1,720,964 research outputs found
On Nonperiodic Euler Flows with Hölder Regularity
Get PDFIn (Isett, Regularity in time along the coarse scale flow for the Euler equations, 2013), the first author proposed a strengthening of Onsager’s conjecture on the failure of energy conservation for incompressible Euler flows with Hölder regularity not exceeding 1/31/3 . This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space L[∞ over t]B[1/3 over 3,∞] due to low regularity of the energy profile. This paper is the first and main paper in a series of two, the results of which may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with Hölder exponent less than 1/51/5 . The main result of the present paper shows that any given smooth Euler flow can be perturbed in C[1/5−ϵ over t,x] on any pre-compact subset of R×R[superscript 3] to violate energy conservation. Furthermore, the perturbed solution is no smoother than C[1/5−ϵ over t,x]. As a corollary of this theorem, we show the existence of nonzero C[1/5−ϵ over t,x] solutions to Euler with compact space-time support, generalizing previous work of the first author (Isett, Hölder continuous Euler flows in three dimensions with compact support in time, 2012) to the nonperiodic setting.National Science Foundation (U.S.) (Award No. DMS-1402370
On the Endpoint Regularity in Onsager\u27s Conjecture
Get PDFOnsager\u27s conjecture states that the conservation of energy may fail for incompressible Euler flows with Hölder regularity below . This conjecture was recently solved by the author, yet the endpoint case remains an interesting open question with further connections to turbulence theory. In this work, we construct energy non-conserving solutions to the incompressible Euler equations with space-time Hölder regularity converging to the critical exponent at small spatial scales and containing the entire range of exponents .
Our construction improves the author\u27s previous result towards the endpoint case. To obtain this improvement, we introduce a new method for optimizing the regularity that can be achieved by a convex integration scheme. A crucial point is to avoid power-losses in frequency in the estimates of the iteration. This goal is achieved using localization techniques of \cite{IOnonpd} to modify the convex integration scheme.
We also prove results on general solutions at the critical regularity that may not conserve energy. These include a theorem on intermittency stating roughly that energy dissipating solutions cannot have absolute structure functions satisfying the Kolmogorov-Obukhov scaling for any if their singular supports have space-time Lebesgue measure zero.Changes to improve presentatio
A Proof of Onsager\u27s Conjecture
Get PDFFor any due to [Eyink] and [Constantin, E, Titi], solves Onsager\u27s conjecture that the exponent marks the threshold for conservation of energy for weak solutions in the class . The previous best results were solutions in the class for , due to the author, and in the class for due to Buckmaster, De Lellis and Székelyhidi, both based on the method of convex integration developed for the incompressible Euler equations by De Lellis and Székelyhidi. The present proof combines the method of convex integration and a new gluing approximation technique. The convex integration part of the proof relies on the Mikado flows introduced by [Daneri, Székelyhidi] and the framework of estimates developed in the author\u27s previous work.References improved. Modified in response to referee
On the Endpoint Regularity in Onsager's Conjecture
Get PDFOnsager's conjecture states that the conservation of energy may fail for 3D incompressible Euler flows with Hölder regularity below 1/3. This conjecture was recently solved by the author, yet the endpoint case remains an interesting open question with further connections to turbulence theory. In this work, we construct energy non-conserving solutions to the 3D incompressible Euler equations with space-time Hölder regularity converging to the critical exponent at small spatial scales and containing the entire range of exponents [0,1/3).
Our construction improves the author's previous result towards the endpoint case. To obtain this improvement, we introduce a new method for optimizing the regularity that can be achieved by a general convex integration scheme. A crucial point is to avoid power-losses in frequency in the estimates of the iteration. This goal is achieved using localization techniques of [IO16b] to modify the convex integration scheme.
We also prove results on general solutions at the critical regularity that may not conserve energy. These include the fact that singularites of positive space-time Lebesgue measure are necessary for any energy non-conserving solution to exist while having critical regularity of an integrability exponent greater than three
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
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
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe 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
Get PDFWe 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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