Magnetic fields and Turbulence in Star Formation using Smoothed Particle
  Hydrodynamics
  Firstly, we give a historical overview of attempts to incorporate magnetic
fields into the Smoothed Particle Hydrodynamics method by solving the equations
of Magnetohydrodynamics (MHD), leading an honest assessment of the current
state-of-the-art in terms of the limitations to performing realistic
calculations of the star formation process. Secondly, we discuss the results of
a recent comparison we have performed on simulations of driven, supersonic
turbulence with SPH and Eulerian techniques. Finally we present some new
results on the relationship between the density variance and the Mach number in
supersonic turbulent flows, finding sigma^2_{ln rho} = ln (1 + b^2 M^2) with
b=0.33 up to Mach~20, consistent with other numerical results at lower Mach
number (Lemaster and Stone 2008) but inconsistent with observational
constraints on sigma_rho and M in Taurus and IC5146.
