Monte-Carlo methods for NLTE spectral synthesis of supernovae

We present JEKYLL, a new code for modelling of supernova (SN) spectra and lightcurves based on Monte-Carlo (MC) techniques for the radiative transfer. The code assumes spherical symmetry, homologous expansion and steady state for the matter, but is otherwise capable of solving the time-dependent radiative transfer problem in non-local-thermodynamic-equilibrium (NLTE). The method used was introduced in a series of papers by Lucy, but the full time-dependent NLTE capabilities of it have never been tested. Here, we have extended the method to include non-thermal excitation and ionization as well as charge-transfer and two-photon processes. Based on earlier work, the non-thermal rates are calculated by solving the Spencer-Fano equation. Using a method previously developed for the SUMO code, macroscopic mixing of the material is taken into account in a statistical sense. In addition, a statistical Markov-chain model is used to sample the emission frequency, and we introduce a method to control the sampling of the radiation field. Except for a description of JEKYLL, we provide comparisons with the ARTIS, SUMO and CMFGEN codes, which show good agreement in the calculated spectra as well as the state of the gas. In particular, the comparison with CMFGEN, which is similar in terms of physics but uses a different technique, shows that the Lucy method does indeed converge in the time-dependent NLTE case. Finally, as an example of the time-dependent NLTE capabilities of JEKYLL, we present a model of a Type IIb SN, taken from a set of models presented and discussed in detail in an accompanying paper. Based on this model we investigate the effects of NLTE, in particular those arising from non-thermal excitation and ionization, and find strong effects even on the bolometric lightcurve. This highlights the need for full NLTE calculations when simulating the spectra and lightcurves of SNe.Comment: Accepted for publication by Astronomy & Astrophysic

An ϵ\epsilon-expansion for Small-World Networks

I construct a well-defined expansion in $\epsilon=2-d$ for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green's function, and is used to calculate the average Green's function and fluctuations to first non-leading order in $\epsilon$, giving results which agree with numerics. This technique is also applicable to other problems of diffusion in random media.Comment: 7 pages Europhysics style, 3 figure

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure

Consensus formation on coevolving networks: groups' formation and structure

We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state. We find that, while on static networks these properties are determined by percolation phenomena, on adaptive networks the rewiring process leads to different behaviors: Adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion, though it also makes possible the division of clusters. We show how the convergence time is determined by the characteristic time of link rearrangement. We finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J. Phys. A covering the "Complex Networks: from Biology to Information Technology" conference (Pula, Italy, 2007

Three-dimensional modeling of Type Ia supernovae - The power of late time spectra

Late time synthetic spectra of Type Ia supernovae, based on three-dimensional deflagration models, are presented. We mainly focus on one model,"c3_3d_256_10s", for which the hydrodynamics (Roepke 2005) and nucleosynthesis (Travaglio et al. 2004) was calculated up to the homologous phase of the explosion. Other models with different ignition conditions and different resolution are also briefly discussed. The synthetic spectra are compared to observed late time spectra. We find that while the model spectra after 300 to 500 days show a good agreement with the observed Fe II-III features, they also show too strong O I and C I lines compared to the observed late time spectra. The oxygen and carbon emission originates from the low-velocity unburned material in the central regions of these models. To get agreement between the models and observations we find that only a small mass of unburned material may be left in the center after the explosion. This may be a problem for pure deflagration models, although improved initial conditions, as well as higher resolution decrease the discrepancy. The relative intensity from the different ionization stages of iron is sensitive to the density of the emitting iron-rich material. We find that clumping, with the presence of low density regions, is needed to reproduce the observed iron emission, especially in the range between 4000 and 6000 AA. Both temperature and ionization depend sensitively on density, abundances and radioactive content. This work therefore illustrates the importance of including the inhomogeneous nature of realistic three-dimensional explosion models. We briefly discuss the implications of the spectral modeling for the nature of the explosion.Comment: 20 pages, 9 figures, resolution of Fig 1 is reduced to meet astro-ph file size restriction, submitted to A&

No trace of a single-degenerate companion in late spectra of SNe 2011fe and 2014J

Left-over, ablated material from a possible non-degenerate companion can reveal itself after about one year in spectra of Type Ia SNe (SNe Ia). We have searched for such material in spectra of SN 2011fe (at 294 days after the explosion) and for SN 2014J (315 days past explosion). The observations are compared with numerical models simulating the expected line emission. The spectral lines sought for are H-alpha, [O I] 6300 and [Ca II] 7291,7324, and the expected width of these lines is about 1000 km/s. No signs of these lines can be traced in any of the two supernovae. When systematic uncertainties are included, the limits on hydrogen-rich ablated gas in SNe 2011fe and 2014J are 0.003 M_sun and 0.0085 M_sun, respectively, where the limit for SN 2014J is the second lowest ever, and the limit for SN 2011fe is a revision of a previous limit. Limits are also put on helium-rich ablated gas. These limits are used, in conjunction with other data, to argue that these supernovae can stem from double-degenerate systems, or from single-degenerate systems with a spun up/spun down super-Chandrasekhar white dwarf. For SN 2011fe, other types of hydrogen-rich donors can likely be ruled out, whereas for SN 2014J a main-sequence donor system with large intrinsic separation is still possible. Helium-rich donor systems cannot be ruled out for any of the two supernovae, but the expected short delay time for such progenitors makes this possibility less likely, especially for SN 2011fe. The broad [Ni II] 7378 emission in SN 2014J is redshifted by about +1300 km/s, as opposed to the known blueshift of roughly -1100 km/s for SN 2011fe. [Fe II] 7155 is also redshifted in SN 2014J. SN 2014J belongs to a minority of SNe Ia that both have a nebular redshift of [Fe II] 7155 and [Ni II] 7378, and a slow decline of the Si II 6355 absorption trough just after B-band maximum.Comment: 13 pages, submitted to A&

Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency

Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and $k_{j}$ being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at $\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of $\beta^{*}$. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.Comment: Papers on related research can be found at http://www.rpi.edu/~korniss/Research

Genetic diversity among twelve grape cultivars indigenous to the Carpathian Basin revealed by RAPD markers

Twelve cultivars (Vitis vinifera L.) were subjected to RAPD analysis in order to estimate the genetic diversity among these genotypes and to analyse their genetic relationships. The study was performed using 28 primers that generated 120 polymorphic fragments. There was genetic variation among the cultivars with values of genetic diversity ranging from 0.419 to 0.642 using the Jaccard coefficient. UPGMA analysis of distance matrix resulted in a dendrogram with three clusters. The dendrogram shows that the cultivars of our study can be distinguished to a relatively high degree. Results were compared with the taxonomic classification and with the synonyms of the cultivars. The RAPD technique was useful for identification and discrimination of these grape cultivars