1,720,967 research outputs found
Una favola epica : Fedro 1,30 e Virgilio
Full text linkIn fable 1,30 Phaedrus merges two Vergilian passages which describe a duel between two bulls: Georg. 3,209-241, where they battle for the love of a heifer, and especially Aen. 12,715-724, where supremacy over the herd is at stake. In this article, I analyze how Phaedrus appropriates this epic theme, paying particular attention to the generic dynamics between fable and epos. By way of conclusion, I turn to Jean de La Fontaine's rewriting of Phaedrus' apologue (Fables 2,4), which creatively reacts to the insertion of the Vergilian subject-matter into the fable
Stationary Solutions of Damped Stochastic 2-dimensional Euler’s Equation
Full text linkExistence 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
Essential self-adjointness of Liouville operator for 2D Euler point vortices
Full text linkWe 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 dxN 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 L2(dxN) associated to said flow, the core being made of observables smooth outside a suitable set on which singularities can occur
Infinitesimal Invariance of Completely Random Measures for 2D Euler Equations
No full textWe consider suitable weak solutions of 2-dimensional Euler equations on bounded domains, and show that the class of completely random measures is infinitesimally invariant for the dynamics. Space regularity of samples of these random fields falls outside of the well-posedness regime of the PDE under consideration, so it is necessary to resort to stochastic integrals with respect to the candidate invariant measure in order to give a definition of the dynamics. Our findings generalize and unify previous results on Gaussian stationary solutions of Euler equations and point vortices dynamics. We also discuss difficulties arising when attempting to produce a solution flow for Euler’s equations preserving independently scattered random measures
Decay of correlation rate in the mean field limit of point vortices ensembles
Full text linkWe consider the Mean Field limit of Gibbsian ensembles of 2-dimensional (2D) point vortices on the torus. It is a classical result that in such limit correlations functions converge to 1, that is, point vortices decorrelate: We compute the rate at which this convergence takes place by means of Gaussian integration techniques, inspired by the correspondence between the 2D Coulomb gas and the Sine-Gordon Euclidean field theory
Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations
Full text linkWe 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
Fluctuations of polyspectra in spherical and Euclidean random wave models
Full text linkWe consider polynomial transforms (polyspectra) of Berry's model - the Euclidean Random Wave model - and of Random Hyperspherical Harmonics. We determine the asymptotic behavior of variance for polyspectra of any order in the high-frequency limit. In particular, we are able to treat polyspectra of any odd order q >= 5, whose asymptotic behavior was left as a conjecture in the case of Random Hyperspherical Harmonics by Marinucci and Wigman (Comm. Math. Phys. 2014). To this end, we exploit a relation between the variance of polyspectra and the distribution of uniform random walks on Euclidean space with finitely many steps, which allows us to rely on technical results in the latter context
Gaussian invariant measures and stationary solutions of 2D Primitive Equations
Full text linkWe 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
Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems
Full text linkWe consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations
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