Gap and out-gap breathers in a binary modulated discrete nonlinear Schr\"odinger model

We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of 'exchange of stability' between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.Comment: 17 pages, 12 figures, submitted to Eur. Phys. J.

Tracing the atomic nitrogen abundance in star-forming regions with ammonia deuteration

Partitioning of elemental nitrogen in star-forming regions is not well constrained. Most nitrogen is expected to be partitioned among atomic nitrogen, molecular nitrogen (N2), and icy N-bearing molecules, such as ammonia (NH3) and N2. Atomic nitrogen is not directly observable in the cold gas. In this paper, we propose an indirect way to constrain the amount of atomic nitrogen in the cold gas of star-forming clouds, via deuteration in ammonia ice, the [ND2H/NH2D]/[NH2D/NH3] ratio. Using gas-ice astrochemical simulations, we show that if atomic nitrogen remains as the primary reservoir of nitrogen during cold ice formation stages, the [ND2H/NH2D]/[NH2D/NH3] ratio is close to the statistical value of 1/3 and lower than unity, whereas if atomic nitrogen is largely converted into N-bearing molecules, the ratio should be larger than unity. Observability of ammonia isotopologues in the inner hot regions around low-mass protostars, where ammonia ice has sublimated, is also discussed. We conclude that the [ND2H/NH2D]/[NH2D/NH3] ratio can be quantified using a combination of VLA and ALMA observations with reasonable integration times, at least toward IRAS 16293-2422 where high molecular column densities are expected.Comment: Accepted for publication in MNRAS, 12 pages, 9 figures, 1 Tabl

Quasiperiodic localized oscillating solutions in the discrete nonlinear Schr\"odinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schr\"odinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.Comment: 4 pages, 4 figures, to be published in Phys. Rev. E. Revised version: change of title, added Figs. 1(b),(c), 4 new references + minor clarification

An analogue of the Magnus problem for associative algebras

We prove an analogue of the Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by n+k generators and k relations and has an n-element system of generators, then this algebra is a free algebra of rank n

Warm water deuterium fractionation in IRAS 16293-2422 - The high-resolution ALMA and SMA view

Measuring the water deuterium fractionation in the inner warm regions of low-mass protostars has so far been hampered by poor angular resolution obtainable with single-dish ground- and space-based telescopes. Observations of water isotopologues using (sub)millimeter wavelength interferometers have the potential to shed light on this matter. Observations toward IRAS 16293-2422 of the 5(3,2)-4(4,1) transition of H2-18O at 692.07914 GHz from Atacama Large Millimeter/submillimeter Array (ALMA) as well as the 3(1,3)-2(2,0) of H2-18O at 203.40752 GHz and the 3(1,2)-2(2,1) transition of HDO at 225.89672 GHz from the Submillimeter Array (SMA) are presented. The 692 GHz H2-18O line is seen toward both components of the binary protostar. Toward one of the components, "source B", the line is seen in absorption toward the continuum, slightly red-shifted from the systemic velocity, whereas emission is seen off-source at the systemic velocity. Toward the other component, "source A", the two HDO and H2-18O lines are detected as well with the SMA. From the H2-18O transitions the excitation temperature is estimated at 124 +/- 12 K. The calculated HDO/H2O ratio is (9.2 +/- 2.6)*10^(-4) - significantly lower than previous estimates in the warm gas close to the source. It is also lower by a factor of ~5 than the ratio deduced in the outer envelope. Our observations reveal the physical and chemical structure of water vapor close to the protostars on solar-system scales. The red-shifted absorption detected toward source B is indicative of infall. The excitation temperature is consistent with the picture of water ice evaporation close to the protostar. The low HDO/H2O ratio deduced here suggests that the differences between the inner regions of the protostars and the Earth's oceans and comets are smaller than previously thought.Comment: Accepted for publication in Astronomy & Astrophysic

How training and testing histories affect generalization: a test of simple neural networks

We show that a simple network model of associative learning can\ud reproduce three findings that arise from particular training and\ud testing procedures in generalization experiments: the effect of 1)\ud ``errorless learning'' and 2) extinction testing on peak shift, and\ud 3) the central tendency effect. These findings provide a true test\ud of the network model, which was developed to account for other\ud penhomena, and highlight the potential of neural networks to study\ud phenomena that depend on sequences of experiences with many stimuli.\ud Our results suggest that at least some such phenomena, e.g.,\ud stimulus range effects, may derive from basic mechanisms of\ud associative memory rather than from more complex memory processes

Discrete Darboux transformation for discrete polynomials of hypergeometric type

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

Atom-atom correlations and relative number squeezing in dissociation of spatially inhomogeneous molecular condensates

We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.Comment: Minor corrections, final published versio

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.Comment: 19 pages, 4 figure

Existence of the Stark-Wannier quantum resonances

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.Comment: 30 pages, 1 figur