1,721,077 research outputs found
Shock waves and time scales to reach equipartition in the Fermi-Pasta-Ulam model
No full textIn a specific continuum limit at intermediate energy, the Fermi-Pasta-Ulam (FPU)-β chain can be described by a nonlinear partial differential equation whose solutions are shock waves. Proper long-wavelength initial conditions of the discrete model show a time evolution in numerical simulations that agrees with the solution of the continuum model where it is single valued. The breakdown times for the occurrence of the shock, when starting from a smooth initial condition, are shown to be relevant time scales for the transition to equipartition of energy, by an analysis of the time evolution of the spectral entropy. A simple time scale tB∼N2/(βkE) is derived in the continuum limit for mode k initial excitations with energy E and N particles. This time scale is tested numerically in the FPU chain. © 1995 The American Physical Society
Lyapunov exponents from unstable periodic orbits
No full textWe propose a method that allows us to analytically compute the largest Lyapunov exponent of a Hamiltonian chaotic system from the knowledge of a few unstable periodic orbits (UPOs). In the framework of a recently developed theory for Hamiltonian chaos, by computing the time averages of the metric tensor curvature and of its fluctuations along analytically known UPOs, we have re-derived the analytic value of the largest Lyapunov exponent for the Fermi-Pasta-Ulam-beta (FPU-beta) model. The agreement between our results and the Lyapunov exponents obtained by means of standard numerical simulations confirms the point of view which attributes to UPOs the special role of efficient probes of general dynamical properties, among them chaotic instability
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Exact solutions in the FPU oscillator chain
No full textAfter a brief comprehensive review of old and new results on the well-known Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU system with quartic nonlinearity and periodic boundary conditions, with explicitly computed mode coupling coefficients. The core of the paper is the proof of the existence of one- and two-mode exact solutions, physically representing nonlinear standing and travelling waves of small wavelength whose explicit lattice representations are obtained, and which are valid also as N → ∞. Moreover, and more generally, we show the presence of multi-mode invariant submanifolds. The full mode-space stability problem of the anharmonic zone-boundary mode is solved, showing that this mode becomes unstable through a mechanism of the modulational Benjamin-Feir type. In the thermodynamic limit the mode is always unstable but with instability growth rate linearly vanishing with energy density. The physical significance of these solutions and of their stability properties, with respect to the previously much more studied equipartition problem for long wavelength initial excitations, is briefly discussed. Copyright © 1997 Elsevier Science B.V. All rights reserved
Variations on the Author
Full text link“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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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