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Aggregation pattern transitions by slightly varying the attractive/repulsive function.

Cheng Z, Zhang HT, Chen MZ, Zhou T, Valeyev NV - PLoS ONE (2011)

Bottom Line: More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster.Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant.Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Digital Manufacturing Equipments and Technology, Huazhong University of Science and Technology, Wuhan, People's Republic of China.

ABSTRACT
Among collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional links between particles play an important role. By slightly changing the cutoff distance of the A/R function, a drastic transition between two distinct aggregation patterns is observed. More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster. Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant. Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations. This work bridges the aggregation phenomena of physical particles and swarming of organisms in nature upon revealing some common mechanism behind them by slightly varying their inter-individual attractive/repulsive functions, and may find its potential engineering applications, for example, in the formation design of multi-robot systems and unmanned aerial vehicles (UAVs).

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(Color online) Crystal-like pattern of  particles with .Subfigures (a), (b) and (c) are the snapshots at the th, th and th running steps, and (d) shows the zoomed in crystal-like cluster. All the other settings are the same as Fig. 2.
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pone-0022123-g003: (Color online) Crystal-like pattern of particles with .Subfigures (a), (b) and (c) are the snapshots at the th, th and th running steps, and (d) shows the zoomed in crystal-like cluster. All the other settings are the same as Fig. 2.

Mentions: A remarkable transition phenomenon from so-called liquid-like pattern to crystal-like one emerges in the numerical simulations along with increasing (see Eq. (3)). In detail, for the liquid-like pattern as shown in Fig. 2 and Fig. 4(a), some small clusters of particles are formed with structures quite similar to liquid drops among which the particle density is decreasing from the drop kernel to the surface due to the “surface tension”. Moreover, when multiple clusters or “drops” encounter, they will merge into a larger ring-shaped cluster or “drop” no matter what the original orientations and velocities the former “drops” were in. In comparison, for the crystal-like pattern, larger clusters are formed with much more evenly distributed particles as shown in Fig. 3 and Fig. 4(b), where a regular lattice-shaped formation emerges, which resembles molecules' distribution in crystal phase. When multiple crystal-like clusters encounter, the merged cluster will form an irregular shape determined by the original orientations and velocities of the previous clusters. Furthermore, the collective dynamics of the self-driven particles is more complex than these two aforementioned patterns, as there still exists a quasi-stable transient intermediate pattern [45] between them as show in Fig. 4(c). This pattern embodies a mixture of the crystal-like internal lattice together with the liquid-like ring-shaped external features. We call it a transient status since such a “partially melted” pattern is much weaker than the liquid- and crystal-like ones, whose corresponding range of is much smaller than those of the two latter ones. Thereby, the dynamics of the self-driven particles is dominated by the liquid-like and crystal-like patterns, whose characteristics are the focus of our investigation.


Aggregation pattern transitions by slightly varying the attractive/repulsive function.

Cheng Z, Zhang HT, Chen MZ, Zhou T, Valeyev NV - PLoS ONE (2011)

(Color online) Crystal-like pattern of  particles with .Subfigures (a), (b) and (c) are the snapshots at the th, th and th running steps, and (d) shows the zoomed in crystal-like cluster. All the other settings are the same as Fig. 2.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3140480&req=5

pone-0022123-g003: (Color online) Crystal-like pattern of particles with .Subfigures (a), (b) and (c) are the snapshots at the th, th and th running steps, and (d) shows the zoomed in crystal-like cluster. All the other settings are the same as Fig. 2.
Mentions: A remarkable transition phenomenon from so-called liquid-like pattern to crystal-like one emerges in the numerical simulations along with increasing (see Eq. (3)). In detail, for the liquid-like pattern as shown in Fig. 2 and Fig. 4(a), some small clusters of particles are formed with structures quite similar to liquid drops among which the particle density is decreasing from the drop kernel to the surface due to the “surface tension”. Moreover, when multiple clusters or “drops” encounter, they will merge into a larger ring-shaped cluster or “drop” no matter what the original orientations and velocities the former “drops” were in. In comparison, for the crystal-like pattern, larger clusters are formed with much more evenly distributed particles as shown in Fig. 3 and Fig. 4(b), where a regular lattice-shaped formation emerges, which resembles molecules' distribution in crystal phase. When multiple crystal-like clusters encounter, the merged cluster will form an irregular shape determined by the original orientations and velocities of the previous clusters. Furthermore, the collective dynamics of the self-driven particles is more complex than these two aforementioned patterns, as there still exists a quasi-stable transient intermediate pattern [45] between them as show in Fig. 4(c). This pattern embodies a mixture of the crystal-like internal lattice together with the liquid-like ring-shaped external features. We call it a transient status since such a “partially melted” pattern is much weaker than the liquid- and crystal-like ones, whose corresponding range of is much smaller than those of the two latter ones. Thereby, the dynamics of the self-driven particles is dominated by the liquid-like and crystal-like patterns, whose characteristics are the focus of our investigation.

Bottom Line: More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster.Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant.Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Digital Manufacturing Equipments and Technology, Huazhong University of Science and Technology, Wuhan, People's Republic of China.

ABSTRACT
Among collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional links between particles play an important role. By slightly changing the cutoff distance of the A/R function, a drastic transition between two distinct aggregation patterns is observed. More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster. Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant. Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations. This work bridges the aggregation phenomena of physical particles and swarming of organisms in nature upon revealing some common mechanism behind them by slightly varying their inter-individual attractive/repulsive functions, and may find its potential engineering applications, for example, in the formation design of multi-robot systems and unmanned aerial vehicles (UAVs).

Show MeSH