597 research outputs found

    Toy Models for Galaxy Formation versus Simulations

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    We describe simple useful toy models for key processes of galaxy formation in its most active phase, at z > 1, and test the approximate expressions against the typical behaviour in a suite of high-resolution hydro-cosmological simulations of massive galaxies at z = 4-1. We address in particular the evolution of (a) the total mass inflow rate from the cosmic web into galactic haloes based on the EPS approximation, (b) the penetration of baryonic streams into the inner galaxy, (c) the disc size, (d) the implied steady-state gas content and star-formation rate (SFR) in the galaxy subject to mass conservation and a universal star-formation law, (e) the inflow rate within the disc to a central bulge and black hole as derived using energy conservation and self-regulated Q ~ 1 violent disc instability (VDI), and (f) the implied steady state in the disc and bulge. The toy models provide useful approximations for the behaviour of the simulated galaxies. We find that (a) the inflow rate is proportional to mass and to (1+z)^5/2, (b) the penetration to the inner halo is ~50% at z = 4-2, (c) the disc radius is ~5% of the virial radius, (d) the galaxies reach a steady state with the SFR following the accretion rate into the galaxy, (e) there is an intense gas inflow through the disc, comparable to the SFR, following the predictions of VDI, and (f) the galaxies approach a steady state with the bulge mass comparable to the disc mass, where the draining of gas by SFR, outflows and disc inflows is replenished by fresh accretion. Given the agreement with simulations, these toy models are useful for understanding the complex phenomena in simple terms and for back-of-the-envelope predictions.Comment: Resubmitted to MNRAS after responding to referee's comments; Revised figure

    Legal Considerations for the Use of Social Media by Public School Educators

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    Isomerisation of cis-9 trans-11 conjugated linoleic acid (CLA) to trans-9 trans-11 CLA during acidic methylation can be avoided by a rapid base catalysed methylation of milk fat

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    This study investigated the evolution of trans-9 trans-11 conjugated linoleic acid (CLA) from cis-9 trans-11 CLA during methylation and its avoidance through a rapid base methylation of milk fat. The study examined three conditions shown to result in loss of cis-9 trans-11 CLA during methylation namely: temperature, methylation time, water contamination in old reagents and acidic conditions. Three techniques currently used for the conversion of milk fat into fatty acid methyl esters for analysis of CLA content by gas liquid chromatography and a fourth procedure designed to eliminate acidic conditions and to limit methylation temperature and time were used. The four methods were: (i) acidic methylation (AM); (ii) acidic and basic bimethylation with fresh reagents (FBM); (iii) acidic and basic bimethylation with pre-prepared reagents (PBM) and (iv) basic methylation (BM). Each regime was carried out on six milk samples over two periods and methylated 1 ml freeze-dried milk (n=12 per regime). Total CLA was not different across methylation regimes (0.30 mg/ml). Isomer cis-9 trans-11 was higher (P <0.01) with BM than the other regimes and lowest with AM: 21.2, 17.8, 18.8 and 14.7 mg/100 ml for BM, FBM, PBM and AM, respectively. The inverse relationship was shown for trans-9 trans-11 with higher (P <0.001) amounts with AM than the other regimes and lowest with BM: 0.57, 2.55, 2.36 and 3.69 mg/100 ml for BM, FBM, PBM and AM, respectively. The trans-10 cis-12 isomer was also shown to alter with methylation procedure being higher (P <0.001) with AM than the other regimes: 0.43, 0.47, 0.29 and 1.20 mg/100 ml for BM, FBM, PBM and AM, respectively. Validation with known CLA free fatty acid and triacylglycerol standards confirmed that AM resulted in conversion of cis-9 trans-11 to trans-9 trans-11, and also elevated trans-10 cis-12 whilst BM of triacylglycerol CLA did not isomerise cis-9 trans-11 and was comparable to FBM

    Algorithms for the Numerical Solution of a Finite-Part Integral Equation

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    The authors investigate a hypersingular integral equation which arises in the study of acoustic wave scattering by moving objects. A Galerkin method and two collocation methods are presented for solving the problem numerically. These numerical techniques are compared and contrasted in three test problems
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