We show that, under a suitable assumption on the pressure tensor, the mass and momentum balance equations of hydrodynamical theory, introduced in the early 1980s by many authors to describe matrix separation, yield the equations of the Madelung fluid that are equivalent to the Schrödinger-like equation with logarithmic nonlinearity. This equation has solitary-waves solutions as required by many experimental volcanic models.
Abstract. We discuss an alternative approach to quintessence modifying the usual equation of state of the cosmological fluid in order to see if going further than the approximation of perfect fluid allows to better reproduce the available data. We consider a cosmological model comprising only two fluids, namely baryons (modelled as dust) and dark matter with a Van der Waals equation of state. First, the general features of the model are presented and then the evolution of the energy density, the Hubble parameter and the scale factor are determined showing that it is possible to obtain accelerated expansion choosing suitably the model parameters. We use the the data on the dimensionless coordinate distances to Type Ia supernovae and distant radio galaxies to see whether Van der Waals quintessence is viable to explain dark energy and to constrain its parameters. We then compare the model predictions with the estimated age of the universe and the position of the first three peaks of the anisotropy spectrum of the cosmic microwave background radiation.
IntroductionIn the last few years an increasing bulk of data have been accumulated favouring the scenario of a spatially flat universe dominated by some form of dark energy. A first strong evidence came from the Hubble diagram of type Ia supernovae (hereafter SNeIa) that turned out to be best fitted by spatially flat accelerating cosmological models † Present address :
[1] We study the volcanic tremor time series recorded by a broadband three-component seismic network installed at Stromboli volcano during 1997. By using decomposition methods in both frequency and time domains, we prove that Strombolian tremor can be described as a linear combination of nonlinear signals in time domain. These ''components'' are similar to those obtained for explosion quakes, with the only difference being the amplitude enhancement. We characterize each of these nonlinear signals both in terms of their wavefield properties as well as dynamic systems. Moreover, we take into account the complex processes of magma flow and turbulent degassing, looking at time and amplitude modulation of tremor on a suitable scale. The distribution of tremor amplitudes is Gaussian while the intertimes between the maxima in a suitable scale are described by a Poisson clustered process. Starting from these analyses, a first approximate model for volcanic tremor field can be deduced. The recorded signals, i.e., the elastic vibrations at a point, can be described by a nonlinear equation which gives limit cycles (different observed ''nonlinear modes''). This equation is governed by a time-dependent threshold which represents the variability of bubble flux. We take into account some inelasticity in the medium perturbing the elastic potential with a Gaussian function on a suitable scale. It acts as a radiance function modulating the frequency of the limit cycle. This proposed model is able to reproduce waveform, Fourier spectrum, and phase space dimension of one of the extracted nonlinear wave packets.
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