Exponential asymptotics for line solitons in two-dimensional periodic potentials

As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multi-scale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multi-line-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.Comment: 27 pages, 8 figures. To appear in Stud. Appl. Mat

From nonlocal gap solitary waves to bound states in periodic media

Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become nonlocal owing to the presence of growing tails of exponentially-small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such nonlocal solitary waves, higher-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two nonlocal solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.Comment: To appear in Proc. Roy. Soc. Lond.

Solitary waves and their linear stability in nonlinear lattices

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, hinge upon a certain recurrence relation which contains information beyond all orders of the usual two-scale perturbation expansion. It follows that only two such positions are permissible, and of those two solitary waves, one is linearly stable and the other unstable. For a cosine lattice, in particular, the two possible solitary waves are centered at a maximum or minimum of the lattice, with the former being stable, and the analytical predictions for the associated linear stability eigenvalues are in excellent agreement with numerical results. Furthermore, a countable set of multi-solitary-wave bound states are constructed analytically. In spite of rather different physical settings, the exponential asymptotics approach followed here is strikingly similar to that taken in earlier studies of solitary wavepackets involving a periodic carrier and a slowly-varying envelope, which underscores the general value of this procedure for treating multi-scale solitary-wave problems.Comment: To appear in Stud. Appl. Mat

Using a Rolling Vector Error Correction Model to Model Static and Dynamic Causal Relations between Electricity Spot Price and Related Fundamental Factors: The Case of Greek Electricity Market

The purpose of this study is to investigate short and long run relationships between electricity spot prices in Greece, Brent oil, natural gas, lignite fuel cost and carbon allowances using daily data from 2007 to 2014. Static and dynamic Johansen test are applied in order to identify long run relations and also to assess the evolution over time in the level of cointegration. Additionally we test for Granger Causality in a Vector error correction model and embrace impulse response and variance decomposition techniques to model the dynamic response of electricity prices in excitation of another variable. Overall our results suggest an important long run relation between spot electricity prices in Greece, natural gas price and carbon allowances, while in the short run electricity prices are not affected by any of the other variables, results that are of practical importance for the market regulator as well as the wholesale market participants. Keywords:  Vector Error Correction, Electricity Markets, Fuel Markets JEL Classifications: C4, C5 & C

AGN dust tori at low and high luminosities

A cornerstone of AGN unification schemes is the presence of an optically and geometrically thick dust torus. It provides the obscuration to explain the difference between type 1 and type 2 AGN. We investigate the influence of the dust distribution on the Eddington limit of the torus. For smooth dust distributions, the Eddingtion limit on the dust alone is 5 orders of magnitudes below the limit for electron scattering in a fully ionized plasma, while a clumpy dust torus has an Eddington limit slightly larger than the classical one. We study the behaviour of a clumpy torus at low and high AGN luminosities. For low luminosities of the order of ~10^42 erg/s, the torus changes its characteristics and obscuration becomes insufficient. In the high luminosity regime, the clumpy torus can show a behaviour which is consistent with the "receding torus" picture. The derived luminosity-dependent fraction of type-2-objects agrees with recent observational results. Moreover, the luminosity-dependent covering factor in a clumpy torus may explain the presence of broad-line AGN with high column densities in X-rays.Comment: 5 pages, 0 figures; Accepted for publication in MNRA

Compton Thick AGN in the XMM-COSMOS survey

Heavily obscured, Compton Thick (CT, NH>10^24 cm^-2) AGN may represent an important phase in AGN/galaxy co-evolution and are expected to provide a significant contribution to the cosmic X-ray background (CXB). Through direct X-ray spectra analysis, we selected 39 heavily obscured AGN (NH>3x10^23 cm^-2) in the 2 deg^2 XMM-COSMOS survey. After selecting CT AGN based on the fit of a simple absorbed two power law model to the XMM data, the presence of CT AGN was confirmed in 80% of the sources using deeper Chandra data and more complex models. The final sample of CT AGN comprises 10 sources spanning a large range of redshift and luminosity. We collected the multi-wavelength information available for all these sources, in order to study the distribution of SMBH and host properties, such as BH mass (M_BH), Eddington ratio (\lambda_Edd), stellar mass (M*), specific star formation rate (sSFR) in comparison with a sample of unobscured AGN. We find that highly obscured sources tend to have significantly smaller M_BH and higher \lambda_edd with respect to unobscured ones, while a weaker evolution in M* is observed. The sSFR of highly obscured sources is consistent with the one observed in the main sequence of star forming galaxies, at all redshift. We also present optical spectra, spectral energy distribution (SED) and morphology for the sample of 10 CT AGN: all the available optical spectra are dominated by the stellar component of the host galaxy, and a highly obscured torus component is needed in the SED of the CT sources. Exploiting the high resolution Hubble-ACS images available, we conclude that these highly obscured sources have a significantly larger merger fraction with respect to other X-ray selected samples of AGN. Finally we discuss implications in the context of AGN/galaxy co-evolutionary models, and compare our results with the predictions of CXB synthesis models.Comment: Revised version after referee comments. Accepted for publication in Astronomy & Astrophysics on 25 November 2014. 23 pages, 2 tables, 16 figure

Cold gas in massive early-type galaxies: The case of NGC 1167

We present a study of the morphology and kinematics of the neutral hydrogen in the gas-rich (M_HI=1.5x10^{10}Msun), massive early-type galaxy NGC 1167, which was observed with the Westerbork Synthesis Radio Telescope (WSRT). The HI is located in a 160kpc disk (~3xD_25) and has low surface density (<2Msun pc^{-2}). The disk shows regular rotation for r<65kpc but several signs of recent and ongoing interaction and merging with fairly massive companions are observed. No population of cold gas clouds is observed - in contrast to what is found in some spiral galaxies. This suggests that currently the main mechanism bringing in cold gas to the disk is the accretion of fairly massive satellite galaxies, rather than the accretion of a large number of small gas clumps. NGC 1167 is located in a (gas-) rich environment: we detect eight companions with a total HI mass of ~6x10^9Msun within a projected distance of 350kpc. Deep optical images show a disrupted satellite at the northern edge of the HI disk. The observed rotation curve shows a prominent bump of about 50km/s (in the plane of the disk) at r=1.3xR_25. This feature in the rotation curve occurs at the radius where the HI surface density drops significantly and may be due to large-scale streaming motions in the disk. We suspect that both the streaming motions and the HI density distribution are the result of the interaction/accretion with the disrupted satellite. Like in other galaxies with wiggles and bumps in the rotation curve, HI scaling describes the observed rotation curve best. We suggest that interactions create streaming motions and features in the HI density distribution and that this is the reason for the success of HI scaling in fitting such rotation curves.Comment: 17 pages, 11 figures; A&A in pres

Hard X-ray Variability of AGN

Aims: Active Galactic Nuclei are known to be variable throughout the electromagnetic spectrum. An energy domain poorly studied in this respect is the hard X-ray range above 20 keV. Methods: The first 9 months of the Swift/BAT all-sky survey are used to study the 14 - 195 keV variability of the 44 brightest AGN. The sources have been selected due to their detection significance of >10 sigma. We tested the variability using a maximum likelihood estimator and by analysing the structure function. Results: Probing different time scales, it appears that the absorbed AGN are more variable than the unabsorbed ones. The same applies for the comparison of Seyfert 2 and Seyfert 1 objects. As expected the blazars show stronger variability. 15% of the non-blazar AGN show variability of >20% compared to the average flux on time scales of 20 days, and 30% show at least 10% flux variation. All the non-blazar AGN which show strong variability are low-luminosity objects with L(14-195 keV) < 1E44 erg/sec. Conclusions: Concerning the variability pattern, there is a tendency of unabsorbed or type 1 galaxies being less variable than the absorbed or type 2 objects at hardest X-rays. A more solid anti-correlation is found between variability and luminosity, which has been previously observed in soft X-rays, in the UV, and in the optical domain.Comment: 9 pages, 7 figures, accepted for publication in A&