1,720,991 research outputs found
Attractors for gradient flows of nonconvex functionals and applications
No full textThis paper addresses the long-time behaviour of gradient flows of nonconvex
functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by
J. M. Ball, we provide some sufficient conditions for the existence of a global
attractor. The abstract results are applied to various classes of nonconvex evolution
problems. In particular, we discuss the long-time behaviour of solutions of
quasistationary phase field models and prove the existence of a global attractor
Motion of vortices for the extrinsic Ginzburg-Landau flow for vector fields on surfaces.
No full textWe consider the gradient flow of a Ginzburg-Landau functional of the type
F_\eps^{\extr}(u):=\frac{1}{2}\int_M \abs{D u}_g^2 + \abs{\Sh u}^2_g
+\frac{1}{2\eps^2}\left(\abs{u}^2_g-1\right)^2\Vg
which is defined for tangent vector fields
(here stands for the covariant derivative) on a closed surface~
and includes extrinsic effects via the shape operator \Sh
induced by the Euclidean embedding of~. The functional depends on the small parameter
\eps>0. When \eps is small it is clear from the structure of the Ginzburg-Landau functional that \abs{u}_g ``prefers'' to be close to . However, due to the incompatibility for vector fields on between the Sobolev regularity and the unit norm constraint, when \eps is close to , it is expected that a finite number of singular points (called vortices) having non-zero index emerges (when the Euler characteristic is non-zero). This intuitive picture has been made precise in the recent work by R. Ignat \& R. Jerrard \cite{JerrardIgnat_full}.
In this paper we are interested the dynamics of vortices generated by F_\eps^{\extr}.
To this end we study the behavior when \eps\to 0 of the solutions of the (properly rescaled) gradient flow of F_\eps^{\extr}.
In the limit \eps\to 0 we obtain the effective dynamics of the vortices. The dynamics, as expected, is influenced by both the intrinsic and extrinsic properties of the surface~
DIMENSIONAL REDUCTION AND EMERGENCE OF DEFECTS IN THE OSEEN-FRANK MODEL FOR NEMATIC LIQUID CRYSTALS
No full textIn this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin slab Omega x (0, h) with Omega subset of R-2 and h > 0 we consider the one-constant approximation of the Oseen-Frank model for nematic liquid crystals. We impose Dirichlet boundary conditions on the lateral boundary and weak anchoring conditions on the top and bottom faces of the cylinder Omega x (0, h). The Dirichlet datum has the form (g, 0), where g: partial derivative Omega -> S-1 has non-zero winding number. Under appropriate conditions on the scaling, in the limit as h -> 0 we obtain a behavior that is similar to the one observed in the asymptotic analysis (see [7]) of the two-dimensional Ginzburg-Landau functional. More precisely, we rigorously prove the emergence of a finite number of defect points in Omega having topological charges that sum to the degree of the boundary datum. Moreover, the position of these points is governed by a Renormalized Energy, as in the seminal results of Bethuel, Brezis and Helein [7]
Convergence of solutions for the fractional Cahn–Hilliard system
No full textThis paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called Łojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but C 1 ) nonlinearities
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
Variational Analysis of Nematic Shells
No full textIn this note we present some recent results on the Mathematical Analysis of Nematic Shells. The type of results we present deal with the analysis of defectless configurations as well as the analysis of defected configurations. The mathematical tools include Topology, Analysis of Partial Differential Equations as well as Variational Techniques like Γ convergence
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