Localized modes and bistable scattering in nonlinear network junctions

We study the properties of junctions created by crossing of N identical branches of linear discrete networks. We reveal that for N>2 such a junction creates a topological defect and supports two types of spatially localized modes. We analyze the wave scattering by the junction defect and demonstrate nonzero reflection for any set of parameters. If the junction is nonlinear, it is possible to achieve the maximum transmission for any frequency by tuning the intensity of the scattering wave. In addition, near the maximum transmission the system shows the bistable behaviour.Comment: 5 pages, 7 figures, submitted to Physical Review

Prediction of narrow N∗N^{*} and Λ∗\Lambda^* resonances with hidden charm above 4 GeV

The interaction between various charmed mesons and charmed baryons are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. Several meson-baryon dynamically generated narrow $N^*$ and $\Lambda^*$ resonances with hidden charm are predicted with mass above 4 GeV and width smaller than 100 MeV. The predicted new resonances definitely cannot be accommodated by quark models with three constituent quarks and can be looked for at the forthcoming PANDA/FAIR experiments.Comment: 4 pages, 3 figure

Fano resonance in quadratic waveguide arrays

We study resonant light scattering in arrays of channel optical waveguides where tunable quadratic nonlinearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for the first observation of Fano resonance in nonlinear optics.Comment: 3 pages, 3 figures, submitted to Optics Letters, slightly revise

Cultivation and anaerobic digestion of Scenedesmus spp. grown in a pilot-scale open raceway

Digestibility of a micro-algal mixture was evaluated by mesophilic anaerobic digestion in continuously-stirred tank reactors. The culture consisted primarily of Scenedesmus spp. continuously cultivated over a 6-month period in a 100 m2 raceway reactor instrumented to record pH, dissolved oxygen and temperature. The raceway received supplementary carbon in the form of flue gas from a diesel boiler (10% CO2) injected into a 1-m deep sump to control pH in the range 7.8–8.0. Dilution was optimised to biomass productivity and gave values of 10–15 and 20–25 g total suspended solids (TSS) m? 2 day? 1 in winter (December–February) and spring (April–May), respectively. The culture for the anaerobic digestion trial was harvested in February by centrifugation to give an algal paste containing 4.3% volatile solids (VS). Semi-continuous digestion at organic loading rates of 2.00, 2.75 and 3.50 g VS l? 1 day? 1 gave volumetric biogas productions of ~ 0.66, ~ 0.83 and ~ 0.99 l l? 1 day? 1, respectively. Specific methane yield ranged from 0.13 to 0.14 l CH4 g? 1 VSadded with biogas methane content ~ 62%. Overall the digestion process was stable, but only ~ 30% VS destruction was achieved indicating low biodegradability, due to the short retention times and the recalcitrant nature of this type of biomas

The γγ\gamma \gamma decay of the f0(1370)f_0(1370) and f2(1270)f_2(1270) resonances in the hidden gauge formalism

Using recent results obtained within the hidden gauge formalism for vector mesons, in which the $f_0(1370)$ and $f_2(1270)$ resonances are dynamically generated resonances from the $\rho \rho$ interaction, we evaluate the radiative decay of these resonances into $\gamma \gamma$. We obtain results for the width in good agreement with the experimental data for the $f_2(1270)$ state and a width about a factor five smaller for the $f_0(1370)$ resonance, which would agree with preliminary results from the Belle collaboration, hinting at an order of magnitude smaller width for this resonance than for the $f_2(1270)$.Comment: 7 pages, 9 figures, proof of gauge invariance adde

Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed

Comments on the dispersion relation method to vector-vector interaction

We study in detail the method proposed recently to study the vector-vector interaction using the $N/D$ method and dispersion relations, which concludes that, while for $J=0$, one finds bound states, in the case of $J=2$, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for $N$ and $D$ and a subtracted dispersion relation for $D$ is used, with subtractions made up to a polynomial of second degree in $s-s_\mathrm{th}$, matching the expression to $1-VG$ at threshold. We study this in detail for the $\rho - \rho$ interaction and to see the convergence of the method we make an extra subtraction matching $1-VG$ at threshold up to $(s-s_\mathrm{th})^3$. We show that the method cannot be used to extrapolate the results down to 1270 MeV where the $f_2(1270)$ resonance appears, due to the artificial singularity stemming from the "on shell" factorization of the $\rho$ exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the $\rho$, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the $(s-s_\mathrm{th})^2$ and $(s-s_\mathrm{th})^3$ expansions lead to a zero of $\mathrm{Re}\,D(s)$, at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large $\mathrm{Im}\,D(s)$ that we discuss is unphysical.Comment: 8 pages, 10 figures, 1 tabl

Hundreds of Low-Mass Active Galaxies in the Galaxy And Mass Assembly (GAMA) Survey

We present an entirely new sample of 388 low-mass galaxies ($M_\star \leq 10^{10} M_\odot$) that have spectroscopic signatures indicating the presence of massive black holes (BHs) in the form of active galactic nuclei (AGNs) or tidal disruption events (TDEs). Of these, 70 have stellar masses in the dwarf galaxy regime with $10^8 \lesssim M_\star/M_\odot \lesssim 10^{9.5}$. We identify the active galaxies by analyzing optical spectra of a parent sample of $\sim$23,000 low-mass emission-line galaxies in the Galaxy and Mass Assembly (GAMA) Survey Data Release 4, and employing four different diagnostics based on narrow emission line ratios and the detection of high-ionization coronal lines. We find that 47 of the 388 low-mass active galaxies exhibit broad H$\alpha$ in their spectra, corresponding to virial BH masses in the range $M_{\rm BH} \sim 10^{5.0-7.7} M_\odot$ with a median BH mass of $\langle M_{\rm BH}\rangle \sim 10^{6.2} M_\odot$. Our sample extends to higher redshifts ($z \le 0.3; \langle z \rangle=0.13$) than previous samples of AGNs in low-mass/dwarf galaxies based on Sloan Digital Sky Survey spectroscopy, which can be attributed to the spectroscopic limit of GAMA being $\sim 2$ magnitudes deeper. Moreover, our multi-diagnostic approach has revealed low-mass active galaxies spanning a wide range of properties, from blue star-forming dwarfs to luminous "miniquasars" powered by low-mass BHs. As such, this work has implications for BH seeding and AGN feedback at low masses.Comment: Accepted for publication in The Astrophysical Journa