Tree-Grass interactions dynamics and Pulse Fires: mathematical and numerical studies

Savannas are dynamical systems where grasses and trees can either dominate or coexist. Fires are known to be central in the functioning of the savanna biome though their characteristics are expected to vary along the rainfall gradients as observed in Sub-Saharan Africa. In this paper, we model the tree-grass dynamics using impulsive differential equations that consider fires as discrete events. This framework allows us to carry out a comprehensive qualitative mathematical analysis that revealed more diverse possible outcomes than the analogous continuous model. We investigated local and global properties of the equilibria and show that various states exist for the physiognomy of vegetation. Though several abrupt shifts between vegetation states appeared determined by fire periodicity, we showed that direct shading of grasses by trees is also an influential process embodied in the model by a competition parameter leading to bifurcations. Relying on a suitable nonstandard finite difference scheme, we carried out numerical simulations in reference to three main climatic zones as observable in Central Africa.Comment: 51 pages, 7 figure

The End of the Lines for OX 169: No Binary Broad-Line Region

We show that unusual Balmer emission line profiles of the quasar OX 169, frequently described as either self-absorbed or double peaked, are actually neither. The effect is an illusion resulting from two coincidences. First, the forbidden lines are quite strong and broad. Consequently, the [N II]6583 line and the associated narrow-line component of H-alpha present the appearance of twin H-alpha peaks. Second, the redshift of 0.2110 brings H-beta into coincidence with Na I D at zero redshift, and ISM absorption in Na I D divides the H-beta emission line. In spectra obtained over the past decade, we see no substantial change in the character of the line profiles, and no indication of intrinsic double-peaked structure. The H-gamma, Mg II, and Ly-alpha emission lines are single peaked, and all of the emission-line redshifts are consistent once they are correctly attributed to their permitted and forbidden-line identifications. A systematic shift of up to 700 km/s between broad and narrow lines is seen, but such differences are common, and could be due to gravitational and transverse redshift in a low-inclination disk. Stockton & Farnham (1991) had called attention to an apparent tidal tail in the host galaxy of OX 169, and speculated that a recent merger had supplied the nucleus with a coalescing pair of black holes which was now revealing its existence in the form of two physically distinct broad-line regions. Although there is no longer any evidence for two broad emission-line regions in OX 169, binary black holes should form frequently in galaxy mergers, and it is still worthwhile to monitor the radial velocities of emission lines which could supply evidence of their existence in certain objects.Comment: 19 pages, 5 figures, accepted for publication in Ap.

The analysis of solar models: Neutrinos and oscillations

Tests of solar neutrino flux and solar oscillation frequencies were used to assess standard stellar structure theory. Standard and non-standard solar models are enumerated and discussed. The field of solar seismology, wherein the solar interior is studied from the measurement of solar oscillations, is introduced

Influence of s,p-d and s-p exchange couplings on exciton splitting in (Zn,Mn)O

This work presents results of near-band gap magnetooptical studies on (Zn,Mn)O epitaxial layers. We observe excitonic transitions in reflectivity and photoluminescence, that shift towards higher energies when the Mn concentration increases and split nonlinearly under the magnetic field. Excitonic shifts are determined by the s,p-d exchange coupling to magnetic ions, by the electron-hole s-p exchange, and the spin-orbit interactions. A quantitative description of the magnetoreflectivity findings indicates that the free excitons A and B are associated with the Gamma_7 and Gamma_9 valence bands, respectively, the order reversed as compared to wurtzite GaN. Furthermore, our results show that the magnitude of the giant exciton splittings, specific to dilute magnetic semiconductors, is unusual: the magnetoreflectivity data is described by an effective exchange energy N_0(beta-alpha)=+0.2+/-0.1 eV, what points to small and positive N_0 beta. It is shown that both the increase of the gap with x and the small positive value of the exchange energy N_0 beta corroborate recent theory describing the exchange splitting of the valence band in a non-perturbative way, suitable for the case of a strong p-d hybridization.Comment: 8 pages, 8 figure

Luxembourg

The 2018 political year was dominated by the parliamentary elections on 14 October2018. The general expectation was that the Christian Democrats (CSV), who had been inopposition since 2013,would win the election and return to government.In the end,they lostvotes and the incumbent coalition of Liberals (DP), Social Democrats (LSAP) and Greens(Déi Gréng) could maintain its majority, allowing the three parties to continue for a secondterm. These elections also led to the rise of the Pirate Party.On the legislative front, several bills on the government’s legislative agenda were votedon by Parliament

Aperiodic Ising model on the Bethe lattice: Exact results

We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences. We present analytical formulae for the continuously varying critical exponents and discuss a relationship with the (surface) critical behavior of the aperiodic quantum Ising chain.Comment: 7 pages, 3 figures, minor correction

Modeling Variable Emission Lines in AGNs: Method and Application to NGC 5548

We present a new scheme for modeling the broad line region in active galactic nuclei (AGNs). It involves photoionization calculations of a large number of clouds, in several pre-determined geometries, and a comparison of the calculated line intensities with observed emission line light curves. Fitting several observed light curves simultaneously provides strong constraints on model parameters such as the run of density and column density across the nucleus, the shape of the ionizing continuum, and the radial distribution of the emission line clouds. When applying the model to the Seyfert 1 galaxy NGC 5548, we were able to reconstruct the light curves of four ultraviolet emission-lines, in time and in absolute flux. This has not been achieved by any previous work. We argue that the Balmer lines light curves, and possibly also the MgII2798 light curve, cannot be tested in this scheme because of the limitations of present-day photoionization codes. Our fit procedure can be used to rule out models where the particle density scales as r^{-2}, where r is the distance from the central source. The best models are those where the density scales as r^{-1} or r^{-1.5}. We can place a lower limit on the column density at a distance of 1 ld, of N_{col}(r=1) >~ 10^{23} cm^{-2} and limit the particle density to be in the range of 10^{12.5}>N(r=1)>10^{11} cm^{-3}. We have also tested the idea that the spectral energy distribution (SED) of the ionizing continuum is changing with continuum luminosity. None of the variable-shape SED tried resulted in real improvement over a constant SED case although models with harder continuum during phases of higher luminosity seem to fit better the observed spectrum. Reddening and/or different composition seem to play a minor role, at least to the extent tested in this work.Comment: 12 pages, including 9 embedded EPS figures, accepted for publication in Ap