Multifractal dimensions for critical random matrix ensembles

Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q \le 2$. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility $\chi$ describing level correlations can be related to $D_q$ in a unified way as $D_q=(1-\chi)[1+(q-1)\chi]^{-1}$, thus generalizing existing relations with relevance to the disorder driven Anderson--transition.Comment: 6 pages, 9 figure

The Radio Galaxy Population in the SIMBA SImulations

We examine the 1.4GHz radio luminosities of galaxies arising from star formation and active galactic nuclei (AGN) within the state-of-the-art cosmological hydrodynamic simulation Simba. Simba grows black holes via gravitational torque limited accretion from cold gas and Bondi accretion from hot gas, and employs AGN feedback including jets at low Eddington ratios. We define a population of radio loud AGN (RLAGN) based on the presence of ongoing jet feedback. Within RLAGN we define high and low excitation radio galaxies (HERGs and LERGs) based on their dominant mode of black hole accretion: torque limited accretion representing feeding from a cold disk, or Bondi representing advection-dominated accretion from a hot medium. Simba predicts good agreement with the observed radio luminosity function (RLF) and its evolution, overall as well as separately for HERGs and LERGs. Quiescent galaxies with AGN-dominated radio flux dominate the RLF at > $\sim 10^{22-23}$ W Hz$^{-1}$, while star formation dominates at lower radio powers. Overall, RLAGN have higher black hole accretion rates and lower star formation rates than non-RLAGN at a given stellar mass or velocity dispersion, but have similar black hole masses. Simba predicts a LERG number density of 8.53 Mpc$^{-3}$, $\sim 10\times$ higher than for HERGs, broadly as observed. While LERGs dominate among most massive galaxies with the largest black holes and HERGs dominate at high specific star formation rates, they otherwise largely populate similar-sized dark matter halos and have similar host galaxy properties. Simba thus predicts that deeper radio surveys will reveal an increasing overlap between the host galaxy demographics of HERGs and LERGs.Comment: 17 pages, 9 figures, Accepted for publication in MNRA

Equivalent layered models for functionally graded plates

Functionally graded plates whose material properties vary continuously through the thickness are modelled as exactly equivalent plates composed of up to four isotropic layers. Separate models are derived for analysis using classical plate theory, first-order and higher-order shear deformation theory. For cases where Poisson’s ratio varies through the thickness, the integrations required to obtain the membrane, coupling and out-of-plane stiffness matrices are performed accurately using a series solution. The model is verified by comparison with well converged solutions from approximate models in which the plate is divided into many isotropic layers. Critical buckling loads and undamped natural frequencies are found for a range of illustrative examples