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The Riemann problem for materials with nonconvex equations of state II: General Flow
No full textAbstractIn Part I, we showed how to construct the solution of the Riemann problem for the equations of isentropic flow without assuming that the pressure is a convex function of the volume. We were also able to eliminate certain extraneous solutions using a viscosity argument. In this paper we show how to proceed when the flow is not isentropic and when there is no restriction on the sign of (∂2p∂v2)s
Theoretical numerical analysis
No full textTheoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matr
The Riemann problem for materials with nonconvex equations of state I: Isentropic flow
No full textAbstractIn the existing literature on nonlinear conservation laws, it is customary to assume that characteristic fields which are not linearly degenerate are in fact genuinely nonlinear. For the equations of compressible flow, this means that the pressure is a convex function of the volume. H. A. Bethe has investigated some of the conditions which cause this assumption to break down, and he has also studied some of the consequences of this breakdown. In this paper, we show that, assuming isentropic flow, one can obtain similarly detailed information about the Riemann problem for nonconvex gases as for convex ones. An important reason for doing this is that in many applications the pressure is given only as a table, and intermediate values are obtained by interpolation. Thus, the pressure used in the computation may not be convex even though the actual pressure is
Theoretical Numerical Analysis
No full textTheoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysi
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Cooperation in a three-way arms race
No full textAbstractA three-way arms race can be modeled as an iterated game with the payoff determined by the average performance over the past. We show that there exists a robust strategy for any one player which cannot be exploited by the other players, but for which mutual disarmament is a global attractor if the strategy is used by all three players
The stability of MacCormack's method for the scalar advection equation
No full textAbstractWe show that MacCormack's method for the scalar advection equation ut = aux+buy is stable if (aΔt/Δx)2 + (bΔt/Δy)2 ≤ 2 1+18 −2≈18. This bound on the mesh ratios is not optimal, since numerical sampling shows that .3266 will do when (aΔt/Δx)2 = (bΔt/Δy)2
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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