On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of references corrected, version to appear in JHE

The Strehl Ratio in Adaptive Optics Images: Statistics and Estimation

Statistical properties of the intensity in adaptive optics images are usually modeled with a Rician distribution. We study the central point of the image, where this model is inappropriate for high to very high correction levels. The central point is an important problem because it gives the Strehl ratio distribution. We show that the central point distribution can be modeled using a non-central Gamma distribution.Comment: 8 pages, 5 figure

Exclusion and zero-range in the rarefaction fan

In these notes we briefly review asymptotic results for the totally asymmetric simple exclusion process and the totally asymmetric constant-rate zero-range process, in the presence of particles with different priorities. We review the Law of Large Numbers for a second class particle added to those systems and we present the proof of crossing probabilities for a second and a third class particles. This is done, for the exclusion process, by means of a particle-hole symmetry argument, while for the zero-range process it is a consequence of a coupling argument.FC

Hadronic interactions of primary cosmic rays with the FLUKA code

The measured fluxes of secondary particles produced by the interactions of cosmic rays with the astronomical environment represent a powerful tool to infer some properties of primary cosmic rays. In this work we investigate the production of secondary particles in inelastic hadronic interactions between several cosmic rays species of projectiles and different target nuclei of the interstellar medium. The yields of secondary particles have been calculated with the FLUKA simulation package, that provides with very good accuracy the energy distributions of secondary products in a large energy range. An application to the propagation and production of secondaries in the Galaxy is presented.Comment: 8 pages, 4 figures; Contribution to the 34th International Cosmic Ray Conference, July 30 to August 6, The Hague, Netherlands; fixing a typo in the y-axis label of Fig.

Atmospheric neutrinos in a Large Liquid Argon detector

In view of the evaluation of the physics goals of a large Liquid Argon TPC, evolving from the ICARUS technology, we have studied the possibility of performing precision measurements on atmospheric neutrinos. For this purpose we have improved existing Monte Carlo neutrino event generators based on FLUKA and NUX by including the 3-flavor oscillation formalism and the numerical treatment of Earth matter effects. By means of these tools we have studied the sensitivity in the measurement of Theta(23) through the accurate measurement of electron neutrinos. The updated values for Delta m^2(23) from Super-Kamiokande and the mixing parameters as obtained by solar and KamLand experiments have been used as reference input, while different values of Theta(13) have been considered. An exposure larger than 500 kton yr seems necessary in order to achieve a significant result, provided that the present knowledge of systematic uncertainties is largely improved.Comment: Talk given at the worksgop "Cryogenic Liquid Detectors for Future Particle Physics", LNGS (Italy) March 13th-14th, 200