A Central Limit Theorem for Gibbsian Invariant Measures of 2D Euler Equations

We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global space average in the bounded domain case (neutrality condition), the ensemble converges to the so-called Energy-Enstrophy Gaussian random distributions. This can be interpreted as describing Gaussian fluctuations around the mean field limit of vortices ensembles. The main argument consists in proving convergence of partition functions of vortices and Gaussian distributions.Comment: 27 pages, to appear on Communications in Mathematical Physic

Gaussian invariant measures and stationary solutions of 2D Primitive Equations

We introduce a Gaussian measure formally preserved by the 2-dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in \cite{GuJa13} for a hyperviscous version of the equations.Comment: 15 page

Octavio Paz e Fabio Morábito, poetastradutores

IX Congresso Brasileiro de Hispanistas realizado nos dias 22 a 25 agosto 2016Ao final do ensaio "El nado del traductor" (2000) o egípcioitaliano Fabio Morábito conclui que a poesia é a "nostalgia" de outras línguas, pois representa o desejo humano de ser ouvido em profundidade. Para esse escritor que escolheu o espanhol como língua de escrita, a poesia imitaria a tradução, pois ambas seriam um "segundo nascimento da língua". Quase trinta anos antes, Octavio Paz, no ensaio Traducción: literatura y literalidad (1971) defendia a tradução e a criação como "operações gêmeas". A comunicação objetiva percorrer os textos em que ambos opinam a respeito da tradução literária, buscando desvelar suas autofigurações enquanto poetastradutores. Além de seu ensaio principal, o discurso de Paz sobre tradução aparece disseminado em livros como Los hijos del limo (1974), El signo y el garabato (1973), assim como nos prólogos e notas de suas traduções, em especial as reunidas em Versiones y diversiones (1974). Fabio Morábito, ademais do ensaio supracitado, manifestouse a respeito no conto "Los Vetriccioli" (1989), no ensaio "Poesía y traducción I: olvidar el original" (2010), na palestra "Traduttore truffatore" (2013) e nos insights de El idioma materno (2014): "Scrittore traditore", "La capa exterior", "Drácula y el idioma" e "Los poetas no escriben libros". Enquanto Paz busca combater um dos lugares comuns da teoria da tradução que afirma a intradutibilidade da poesia, Morábito descreve o momento em que sua experiência pessoal de tradutor se faz presente através de duas metáforas interrelacionadas. Por um lado, o esforço de atenção prestado a um som débil – sussurrado ou ouvido –, por outro, sua necessidade, enquanto tradutor, de um lugar que lhe seja próprioUNILA­-UNIOEST

Stationary Solutions of Damped Stochastic 2-dimensional Euler's Equation

Existence of stationary point vortices solution to the damped and stochastically driven Euler's equation on the two dimensional torus is proved, by taking limits of solutions with finitely many vortices. A central limit scaling is used to show in a similar manner the existence of stationary solutions with white noise marginals.Comment: 24 page

Essential Self-Adjointness of Liouville Operator for 2D Euler Point Vortices

We analyse the 2-dimensional Euler point vortices dynamics in the Koopman-Von Neumann approach. Classical results provide well-posedness of this dynamics involving singular interactions for a finite number of vortices, on a full-measure set with respect to the volume measure $dx^N$ on the phase space, which is preserved by the measurable flow thanks to the Hamiltonian nature of the system. We identify a core for the generator of the one-parameter group of Koopman-Von Neumann unitaries on $L^2(dx^N)$ associated to said flow, the core being made of observables smooth outside a suitable set on which singularities can occur.Comment: 17 page

Cognitive network structure: an experimental study

In this paper we present first experimental results about a small group of people exchanging private and public messages in a virtual community. Our goal is the study of the cognitive network that emerges during a chat seance. We used the Derrida coefficient and the triangle structure under the working assumption that moods and perceived mutual affinity can produce results complementary to a full semantic analysis. The most outstanding outcome is the difference between the network obtained considering publicly exchanged messages and the one considering only privately exchanged messages: in the former case, the network is very homogeneous, in the sense that each individual interacts in the same way with all the participants, whilst in the latter the interactions among different agents are very heterogeneous, and are based on "the enemy of my enemy is my friend" strategy. Finally a recent characterization of the triangular cliques has been considered in order to describe the intimate structure of the network. Experimental results confirm recent theoretical studies indicating that certain 3-vertex structures can be used as indicators for the network aging and some relevant dynamical features.Comment: 15 pages, 5 figures, 3 table

Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations

We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist configurations of arbitrarily many vortices in which three of them collapse in finite time. As an intermediate step, we show that well-known self-similar bursts and collapses of three isolated vortices in the plane persist under a sufficiently regular external perturbation. We also discuss how our results produce examples of non-unique weak solutions to 2-dimensional Euler's equations -- in the sense introduced by Schochet -- in which energy is dissipated.Comment: 30 page

Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations

We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to the first integrals energy and enstrophy are Gaussian measures supported by distributional spaces. We define a suitable weak formulation for barotropic equations, and prove existence of a stationary solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.Comment: 18 page