Newtonian kinematical backreaction in cosmological $N$-body simulations
  with Delaunay Tesselation: "zero test" and scale dependence
  The backreaction of inhomogeneities describes the effect of inhomogeneous
structure on average properties of the Universe. We investigate this approach
by testing the consistency of cosmological $N$-body simulations as non-linear
structure evolves. Using the Delaunay Tessellation Field Estimator (DTFE), we
calculate the kinematical backreaction $Q$ from simulations on different scales
in order to measure how much $N$-body simulations should be corrected for this
effect. This is the first step towards creating fully relativistic and
inhomogeneous $N$-body simulations. In this paper we compare the interpolation
techniques available in DTFE and illustrate the statistical dependence of $Q$
as a function of length scale.
