1,721,038 research outputs found
Correction to: Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons (Nonlinear Differential Equations and Applications NoDEA, (2021), 28, 1, (9), 10.1007/s00030-020-00668-2)
No full textThis erratum corrects some errors which appear in [Dohnal T., Romani G., Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons, Nonlinear Differ. Equ. Appl. 28, 9 (2021).]. In particular, it replaces the (unsuitable) definition of isolatedness of the linear eigenvalue, from which the bifurcation occurs
Justification of the asymptotic Coupled Mode approximation of out-of-plane gap solitons in Maxwell equations
Full text linkIn periodic media gap solitons with frequencies inside a spectral gap but close to a spectral band can be formally approximated by a slowly varying envelope ansatz. The ansatz is based on the linear Bloch waves at the edge of the band and on effective coupled mode equations (CMEs) for the envelopes. We provide a rigorous justification of such CME asymptotics in two-dimensional photonic crystals described by the Kerr nonlinear Maxwell system. We use a Lyapunov-Schmidt reduction procedure and a nested fixed point argument in the Bloch variables. The theorem provides an error estimate in H-2(R-2
Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons
Full text linkWe consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter (“doubly” nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the linear problem using a Lyapunov–Schmidt reduction and provide an expansion of both the nonlinear eigenvalue and the solution. We further prove that if the linear eigenvalue is real and the nonlinear problem PT-symmetric, then the bifurcating nonlinear eigenvalue remains real. These general results are then applied in the context of surface plasmon polaritons (SPPs), i.e. localized solutions for the nonlinear Maxwell’s equations in the presence of one or more interfaces between dielectric and metal layers. We obtain the existence of transverse electric SPPs in certain PT-symmetric configurations
A quasilinear transmission problem with application to Maxwell equations with a divergence-free D-field
Full text linkMaxwell equations in the absence of free charges require initial data with a divergence-free displacement field D. In materials in which the dependence D=D(E) is nonlinear the quasilinear problem ∇⋅D(E)=0 is hence to be solved. In many applications, e.g. in the modelling of wave packets, an approximative asymptotic ansatz of the electric field E is used, which satisfies this divergence condition at t=0 only up to a small residual. We search then for a small correction of the ansatz to enforce ∇⋅D(E)=0 at t=0 and choose this correction in the form of a gradient field. In the usual case of a power type nonlinearity in D(E) this leads to the sum of the Laplace and p-Laplace operators. We also allow for the medium to consist of two different materials so that a transmission problem across an interface is produced. We prove the existence of the correction term for a general class of nonlinearities and provide regularity estimates for its derivatives, independent of the L2-norm of the original ansatz. In this way, when applied to the wave packet setting, the correction term is indeed asymptotically smaller than the original ansatz. We also provide numerical experiments to support our analysis
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
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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