A simple simulation of cosmic shock waves in the formation of the large scale structure of the universe

I present here a simplified model of the large scale structure in two dimensions, using a series of matter waves, stationary in time, each originating from a different position and with a slightly different wavelength. The position of each wave is chosen at random. Different methods for producing random numbers are used, and each compared with more advanced N-body simulations. This simplified model does provide a reasonable model for the formation of galactic clusters, tuning the simulation by changing the wavelength of each wave. Introduction The distribution of galaxies through the observable universe is non uniform. Astronomers have been gathering evidence for around 20 years, on the large scale structure of the universe. They observe large clusters of galaxies (superclusters), filaments and walls between these clusters, as well as voids; large space in between galactic clusters [1]. An interesting way to model this large scale structure is to propagate shock waves through a simulation of the early universe [2]. The shock waves result from the accretion accumulation of matter onto sheets, filaments and knots. These accretions cause further shock waves, due to asymmetric flow of matter along a filament. Collisions and merges between large objects cause further shock waves[2]. Shock waves are also formed by mass in a void accreting onto a filament, knot or sheet[2][3]. The structure of these shock waves of thus highly complex. Traditionally N-body simulations have been used to model these shock waves, and their effect on the large scale structure of the universe. Hydrodynamics and fluid flow are included in the models, which provide very useful results [3]. A sin wave in cylindrical coordinates (Figure 1(a)) can be used to model a cosmological shock wave. By adding even a very small number of these shock waves, the overall structure of the original wave is quickly lost Figure 1(b). Figure 1 is a contour plot of the following equations: sin (√ x2 + y2 ) and: sin (√ x2 + y2 ) +sin (√ (x + 2) + (y − 3) ) +sin (√ (x + 1) + (y + 1) ) +sin (√ (x + 4) + (y − 5) )