1,720,965 research outputs found
Geometric and Topological Aspects of Mimetic Numerical Schemes
No full textMimetic or compatible numerical schemes are designed to preserve the fundamental properties of physical and mathematical models, such as conservation laws, at the discrete level. To this end, methods of algebraic topology and differential geometry play a fundamental role to design its basic building blocks, like reconstruction operators or discrete Hodge operators and their algebraic realization given by mass matrices.
In this thesis we provide new geometric viewpoints of low-order compatible numerical schemes. In particular, two key principles will guide our constructions.
First, a tight relation between reconstruction operators and geometric elements of the barycentric dual grid. Second, a decomposition of mass matrices as the sum of a consistent and a stabilization part. We will use these principles to extended and improve the basic building blocks at the core of mimetic numerical schemes as well as their range of applicability.
We introduce the novel geometric concept of P_0-consistency which generalizes the standard consistency requirement of the mimetic methods. Fundamentally, it shows that geometric elements of a secondary grid, precisely, a barycentric dual grid, are not only useful but they are implicitly present in low-order mimetic numerical schemes, even if not made explicit. This fact has two consequences. First, it provides the equivalence between mimetic numerical schemes and discrete geometric approaches. Second, it is the key principle to extend the classical mimetic methods to grids having curved faces. Indeed, all standard mimetic methods only deal with polyhedral grids, thus having planar faces.
Then, we introduce a new construction of sparse inverse mass matrices for arbitrary tetrahedral grids and possibly inhomogeneous and anisotropic materials, debunking the conventional wisdom that the barycentric dual grid prohibits a sparse representation for inverse mass matrices. In particular, we provide a unified framework for the construction of both edge and face mass matrices and their sparse inverses as the sum of consistent and a stabilization part.
Next, we address the problem of computing discrete vector potentials. Currently, the most efficient methods to compute them are based on the so-called tree-cotree decomposition. However, tree-cotree techniques suffer from well-known termination problems that we show be related to topological obstructions of the three-dimensional space. We propose a new algorithm based on discrete Morse theory that is able to deal with such topological obstructions.
Finally, we extend the range of applicability of mimetic numerical schemes by introducing a novel mimetic volume integral method to solve eddy current problems. Integral methods for solving eddy current problems use Biot-Savart law to produce non-local constitutive relations that lead to fully populated generalized mass matrices. Yet, these formulations are very appealing because only the mesh of conductors is needed. We show how our novel mimetic method solves the three main problems of volume integral methods. First, the computation of the inductance matrix elements is slow and also delicate because of the singularity in the integral equation. We exploit constant basis functions that allow a much faster inductance matrix construction with respect to the standard one based on the Rao-Wilton-Glisson (RWG) or Raviart-Thomas (RT) basis functions. Second, our basis functions work for polyhedral elements while producing the same results as RWG and RT basis functions for tetrahedral grids. Third, the new basis functions allow to factorize the inductance matrix and to introduce a novel family of groundbreaking low-rank inductance matrix compression techniques that show several orders of magnitude improvement in memory occupation and computational effort than state-of-the-art alternatives, allowing to solve problems that otherwise cannot be faced
BIOSENSORE E RELATIVO PROCEDIMENTO
No full textIl presente trovato è relativo ad un biosensore elettrochimico per il
tracciamento della posizione di una o più particelle isolanti che scorrono
in un fluido conduttore comprendente una molteplicità di elettrodi, di cui due elettrodi attivi ed almeno una coppia di elettrodi di
misura e riferimento. Il trovato si riferisce altresì ad un
procedimento di utilizzo del biosensore
Fake Conductivity or Cohomology: Which to Use When Solving Eddy Current Problems With -Formulations?
No full text
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
Generators of with for Triangulated Surfaces : Construction and Classification of Global Loops
No full textGiven a compact surface embedded in with boundary , our goal is to construct a set of representatives for a basis of the relative cohomology group , where is a specified subset of . To achieve this, we propose a novel graph-based algorithm with two key features: it is applicable to non-orientable surfaces, thereby generalizing previous approaches, and it has a worst-case time complexity that is linear in the number of edges of the mesh triangulating . Importantly, this algorithm serves as a critical pre-processing step to address the low-frequency breakdown encountered in boundary element discretizations of integral equation formulations
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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