Theoretical galaxy formation models are an established and powerful tool for interpreting the astrophysical significance of observational data, particularly galaxy surveys. Such models have been utilised with great success by optical surveys such as
2dFGRS and SDSS, but their application to radio surveys of cold gas in galaxies has been limited. In this chapter we describe recent developments in the modelling of the cold gas properties in the models, and how these developments are essential if they are to be applied to cold gas surveys of the kind that will be carried out with the SKA. By linking explicitly a galaxys star formation rate to the abundance of molecular hydrogen in the galaxy rather than cold gas abundance, as was assumed previously, the latest models reproduce naturally many of the global atomic and molecular hydrogen properties of observed galaxies. We review some of the key results of the latest models and highlight areas where further developments are necessary. We discuss also how model predictions can be most accurately compared with observational data, what challenges we expect when creating synthetic galaxy surveys in the SKA era, and how the SKA can be used to test models of dark matter.
Abridged: We simulate a massive galaxy cluster in a LCDM Universe using three different approaches to solving the equations of non-radiative hydrodynamics: `classic Smoothed Particle Hydrodynamics (SPH); a novel SPH with a higher order dissipation sw
itch (SPHS); and adaptive mesh refinement (AMR). We find that SPHS and AMR are in excellent agreement, with both forming a well-defined entropy core that rapidly converges with increasing mass and force resolution. By contrast, SPH exhibits rather different behaviour. At low redshift, entropy decreases systematically with decreasing cluster-centric radius, converging on ever lower central values with increasing resolution. At higher redshift, SPH is in better agreement with SPHS and AMR but shows much poorer numerical convergence. We trace these discrepancies to artificial surface tension in SPH at phase boundaries. At early times, the passage of massive substructures close to the cluster centre stirs and shocks gas to build an entropy core. At later times, artificial surface tension causes low entropy gas to sink artificially to the centre of the cluster. We use SPHS to study the contribution of numerical versus physical dissipation on the entropy core, and argue that numerical dissipation is required to ensure single-valued fluid quantities in converging flows. However, provided this dissipation occurs only at the resolution limit, and provided that it does not propagate errors to larger scales, its effect is benign. There is no requirement to build `sub-grid models of unresolved turbulence for galaxy cluster simulations. We conclude that entropy cores in non-radiative simulations of galaxy clusters are physical, resulting from entropy generation in shocked gas during cluster assembly, putting to rest the long-standing puzzle of cluster entropy cores in AMR simulations versus their apparent absence in classic SPH simulations.
We investigate the impact of feedback - from supernovae (SNe), active galactic nuclei (AGN) and a photo-ionizing background at high redshifts - on the neutral atomic hydrogen (HI) mass function, the $b_{rm J}$ band luminosity function, and the spatia
l clustering of these galaxies at $z$=0. We use a version of the semi-analytical galaxy formation model GALFORM that calculates self-consistently the amount of HI in a galaxy as a function of cosmic time and links its star formation rate to its mass of molecular hydrogen (H$_2$). We find that a systematic increase or decrease in the strength of SNe feedback leads to a systematic decrease or increase in the amplitudes of the luminosity and HI mass functions, but has little influence on their overall shapes. Varying the strength of AGN feedback influences only the numbers of the brightest or most HI massive galaxies, while the impact of varying the strength of photo-ionization feedback is restricted to changing the numbers of the faintest or least HI massive galaxies.Our results suggest that the HI mass function is a more sensitive probe of the consequences of cosmological reionization for galaxy formation than the luminosity function. We find that increasing the strength of any of the modes of feedback acts to weaken the clustering strength of galaxies, regardless of their HI-richness. In contrast, weaker AGN feedback has little effect on the clustering strength whereas weaker SNe feedback increases the clustering strength of HI-poor galaxies more strongly than HI-rich galaxies. These results indicate that forthcoming HI surveys on next generation radio telescopes such as the Square Kilometre Array and its pathfinders will be exploited most fruitfully as part of multiwavelength survey campaigns.
Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are
obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.
We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form [ L_{e_i}L_{f_j} = sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}] where $u= (u_{i,j,k,l})$ is an $n
m times nm$ unitary matrix. These algebras, which generalise the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to isometric isomorphism in terms of the matrix $u$.
