The main following implemented functionalities are specifically directed at cosmological simulation data outputs. Some of them are statistical tools that one can deploy in order to discriminate among different cosmological models.

**Particles Mass Density and Gravitational Field Calculations**
By using an *eight-point Cloud-in-Cell* smoothing algorithm, AstroMD computes the mass density field
associated to the particle distribution by distributing the mass of each particle over the computational
mesh. The computation can be done with the maximum accuracy, that is by considering all the particles over a uniform high
resolution mesh. The user can also use a sample of the whole set of particles thus reducing the CPU time
consumption and the memory request. The smoothing of the masses can be generally performed by using a coarse grid that can
be refined where high resolution is necessary.

**Power Spectrum and Correlation Function** -
The quantity is used to calculate the Power Spectrum of the matter distribution, which is defined as
the average value of the square norm of :

(2) |

Several estimators have been used in the literature to measure, in particular, the two-point Correlation Function, that is defined in terms of probability of finding a point in a randomly-chosen volume and a point in another volume separated by a distance .

The two-point Correlation Function of AstroMD is based on the three-dimensional counterpart of the

(3) |

**Minkowski Functionals**
The Minkowski Functionals (*MFs*) provide a novel tool to
characterize the Large Scale Structure of the Universe.
They describe the Geometry, the Curvature and the Topology of a point-set.

In a three-dimensional Euclidean space, these functionals have a direct geometric
interpretation as listed in Table 1.
The *MFs* algorithm inside AstroMD associates a ball of radius to each point of the point distribution. The size, the
shape and the connectivity of the spatial pattern, formed by the union-set of these balls, change with the radius, which can
be employed as a diagnostic parameter.

geometric quantity | ||||

V volume | ||||

A surface | ||||

H mean curvature |

**Friend-of-Friend Algorithm**
Dynamical studies of groups of galaxies are an important method for estimating galaxy masses.
The most common group-finding algorithm is known as *Friend-of-Friend* (*FoF*).
This technique was first used by Huchra & Geller. A particle belongs to an *FoF* group if it lies within
some linking length of any other
particle in the group.

After all such groups are found, those with less than a specified minimum
number of group members are rejected.

AstroMD visualizes the positions of all grouped particles ,each of them being marked with their group identifier (see
figure 1.33), and the positions of all centers of mass that are associated with the number of particles in the
group; the radius, velocity (if present in input) and total mass are also visualized.