345 research outputs found

    A Flow Tangent to the Ricci Flow via Heat Kernels and Mass Transport

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    We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non–smooth metric measure spaces with Ricci curvature bounded from below

    Compositional Optimization and Structural Properties of the Filled Skutterudite Smy(FexNi1−x)4Sb11.5Sn0.5

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    A compositional and crystallographic study was carried out on the Smy(FexNi1−x)4Sb11.5Sn0.5 filled skutterudite system (0.40 ≤ x ≤ 0.80) with the aim to determine the equilibrium Sm filling fraction (y) within the considered x range. The relevance of the material lies in its potential thermoelectric properties: in analogy with similar skutterudites systems, these features should in fact result as being improved with respect to the ones of the corresponding Sn-free system thanks to the partial substitution of Sn for Sb, which is expected to lower the phonon thermal conductivity. The results of Rietveld refinements allowed us to study the skutterudite structural properties and to discuss them, adopting a comparative approach with respect to the ones of the Sn-free system Smy(FexNi1−x)4Sb12. Relying on the refined Sm occupancy factors, the p/n crossover is shown to be located at x ~ 0.53, meaning that the introduction of Sn induces an enlargement of the p-region; moreover, at variance with the Sn-free system, the coefficient of thermal expansion does not show any significant mismatch between n- and p-compositions, which should ensure a prolonged lifetime of a device made of n- and p-legs that both derive from the studied system

    New Women for New Families

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    The crisis of the family, at least as it is understood traditionally, is a concept that has been taken on board by public opinion. It is undergoing a redefinition of roles, values, relationships. The author makes a number of considerations of a pedagogical nature. Firstly we need to re-evaluate in a positive way the aptitude of women for looking after he needs of others, and in offering emotional support within the family unit

    Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric

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    As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto, Commun Pure Appl Math, 1999). In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation

    Gromov-Hausdorff convergence of discrete transportation metrics

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    This paper continues the investigation of discrete transportation distances initiated in [13] and further studied in [8] (see also [5] and [14]). We prove that the discrete transportation metrics on the d-dimensional discrete torus with mesh size 1/N converge, when N goes to infinity to the standard 2-Wasserstein distance on the continuous torus. This is the first result of a passage to the limit from a discrete transportation problem to a continuous one, and proves that the theory built by the second author is fully compatible with the continuous case. © 2013 Society for Industrial and Applied Mathematics

    A user's guide to optimal transport

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    This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below

    Pelle (Arthur Schopenhauer)

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    Attraverso l'analisi dei passaggi che Schopenhauer dedica agli zingari nel "Mondo" e nei "Parerga" è possibile tracciare una filosofia della pelle che porta ad una secca alternativa finale tra l'economicismo meccanicistico della natura (Schopenhauer) e la libertà che quella stessa natura mostra nella parabola dei gigli del campo (Kierkegaard)
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