Soliton dynamics in damped and forced Boussinesq equations

We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case

Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry

We discuss the effect of small perturbation on nodeless solutions of the nonlinear \Schrodinger\ equation in 1+1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier [Phys.~Rev.~E 92, 042901 (2015)]. In particular we consider the nonlinear partial differential equation \{ \, \rmi \, \partial_t + \partial_x^2 + g |\psi(x,t)|^2 - V^{+}(x) \, \} \, \psi(x,t) = 0, where V^{+}(x) = \qty( -b^2 - m^2 + 1/4 ) \, \sech^2(x) - 2 i \, m \, b \, \sech(x) \, \tanh(x) represents the complex potential. Here we study the perturbations as a function of $b$ and $m$ using a variational approximation based on a dissipation functional formalism. We compare the result of this variational approach with direct numerical simulation of the equations. We find that the variational approximation works quite well at small and moderate values of the parameter $b m$ which controls the strength of the imaginary part of the potential. We also show that the dissipation functional formalism is equivalent to the generalized traveling wave method for this type of dissipation.Comment: 18 pages, 6 figure

Electron neutrino tagging through tertiary lepton detection

We discuss an experimental technique aimed at tagging electron neutrinos in multi-GeV artificial sources on an event-by-event basis. It exploits in a novel manner calorimetric and tracking technologies developed in the framework of the LHC experiments and of rare kaon decay searches. The setup is suited for slow-extraction, moderate power beams and it is based on an instrumented decay tunnel equipped with tagging units that intercept secondary and tertiary leptons from the bulk of undecayed \pi^+ and protons. We show that the taggers are able to reduce the \nue contamination originating from K_e3 decays by about one order of magnitude. Only a limited suppression (~60%) is achieved for \nue produced by the decay-in-flight of muons; for low beam powers, similar performance as for K_e3 can be reached supplementing the tagging system with an instrumented beam dump.Comment: 19 pages, 7 figures; minor changes, version to appear in EPJ

Growing supermassive black holes in the late stages of galaxy mergers are heavily obscured

Mergers of galaxies are thought to cause significant gas inflows to the inner parsecs, which can activate rapid accretion onto supermassive black holes (SMBHs), giving rise to Active Galactic Nuclei (AGN). During a significant fraction of this process, SMBHs are predicted to be enshrouded by gas and dust. Studying 52 galactic nuclei in infrared-selected local Luminous and Ultra-luminous infrared galaxies in different merger stages in the hard X-ray band, where radiation is less affected by absorption, we find that the amount of material around SMBHs increases during the last phases of the merger. We find that the fraction of Compton-thick (CT, $N_{\rm\,H}\geq 10^{24}\rm\,cm^{-2}$) AGN in late merger galaxies is higher ($f_{\rm\,CT}=65^{+12}_{-13}\%$) than in local hard X-ray selected AGN ($f_{\rm\,CT}=27\pm 4\%$), and that obscuration reaches its maximum when the nuclei of the two merging galaxies are at a projected distance of $D_{12}\simeq0.4-10.8$ kiloparsecs ($f_{\rm\,CT}=77_{-17}^{+13}\%$). We also find that all AGN of our sample in late merger galaxies have $N_{\rm\,H}> 10^{23}\rm\,cm^{-2}$, which implies that the obscuring material covers $95^{+4}_{-8}\%$ of the X-ray source. These observations show that the material is most effectively funnelled from the galactic scale to the inner tens of parsecs during the late stages of galaxy mergers, and that the close environment of SMBHs in advanced mergers is richer in gas and dust with respect to that of SMBHs in isolated galaxies, and cannot be explained by the classical AGN unification model in which the torus is responsible for the obscuration.Comment: Final version matching the article published in MNRAS - 30 pages, 16 figure

Equivalent layered models for functionally graded plates

Functionally graded plates whose material properties vary continuously through the thickness are modelled as exactly equivalent plates composed of up to four isotropic layers. Separate models are derived for analysis using classical plate theory, first-order and higher-order shear deformation theory. For cases where Poisson’s ratio varies through the thickness, the integrations required to obtain the membrane, coupling and out-of-plane stiffness matrices are performed accurately using a series solution. The model is verified by comparison with well converged solutions from approximate models in which the plate is divided into many isotropic layers. Critical buckling loads and undamped natural frequencies are found for a range of illustrative examples

Swallowing Activity Assessed by Ambulatory Impedance-pH Monitoring Predicts Awake and Asleep Periods at Night

Introduction: Voluntary muscle activity, including swallowing, decreases during the night. The association between nocturnal awakenings and swallowing activity is under-researched with limited information on the frequency of swallows during awake and asleep periods. Aim: The aim of this study was to assess nocturnal swallowing activity and identify a cut-off predicting awake and asleep periods. Methods: Patients undergoing impedance-pH monitoring as part of GERD work-up were asked to wear a wrist activity detecting device (Actigraph®) at night. Swallowing activity was quantified by analysing impedance changes in the proximal esophagus. Awake and asleep periods were determined using a validated scoring system (Sadeh algorithm). Receiver operating characteristics (ROC) analyses were performed to determine sensitivity, specificity and accuracy of swallowing frequency to identify awake and asleep periods. Results: Data from 76 patients (28male, 48 female; mean age 56±15years) were included in the analysis. The ROC analysis found that 0.33sw/min (i.e. one swallow every 3min) had the optimal sensitivity (78%) and specificity (76%) to differentiate awake from asleep periods. A swallowing frequency of 0.25sw/min (i.e. one swallow every 4min) was 93% sensitive and 57% specific to identify awake periods. A swallowing frequency of 1sw/min was 20% sensitive but 96% specific in identifying awake periods. Summary and Conclusion: Impedance-pH monitoring detects differences in swallowing activity during awake and asleep periods. Swallowing frequency noticed during ambulatory impedance-pH monitoring can predict the state of consciousness during nocturnal period