1,158 research outputs found

    The Principle of Similitude in Biology: From Allometry to the Formulation of Dimensionally Homogenous `Laws'

    Full text link
    Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the Π\rm \Pi theorem (Vaschy 1892; Buckingham 1914). However, most relations in allometry do not satisfy this basic requirement, including the `3/4 Law' (Kleiber 1932) that relates the basal metabolic rate and body mass, which it is sometimes claimed to be the most fundamental biological rate (Brown et al. 2004) and the closest to a law in life sciences (West \& Brown 2004). Using the Π\rm \Pi theorem, here we show that it is possible to construct a unique homogeneous equation for the metabolic rates, in agreement with data in the literature. We find that the variations in the dependence of the metabolic rates on body mass are secondary, coming from variations in the allometric dependence of the heart frequencies. This includes not only different classes of animals (mammals, birds, invertebrates) but also different exercise conditions (basal and maximal). Our results demonstrate that most of the differences found in the allometric exponents (White et al. 2007) are due to compare incommensurable quantities and that our dimensionally homogenous formula, unify these differences into a single formulation. We discuss the ecological implications of this new formulation in the context of the Malthusian's, Fenchel's and the total energy consumed in a lifespan relations.Comment: A accepted for publication in Theoretical Ecology. Comments are welcome ([email protected]

    On the Fueling of Massive Black Holes and the Properties of their Host Spheroids

    Get PDF
    We study the relation between nuclear massive black holes and their host spheroid gravitational potential. Using simple models, we analyze how gas is expected to be transported in the nuclear regions of galaxies. When we couple it with the expected gas lifetime given by the Kennicutt-Schmidt Law, this naturally leads to the `M_BH - M_virial' and `M_BH - sigma' relations. We also numerically test, using AMR simulations, our simple models for the mass transport with satisfactory results.Comment: Reduced version that fit the 4-page limit. In press ApJ Letter

    Multiscale mass transport in z~6 galactic discs: fueling black holes

    Full text link
    By using AMR cosmological hydrodynamic N-body zoom-in simulations, with the RAMSES code, we studied the mass transport processes onto galactic nuclei from high redshift up to z6z\sim6. Due to the large dynamical range of the simulations we were able to study the mass accretion process on scales from 50[kpc]\sim50[kpc] to \sim few 1[pc]1[pc]. We studied the BH growth on to the galactic center in relation with the mass transport processes associated to both the Reynolds stress and the gravitational stress on the disc. Such methodology allowed us to identify the main mass transport process as a function of the scales of the problem. We found that in simulations that include radiative cooling and SNe feedback, the SMBH grows at the Eddington limit for some periods of time presenting fEDD0.5\langle f_{EDD}\rangle\approx 0.5 throughout its evolution. The α\alpha parameter is dominated by the Reynolds term, αR\alpha_R, with αR1\alpha_R\gg 1. The gravitational part of the α\alpha parameter, αG\alpha_G, has an increasing trend toward the galactic center at higher redshifts, with values αG1\alpha_G\sim 1 at radii <\sim few 101[pc] 10^1[pc] contributing to the BH fueling. In terms of torques, we also found that gravity has an increasing contribution toward the galactic center at earlier epochs with a mixed contribution above 100[pc]\sim 100 [pc]. This complementary work between pressure gradients and gravitational potential gradients allows an efficient mass transport on the disc with average mass accretion rates of the order \sim few 1[M/yr]1 [M_{\odot}/yr]. These level of SMBH accretion rates found in our cosmological simulations are needed in all models of SMBH growth that attempt to explain the formation of redshift 676-7 quasars

    Gravitational Fragmentation in Galaxy Mergers: A Stability Criteria

    Full text link
    We study the gravitational stability of gaseous streams in the complex environment of a galaxy merger, because mergers are known to be places of ongoing massive cluster formation and bursts of star formation. We find an analytic stability parameter for case of gaseous streams orbiting around the merger remnant. We test our stability criteria using hydrodynamical simulations of galaxy mergers, obtaining satisfactory results. We find that our criteria successfully predicts the streams that will be gravitationally unstable to fragment into clumps.Comment: 10 pages, 2 figures. After 2nd referee repor


    Get PDF
    The Luntian Multi-Purpose Cooperative located in Tiaong, Quezon, Philippines. The Luntian Multi-Purpose cooperative focuses more on feed production as well as hog fattening. The LMC applied the vertical integration to develop the cooperative. They have their members as their primary costumers of their feeds. The cooperative’s business activity includes also meat shop, granting of production loan, micro-finance, mobilization of saving deposits, aside from feed milling and hog fattening. Different agencies, industry organizations and private institutions provide trainings, seminars, assistance, as well as credit for the cooperative.The aims of the study was to determine the present and discuss a noteworthy business issue (s) of Luntian Multipurpose Cooperative, evaluate the business environment prevailing at a particular time of this case , assess the cooperative’s performance in terms of the four business functions , define the problem relevant to the business issue(s) being studied. The study used primary and secondary data. Primary data were gathered through interviews with the key personnel, managers, and other informants of the Luntian Multipurpose Cooperative in order to obtain responses regarding the overall status of the cooperative including its problem and plans. Secondary data were taken from files and documents, especially the history, background information and financial statements. Other data were taken through research materials such as book, unpublished special problems and from some government institutions. The recommendation of this research showed that Luntian MPC should engage in establishing a communal farm as to become the primary source of hybrid piglets that their members would raised. The alternatives solution was establishing a breeding farm that would ask for initial investment. Keywords: cooperative, vertical integration, case study, por