The free streaming of warm dark matter particles dampens the fluctuation spectrum, flattens the mass function of haloes and set a fine grained phase density limit for dark matter structures. The phase space density limit is expected to imprint a constant density core at the halo center on the contrary to what happens for cold dark matter. We explore these effects using high resolution simulations of structure formation in different warm dark matter scenarios. We find that the size of the core we obtain in simulated haloes is in good agreement with theoretical expectations based on Liouville's theorem. However, our simulations show that in order to create a significant core, (r c ∼ 1 kpc), in a dwarf galaxy (M ∼ 10 10 M ⊙ ), a thermal candidate with a mass as low as 0.1 keV is required. This would fully prevent the formation of the dwarf galaxy in the first place. For candidates satisfying large scale structure constrains (m ν larger than ≈ 1 − 2 keV) the expected size of the core is of the order of 10 (20) pc for a dark matter halo with a mass of 10 10 (10 8 ) M ⊙ We conclude that "standard" warm dark matter is not viable solution for explaining the presence of cored density profiles in low mass galaxies.

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On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions.

In recent years, warm dark matter models have been studied as a viable alternative to the cold dark matter models. The warm dark matter particle properties are expected to imprint distinct signatures on the structure formation at both large and small scales and there have been many attempts to study these properties with numerical simulations. In this paper, we review and update on warm dark matter simulation studies from the past two decades and their most significant results: structure formation mechanisms, halos evolution, sizes and distribution, and internal structure properties. We discuss the theoretical assumptions and the limitations of the methods employed. In this context, several controversial claims are scrutinized in the attempt to clarify these confusing and sometimes even contradictory conclusions in the numerical simulation literature. We address the circumstances in which a promising keV dark matter candidate should be properly treated in the simulations.