Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution

Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (twodimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that “drops are (hierarchically) clustered” and that “inhomogeneity in rain is likely to extend down to millimeter scales”. Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression ( r2−8r3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells.Postprint (published version

Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

A Dust-Penetrated Classification Scheme for Bars as Inferred from their Gravitational Force Fields

The division of galaxies into ``barred'' (SB) and ``normal'' (S) spirals is a fundamental aspect of the Hubble galaxy classification system. This ``tuning fork'' view was revised by de Vaucouleurs, whose classification volume recognized apparent ``bar strength'' (SA, SAB, SB) as a continuous property of galaxies called the ``family''. However, the SA, SAB, and SB families are purely visual judgments that can have little bearing on the actual bar strength in a given galaxy. Until very recently, published bar judgments were based exclusively on blue light images, where internal extinction or star formation can either mask a bar completely or give the false impression of a bar in a nonbarred galaxy. Near-infrared camera arrays, which principally trace the old stellar populations in both normal and barred galaxies, now facilitate a quantification of bar strength in terms of their gravitational potentials and force fields. In this paper, we show that the maximum value, Qb, of the ratio of the tangential force to the mean radial force is a quantitative measure of the strength of a bar. Qb does not measure bar ellipticity or bar shape, but rather depends on the actual forcing due to the bar embedded in its disk. We show that a wide range of true bar strengths characterizes the category ``SB'', while de Vaucouleurs category ``SAB'' corresponds to a much narrower range of bar strengths. We present Qb values for 36 galaxies, and we incorporate our bar classes into a dust-penetrated classification system for spiral galaxies.Comment: Accepted for publication in the Astrophysical Journal (LaTex, 30 pages + 3 figures); Figs. 1 and 3 are in color and are also available at http://bama.ua.edu/~rbuta/bars

The Eastern Arm of M83 Revisited: High-Resolution Mapping of 12CO 1-0 Emission

We have used the Owens Valley Millimeter Array to map 12CO (J=1-0) along a 3.5 kpc segment of M83's eastern spiral arm at resolutions of 6.5"x3.5", 10", and 16". The CO emission in most of this segment lies along the sharp dust lane demarking the inner edge of the spiral arm, but beyond a certain point along the arm the emission shifts downstream from the dust lane to become better aligned with the young stars seen in blue and H-beta images. This morphology resembles that of the western arm of M100. Three possibilities, none of which is wholly satisfactory, are considered to explain the deviation of the CO arm from the dust lane: heating of the CO by UV radiation from young stars, heating by low-energy cosmic rays, and a molecular medium consisting of two (diffuse and dense) components which react differently to the density wave. Regardless, the question of what CO emission traces along this spiral arm is a complicated one. Strong tangential streaming is observed where the arm crosses the kinematic major axis of the galaxy, implying that the shear becomes locally prograde in the arms. Inferred from the streaming is a very high gas surface density of about 230 solar masses/pc**2 and an arm-interarm contrast greater than 2.3 in the part of the arm near the major axis. Using two different criteria, we find that the gas at this location is well above the threshold for gravitational instability -- much more clearly so than in either M51 or M100.Comment: Accepted for publication in ApJ. 25 pages, 5 figures. Manuscript in LaTeX, figures in pdf. Fig 3 in colo

HII regions in spiral galaxies: Size distribution, luminosity function, and new isochrone diagnostics of density wave kinematics

We investigate the relationship of the HII region luminosity function (HII LF) to the HII region size distribution and density wave triggering in grand-design spiral galaxies. We suggest that the differential nebular size distribution is described by a power law of slope ~ -4, with flattening at radii below ~ 130 pc. This contrasts with the conventional exponential description, but it is physically and quantitatively consistent with the typical observed value of -2 for the HII LF slope. We have developed an interactive code that computes spatial isochrones for the evolving loci of spiral density waves in disk galaxies. This allows comparison of the nebular spatial distribution with the spatial isochrones for simple rotation curve parameters. Our comparisons for four grand-design galaxies suggest that the corotation radius r_co coincides with the outer ends of the star-forming arms. This value for r_co yields the best spatial correspondence between the HII regions and the isochrones, and also appears to yield a coincidence between the Inner Lindblad Resonance with the radial onset of star formation in the arms. Thus, we suggest that isochrones offer a new, simple, and effective technique for determining r_co, and thus the spiral pattern speed. However, application of the isochrones also demonstrates that evolution of the nebular population is difficult to spatially isolate in these galaxies.Comment: 15 pp, 8 figs, uses emulateapj. Accepted to A

Criteri topologici per l'ottimizzazione sicura di reazioni potenzialmente fuggitive

In this work, optimization procedures, particurarly suitable for potentially runaway reactions carried out in indirectly cooled semibatch reactors operated in isoperibolic temperature control mode, have been developed. Such optimization procedures based on a particular criterion, referred to as "topological", in order tio select a set of operating conditions which is able of ensuring both process thermochemical stability and high productivity and selectivity with respect the desired product. This topological approach has been validated both experimentally and theoretically by studing kinetic schemes characterized by different complexity degrees. As an example, the relevant case study of the free radical emulsion polymerization of vinyl acetate has been analyzed and reported

Removal of a mixture of oxygenated VOCs in a biotrickling filter

[Abstract] Laboratory scale-studies on the biodegradation of a 1:1:1 wt mixture of three oxygenated volatile organic compounds (VOCs), ethanol, ethyl acetate and methyl-ethyl ketone (MEK) in a biotrickling filter were carried out using two identically sized columns, filled with different polypropylene rings. The reactors were seeded with a two-month preconditioned culture from activated sludge. The performance of the biotrickling filters was examined for a continuous period of 4 months at VOC concentration from 125 mg-C/m3 to 550 mg-C/m3 and at gas flow rates of around 1.0 m3/h, 2.0 m3/h and 4.6 m3/h, which correspond to gas empty bed residence times (EBRT) of 68 s, 33 s and 16 s, respectively. Similar performance was obtained for both supports. Intermittent flow rate of trickling liquid was shown as beneficial to improve the removal efficiency of the system. A stratification in the substrate consumption was observed from gas composition profiles, with MEK % in the emission greater than 78%. Continuous VOC feeding resulted in an excessive accumulation of biomass and high pressure drop was developed in less than 20-30 days of operation. Intermittent VOC loading with night and weekend feed cut-off periods passing dried air, but without water addition, was shown as a successful operational mode to control the biofilm thickness. In this case, operation at high inlet loads was extended for more than 50 days maintaining high removal efficiencies and low pressure drops

Dark matter within high surface brightness spiral galaxies

We present results from a detailed dynamical analysis of five high surface brightness, late type spirals, studied with the aim to quantify the luminous-to-dark matter ratio inside their optical radii. The galaxies' stellar light distribution and gas kinematics have been observed and compared to hydrodynamic gas simulations, which predict the 2D gas dynamics arising in response to empirical gravitational potentials, which are combinations of differing stellar disk and dark halo contributions. The gravitational potential of the stellar disk was derived from near-infrared photometry, color-corrected to constant (M/L); the dark halo was modelled by an isothermal sphere with a core. Hydrodynamic gas simulations were performed for each galaxy for a sequence of five different mass fractions of the stellar disk and for a wide range of spiral pattern speeds. These two parameters mainly determine the modelled gas distribution and kinematics. The agreement between the non-axisymmetric part of the simulated and observed gas kinematics permitted us to conclude that the galaxies with the highest rotation velocities tend to possess near-maximal stellar disks. In less massive galaxies, with v_max<200 km/s, the mass of the dark halo at least equals the stellar mass within 2-3 R_disk. The simulated gas morphology provides a powerful tool to determine the dominant spiral pattern speed. The corotation radius for all galaxies was found to be constant at R_corotation ~ 3 R_disk and encloses the strong part of the stellar spiral in all cases.Comment: 28 pages, 7 figures; to appear in the Astrophysical Journal, Vol. 586, March 200