With Count Probability as the Probability Mode, the Probability value in the distribution table (first column) refers to the number of spheres of a type.

With Volume Probability, it refers to the volume of spheres of a type.

The Draw Mode controls how the number of each sphere type is determined:

• Draw Spheres: A random generator sets the type of each sphere in the structure depending on the given probabilities. Thus, the number of spheres of each type depends on the Random Seed.
• Compute Sphere Type Numbers: The number of spheres for each type is computed analytically, based on the probabilities, but without a random generator. The number of spheres of each type is the same for different Random Seeds.

For example, choosing Count Probability and Compute Sphere Type Numbers and specifying that of 100 spheres, 70% should be 1 mm and 30% should be 0.5 mm, exactly 70 spheres have a diameter of 1 mm and 30 spheres have a diameter of 0.5 mm.

In contrast, selecting Draw Spheres determines that for each of the 100 spheres in the example the type is randomly drawn. Thus, each sphere has a 70% probability to have a diameter of 100 µm, and a 30% probability to have a diameter of 50 µm. Therefore, the Achieved Distribution of type 1 is dependent on the Random Number, and binomially distributed around an expectation value of 0.7.

Enter the number of spheres to be packed.

When working with Volume probability and strongly differing sphere diameters, it might happen that only a very small number of the larger spheres appears in the structure, or that they are completely missing.

By clicking Suggest Sphere Number a number of spheres is proposed so that ratios close to the desired probabilities can be reached. Depending on the chosen parameters (for example Volume Probability and strongly differing diameters), the suggested number of spheres might be large.

Determine the number of different sphere types to be packed. Increasing the number adds rows in the distribution table below.

The distribution table contains the parameters for the different sphere types to be packed. The parameters for up to 255 sphere types can be entered in the table, when selecting Material ID per Object Type and up to 1000 when selecting Material ID per Material for material mode.

The table consists of the following columns:

• Enter the Probability of the sphere type.
• Enter the Diameter of the sphere type in the chosen unit.
• The Achieved Distribution is drawn automatically given the previously entered number of spheres, and the values for diameter and probability for the distinct sphere types and shows the achieved ratio of the respective sphere types.
• The Sphere Number is also drawn automatically and shows the number of spheres of that type.
• The Material ID is chosen automatically counting the sphere types or materials depending on the material mode.
• Select the Material from the GeoDict material database by clicking on it.

Click the Edit / Paste Distribution Table button to edit the values for Diameter and Probability (depending on the choice for probability mode) in the Edit Sphere Distribution dialog.

Clicking Normalize ensures that the Probability values sum up to one.

Alternatively, the distribution can be pasted from other software, for example from Microsoft Excel, or it can be loaded from a *.txt-file. With the Save… button, the distribution table can be written to a *.txt file.

The given Sphere Material is applied to all sphere types. If different materials should be present in the structure, change the according materials afterward.

Checking Apply Gravity includes a simulation of gravitational force on the packed spheres after the packing process, so that the spheres “fall down” in the Z-direction from their positions in the packing. The effect of applying gravity to a packed structure is obvious for low packing density (under 30%). As the domain is always periodic for the packing, the spheres cutting the bottom of the domain reappear in the top. If this is not desired, use ProcessGeo - Crop to crop the top of the domain.