Asymptotic of grazing collisions and particle approximation for the Kac equation without cutoff

The subject of this article is the Kac equation without cutoff. We first show that in the asymptotic of grazing collisions, the Kac equation can be approximated by a Fokker-Planck equation. The convergence is uniform in time and we give an explicit rate of convergence. Next, we replace the small collisions by a small diffusion term in order to approximate the solution of the Kac equation and study the resulting error. We finally build a system of stochastic particles undergoing collisions and diffusion, that we can easily simulate, which approximates the solution of the Kac equation without cutoff. We give some estimates on the rate of convergence.Comment: 37 pages, 6 figure

Mixing of shear Alfven wave packets

The propagation of shear Alfven wave packets in inhomogeneous magnetic fields, at the origin of their distortion, regardless of the occurrence of non-linear coupling, is considered. It is shown that the distortion mechanism can be regarded as mixing process and hence, standard "phase mixing" corresponds to the effect of an "Alfvenic" shear flow while enhanced dissipation at a magnetic X-point corresponds to mixing by an "Alfvenic" strain flow. The evolution of the global wave field is supposed to result from the dynamics of a superposition of wave packets and a kinetic equation for the wave energy is obtained following this eikonal (WKB) description. Since shear Alfven wave packets experience continuous shearing/straining while transported by an inhomogeneous Alfvenic flow $\mathbf{V}_{A}$, their mixing process, in physical space, is also a cascade of wave energy in k-space. The wave energy spectrum resulting from this linear mechanism of energy transfer is determined for the special case of waves propagating along chaotic magnetic field lines, the analog of a chaotic mixing process. The latter follows a $k^{-1}$ power-law, in the energy conserving range in $k$ space.Comment: revised, final version, Astron. Astrophys. in pres

Cinara tujafilina (del Guercio, 1909) - a new aphid record for Malta (Aphididae, Lachninae)

The aphidofauna of the Maltese archipelago is currently composed of some one hundred recorded species (Mifsud & Pérez Hidalgo, 2011; Mifsud et al. 2011) of which only six species are associated with conifers. Of these, three species belong to the genus Cinara: C. maghrebica, C. palaestinensis (both recorded on Pinus halepensis) and C. cupressi (recorded on Cupressus sempervirens). Identification of a recently captured single alate viviparous female of Cinara, based on Binazzi & Scheurer (2009) and Nieto Nafría et al., (2003), proved to be Cinara (Cupressobium) tujafilina (del Guercio, 1909), a species not previously recorded from Malta.peer-reviewe

The grapevine aphid Aphis illinoisensis : a good example of recent invasion and rapid colonization by aphids

Aphis illinoisensis represents one of the most recent aphid invaders from the New World to the Mediterranean Region. This aphid, which is native to North America and is now widely distributed in Central and South America, was first found in Southern Turkey in 2002, and in 2005 it was also found in Crete (Greece). Thereafter it was recorded from Northern Cyprus, Israel, Tunisia, Algeria, Montenegro and Libya, and is now probably present throughout the Mediterranean. The present work provides data on the presence of this aphid in the Maltese islands, a group of low-lying islands situated in the central Mediterranean Basin.peer-reviewe

First field records of the sexuales (males and oviparae) of Toxoptera aurantii (Hemiptera : Aphididae)

Toxoptera aurantii (Boyer de Fonscolombe) is an aphid pest of great agricultural importance, not only due to its polyphagy but mostly due to its ability to transmit various plant viruses e.g. Citrus tristeza virus on Citrus (Blackman & Eastop, 2000). Blackman & Eastop (2000) considered this aphid to be entirely anholocyclic, because no sexual morphs have ever been observed in the field.peer-reviewe