117,439 research outputs found
The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.
No full textIn this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment.
We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided
On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity
No full textIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain Ω of the plane taking values in the real plane and discontinuous on a simple curve, with two endpoints. We show that, under certain assumptions, the relaxed area does not exceed the area of the regular part of the function, with the addition of a singular term measuring the area of a disk-type solution of the Plateau's problem spanning the two traces of the function across the jump set. The result is valid also when the minimal surface has self-intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of the minimal surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some results from Morse theory
Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity
No full textIn this paper, we estimate the area of the graph of a map u: Ω⊂ R2→ R2 discontinuous on a segment Ju, with Ju either compactly contained in the bounded open set Ω , or starting and ending on ∂Ω. We characterize A ̄ ∞(u, Ω) , the relaxed area functional in a sort of uniform convergence, in terms of the infimum of the area of those surfaces in R3 spanning the graphs of the traces of u on the two sides of Ju and having what we have called a semicartesian structure. We exhibit examples showing that A ̄ (u, Ω) , the relaxed area in L1(Ω; R2) , may depend on the values of u far from Ju and also on the relative position of Ju with respect to ∂Ω. These examples confirm the highly non-local behavior of A ̄ (u, ·) and justify the interest in the study of A ̄ ∞. Finally we prove that A ̄ (u, ·) is not subadditive for a rather large class of discontinuous maps u
A Bioinspired Cownose Ray Robot for Seabed Exploration
No full textThis article presents the design and the experimental tests of a bioinspired robot mimicking the cownose ray. These fish swim by moving their large and flat pectoral fins, creating a wave that pushes backward the surrounding water so that the fish is propelled forward due to momentum conservation. The robot inspired by these animals has a rigid central body, housing motors, batteries, and electronics, and flexible pectoral fins made of silicone rubber. Each of them is actuated by a servomotor driving a link inside the leading edge, and the traveling wave is reproduced thanks to the flexibility of the fin itself. In addition to the pectoral fins, two small rigid caudal fins are present to improve the robot’s maneuverability. The robot has been designed, built, and tested underwater, and the experiments have shown that the locomotion principle is valid and that the robot is able to swim forward, perform left and right turns, and do floating or diving maneuvers
Lattice effects in cubicLa2Mo2O9: effect of vacuum and correlation with transport properties
No full textThis study aims to investigate correlations between lattice effects and transport properties in cubic La2Mo2O9. High temperature neutron diffraction data, recorded in air and under vacuum, are used to follow the evolution with temperature of selected structural parameters, i.e. bond lengths and angles. Results suggest a possible correlation with the experimentally observed decrease of the
activation energy for oxygen migration at high temperature. The effect on the structural properties of the low oxygen partial pressure used during the measurements in vacuum is negligible and this represents a valuable information in view of possible applications of the material in solid state devices.
r 2008 Elsevier Inc. All rights reserved
Anisotropic mean curvature on facets and relations with capillarity
No full textGiven an anisotropy φ on R3, we discuss the relations between the φ-calibrability of a facet F ⊂ ∂E of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet B̃Fφ of the unit ball of φ, φ-calibrability is equivalent to show the existence of a φ-subunitary vector field in F, with suitable normal trace on ∂F, and with constant divergence equal to the φ-mean curvature of F. Assuming E convex at F, B̃Fφ a disk, and F (strictly) φ-calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict φ-calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C1,1, the solution of the total variation flow starting at 1F
Perovskite solid solutions–a Monte Carlo study of the deep earth analogue (K, Na)MgF<sub>3</sub>
No full textUnderstanding the behaviour of solid solutions over wide ranges of temperature and pressure remains a major challenge to both theory and experiment. Here we report a detailed exchange Monte Carlo study using a classical ionic model of the model perovskite parascandolaite-neighborite (K,Na)MgF3 solid solution and its end-members for temperatures in the range 300-1000 K and pressures from 0-8 GPa. Full account is taken of the local environment of the individual cations, clustering and thermal effects. Properties considered include the crystal structure, phase transitions, the thermodynamics of mixing and the non-ideality of the solid solution. Clustering of the potassium ions is examined via a short-range order parameter. Where experimental data are available for comparison, agreement is very good.</p
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe 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
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