The role of differential rotation in the evolution of the r-mode instability

We discuss the role of differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly-rotating neutron star. It is shown that the amplitude of the r-mode saturates in a natural way at a value that depends on the amount of differential rotation at the time the instability becomes active. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to a rotation rate that is comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants.Comment: 4 pages, 2 figures, in Proceedings of the 5th International Workshop "New Worlds in Astroparticle Physics", Faro, Portugal, 8-10 January 200

On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a square lattice is found to be c_0=0.1765005(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda_c = (1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) = 0.538410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the 2-d percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.Comment: 9 pages, 5 figures. Accepted for publication, Physical Review

Aging and fluctuation-dissipation ratio in a nonequilibrium qq-state lattice model

A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model

Finite-size scaling of the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same as for site and bond percolation, confirming further that the SIR model is also in the percolation class

Nonlinear evolution of r-modes: the role of differential rotation

Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the l=2 r-mode instability of a newly born, hot, rapidly rotating neutron star. It is shown that the amplitude of the r-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the r-mode and, consequently, almost none is carried away by gravitational radiation.Comment: 10 pages, 5 figure

Anomalous magnetic and weak magnetic dipole moments of the τ\tau lepton in the simplest little Higgs model

We obtain analytical expressions, both in terms of parametric integrals and Passarino-Veltman scalar functions, for the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) of a charged lepton in the framework of the simplest little Higgs model (SLHM). Our results are general and can be useful to compute the weak properties of a charged lepton in other extensions of the standard model (SM). As a by-product we obtain generic contributions to the anomalous magnetic dipole moment (AMDM), which agree with previous results. We then study numerically the potential contributions from this model to the $\tau$ lepton AMDM and AWMDM for values of the parameter space consistent with current experimental data. It is found that they depend mainly on the energy scale $f$ at which the global symmetry is broken and the $t_\beta$ parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the $\tau$ AMDM is of the order of $10^{-9}$, the real (imaginary) part of its AWMDM is of the order of $10^{-9}$ ($10^{-10}$). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.Comment: 23 pages, 11 figures, new analysis and References adde

The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.Comment: Accepted for publication (Physical Review E