Dynamic Interaction between Molecule Clusters

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filtering steps should be performed to remove unnecessary data. First, flow groups which contain too few molecules can be omitted, as their relevance is too low com-pared to the risk of cluttering the image. Second, flow groups traveling over a time too long should also be removed, as these molecules more likely just evaporated into the bulk and only by chance joined a second cluster at a later time step. These two aspects are not independent, however. Flow groups existing only for a very short time might be of interest even if they only contain very few molecules, only a single molecule in the extreme case. On the other hand, flow groups existing for a long time and consisting of very many molecules may indicate a directed, struc-tured behaviour or a severe malfunction in the cluster detection criterion and should therefore not be removed.

Figure 75: Clusters with colours between yellow and red are decaying (left), while clusters with colours between yellow and green are growing (right). Evaporating molecular cluster (in the middle of the left image) leaving a flow group (blue arrow, centre image) containing almost all molecules of the evaporated cluster (indicated by the similar size), moving slowly and forming a new cluster (right image). This behaviour hints at a cluster detection problem.

Molecule clusters and flow groups can be shown in the 3D space (cf. Figure 75), providing an easy interpretation, or in an abstract diagram (cf. Figure 76). Of course, both representations can be combined by coordinated views providing linking and brushing, e.g. for selection of clusters and correspond-ing filtercorrespond-ing. Uscorrespond-ing such a tool a user can easily get more information about the detected clusters, their evolution over time and their interaction with each other and with the surrounding monomers.

In the 3D space representation, molecule clusters can simply be shown as el-lipsoids (cf. Chapter 3.1.1). To emphasise the evolution, a special colour coding can be used. Three user-defined colours represent the major evolution tendencies of clus-ters. The default colours are yellow for clusters keeping their size, green for growing and red for decaying clusters. These colours are interpolated accordingly: e.g. slight-ly shrinking clusters are coloured in orange. The surrounding vapour can be shown by different metaphors including point-based GPU ray cast spheres. Details can be

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found in the original publication [GRVE07]. For easier viewing of the elements of interest, i.e. clusters’ ellipsoids and flow groups, all remaining molecules can be filtered. The flow groups can be shown using arrows glyphs (cf. Chapter 2.5 for GPU ray casting). As these arrows are based on many individual molecules, their move-ment is averaged and abstracted: the flow groups’ arrows move linearly from their emerging position, averaged over the position of all atoms at the time frame A", to their vanishing position, averaged from all atoms at time frame A-. The sizes of the arrows are given by the number of molecules the flow groups contain, scaled ac-cordingly (based on cubic-root and considering HCP) making them visually compa-rable to the ellipsoids. The remaining parameters of the arrow, length and radii of arrow head and tail, are chosen relative to the main size value, such that the overall impression corresponds to the sizes and impressions of the molecule cluster ellip-soids. Figure 75 shows an exemplary flow group connecting two clusters. All three elements are of almost equal size, which means that they are likely to all represent the same set of molecules. This indicates a cluster detection failure, but can also be because of normal density fluctuations, because all elements are rather small. To further increase the information coupling between the arrows and the ellipsoids, the colour coding of the arrows is chosen to represent the fraction of molecules in the flow group and in the cluster. A value of 1, meaning all molecules of the cluster join into the same flow group, is represented by blue (which is not used by the colour coding for the ellipsoids). The value of zero is shown by a red colour. Small values close to zero mean that only very few molecules of the cluster join in the corresponding flow group. The colours are chosen in relation to the clusters + and and are interpolated as the flow group moves. The flow group shown in Figure 75 being clear blue further emphasises the fact that it contains all atoms of both corre-sponding clusters.

The schematic view of the dynamics of the data set is shown in Figure 76.

The horizontal axis represents time. Molecule clusters are represented as horizontal lines of varying thickness, encoding the number of contained molecules. The verti-cal arrangement of the clusters is initially based on the cluster IDs, but can be man-ually adjusted by the user. The clusters do not have a further colour coding and are shown black, with the only exception that selected clusters are shown in red. Se-lected clusters in the 3D visualization are rendered with a halo, as colour modula-tion does not provide enough distincmodula-tion. Molecule cluster lines can be selected by either clicking on the line in the schematic view or by picking the corresponding ellipsoid. Flow groups are shown by Bézier curves. Their start and end points are given by their clusters and the corresponding time frames. The thickness is derived from the number of molecules using the same mapping as for the lines represent-ing the clusters themselves. So the amount of molecules leavrepresent-ing the cluster at a time, represented by the decrease in the line width, can be compared to the amount of molecules contained in a flow group. The schematic view can be interactively zoomed and panned and can be filtered to only show the selected cluster lines, the

connected flow groups, and the cluster lines directly connected to the shown flow groups.

Figure 76: The schematic view of the molecule cluster evolution with two selected clusters (red) and all corresponding flow groups connecting to other clusters (black) shows a 10,000 methane nucleation dataset with geometrical cluster detection. The colour of the flow groups are based on the IDs and of the clusters they are leaving and joining to allow for visual grouping.

The fluctuation in molecule clusters, e.g. shown in Figure 75, also manifests for larger clusters, which are always surrounded by small flow groups. This effect is partially expected as molecules may collide rather fast with these clusters, but cannot join them immediately because of too different speeds and energy levels.

Instead, they rebound, get slowed down, and then join the cluster some time steps later. There are different cluster detection criteria, which handle effects like this differently. As a matter of fact there is no thermodynamically correct detection algorithm. Each method is an approximation of quantum mechanics and has ad-vantages and disadad-vantages. Although in the application domain there exists de-tailed knowledge of the limitations of these methods, comparing results of different detection criteria on the same data set is important to judge the quality of the found molecule clusters and the derived values, e.g. nucleation rate and critical cluster size.

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Figure 77: Schematic views of two clustering algorithms applied to a 50,000 methane nucle-ation dataset. The top images show the results of a pure geometric clustering, and the lower images show the results of a clustering based on energy levels. The images below the dia-grams show zoomed-in views of the selected cluster (marked red in the diadia-grams) at differ-ent time frames. The geometrical clustering detects large and unstable clusters. The select-ed cluster is temporarily split into two. The thick green flow groups and the corresponding dent in the lower cluster line indicate a detection problem. The energy-based clustering (right) is more stable in this respect but results in smaller clusters.

Figure 77 shows the schematic views for a methane nucleation simulation data set with 50,000 molecules comparing two cluster detection algorithms. The top images are generated based on a simple geometric distance criterion. A mole-cule with four neighbours within a distance threshold is considered to be part of the liquid phase. All molecules within this neighbourhood and which are in liquid phase form a cluster. The algorithm used for the bottom images defines two mole-cules as clustered if the sum of their potential energy and their relative kinetic energy is negative (cf. [Hil55]). The geometrical criterion detects larger and more clusters than the energy-based approach does (cf. Figure 77 in which the same clus-ter is selected, which is number 2912 if using the geometrical criclus-terion and number 689 if using the energy-based criterion). It also often creates multiple clusters, close together, instead of a single one. The small cluster at the top of the top image in Figure 77 (ID 3007) is such an example. The line of this cluster is connected to the lower and bigger cluster (ID 2912) with thick flow groups, indicating that almost all molecules came from and re-join that cluster. At the same time (time frame 91) the big cluster (2912) shows a dent in its size corresponding to the size of the small clus-ter (3007). The energy-based clusclus-ter detection shown in the bottom diagram does not exhibit such splitting.

Figure 78: Schematic view of a R-152a nucleation simulation (Figure 4; right). Almost all molecules are very quickly clustered in many rather small and stable clusters. Greater changes only happen when two clusters merge, which is clearly indicated by the correspond-ing thick flow groups in the schematic view.

A second, interesting observation in the top image of Figure 77 is the black cluster (ID 2805) which disappears and feeds all molecules with several flow groups to the big, red cluster (ID 2912) over a time of about four time steps before it

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pletely vanishes. The coupling with the direct 3D view revealed the simple reason behind this behaviour: The cluster (ID 2805) became rather slim and elongated at time frame 88, such that the geometrical method failed to get the required four neighbours for some molecules to cleanly detect the cluster. Instead, two clusters are detected. When the cluster changed back into a more elliptical shape, the detec-tion criterion did not re-assign all molecules to the original cluster but to the new one. A similar effect can be seen in Figure 76 between the two selected, red clusters.

The schematic view does successfully represent the behaviour of the data set. A further example is shown in Figure 78. This data set, also shown in the right image of Figure 4, is a nucleation simulation of the cooling agent Difluoroethane (R-152a). Early in the simulation, most molecules cluster in rather small droplets of only few molecules each. Later on, almost no fluctuations between the clusters take place, but clusters coalesce with each other. This is clearly visible in the schematic view by flow groups at the end of the cluster lines, which are of same size as the clusters themselves and which connect to a larger cluster within a very small period of time (usually only a single time step).

This exemplary, abstract visualization of the dynamic of MD data sets can be extended to other types of data and other application fields. However, what be-comes evident is that a generic visualization cannot be optimal in all cases. Instead, visualizations optimized for specific problems and designed and developed in close collaboration between visualization experts and research partners from the corre-sponding application domains will usually yield better results.

4 MegaMol

To recapitulate one important statement of the introduction: The purpose of visual-ization is to gain insight into large data sets from diverse applications (cf. [CMS99], [JH04], and Chapter 1). As such, visualization needs, apart from presenting some novelty, to work with real-world data sets and needs to be applied to real-world problems to advance the scientific field itself. To be able to handle the continuously growing data sets and problem sizes the software complexity also increases to achieve the required solutions. Software systems emerge to cope with this situation and are quickly gaining importance, which can be seen in the fact that major visu-alization venues recently introduced the system paper type. However, such software systems tend to be huge, continuously growing, and more long-lasting than origi-nally intended and expected [Phi98]. Creating such a large software system benefits from expertise beyond the field of visualization itself: namely from a deeper under-standing of software design and the principles of software engineering (SE). In this chapter this concept is detailed by the example of MegaMol [Meg], a visualization system focused on particle-based visualization for MD data sets. Almost all visuali-zations presented in this thesis were implemented as part of MegaMol.