Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimum time-stepping scheme for N-body simulations   We present a new time-stepping criterion for N-body simulations that is based
on the true dynamical time of a particle. This allows us to follow the orbits
of particles correctly in all environments since it has better adaptivity than
previous time-stepping criteria used in N-body simulations. Furthermore, it
requires far fewer force evaluations in low density regions of the simulation
and has no dependence on artificial parameters such as, for example, the
softening length. This can be orders of magnitude faster than conventional
ad-hoc methods that employ combinations of acceleration and softening and is
ideally suited for hard problems, such as obtaining the correct dynamics in the
very central regions of dark matter haloes. We also derive an eccentricity
correction for a general leapfrog integration scheme that can follow
gravitational scattering events for orbits with eccentricity e -> 1 with high
precision. These new approaches allow us to study a range of problems in
collisionless and collisional dynamics from few body problems to cosmological
structure formation. We present tests of the time-stepping scheme in N-body
simulations of 2-body orbits with eccentricity e -> 1 (elliptic and
hyperbolic), equilibrium haloes and a hierarchical cosmological structure
formation run.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci