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Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this Letter, we demonstrate that recurrence networks obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with scaling exponents $\gamma$ that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that $\gamma$ is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent $\gamma$ depending on a suitable notion of local dimension, and such with fixed $\gamma=1$., Comment: 6 pages, 7 figures

Measurements of low temperature transport and thermodynamic properties have been used to characterize the non-Fermi liquid state of the itinerant ferromagnet ZrZn$_2$. We observe a $T^{5/3}$ temperature dependence of the electrical resistivity at zero field, which becomes $T^2$ like in an applied field of 9 T. In zero field we also measured the thermal conductivity, and we see a novel linear in $T$ dependence of the difference between the thermal and electrical resistivities. Heat capacity measurements, also at zero field, reveal an upturn in the electronic contribution at low temperatures when the phonon term is subtracted. Taken together, we argue that these properties are consistent with a marginal Fermi liquid state which is predicted by a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions. We compare our data to quantitative predictions and establish this model as a compelling theoretical framework for understanding ZrZn$_2$., Comment: 10 pages, 10 figures

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis.

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potentials of these complex network measures for detecting dynamical transitions. Finally we apply the proposed approach to a marine palaeo-climate record and identify subtle changes of the climate regime., Comment: 23 pages, 7 figures

Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosity of neutrino annihilation is greatly augmented; (ii) the disk becomes thermally and viscously unstable in the inner region, and behaves S-Shape of the surface density versus accretion rate. It turns out that magnetically torqued NDAF can be invoked to interpret the variability of gamma-ray luminosity. In addition, we discuss the possibility of restarting the central engine to produce the X-ray flares with required energy., Comment: 26 pages, 5 figures, accepted for publication in ApJ

The extremely bright optical flash that accompanied GRB 080319B suggested, at first glance, that the prompt $\gamma$-rays in this burst were produced by Synchrotron self Compton (SSC). We analyze here the observed optical and $\gamma$ spectrum. We find that the very strong optical emission poses, due to self absorption, very strong constraints on the emission processes and put the origin of the optical emission at a very large radius, almost inconsistent with internal shock. Alternatively it requires a very large random Lorentz factor for the electrons. We find that SSC could not have produced the prompt $\gamma$-rays. We also show that the optical emission and the $\gamma$ rays could not have been produced by synchrotron emission from two populations of electron within the same emitting region. Thus we must conclude that the optical and the $\gamma$-rays were produced in different physical regions. A possible interpretation of the observations is that the $\gamma$-rays arose from internal shocks but the optical flash resulted from external shock emission. This would have been consistent with the few seconds delay observed between the optical and $\gamma$-rays signals.

Using the conservation of energy and momentum during collisions of any two shells, we consider the efficiency of gamma-ray bursts by assuming that the ejecta from the central engine are equally massive and have the same Lorentz factors. We calculate the efficiency and the final Lorentz factor of the merged whole shell for different initial diversities of Lorentz factors and for different microscopic radiative efficiency. As a result, a common high efficiency in the range of 0.1 to 0.9 is considerable, and a very high value near 100% is also reachable if the diversity of the Lorentz factors is large enough., Comment: 12 pages, 6 figures, accepted by JASR

Similar to the pulsar, the magnetic axis and the spin axis of the gamma-ray burst source may not lie on the same line. This may cause a ring-like jet due to collimation of the precessing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with temporal index equal to -1/2 if the Lorentz factor of the ejecta is not very high. This phase is consistent with the shallow decay phase of some early X-ray afterglow detected by {\it{swift}}. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709., Comment: 6 pages, 2 figures. Accepted by ChJAA

By neglecting sideways expansion of gamma-ray burst (GRB) jets and assuming their half-opening angle distribution, we estimate the detectability of orphan optical afterglows. This estimation is carried out by calculating the durations of off-axis optical afterglows whose flux density exceeds a certain observational limit. We show that the former assumption leads to more detectable orphans, while the latter suppresses the detectability strongly compared with the model with half-opening angle $\theta_j=0.1$. We also considered the effects of other parameters, and find that the effects of the ejecta energy $E_j$ and post-jet-break temporal index $-\alpha_2$ are important but that the effects of the electron-energy distribution index $p$, electron energy equipartition factor $\epsilon_e$, and environment density $n$ are insignificant. If $E_j$ and $\alpha_2$ are determined by other methods, one can constrain the half-opening angle distribution of jets by observing orphan afterglows. Adopting a set of "standard" parameters, the detectable rate of orphan afterglows is about $1.3\times 10^{-2} {deg}^{-2} {yr}^{-1}$, if the observed limiting magnitude is 20 in R-band., Comment: 6 pages, 5 figures. Accepted by A&A

The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to competition for processing capacity among the items produced, which significantly impacts their throughput time (TPT). Such production models naturally exhibit two time scales: a short one, characteristic of single items processed through individual machines, and a longer one, characteristic of the response time of the entire factory. Coarse-grained partial differential equations for the spatio-temporal evolution of a "phase density" were obtained through a kinetic theory approach in Armbruster et al. [2]. We take advantage of the time scale separation to directly solve such coarse-grained equations, even when we cannot derive them explicitly, through an equation-free computational approach. Short bursts of appropriately initialized stochastic fine-scale simulation are used to perform coarse projective integration on the phase density. The key step in this process is lifting: the construction of fine-scale, discrete realizations consistent with a given coarse-grained phase density field. We achieve this through computational evaluation of conditional distributions of a "phase velocity" at the limit of large item influxes., Comment: 14 pages, 17 figures

By considering synchrotron radiative process in the internal shock model and assuming that all internal shocks are nearly equally energetic, we analyze the gamma-ray burst (GRB) emission at different radii corresponding to different observed times. We apply this model to GRB 050904 and find that our analytical results can provide a natural explanation for the multi-band observations of GRB 050904. This suggests that the X-ray flare emission and the optical emission of this burst could have originated from internal shocks being due to collisions among nearly-equally-energetic shells ejected from the central engine. Thus GRB 050904 appears to be a burst with super-long central engine activity., Comment: 16 pages, 4 figure. Submitted on Oct. 21, 2005, accepted by ApJ

When a cold shell sweeps up the ambient medium, a forward shock and a reverse shock will form. We analyze the reverse-forward shocks in a wind environment, including their dynamics and emission. An early afterglow is emitted from the shocked shell, e.g., an optical flash may emerge. The reverse shock behaves differently in two approximations: relativistic and Newtonian cases, which depend on the parameters, e.g., the initial Lorentz factor of the ejecta. If the initial Lorentz factor is much less than $114 E_{53}^{1/4} \Delta_{0,12}^{-1/4} A_{*,-1}^{-1/4}$, the early reverse shock is Newtonian. This may take place for the wider of a two-component jet, an orphan afterglow caused by a low initial Lorentz factor, and so on. The synchrotron self absorption effect is significant especially for the Newtonian reverse shock case, since the absorption frequency $\nu_a$ is larger than the cooling frequency $\nu_c$ and the minimum synchrotron frequency $\nu_m$ for typical parameters. For the optical to X-ray band, the flux is nearly unchanged with time during the early period, which may be a diagnostic for the low initial Lorentz factor of the ejecta in a wind environment. We also investigate the early light curves with different wind densities, and compare them with these in the ISM model., Comment: 14 pages, 7 figures, 2 tables, accepted for publication in MNRAS

Based on 1.35 million polarized $\Xi^{-}$ events, we measure the parameter $\phi_{\Xi}$ to be $-1.61^{\circ} \pm 2.66^{\circ} \pm 0.37^{\circ}$ for $\Xi^{-} \to \Lambda \pi^{-}$ decay. New results for the parameters $\beta_{\Xi}$ and $\gamma_{\Xi}$ are also presented. Assuming that the CP-violating phase-shift difference is negligible, we deduce the strong phase-shift difference between the P-wave and S-wave amplitudes of the $\Lambda\pi$ final state to be $3.17^{\circ} \pm 5.28^{\circ} \pm 0.73^{\circ}$. This strong phase-shift difference reduces the theoretical uncertainty in estimating the level of CP violation in $\Xi$-hyperon decay., Comment: To be published in Physical Review Letters