently many concrete logics to make some generalizations. Instead of proving the same sort of theorems for each logic separately, we can consider big classes of logics and try to develop general methods for investigating their propertiesen masse.In this chapter we introduce rather abstract concepts of superintuitionistic and modal logics and discuss the general settings of problems associated with them to be examined in the rest of the book.
Effective algebras
Authors: Stoltenberg-Hansen V , Tucker J V 
Published: November 2023

Abstract
The theory of the computable functions establishes the scope and limits of computation by means of algorithms on the set N = (0,1,2,...) of natural numbers. It is based on the assumption that this set of data, equipped with some very simple operations, forms an algebraic structure that is computable in some absolute sense: the data are concrete objects and the operations on the data are computable. An objective of the theory is to analyse and classify the functions and sets that can be defined, using a variety of models of computation and formal systems, over some fundamental algebras of natural numbers.
Getting started
Authors: Clark Malcolm 
Published: November 2023

Abstract
Tex can do all sorts of very clever things, but it seems sensible to try to do all sorts of ordinary things first, and then migrate to the more esoteric later. Experience is a potential, if expensive, teacher; let us examine what happens when we run some text through Tex-An example input file, named EXAMPLE, is listed in Figure 2.1, and the result of running that file through Tex is shown in Figure 2.2. The text presented was prepared using an ordinary editor, and was simply typed in without any particular attention to line endings, or any sort of ‘formatting’. The ‘formatting’ will be Tex’s concern, not ours. The only concession to the ‘logical’ structure of the text has been to divide the text into paragraphs, by leaving a blank line at the end of each paragraph.
More Maths
Authors: Clark Malcolm 
Published: November 2023

Abstract
This chapter draws together some more of ‘IEX’s wide range of facilities for mathematics, filling in some of the features which provide the flexibility needed to support a very diverse area of technical typesetting. Some of these features help to lay the groundwork for an understanding of the way that ‘IEX really does work. Such an understanding may not be necessary for the vast majority of tasks to which we put ‘IEX, but may give us the confidence to believe that we can handle the exceptional or novel situations too.
Tables by tabs
Authors: Clark Malcolm 
Published: November 2023

Abstract
One reason for tackling matrices before tables was to demonstrate how straightforward it is to obtain aligned entries. There is very little difference between a matrix and a table - at least, not from the way it is laid out. From a mathematical point of view they may have rather different properties, if they do indeed contain numerical information. Of course, many tables will contain no numerical information at all. Two elements will be preserved in any discussion of Tex’s tabular facilities, the & and the \er. Before looking at Tex’s handling of tabular material, consider this quotation from Richard Beach (1986): Designing table typography is a hard problem. There are many formatting details to get right and there is only a small amount of space with which to work. The two-dimensional nature of tables requires alignment of information in both directions at the same time. It is very important to maintain control over placement because the organization of information in tables is part of the message. Juxtaposition and other spatial relationships within tables have an important impact on the way in which tables convey information.
The Restricted Burnside Problem
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
The first edition of this book provided an account of the restricted Burnside problem making extensive use of Lie ring techniques to provide a uniform treatment of the field. It also included Kostrikin's theorem for groups of prime exponent. The second edition, as well as providing general updating, contains a new chapter on E.I. Zelmanov's highly acclaimed and recent solution to the Restricted Burnside Problem for arbitrary prime-power exponent. This material is currently only available in papers in Russian journals. This proof of Zelmanov's theorem given in the new edition is self contained, and (unlike Zelmanov's original proof) does not rely on the theory of Jordan algebras.
Basic concepts
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
In 1902 William Burnside [5] wrote’A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite, while the order of every operation it contains is finite’. In modern terminology the most general form of the problem is ‘Can a finitely generated group be infinite while every element in the group has finite order?’. This question was answered in 1964 by Golod [10], who constructed finitely generated infinite p-groups.
Belief Revision
Authors: Gardenfors Peter , Rott Hans 
Published: November 2023

Abstract
The bird caught in the trap is white. C Now suppose that, as a matter of fact, the bird caught in the trap turns out to be black. This means that you want to add the fact -&gt;C, i.e., the negation of C, to the database. But then the database becomes inconsistent. If you want to keep the database consistent—which is normally a sound methodology—you need to revise it. This means that some of the beliefs in the original database must be retracted. You don’t want to give up all of the beliefs since this would be an unnecessary loss of valuable information. So you have to choose between retracting A, B1, B1 -&gt; B, or A A B C. When giving up a belief you have to decide which of the reasons for this belief to retain and which to retract (this is the backward direction).
The Complex Projective Line
Authors: Goldman William m. 
Published: November 2023

Abstract
This preliminary section discusses 1-dimensional complex geometry from the point of view adopted in this book. We begin with projective geometry, from which both complex elliptic and hyperbolic I-dimensional geometry derive. We base our treatment on the books of Cartan [24] and Coolidge [31]. For an excellent treatment of projective geometry in the real ca.5e, see Coxeter (34). A principal geometric object is a circle (which Cartan calls a “chain” in [24}) which is just a Euclidean circle or straight line. We find several algebraic ways of describing circles, which will be useful in the sequel. In particular we describe circles in terms of 2 x 2 Hermitian matrices. We shall make essential use of the null polarity (the unique object in projective geometry corresponding to the symplectic structure on ℂ) to identify anti-polarities with anti-involutions. Furthermore, elliptic and hyperbolic geometry are developed in terms of anti-polarities which are the projective counterpart of Hermitian forms.