Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated using the following PO formulas: (a) The curvature expansion of the Ruelle zeta function. (b) The average of the PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b) agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (c) gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to {\em uniformity sum rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum rules follow from general arguments and are supported by much numerical evidence.Comment: 6 Tables, 2 Figures (postscript); To appear in Physical Review

A comparison of the PARET/ANL and RELAP5/MOD3 codes for the analysis of IAEA benchmark transients

The PARET/ANL and RELAP5/MOD3 codes are used to analyze the series of benchmark transients specified for the IAEA Research Reactor Core Conversion Guidebook (IAEA-TECDOC-643, Vol. 3). The computed results for these loss-of-flow and reactivity insertion transients with scram are in excellent agreement and agree well with the earlier results reported in the guidebook. Attempts to also compare RELAP5/MOD3 with the SPERT series of experiments are in progress

Understanding Galaxy Formation and Evolution

The old dream of integrating into one the study of micro and macrocosmos is now a reality. Cosmology, astrophysics, and particle physics intersect in a scenario (but still not a theory) of cosmic structure formation and evolution called Lambda Cold Dark Matter (LCDM) model. This scenario emerged mainly to explain the origin of galaxies. In these lecture notes, I first present a review of the main galaxy properties, highlighting the questions that any theory of galaxy formation should explain. Then, the cosmological framework and the main aspects of primordial perturbation generation and evolution are pedagogically detached. Next, I focus on the ``dark side'' of galaxy formation, presenting a review on LCDM halo assembling and properties, and on the main candidates for non-baryonic dark matter. It is shown how the nature of elemental particles can influence on the features of galaxies and their systems. Finally, the complex processes of baryon dissipation inside the non-linearly evolving CDM halos, formation of disks and spheroids, and transformation of gas into stars are briefly described, remarking on the possibility of a few driving factors and parameters able to explain the main body of galaxy properties. A summary and a discussion of some of the issues and open problems of the LCDM paradigm are given in the final part of these notes.Comment: 50 pages, 10 low-resolution figures (for normal-resolution, DOWNLOAD THE PAPER (PDF, 1.9 Mb) FROM http://www.astroscu.unam.mx/~avila/avila.pdf). Lectures given at the IV Mexican School of Astrophysics, July 18-25, 2005 (submitted to the Editors on March 15, 2006

Measurement of the mass difference between top quark and antiquark in pp collisions at root s=8 TeV

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Unveiling the impact of Fe-doping concentration on the local structure and morphological evolution of Cr2O3 nanoparticles

A series of Cr2−xFexO3 (0.0 ≤ x ≤ 0.3) nanoparticles were successfully synthesized using a sol-gel-based method. Analysis through XRD and SAED of both pure and Fe-doped Cr2O3 nanoparticles revealed a rhombohedral structure belonging to the R 3‾cD3d6 space group, without the formation of secondary phases or Fe clusters. Fe ions were well integrated, as indicated by fluctuations in lattice parameters, and lattice strain. The crystallite size decreased from 38.42 to 27.54 nm with increasing doping concentration. HRTEM images depicted evenly distributed nanoparticles. At lower dopant concentrations (x = 0.1), smaller and more heterogeneous nanorod-like structures emerged, with average sizes and lengths of 36.56 and 39 nm, respectively. Increasing the doping content to x = 0.2 resulted in a morphological shift towards semi-spherical and ellipsoidal shapes, with average dimensions of 22.84 and 31 nm, respectively. At higher doping levels (x = 0.3), nanoparticles grew to 66.5 nm in size and exhibited a spherical morphology. Raman and Fourier transform infrared spectra showed red-shifting of absorption bands with increasing Fe content, attributed to variations in bond length and Cr/Fe–O–Cr/Fe structural perturbation. XPS and Mössbauer spectroscopy analyses confirmed the oxidation states of Fe3+ and ionized oxygen vacancies in the crystal lattice of Cr2O3 nanoparticles. Higher values of quadrupolar splitting Δ indicated greater structural disorder induced by Fe3+ in octahedral positions and in an oxygen-deficient environment. Atomistic simulations confirmed that Fe3+ dopants can induce the presence of vacancy-complexes, forming a stable double-defect configuration with vacant Cr sites along the c-axis, proximal to oxygen vacancies with a single positive charge. These findings offer both experimental and theoretical insights into the dynamics of structural defects in trivalent transition metal doping of Cr2O3 nanoparticles, which holds significant implications for spintronics research. © 2024 Elsevier Ltd and Techna Group S.r.l.This research was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-CNPq (grant no. 309184/2022-3) . The authors acknowledge the use of the Multiuser Central Facilities at Federal University of ABC (CEM-UFABC) .Peer reviewe