5,148 research outputs found

    Levi harmonic maps of contact Riemannian manifolds

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    We study Levi harmonic maps i.e. C∞C^\infty solutions f:M→M′f : M \to M^\prime to \tau_\mathcal{H} (f) \equiv \mathr{trace}_{g} ( \Pi_\mathcal{H}\beta_f ) = 0, where (M,η,g)(M , \eta, g) is an (almost) contact (semi) Riemannian manifold, M′M^\prime is a (semi) Riemannian manifold, βf\beta_f is the second fundamental form of ff, and ΠHβf\Pi_\mathcal{H} \beta_f is the restriction of βf\beta_f to the Levi distribution H=Ker(η)\mathcal{H} = \mathrm{Ker}(\eta ). Many examples are exhibited e.g. the Hopf vector field on the unit sphere S2n+1S^{2n+1}, immersions of Brieskorn spheres, and the geodesic flow of the tangent sphere bundle over a Riemannnian manifold of constant curvature 11 are Levi harmonic maps. A CR map ff of contact (semi) Riemannian manifolds (with spacelike Reeb fields) is pseudoharmonic if and only if ff is Levi harmonic. We give a variational interpretation of Levi harmonicity. Any Levi harmonic morphism is shown to be a Levi harmonic map

    Visibility analysis of boundary layer transition

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    We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs are constructed from each time series. The latter are, thus, transformed into a geometrical object, whose main features can be explored using measures typical of network science that provide a reduced order representation of the underlying flow properties. Using these metrics, we observe the evolution of the flow from laminarity to turbulence and the effects exerted by the free-stream turbulence. Different from other methods requiring an extensive amount of spatiotemporal data (e.g., full velocity field) or a set of parameters and thresholds arbitrarily chosen by the user, the present network-based approach is able to identify the onset markers for transition by means of the streamwise velocity time-series alone. Published under an exclusive license by AIP Publishing

    Evaluating collapse fragility curves for existing buildings retrofitted using seismic isolation

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    Few studies have investigated so far the collapse capacity of buildings with base-isolation. In such studies, preliminary considerations have been drawn based on a number of assumptions regarding: (i) the methodology used for assessing the collapse capacity, (ii) the collapse conditions and failure modes assumed for both superstructure and isolation system, and (iii) the numerical modeling assumptions. The main results pointed out that the collapse conditions of base-isolated buildings may occur for intensity levels slightly higher than those associated with the design earthquake. In this paper, further developments are made through the use of enhanced models for the description of the behavior of a rubber-based isolation system and the assumption of more rational collapse conditions. Collapse fragility functions, in terms of mean and dispersion values, are proposed for two archetypes representative of existing buildings retrofitted using the seismic isolation technique. The collapse margin ratio (median collapse capacity Sa, C, namely the spectral acceleration associated to a probability of exceedance equal to 50%, divided by the design spectral acceleration at the collapse prevention limit state) has been evaluated for each examined case-study. Values ranging from 1.10 to 1.45 were found

    Radial evolution of the solar wind in pure high-speed streams: HELIOS revised observations

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    Spacecraft observations have shown that the proton temperature in the solar wind falls off with radial distance more slowly than expected for an adiabatic prediction. Usually, previous studies have been focused on the evolution of the solar-wind plasma by using the bulk speed as an order parameter to discriminate different regimes. In contrast, here, we study the radial evolution of pure and homogeneous fast streams (i.e. well-defined streams of coronal-hole plasma that maintain their identity during several solar rotations) by means of re-processed particle data, from the HELIOS satellites between 0.3 and 1 au. We have identified 16 intervals of unperturbed high-speed coronal-hole plasma, from three different sources and measured at different radial distances. The observations show that, for all three streams, (i) the proton density decreases as expected for a radially expanding plasma, unlike previous analysis that found a slower decrease; (ii) the magnetic field deviates from the Parker prediction, with the radial component decreasing more slowly and the tangential more quickly than expected; (iii) the double-adiabatic invariants are violated and an increase of entropy is observed; (iv) the collisional frequency is not constant, but decreases as the plasma travels away from the Sun. This work provides an insight into the heating problem in pure fast solar wind, fitting in the context of the next solar missions, and, especially for Parker Solar Probe, it enables us to predict the high-speed solar-wind environment much closer to the Sun

    Performance analysis of peak tracking techniques for fiber Bragg grating interrogation systems

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    In this paper, we propose a spectral correlation-based technique for tracking the wavelength shift of a fiber Bragg grating. We compared this approach, by means of a Monte Carlo numerical simulation, to the typical peak tracking techniques applied in classic interrogation systems. As result, we obtained a considerable gain in terms of noise tolerance (about 20 dB), which can be further incremented by selecting large-bandwidth gratings. This permits to increase the power budget of a fiber Bragg grating interrogator without changing the optical layout, overcoming classical limitations of commercial and custom systems. Penalties due to the non-idealities have been evaluated through the same Monte Carlo approach. Finally, we discuss a practical application of the peak tracking techniques to a fiber Bragg grating-based weight sensor, in which we applied the spectral correlation to track both the Bragg wavelength position, spectral deformations due to high strain, and spectral non-linearity

    Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

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    Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

    Three-dimensional curvature homogeneous hypersurfaces

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    summary:This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers
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