Numerical simulations using the N-body method are the primary instrument used to probe the non-linear regime of structure formation in cosmology and provide the basis for all theoretical predictions for the distribution of dark matter at the corresponding physical scales. Over the last few decades, such simulations have gained in refinement and complexity and have allowed the exploration of an ever larger range of scales.

**Nevertheless, the understanding of their precision and their convergence toward the continuum limit remains, at very least, incomplete, in particular for smaller scales.**Indeed, numerical simulations of structure formation in the universe in cosmology use the N body method in which the continuum density field of dark matter is represented by a finite number of discrete particles interacting by a smoothed Newtonian two body potential.

**It is evidently of importance to control as much as possible for their precision and reliability. Specifically, beyond issues of numerical convergence, it is important to understand the limits imposed on the accuracy**of results by the use of a finite number of particles to represent the theoretical continuum density field, and the associated introduction of a smoothing scale (or equivalent) in the gravitational force.### Papers

*Stable clustering and the resolution of dissipationless cosmological N-body simulations*David Benhaiem, Michael Joyce, Francesco Sylos Labini, Mon.Not.R.Acad.Soc in the press 2017*Particle ejection during mergers of dark matter halos,*Isabella P. Carucci, Martin Sparre, Steen H. Hansen, Michael Joyce, JCAP06(2014)057- A toy model to test the accuracy of cosmological N-body simulations, Francesco Sylos Labini, Astronomy & Astrophysics, Volume 552, id.A36, 16 pp 2013
- Self-similarity and stable clustering in a family of scale-free cosmologies, David Benhaiem, Michael Joyce, Bruno Marcos, MNARS 2013
- Evolution of isolated overdensities as a control on cosmological N body simulations, Michael Joyce, Francesco Sylos Labini, MNRAS (February 21, 2013) 429 (2): 1088-1101
- Cosmological simulations of structure formation and the Vlasov equation

Michael Joyce, Commun.NonlinearSci.Numer.Simul.13:100,2008 - Infinite self-gravitating systems and cosmological structure formation, Michael Joyce, American Institute of Physics Conference proceedings, 970 (2008).
- Towards quantitative control on discreteness error in the non-linear regime of cosmological N body simulations, Michael Joyce, Bruno Marcos, Thierry Baertschiger, Mon.Not.R.Astron.Soc, 2008
- Quantification of discreteness effects in cosmological N-body simulations: II. Evolution up to shell crossing, Michael Joyce, Bruno Marcos, Phys.Rev.D76:103505,2007
- An alternative to grids and glasses: Quaquaversal pre-initial conditions for N-body simulations, Steen H. Hansen, Oscar Agertz, Michael Joyce, Joachim Stadel, Ben Moore, Doug Potter, Astrophys.J.656:631-635,2007
- Linear perturbative theory of the discrete cosmological N-body problem, B. Marcos, T. Baertschiger, M. Joyce, A. Gabrielli, F. Sylos Labini, Phys.Rev. D73 (2006) 103507
- A method of generating initial conditions for cosmological N body simulations, M. Joyce, D. Levesque, B. Marcos, Phys.Rev. D72 (2005) 103509
- Reply to the comment on ”On the problem of initial conditions in cosmological N-body simulations”, Thierry Baertschiger, Francesco Sylos Labini, Europhys.Lett.63:633-634,2003
- Power-law correlation and discreteness in cosmological N-body simulations, Thierry Baertschiger, Michael Joyce, Francesco Sylos Labini, Astrophys.J. 581 (2002) L63-L66
- On the problem of initial conditions in cosmological N-body simulations, Thierry Baertschiger, Francesco Sylos Labini, Europhys.Lett.57:322-328,2002