1,720,989 research outputs found
Horses in the Tempest: the Shape(s) of the Winds in Aeneid Book 1
No full textThis article discusses the horse imagery related to the winds in the storm episode at the beginning of Virgil’s Aeneid. A close analysis of Aen. 1.50–86 brings to light the pervasiveness of this imagery, only partly noticed by scholars, who have regarded it as metaphorical (§1). It is here suggested that the winds released by Aeolus could instead be considered as real horses. A reassessment of the ancient literary—and, briefly, iconographic—evidence of the depiction of the winds as horses, horsemen or charioteers is proposed; Virgil fits into a longstanding tradition of Homeric ancestry, which represents the winds as horses (§2). This allows a better understanding of the narrative dynamic which in Aeneid 1 opposes Aeolus to Neptune, the god of the sea as well as of the horses; moreover, the equestrian (and circus) imagery evoked by Virgil contributes to the political and cosmic significance of the tempest episode (§3)
The ignis sacer : a miniature giant? On Lucr. VI 660-661 (and 547)
No full textIn De rerum natura VI 660-661 Lucretius characterises the disease named ignis sacer as a burning snake, a choice justified by the “fiery” and “creeping” nature of that disorder. In this note, I suggest a parallelism between such imagery and the traditional depiction
of Typhon – or, alternatively, the Giant Enceladus –, the serpent-like creature which was thought to be buried under Mount Etna and whose movements were supposed to cause volcanic eruptions. The verb disserpunt at VI 547, used to describe the propagation of seismic tremors, could also be suggestive of similar mythological associations
Decay of time correlations in point vortex systems
No full textThe dynamics of a large point vortex system whose initial configuration consists in uniformly distributed independent positions is investigated. Time correlations of local observables of the vortex configuration are shown to be compatible with power law decay 1/t, providing additional insight on ergodicity and mixing properties of equilibrium dynamics in point vortex models
Invariant measures and stationary solutions of 2-dimensional Euler equations and related models
Full text linkBurst of Point Vortices and Non-uniqueness of 2D Euler Equations
Full text linkWe 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; equivalently we show 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
Gibbs equilibrium fluctuations of point vortex dynamics
Full text linkWe consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature β≥0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N→∞ a generalized version of two-dimensional Euler dynamics preserving the Gaussian energy-enstrophy ensemble
Random splitting of point vortex flows
Full text linkWe consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which single components of the vector field are randomly switched diverges, and therefore it provides an alternative discretization of 2D Euler equations. The random vortex system we introduce preserves microcanonical statistical ensembles of the point vortex system, hence constituting a simpler alternative to the latter in the statistical mechanics approach to 2D turbulence
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
An example of intrinsic randomness in deterministic PDES
No full textFlandoli F, Gess B, Grotto F. An example of intrinsic randomness in deterministic PDES. Stochastics and Dynamics. 2022: 2240023.A new mechanism leading to a random version of Burgers' equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically stochastic, non-entropic weak solution of Burgers' equation on R. In this interpretation, the appearance of randomness in the Burgers' dynamics is caused by random additions of jumps to the solution, corresponding to the random effects in TASEP
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