We investigate the dependence of the galaxy properties on cosmic web environments using the most up-to-date hydrodynamic simulation: Evolution and Assembly of Galaxies and their Environments (EAGLE). The baryon fractions in haloes and the amplitudes of the galaxy luminosity function decrease going from knots to filaments to sheets to voids. Interestingly, the value of L* varies dramatically in different cosmic web environments. At z = 0, we find a characteristic halo mass of $10^{12} h^{-1}\rm M_{\odot }$, below which the stellar-to-halo mass ratio is higher in knots while above which it reverses. This particular halo mass corresponds to a characteristic stellar mass of $1.8\times 10^{10} h^{-1}\rm M_{\odot }$. Below the characteristic stellar mass central galaxies have redder colors, lower sSFRs and higher metallicities in knots than those in filaments, sheets and voids, while above this characteristic stellar mass, the cosmic web environmental dependences either reverse or vanish. Such dependences can be attributed to the fact that the active galaxy fraction decreases along voids, sheets, filaments and knots. The cosmic web dependences get weaker towards higher redshifts for most of the explored galaxy properties and scaling relations, except for the gas metallicity vs. stellar mass relation.

Gravitational softening length is one of the key parameters to properly set up a cosmological N-body simulation. In this paper, we perform a large suit of high-resolution N-body simulations to revise the optimal softening scheme proposed by Power et al. (P03). Our finding is that P03 optimal scheme works well but is over conservative. Using smaller softening lengths than that of P03 can achieve higher spatial resolution and numerically convergent results on both circular velocity and density profiles. However using an over small softening length overpredicts matter density at the inner most region of dark matter haloes. We empirically explore a better optimal softening scheme based on P03 form and find that a small modification works well. This work will be useful for setting up cosmological simulations.