Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it depends on a shock detector. Further, the resulting method is linearity preserving. The same shock detector is used to gradually lump the mass matrix. The resulting method is LED, positivity preserving, and also satisfies a global DMP. Lipschitz continuity has also been proved. However, the resulting scheme is highly nonlinear, leading to very poor nonlinear convergence rates. We propose a smooth version of the scheme, which leads to twice differentiable nonlinear stabilization schemes. It allows one to straightforwardly use Newton’s method and obtain quadratic convergence. In the numerical experiments, steady and transient linear transport, and transient Burgers’ equation have been considered in 2D. Using the Newton method with a smooth version of the scheme we can reduce 10 to 20 times the number of iterations of Anderson acceleration with the original non-smooth scheme. In any case, these properties are only true for the converged solution, but not for iterates. In this sense, we have also proposed the concept of projected nonlinear solvers, where a projection step is performed at the end of every nonlinear iterations onto a FE space of admissible solutions. The space of admissible solutions is the one that satisfies the desired monotonic properties (maximum principle or positivity).Peer ReviewedPostprint (author's final draft

Normative Power is in the Eye of the Beholder: An Empirical Assessment of Perceptions of EU Identity at the WTO

The concept "normative power" is developed to grasp the EU's identity, role and concomittant practice in world politics. The EU's ability to define the normal in world politics' depends on others' perceptions of it and its external practice. Normative power requires that non-EU states perceive the EU as embodying the norms it espouses, to perceive those norms as attractive for emulation, and to perceive EU action to be norm-driven (as opposed to interest-driven), and based on universally valid norms. To assess non-EU state elites' perceptions of EU identity, we conduct a series of interviews with WTO negotiators and former negotiators with experience of negotiating with the EU. We find that, while third country elites do perceive the EU as embodying the norms central to its identity and, to some extent, see those norms as attractive for emulation, they do not perceive EU action as distinct and predominantly norm-driven or based on universal norms. Our research qualifies the understanding of the EU as normative power.Normative Power, NPEU, EU Identity, WTO, Trade Policy Making, Perceptions of the EU

Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction

The interplay between the quantum interferences responsible for one particle localization over a length L_1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L_2 > L_1, is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t_1 necessary to propagate over L_1, the interaction slows down the ballistic motion. On the contrary, after t_1 the interaction favors a very slow delocalization, characterized by a $\log(t)$ spreading of the center of mass, until L_2 is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U.Comment: Published version, 10 LaTeX pages and 10 figures. Third paper of a series of fou

Transgender children: born in the wrong body or in the wrong society?

Algunos niños/as tienen una identidad de género que difiere de su sexo biológico. Ellos y ellas, los niños/as transgéneros, son a menudo vistos como problemáticos dado que amenazan la construcción de género binaria predominante en la sociedad. Sin embargo, en vez de ser una amenaza, los niños/as transgéneros son parte de la diversidad humana y nos hace comprender la identidad de género como un conjunto de posibilidades. El objetivo de este ensayo fue explorar en el desarrollo de los niños transgéneros a la luz de influyentes teorías, enfatizando sus limitaciones y fortalezas, junto con reflexionar sobre algunos elementos a considerar en el espacio terapéutico con niños transgéneros en el contexto escolar. Para ello se examinó qué es lo que se conoce actualmente acerca de los niños/as transgéneros y las dificultades que ellos y ellas tienen que enfrentar en las distintas etapas de su desarrollo.Some children have a gender identity that does not match their anatomical sex. Trangender children are often seen as problematic because they threaten the binary construction of gender embedded in the society. However, rather than a threat, transgender children are part of the human diversity, and make us understand that gender identity is a fluid continuum. The aim of this essay was to explore in the transgender child’s development in light of relevant theories, emphasizing their limitations and assertiveness, in addition to some elements to consider when counselling transgender children in a school setting. This essay examined what is currently known about transgender children and the difficulties that they have to cope with in the different stages of their development