Solar Atmospheric Oscillations and the Chromospheric Magnetic Topology

We investigate the oscillatory properties of the quiet solar chromosphere in relation to the underlying photosphere, with particular regard to the effects of the magnetic topology. We perform a Fourier analysis on a sequence of line-of-sight velocities measured simultaneously in a photospheric (Fe I 709.0 nm) and a chromospheric line (Ca II 854.2 nm). The velocities were obtained from full spectroscopic data acquired at high spatial resolution with the Interferometric BIdimensional Spectrometer (IBIS). The field of view encompasses a full supergranular cell, allowing us to discriminate between areas with different magnetic characteristics. We show that waves with frequencies above the acoustic cut-off propagate from the photosphere to upper layers only in restricted areas of the quiet Sun. A large fraction of the quiet chromosphere is in fact occupied by ``magnetic shadows'', surrounding network regions, that we identify as originating from fibril-like structures observed in the core intensity of the Ca II line. We show that a large fraction of the chromospheric acoustic power at frequencies below the acoustic cut-off, residing in the proximity of the magnetic network elements, directly propagates from the underlying photosphere. This supports recent results arguing that network magnetic elements can channel low-frequency photospheric oscillations into the chromosphere, thus providing a way to input mechanical energy in the upper layers.Comment: 4 pages, 3 figure, A&A Letters in pres

The Kato square root problem on vector bundles with generalised bounded geometry

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.Comment: Slight technical modification of the notion of "GBG constant section" on page 7, and a few technical modifications to Proposition 8.4, 8.6, 8.

Two-fluid matter-quintessence FLRW models: energy transfer and the equation of state of the universe

Recent observations support the view that the universe is described by a FLRW model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w \leq -1/3$ at the present epoch. There are several theoretical suggestions for the cosmological $\Lambda$ component and for the particular form of the energy transfer between this dark energy and matter. This gives a strong motive for a systematic study of general properties of two-fluid FLRW models. We consider a combination of one perfect fluid, which is quintessence with negative pressure ($p_Q = w\epsilon_Q$), and another perfect fluid, which is a mixture of radiation and/or matter components with positive pressure ($p = \beta \epsilon_m$), which define the associated one-fluid model ($p = \gamma \epsilon$). We introduce a useful classification which contains 4 classes of models defined by the presence or absence of energy transfer and by the stationarity ($w = const.$ and $\beta = const.$) or/and non stationarity ($w$ or $\beta$ time dependent) of the equations of state. It is shown that, for given $w$ and $\beta$, the energy transfer defines $\gamma$ and, therefore, the total gravitating mass and dynamics of the model. We study important examples of two-fluid FLRW models within the new classification. The behaviour of the energy content, gravitating mass, pressure, and the energy transfer are given as functions of the scale factor. We point out three characteristic scales, $a_E$, $a_{\cal P}$ and $a_{\cal M}$, which separate periods of time in which quintessence energy, pressure and gravitating mass dominate. Each sequence of the scales defines one of 6 evolution types

Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions

A simple and commonly employed approximate technique with which one can examine spatially disordered systems when strong electronic correlations are present is based on the use of real-space unrestricted self-consistent Hartree-Fock wave functions. In such an approach the disorder is treated exactly while the correlations are treated approximately. In this report we critique the success of this approximation by making comparisons between such solutions and the exact wave functions for the Anderson-Hubbard model. Due to the sizes of the complete Hilbert spaces for these problems, the comparisons are restricted to small one-dimensional chains, up to ten sites, and a 4x4 two-dimensional cluster, and at 1/2 filling these Hilbert spaces contain about 63,500 and 166 million states, respectively. We have completed these calculations both at and away from 1/2 filling. This approximation is based on a variational approach which minimizes the Hartree-Fock energy, and we have completed comparisons of the exact and Hartree-Fock energies. However, in order to assess the success of this approximation in reproducing ground-state correlations we have completed comparisons of the local charge and spin correlations, including the calculation of the overlap of the Hartree-Fock wave functions with those of the exact solutions. We find that this approximation reproduces the local charge densities to quite a high accuracy, but that the local spin correlations, as represented by , are not as well represented. In addition to these comparisons, we discuss the properties of the spin degrees of freedom in the HF approximation, and where in the disorder-interaction phase diagram such physics may be important

The U-band Galaxy Luminosity Function of Nearby Clusters

Despite the great potential of the U-band galaxy luminosity function (GLF) to constrain the history of star formation in clusters, to clarify the question of variations of the GLF across filter bands, to provide a baseline for comparisons to high-redshift studies of the cluster GLF, and to estimate the contribution of bound systems of galaxies to the extragalactic near-UV background, determinations have so far been hampered by the generally low efficiency of detectors in the U-band and by the difficulty of constructing both deep and wide surveys. In this paper, we present U-band GLFs of three nearby, rich clusters to a limit of M_U=-17.5 (M*_U+2). Our analysis is based on a combination of separate spectroscopic and R-band and U-band photometric surveys. For this purpose, we have developed a new maximum-likelihood algorithm for calculating the luminosity function that is particularly useful for reconstructing the galaxy distribution function in multi-dimensional spaces (e.g., the number of galaxies as a simultaneous function of luminosity in different filter bands, surface brightness, star formation rate, morphology, etc.), because it requires no prior assumptions as to the shape of the distribution function. The composite luminosity function can be described by a Schechter function with characteristic magnitude M*_U=-19.82+/-0.27 and faint end slope alpha_U=-1.09+/-0.18. The total U-band GLF is slightly steeper than the R-band GLF, indicating that cluster galaxies are bluer at fainter magnitudes. Quiescent galaxies dominate the cumulative U-band flux for M_U<-14. The contribution of galaxies in nearby clusters to the U-band extragalactic background is <1% Gyr^-1 for clusters of masses ~3*10^14 to 2*10^15 M_solar.Comment: 44 pages, 11 figures, accepted for publication in Ap

Experimental determination of the quasi-projectile mass with measured neutrons

The investigation of the isospin dependence of multifragmentation reactions relies on precise reconstruction of the fragmenting source. The criteria used to assign free emitted neutrons, detected with the TAMU Neutron Ball, to the quasi-projectile source are investigated in the framework of two different simulation codes. Overall and source-specific detection efficiencies for multifragmentation events are found to be model independent. The equivalence of the two different methods used to assign experimentally detected charged particles and neutrons to the emitting source is shown. The method used experimentally to determine quasi-projectile emitted free neutron multiplicity is found to be reasonably accurate and sufficiently precise as to allow for the study of well-defined quasi-projectile sources.Comment: 10 pages, 8 figures. To be submitted to Nucl. Instr. and Meth.

Millimeter Wave Localization: Slow Light and Enhanced Absorption

We exploit millimeter wave technology to measure the reflection and transmission response of random dielectric media. Our samples are easily constructed from random stacks of identical, sub-wavelength quartz and Teflon wafers. The measurement allows us to observe the characteristic transmission resonances associated with localization. We show that these resonances give rise to enhanced attenuation even though the attenuation of homogeneous quartz and Teflon is quite low. We provide experimental evidence of disorder-induced slow light and superluminal group velocities, which, in contrast to photonic crystals, are not associated with any periodicity in the system. Furthermore, we observe localization even though the sample is only about four times the localization length, interpreting our data in terms of an effective cavity model. An algorithm for the retrieval of the internal parameters of random samples (localization length and average absorption rate) from the external measurements of the reflection and transmission coefficients is presented and applied to a particular random sample. The retrieved value of the absorption is in agreement with the directly measured value within the accuracy of the experiment.Comment: revised and expande