1,720,964 research outputs found
Topological Calculus: between Algebraic Topology and Electromagnetic Fields
No full textTopological behaviour of self-similar spectra for fractal domains is shown and applied to solve electromagnetic problems on fractal geometries, like for example the Sierpinski gasket.. Two different mathematical tools are employed: the Topological Calculus, which frames a topology-consistent, discrete counterpart to domains and operators and the Iterated Function Systems (IFSs) to produce fractals as limit sets of simple recursion mappings. Topological invariants and Analytical features of a set can be easily extracted from such a discrete model, even for complex geometries like fractal ones.One of the targets of this work is to show how recursion symmetries of a (pre-) fractal set, mathematically coded by "algebraic" relationships between its parts, are sole responsible for the self-similar distribution of its (laplacian) eigenvalues: no metric information is needed for this property to be observed.Another primary target is to show how Topological Calculus easily allows for an almost instantaneous discretization of contoinuum equations of any (topological) field theory. Investigating the natural modes of self-similar domains is important to many applications whose core geometry is prefractal or at least highly irregular. Most recently, transport and electromagnetic pehnomena were focused: IFS-generated waveguides, resonators and antennas(9) exhibiting multi-band properties. Such complex domains need careful mathematical formulations in order to transfer traditional-geometric properties to them; Topological Calculus is one of such discrete formulations
Spectral analysis of Šerpinskij carpet-like prefractal waveguides and resonators
No full textExact results on some modal properties of waveguides and resonators is studied, whose geometry is derived from "Šerpinskij carpet-like" prefractals (Serpinskij carpet and sponge; Menger sponge). The study is biased to the closed-form computation of specific resonances and eigenmodes (called "diaperiodic"), and to the relation existing between their topology and the existence of a finite set of transverse electromagnetic modes
Can you hear the fractal dimension of a drum?
No full textElectromagnetics and Acoustics on a bounded domain are governed by the
Helmholtz's equation; when such a domain is a [pre-]fractal described by means
of a `just-touching' Iterated Function System (IFS) spectral decomposition of
the Helmholtz's operator is self-similar as well. Renormalization of the
Green's function proves this feature and isolates a subclass of eigenmodes,
called ``diaperiodic'', whose waveforms and eigenvalues can be recursively
computed applying the IFS to the initiator's eigenspaces. The definition of
``spectral dimension'' is given and proven to depend on diaperiodic modes only
for a wide class of IFSs. Finally, asymptotic equivalence between box-counting
and spectral dimensions in the fractal limit is proven. As the `self-similar'
spectrum of the fractal is enough to compute box-counting dimension, positive
answer is given to title question
On models of fractal networks
No full textA couple of iterative models for the theoretical study of fractal networks whose topologies are generated via iterated function systems is presented: a lumped-parameter impedor-oriented one and a two-portnetwork-
oriented one. With the former, the voltage and current patterns give a detailed understanding of the electromagnetic fields’ self-similar distribution throughout the network; on the other hand, model complexity exponentially increases with the prefractal iteration order. The latter ‘black-box’ model only controls port-oriented global parameters that are the ones commonly used in the integration of different electronic systems, and its complexity is independent of prefractal order. Sierpinski gasket and carpet topologies are reported as examples
Electromagnetic radiation from moving fractal sources: A plane-wave spectral approach
No full textIn this work the solution to the problem of electromagnetic radiation from (pre-) fractal antennas is performed by means of Plane-Wave field representation based on closed-form Fourier transforms of the self-similar current patterns. The generalization to the case of uniformly translating antennas is then accomplished through the Frame-Hopping Method by exploiting special-relativistic covariance properties of Plane-Wave spectra
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
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