Extending canonical Monte Carlo methods II

Previously, we have presented a methodology to extend canonical Monte Carlo methods inspired on a suitable extension of the canonical fluctuation relation $C=\beta^{2}$ compatible with negative heat capacities $C<0$. Now, we improve this methodology by introducing a better treatment of finite size effects affecting the precision of a direct determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$, as well as a better implementation of MC schemes. We shall show that despite the modifications considered, the extended canonical MC methods possibility an impressive overcome of the so-called \textit{super-critical slowing down} observed close to the region of a temperature driven first-order phase transition. In this case, the dependence of the decorrelation time $\tau$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $\tau(N)\propto N^{\alpha}$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $\alpha=0.14-0.18$.Comment: Version submitted to JSTA

Equilibrium fluctuation theorems compatible with anomalous response

Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations $C=\beta^{2}<\delta U^{2}>$, which is able to describe the existence of macrostates with negative heat capacities $C<0$. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the \textit{fundamental and the complementary fluctuation theorems}, which represent the generalization of two fluctuation identities already obtained in previous works, and the \textit{associated fluctuation theorem}, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of 2D Ising model.Comment: Extended version of the paper published in JSTA

A precessing jet model for the PN K 3-35: simulated radio-continuum emission

The bipolar morphology of the planetary nebula (PN) K 3-35 observed in radio-continuum images was modelled with 3D hydrodynamic simulations with the adaptive grid code yguazu-a. We find that the observed morphology of this PN can be reproduced considering a precessing jet evolving in a dense AGB circumstellar medium, given by a mass loss rate \dot{M}_{csm}=5x10^{-5}M_{\odot}/yr and a terminal velocity v_{w}=10 km/s. Synthetic thermal radio-continuum maps were generated from numerical results for several frequencies. Comparing the maps and the total fluxes obtained from the simulations with the observational results, we find that a model of precessing dense jets, where each jet injects material into the surrounding CSM at a rate \dot{M}_j=2.8x10^{-4} {M_{\odot}/yr (equivalent to a density of 8x10^{4} {cm}^{-3}, a velocity of 1500 km/s, a precession period of 100 yr, and a semi-aperture precession angle of 20 degrees agrees well with the observations.Comment: 6 pages, 4 figures, accepted to MNRA

Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Asymmetric supernova remnants generated by Galactic, massive runaway stars

After the death of a runaway massive star, its supernova shock wave interacts with the bow shocks produced by its defunct progenitor, and may lose energy, momentum, and its spherical symmetry before expanding into the local interstellar medium (ISM). We investigate whether the initial mass and space velocity of these progenitors can be associated with asymmetric supernova remnants. We run hydrodynamical models of supernovae exploding in the pre-shaped medium of moving Galactic core-collapse progenitors. We find that bow shocks that accumulate more than about 1.5 Mo generate asymmetric remnants. The shock wave first collides with these bow shocks 160-750 yr after the supernova, and the collision lasts until 830-4900 yr. The shock wave is then located 1.35-5 pc from the center of the explosion, and it expands freely into the ISM, whereas in the opposite direction it is channelled into the region of undisturbed wind material. This applies to an initially 20 Mo progenitor moving with velocity 20 km/s and to our initially 40 Mo progenitor. These remnants generate mixing of ISM gas, stellar wind and supernova ejecta that is particularly important upstream from the center of the explosion. Their lightcurves are dominated by emission from optically-thin cooling and by X-ray emission of the shocked ISM gas. We find that these remnants are likely to be observed in the [OIII] lambda 5007 spectral line emission or in the soft energy-band of X-rays. Finally, we discuss our results in the context of observed Galactic supernova remnants such as 3C391 and the Cygnus Loop.Comment: 21 pages, 16 figure