1,721,003 research outputs found
A Metric Approach to Elastic Reformations
No full textWe study a variational framework to compare shapes, modeled as Radon measures on RN, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as integral functionals having some kind of isometries as minimizers. The approach pursued is based on the notion of pointwise Lipschitz constant leading to a matric space framework. In particular, to compare general shapes, we study this reformation problem by using the notion of transport plan and Wasserstein distances as in optimal mass transportation theory
Optimal shapes in force fields
No full textWe study a variational problem involving material shapes, modeled as Radon measures on a given ambient space, in a force vector field. We prove some properties of absolutely continuity of the optimal shapes in dependence on the distributions of the zeros of the force field. More regularity properties of the optimal shapes, as well as simple geometrical characterizations, are established in the case of central force fields, in dependence on the regularity of the field and on the choice of the ambient space
On some variational problems involving volume and surface energies
No full textWe show how some problems coming from different fields of applied sciences, such as physics, engineering, biology, admit a common variational formulation characterized by the competition of two energetic terms. We discuss related problems and techniques studied by the authors and collaborators in the recent past as well open problems and further possible research directions in these topics
Transport problems and disintegration maps
Get PDFBy disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case
A surface energy approach to the mass reduction problem for elastic bodies
No full textWe consider the problem of mass reduction for elastic bodies by appearance of cavities. In this work, this problem is related to the minimization of a surface energy, depending on the stress tensor in the original equilibrium configuration. Special cases of mechanical interest are also analysed
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Minimal Measures, one dimensional currents and the Monge-Kantorovich Problem
Get PDFIn recent works L.C. Evans has noticed a strong analogy between Mather’s theory of minimal measures in Lagrangian dynamic and the theory devel- oped in the last years for the optimal mass transportation (or Monge–Kantorovich) problem. In this paper we start to investigate this analogy by proving that to each minimal measure it is possible to associate, in a natural way, a family of curves on the space of probability measures. These curves are absolutely continuous with respect to the metric structure related to the optimal mass transportation problem. Some minimality properties of such curves are also addressed
Reformation Instability in Elastic Solids
No full textThe reformation of a body fundamentally involves the mapping of one natural reference configuration of it into another natural reference configuration. The mass and the constitutive properties of the material remain unaltered, but the overall shape of the reference configuration generally changes. If, when a natural reference configuration is distorted, there is a portion of the boundary of the body that is displacement controlled, then a reformation of the body must be such that the original displacement controlled part of the boundary and its reformation are identical. In common applications that involve reformation, the remainder of the boundary is traction-free and a reformation essentially involves a change of the morphology of this traction-free surface. For example, undulations are often a characteristic feature of the reformation of a free, plane boundary surface. Reformations are a result of a material instability and they may associate with a chemically induced diffusive processes in which particles of the body move into preferred places. Fundamentally, a reformation is generated in response to the drive to lower the total stored energy of the body. In this work we are not concerned with the physical processes that take place during reformation, but rather we are concerned with characterizing the onset of the instability. We develop a variational characterization of the reformation instability for a nonlinear elastic body and we include the effect of surface energy. As an example, we consider the axial deformation of a circular cylinder and argue that small scale nano-wires, for which the diameter-to-length ratio is sufficiently small, are expected to be stable with respect to spatial variations when extended. Moreover, we observe that if the surfacial energy function is sufficiently convex at the undistorted state such wires may also be stable with respect to spatial variations when compressed. We then show that such small scale nano-wires are unstable with respect to reformation when either extended or compressed. © 2011 Springer Science+Business Media B.V
Variations on the Author
Get PDF“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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