1,721,045 research outputs found
On representation of boundary integrals involving the mean curvature for mean-convex domains
No full textMatteo Novaga
No full text. -- In the present paper, we motivate and describe a numerical approach in order to detect the creation of fractures in a facet of a crystal evolving by anisotropic mean curvature. The result appears to be in accordance with the known examples of facet-breaking. Graphical simulations are included. Key Words: Nonlinear partial differential equations of parabolic type; Crystal growth; Non-smooth analysis. Riassunto. -- Un approccio numerico alle fratture nella crescita di cristalli. In questo lavoro, presentiamo e discutiamo un approccio numerico al problema di individuare la nascita di fratture in una faccia di un cristallo che si evolve per curvatura media anisotropa. I risultati sono in accordo con gli esempi noti fino ad ora di frattura di facce. Sono inoltre incluse alcune simulazioni grafiche. 0. Introduction We model crystal growth in R 3 as an anisotropic evolution by mean curvature when the ambient space is endowed with a convex onehomogeneous function whose unit ball (usu..
Conducting Flat Drops in a Confining Potential
Full text linkWe study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a parameter measuring the relative strength of the Coulomb interaction. As a consequence, when the potential is confining and the Coulomb repulsion strength is below a critical value, we show existence and regularity estimates for volume-constrained minimizers. We also derive the Euler-Lagrange equation satisfied by regular critical points, expressing the first variation of the Coulombic energy in terms of the normal 1/2-derivative of the capacitary potential
Motion by curvature of planar networks
Full text linkWe consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional.
Such a flow represents the evolution of a two-dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries.
Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which are "essentially" non regular.
As a first step, in this paper we study in detail the case of three-curves in the plane meeting at a single triple junction and with the other ends fixed. We show some results about the existence, uniqueness and, in particular, the global regularity of the flow, following the line of analysis carried on in the last years for the evolution by mean curvature of smooth curves and hypersurfaces
A symmetry result for the Ornstein-Uhlenbeck operator
No full textIn 1978 E. De Giorgi formulated a conjecture concerning the onedimensional symmetry of bounded solutions to the elliptic equation u = F0(u), which are monotone in some direction. In this paper we prove the analogous statement for the equation uδ hx;ruiu = F0(u), where the Laplacian is replaced by the Ornstein-Uhlenbeck operator. Our theorem holds without any restriction on the dimension of the ambient space, and this allows us to obtain an similar result in innite dimensions by a limit procedure
Motion by Curvature of Planar Networks II
Full text linkWe prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth as long as the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints
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
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