48,600 research outputs found

    Slowly varying control parameters, delayed bifurcations and the stability of spikes in reaction-diffusion systems

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    We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of ODE's in [P.Mandel, T.Erneux, J.Stat.Phys, 1987]. It was found that the instability would not be fully realized until the system had entered well into the unstable regime. The bifurcation is said to have been "delayed" relative to the threshold value computed directly from a linear stability analysis. In contrast, we analyze the delay effect in systems of PDE's. In particular, for spike solutions of singularly perturbed generalized Gierer-Meinhardt (GM) and Gray-Scott (GS) models, we analyze three examples of delay resulting from slow passage into regimes of oscillatory and competition instability. In the first example, for the GM model on the infinite real line, we analyze the delay resulting from slowly tuning a control parameter through a Hopf bifurcation. In the second example, we consider a Hopf bifurcation on a finite one-dimensional domain. In this scenario, as opposed to the extrinsic tuning of a system parameter through a bifurcation value, we analyze the delay of a bifurcation triggered by slow intrinsic dynamics of the PDE system. In the third example, we consider competition instabilities of the GS model triggered by the extrinsic tuning of a feed rate parameter. In all cases, we find that the system must pass well into the unstable regime before the onset of instability is fully observed, indicating delay. We also find that delay has an important effect on the eventual dynamics of the system in the unstable regime. We give analytic predictions for the magnitude of the delays as obtained through analysis of certain explicitly solvable nonlocal eigenvalue problems. The theory is confirmed by numerical solutions of the full PDE systems.Comment: 31 pages, 20 figures, submitted to Physica D: Nonlinear Phenomen

    Ecologic Relationships Between Bacteria and Algae in Mass Culture

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    Ecological relationships between bacteria and algae in mass cultur

    Highly Ionised Gas as a Diagnostic of the Inner NLR

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    The spectra of AGN from the ultraviolet to the near infrared, exhibit emission lines covering a wide range of ionisation states, from neutral species such as [O I] 6300A, up to [Fe XIV] 5303A. Here we report on some recent studies of the properties of highly ionised lines (HILs), plus two case studies of individual objects. Future IFU observations at high spatial and good spectral resolution, will probe the excitation and kinematics of the gas in the zone between the extended NLR and unresolved BLR. Multi-component SED fitting can be used to link the source of photoionisation with the strengths and ratios of the HILs.Comment: Proceedings of the IAU Symposium: Co-evolution of Central Black Holes and Galaxie

    Remote sensing of changes in morphology and physiology of trees under stress Annual progress report

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    Remote sensing of morphological and physiological changes in trees under stres

    Strong variability of the coronal line region in NGC 5548

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    We present the second extensive study of the coronal line variability in an active galaxy. Our data set for the well-studied Seyfert galaxy NGC 5548 consists of five epochs of quasi-simultaneous optical and near-infrared spectroscopy spanning a period of about five years and three epochs of X-ray spectroscopy overlapping in time with it. Whereas the broad emission lines and hot dust emission varied only moderately, the coronal lines varied strongly. However, the observed high variability is mainly due to a flux decrease. Using the optical [FeVII] and X-ray OVII emission lines we estimate that the coronal line gas has a relatively low density of n~10^3/cm^3 and a relatively high ionisation parameter of log U~1. The resultant distance of the coronal line gas from the ionising source of about eight light years places this region well beyond the hot inner face of the dusty torus. These results imply that the coronal line region is an independent entity. We find again support for the X-ray heated wind scenario of Pier & Voit; the increased ionising radiation that heats the dusty torus also increases the cooling efficiency of the coronal line gas, most likely due to a stronger adiabatic expansion. The much stronger coronal line variability of NGC 5548 relative to that of NGC 4151 can also be explained within this picture. NGC 5548 has much stronger coronal lines relative to the low ionisation lines than NGC 4151 indicating a stronger wind, in which case a stronger adiabatic expansion of the gas and so fading of the line emission is expected.Comment: 10 pages, 6 figures; accepted for publication in MNRAS. arXiv admin note: substantial text overlap with arXiv:1501.0292

    Variability of the coronal line region in NGC 4151

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    We present the first extensive study of the coronal line variability in an active galaxy. Our data set for the nearby source NGC 4151 consists of six epochs of quasi-simultaneous optical and near-infrared spectroscopy spanning a period of about eight years and five epochs of X-ray spectroscopy overlapping in time with it. None of the coronal lines showed the variability behaviour observed for the broad emission lines and hot dust emission. In general, the coronal lines varied only weakly, if at all. Using the optical [Fe VII] and X-ray O VII emission lines we estimate that the coronal line gas has a relatively low density of n~10^3 cm^-3 and a relatively high ionisation parameter of log U~1. The resultant distance of the coronal line gas from the ionising source is about two light years, which puts this region well beyond the hot inner face of the obscuring dusty torus. The high ionisation parameter implies that the coronal line region is an independent entity rather than part of a continuous gas distribution connecting the broad and narrow emission line regions. We present tentative evidence for the X-ray heated wind scenario of Pier & Voit. We find that the increased ionising radiation that heats the dusty torus also increases the cooling efficiency of the coronal line gas, most likely due to a stronger adiabatic expansion.Comment: 12 pages, 9 figures; accepted by MNRA

    Origin and roles of a strong electron-phonon interaction in cuprate oxide superconductors

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    A strong electron-phonon interaction arises from the modulation of the superexchange interaction by phonons. As is studied in Phys. Rev. B 70, 184514 (2004), Cu-O bond stretching modes can be soft around (pm pi/a, 0) and (0, pm pi/a), with a the lattice constant of CuO_2 planes. In the critical region of SDW, where antiferromagnetic spin fluctuations are developed around nesting wave numbers Q of the Fermi surface, the stretching modes can also be soft around 2Q. Almost symmetric energy dependences of the 2Q component of the density of states, which are observed in the so called stripe and checker-board states, cannot be explained by CDW with 2Q following the complete softening of the 2Q modes, but they can be explained by a second-harmonic effect of SDW with Q. The strong electron-phonon interaction can play no or only a minor role in the occurrence of superconductivity.Comment: 5 pages, 1 fugur

    Matrix Big Brunch

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    Following the holographic description of linear dilaton null Cosmologies with a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and Verlinde, we propose an extended background describing a Universe including both Big Bang and Big Crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using Matrix String Theory. We provide a simple theory capable of describing the complete evolution of this closed Universe.Comment: 15 pages, no figures. References adde
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