Rosenblatt distribution subordinated to gaussian random fields with long-range dependence

The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on R^d displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d=1. Several properties of this new distribution are obtained. Specifically, its series representation in terms of independent chi-squared random variables is given, the asymptotic behavior of the eigenvalues, its L\`evy-Khintchine representation, as well as its membership to the Thorin subclass of self-decomposable distributions. The existence and boundedness of its probability density is then a direct consequence.Comment: This paper has 40 pages and it has already been submitte

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

Study of the derivative expansions for the nuclear structure functions

We study the convergence of the series expansions sometimes used in the analysis of the nuclear effects in Deep Inelastic Scattering (DIS) proccesses induced by leptons. The recent advances in statistics and quality of the data, in particular for neutrinos calls for a good control of the theoretical uncertainties of the models used in the analysis. Using realistic nuclear spectral functions which include nucleon correlations, we find that the convergence of the derivative expansions to the full results is poor except at very low values of $x$

Binary neutron star mergers: a jet engine for short gamma-ray bursts

We perform magnetohydrodynamic simulations in full general relativity (GRMHD) of quasi-circular, equal-mass, binary neutron stars that undergo merger. The initial stars are irrotational, $n=1$ polytropes and are magnetized. We explore two types of magnetic-field geometries: one where each star is endowed with a dipole magnetic field extending from the interior into the exterior, as in a pulsar, and the other where the dipole field is initially confined to the interior. In both cases the adopted magnetic fields are initially dynamically unimportant. The merger outcome is a hypermassive neutron star that undergoes delayed collapse to a black hole (spin parameter $a/M_{\rm BH} \sim 0.74$) immersed in a magnetized accretion disk. About $4000M \sim 60(M_{\rm NS}/1.625M_\odot)$ ms following merger, the region above the black hole poles becomes strongly magnetized, and a collimated, mildly relativistic outflow --- an incipient jet --- is launched. The lifetime of the accretion disk, which likely equals the lifetime of the jet, is $\Delta t \sim 0.1 (M_{\rm NS}/1.625M_\odot)$ s. In contrast to black hole--neutron star mergers, we find that incipient jets are launched even when the initial magnetic field is confined to the interior of the stars.Comment: 6 pages, 3 figures, 1 table, matches published versio

Stabilized mixed explicit finite element formulation for compressible and nearly-incompressible solids

El presente estudio presenta una formulación mixta de elementos finitos capaz de abordar problemas quasiincompresibles en forma explícita. Esta formulación se aplica a elementos con interpolaciones independientes e iguales de desplazamientos y deformaciones, estabilizadas mediante subescalas variacionales (VMS). Como continuación del estudio presentado en la referencia [23] , en la que se introdujo la subescala de las deformaciones, en este trabajo se incluyen los efectos de la sub-escala de los desplazamientos, con el fin de estabilizar el campo de las presiones. La formulación evita la condición de Ladyzhenskaya-Babuska-Brezzi (LBB) y sólo requiere la resolución de un sistema diagonal de ecuaciones. En este artículo se tratan también los principales aspectos de implementación. Finalmente, ejemplos de validación numérica muestran el comportamiento de estos elementos en comparación con la formulación irreducible.This study presents a mixed finite element formulation able to address nearly-incompressible problems explicitly. This formulation is applied to elements with independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). As a continuation of the study presented in reference [23], in which the strains sub-scale was introduced, in this work the effects of sub-scale displacements are included, in order to stabilize the pressure field. The formulation avoids the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and only requires the solution of a diagonal system of equations. The main aspects of implementation are also discussed. Finally, numerical examples validate the behaviour of these elements compared with the irreductible formulation.Peer ReviewedPostprint (published version

Pressure-induced transformations in LiCl–H2O at 77 K

A systematic study of the properties of high-density amorphous ice (HDA) in the presence of increasing amounts of salt is missing, especially because it is challenging to avoid ice crystallization upon cooling the pressurized liquid. In order to be able to study HDA also in the presence of small amounts of salt, we have investigated the transformation behaviour of quenched aqueous LiCl solutions (mole fraction x 1 GPa. The observed densification is consistent with the idea that a freeze concentrated LiCl solution of x = 0.14 (R = 6) segregates, which transforms to the glassy state upon cooling, and that the densification is only due to the Ih → HDA transition. Also the XRD patterns and DSC scans are almost unaffected by the presence of the segregated glassy LiCl solution. Upon heating at ambient pressure HDA experiences the polyamorphic transition to low-density amorphous ice (LDA) at ∼120 K, even at x ∼ 0.10. Based on the latent heat evolved in the transition we suggest that almost all water in the sample transforms to an LDA-like state, even the water in the vicinity of the ions. The glassy LiCl solution acts as a spectator that does not shift the transformation temperature significantly and experiences a glass-to-liquid transition at ∼140 K prior to the crystallization to cubic ice. By contrast, at x > 0.12 the phenomenology completely changes and is now dominated by the salt. Hexagonal ice no longer forms upon quenching the LiCl solution, but instead LDA forms. A broad pressure-induced transformation at >0.6 GPa can be attributed to the densification of LDA, the glassy LiCl solution and/or glassy hydrates.Fil: Ruiz, G. N.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentina. Universidad de Innsbruck; AustriaFil: Bove, L. E.. Universite Pierre et Marie Curie; Francia. Ecole Polytechnique Federale de Lausanne; SuizaFil: Corti, Horacio Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Loerting, T.. Universidad de Innsbruck; Austri