Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density $\theta_c$. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of $\theta_c$ on $k$, being $\theta_c(k) \propto k^{-1}$. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of $k$ ($k_{min}=7$), which allows the formation of a nematic phase on a triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic

Entropy-driven phase transition in a system of long rods on a square lattice

The isotropic-nematic (I-N) phase transition in a system of long straight rigid rods of length k on square lattices is studied by combining Monte Carlo simulations and theoretical analysis. The process is analyzed by comparing the configurational entropy of the system with the corresponding to a fully aligned system, whose calculation reduces to the 1D case. The results obtained (1) allow to estimate the minimum value of k which leads to the formation of a nematic phase and provide an interesting interpretation of this critical value; (2) provide numerical evidence on the existence of a second phase transition (from a nematic to a non-nematic state) occurring at density close to 1 and (3) allow to test the predictions of the main theoretical models developed to treat the polymers adsorption problem.Comment: 14 pages, 6 figures. Accepted for publication in JSTA

Constraining the properties of neutron star crusts with the transient low-mass X-ray binary Aql X-1

Aql X-1 is a prolific transient neutron star low-mass X-ray binary that exhibits an accretion outburst approximately once every year. Whether the thermal X-rays detected in intervening quiescent episodes are the result of cooling of the neutron star or due to continued low-level accretion remains unclear. In this work we use Swift data obtained after the long and bright 2011 and 2013 outbursts, as well as the short and faint 2015 outburst, to investigate the hypothesis that cooling of the accretion-heated neutron star crust dominates the quiescent thermal emission in Aql X-1. We demonstrate that the X-ray light curves and measured neutron star surface temperatures are consistent with the expectations of the crust cooling paradigm. By using a thermal evolution code, we find that ~1.2-3.2 MeV/nucleon of shallow heat release describes the observational data well, depending on the assumed mass-accretion rate and temperature of the stellar core. We find no evidence for varying strengths of this shallow heating after different outbursts, but this could be due to limitations of the data. We argue that monitoring Aql X-1 for up to ~1 year after future outbursts can be a powerful tool to break model degeneracies and solve open questions about the magnitude, depth and origin of shallow heating in neutron star crusts.Comment: 14 pages, 5 figures, 3 tables, accepted to MNRA

Well-posedness and stability results for the Gardner equation

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App

On the Benjamin and related equations

We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension.They concern the Cauchy problem, including the long time dynamic, localized solitons or multisolitons, the soliton resolution property. We survey known results, present a few new ones together with open questions and conjectures motivated by numerical simulations. A major issue is to emphasize the differences of the qualitative behavior of solutions with those of the same equations without the capillary term

Microscopic cluster model for the description of (18O,16O) two-neutron transfer reactions

Excitation energy spectra and absolute cross-section angular distributions were measured for the 13C(18O,16O)15C two-neutron transfer reaction at 84 MeV incident energy. Exact finite-range coupled reaction channel calculations are used to analyse the data considering both the direct two-neutron transfer and the two-step sequential mechanism. For the direct calculations, two approaches are discussed: The extreme cluster and the newly introduced microscopic cluster. The latter makes use of spectroscopic amplitudes in the centre-of-mass reference frame, derived from shell-model calculations. The results describe well the experimental cross sections

Microscopic cluster model for the description of new experimental results on the C 13 (O 18, O 16) C 15 two-neutron transfer at 84 MeV incident energy

The C13(O18,O16)C15 reaction is studied at 84 MeV incident energy. Excitation energy spectra and absolute cross-section angular distributions for the strongest transitions are measured with good energy and angular resolutions. Strong selectivity for two-neutron configurations in the states of the residual nucleus is found. The measured cross-section angular distributions are analyzed by exact finite-range coupled reaction channel calculations. The two-particle wave functions are extracted using the extreme cluster and the independent coordinate scheme with shell-model derived coupling strengths. A new approach also is introduced, the microscopic cluster, in which the spectroscopic amplitudes in the center-of-mass reference frame are derived from shell-model calculations using the Moshinsky transformation brackets. This new model is able to describe well the experimental cross section and to highlight cluster configurations in the involved wave functions