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Stars can be ripped apart by tidal forces in the vicinity of a massive black hole (MBH), causing luminous flares known as tidal disruption events (TDEs). These events could be contributing to the mass growth of intermediate-mass MBHs, and new samples from transient surveys can provide useful information on this growth channel. This work aims to study the demographics of TDEs by modeling the co-evolution of MBHs and their galactic environments in a cosmological framework. We use the semi-analytic galaxy formation model \emph{L-Galaxies}BH, which follows the evolution of galaxies as well as of MBHs, including multiple scenarios for MBH seeds and growth, spin evolution, and binary MBH dynamics. Time-dependent TDE rates are associated with each MBH depending on the stellar environment, following the solutions to the 1-D Fokker Planck equation solved with \textsc{PhaseFlow}. Our model produces volumetric rates that are in agreement with the latest optical and previous X-ray samples. This agreement requires a high occupation fraction of nuclear star clusters with MBHs since these star reservoirs host the majority of TDEs at all mass regimes. We predict that TDE rates are an increasing function of MBH mass up to $\sim\, 10^{5.5}$M$_\odot$, beyond which the distribution flattens and eventually drops for $>\,10^{7}$M$_\odot$. In general, volumetric rates are predicted to be redshift-independent at $z\,{<}\,1$. We discuss how the spin distribution of MBHs around the event horizon suppression can be constrained via TDE rates and what is the average contribution of TDEs to the MBH growth. In our work, the majority of low-mass galaxies host nuclear star clusters that have their loss-cone depleted by $z\,=\,0$, explaining why TDEs are rare in these systems. This highlights that time-dependent TDE rates are essential for any model to be in good agreement with observations at all mass regimes., Comment: 26 pages, 11 figures

Decade-long monitoring of blazars at optical and infrared (OIR) wavelengths with the Small and Moderate Aperture Research Telescope System (SMARTS) in Chile and in $\gamma$-rays with the Fermi Large Area Telescope (LAT) has enabled the systematic study of their multi-wavelength long-term variability. In this work we investigate, from a theoretical perspective, the long-term variability properties of blazar emission by introducing an observationally motivated time-dependence to four main parameters of the one-zone leptonic model: injection luminosity of relativistic electrons, strength of magnetic field, Doppler factor, and external photon field luminosity. For the first time, we use both the probability density function and the power spectral density of the 10 year-long Fermi-LAT light curves to create variation patterns for the model parameters. Using as test beds two bright blazars from the SMARTS sample (PKS 2155-304 and 3C 273), we compute 10 year-long OIR, X-ray, and $\gamma$-ray model light curves for different varying parameters. We compare the findings of our theoretical investigation with multi-wavelength observations using various measures of variability. While no single-varying parameter simulation can explain all multi-wavelength variability properties, changes in the electron luminosity and external radiation field in PKS 2155-304 and 3C 273, respectively, can account for most of them. Our results motivate future time-dependent studies with coupling between two or more physical parameters to describe the multi-wavelength long-term blazar variability., Comment: 20 pages, 11 figures, accepted for publication in MNRAS, minor changes from v1, added video links