A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent and we investigate the subsequent evolution of the density field. Photon paths are also calculated, allowing a detailed consideration of gravitational lensing effects and microwave background anisotropies induced by the cluster. We apply the method to modelling high-redshift clusters and, in particular, we consider the reported microwave decrement observed towards the quasar pair PC1643+4631 A&B. We also consider the effect on the primordial microwave background power spectrum due to gravitational lensing by a population of massive high-redshift clusters.

Y.Dabrowski, M.P. Hobson, A.N. Lasenby and C.J.L. Doran, **Microwave Background Anisotropies and Nonlinear Structures II. Numerical computations, ***Mon. Not. R. Astron. Soc.* **302**, 757–770 (1999)