It is possible to configure a lattice for the 3D space, which can be useful to speed up the computation of the potentials. Note though, that this goes in hand with a loss of accuracy: If the lattice is applied, the evaluation of the potentials is carried out only on the nodes of the lattice. Intermediate values are interpolated.

The configuration of a lattice is usually not necessary, it is however required if the Thermodynamic VTK Output, the Thermodynamic Lattice Output, the Potentials_Affect_Thresholds, the Coulomb potentials, or the Coulomb VTK output option is enabled. To configure the thermodynamic output, use the Output section.

To enable a lattice it is necessary to add a Lattice section with the following parameters. If no Lattice section is used in the configuration, no lattice will be used at all.

Automatic — bool, required — Conditions on key value: None

Whether to automatically determine the geometry of the lattice. If set to False, both Cell_Number and Origin and Sizes keys must be specified. If set to True at least one of the geometrical properties must be omitted. SMASH will determine the missing properties as described in Lattice default parameters.

Attention: Specifying only some geometrical parameters (among Cell_Number, Origin and Sizes) and letting SMASH determine the remaining ones should be carefully done as it might give an undesired result. This is due to the fact that SMASH determines the full geometry of the lattice as described in Lattice default parameters and only afterwards the provided keys are overwriting the calculated ones. Therefore, for example, specifing only the Origin will shift the automatically determined lattice and this might not be the desired effect.

Cell_Number — list of 3 ints, optional, default = depends on Modus — Conditions on key value: \(x_i>0\) (see Lattice default parameters)

Number of cells in x, y, z directions.

Attention: Lattice is used to calculate bulk quantities such as baryon density or energy density. The choice of the number of cells, together with the chosen lattice size, affects the results: too coarse of a lattice will average over large volumes of space (which may yield dubious results), while too fine of a lattice may lead the calculation toward Poisson-like noise (because there is not enough particles to provide the necessary statistics). As guidance, one can argue that microscopic hadronic transport should resolve structures on the order of about 1 fm, so that one should choose lattice cell number and lattice size that result in cell size of about 1 fm. Using lattices corresponding to larger cell sizes can be fine if this is what is intended. Using lattices with cell sizes of about 0.5 fm may be risky, and smaller lattice sizes are not not advised.

Note: A too large number of cells can lead to long runtime and/or large memory usage. This aspect is clearly related to the choice of the Sizes key and these two keys should be chosen together. Make sure to choose the lattice geometry carefully and check the results for convergence with respect to it.

Origin — list of 3 doubles, optional, default = depends on Modus — Conditions on key value: None (see Lattice default parameters)

The lattice covers a cuboid region whose vertices \(V_n\) are uniquely identified by the origin coordinates \((O_x, O_y, O_z)\) and the lattice sizes \((L_x, L_y, L_z)\) as follows:

\[ V_n = (O_x+i\cdot L_x, O_y+j\cdot L_y, O_z+k\cdot L_z) \]

where \((i,j,k)\in\{0,1\}\times\{0,1\}\times\{0,1\}\). Coordinates of the lattice are given in fm.

Periodic — bool, optional, default = (Modus == "Box" || Modus == "ListBox") — Conditions on key value: None

Use periodic continuation or not. With periodic continuation \((x,y,z) + (i\cdot L_x,\,j\cdot L_y,\,k\cdot L_z) \equiv (x,y,z)\) with \(i,\,j,\,k\in\mathbb{Z}\) and \(L_x,\,L_y,\,L_z\) being the lattice sizes.

Potentials_Affect_Thresholds — bool, optional, default = false — Conditions on key value: None

Include potential effects, since mean field potentials change the threshold energies of the actions.

Sizes — list of 3 doubles, optional, default = depends on Modus — Conditions on key value: \(x_i>0\) (see Lattice default parameters)

Sizes of lattice in x, y, z directions in fm.

Note: Lattice is used to calculate bulk quantities such as baryon density or energy density and the choice of its size can have a significant impact on the results. A too small lattice size may lead to inaccurate results, becuase part of the system might not be covered, while a too large lattice size may lead to long runtime and large memory usage, depending on the value of the Cell_Number key. These two keys should be chosen together. Make sure to choose the lattice geometry carefully and check the results for convergence with respect to it.

Configuring the Lattice

The following example configures the lattice with the origin in (0,0,0), 20 cells of 10 fm size in each direction and with periodic boundary conditions. The potential effects on the thresholds are taken into consideration. Note that, as the origin is by definition the left down near corner of the cell, center is located at (5, 5, 5).

Lattice:
    Automatic: False
    Origin: [0.0, 0.0, 0.0]
    Sizes: [10.0, 10.0, 10.0]
    Cell_Number: [20, 20, 20]
    Periodic: True
    Potentials_Affect_Thresholds: True

A default lattice is also available for each modus. In this case the lattice is setup automatically with reasonable size, cell number and placement. See Lattice default parameters for more details on the defaults. The default lattice is used if the "Lattice" section in the configuration is given as shown in the following example.

Lattice:
    Automatic: True

It is also possible to explicity set some lattice parameters and use the default for the rest. See the following example for the "Box" modus:

Lattice:
    Automatic: True
    Cell_Number: [20, 20, 20]

As explicitly specified, there will be twenty cells for each direction. The origin and the sizes of the lattice are automatically set such that the lattice exactly covers the entire box.