1,720,964 research outputs found
Regularity estimates for the flow of BV autonomous divergence-free vector fields in R^2
No full textWe consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in time. As a consequence we deduce that both geometric and analytical mixing have a lower bound of order (Formula presented.) as (Formula presented.)
FORWARD UNTANGLING AND APPLICATIONS TO THE UNIQUENESS PROBLEM FOR THE CONTINUITY EQUATION
Full text linkWe introduce the notion of forward untangled Lagrangian representation of a measure-divergence vector-measure rho(1, b), where rho is an element of M+(Rd+1) and b : Rd+1 -> R-d is a rho-integrable vector field with div(t,x)(rho(1, b)) = mu is an element of M(R x R-d): forward untangling formalizes the notion of forward uniqueness in the language of Lagrangian representations. We identify local conditions for a Lagrangian representation to be forward untangled, and we show how to derive global forward untangling from such local assumptions. We then show how to reduce the PDE div(t,x)(rho(1, b)) = mu on a partition of R+ x R-d obtained concatenating the curves seen by the Lagrangian representation. As an application, we recover known well posedeness results for the flow of monotone vector fields and for the associated continuity equation
A uniqueness result for the decomposition of vector fields in Rd
Full text linkGiven a vector field ρ(1,b)∈Lloc1(R+×Rd,Rd+1) such that divt,x(ρ(1,b)) is a measure, we consider the problem of uniqueness of the representation η of ρ(1 , b) Ld+1 as a superposition of characteristics γ:(tγ-,tγ+)→Rd, γ ̇ (t) = b(t, γ(t)). We give conditions in terms of a local structure of the representation η on suitable sets in order to prove that there is a partition of Rd+1 into disjoint trajectories ℘a, a∈ A, such that the PDE divt,x(uρ(1,b))∈M(Rd+1),u∈L∞(R+×Rd),can be disintegrated into a family of ODEs along ℘a with measure r.h.s. The decomposition ℘a is essentially unique. We finally show that b∈Lt1(BVx)loc satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible BV vector fields
Analysis of an integral equation arising from a variational problem
No full textRapporto Interno, Dipartimento di Matematica, Politecnico di Torin
Weak and parabolic solutions of advection-diffusion equations with rough velocity field
Full text linkWe study the Cauchy problem for the advection-diffusion equation partial derivative(t)u + div(ub) = Delta u associated with a merely integrable divergence-free vector field b defined on the torus. We discuss existence, regularity and uniqueness results for distributional and parabolic solutions, in different regimes of integrability both for the vector field and for the initial datum. We offer an up-to-date picture of the available results scattered in the literature, and we include some original proofs. We also propose some open problems, motivated by very recent results which show ill-posedness of the equation in certain regimes of integrability via convex integration schemes
On the advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity
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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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