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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) The distance  distribution with increasing .Here, the particle number  and . (a) “Liquid-like” pattern with , (b) “Crystal-like” pattern with , (c) Intermediate pattern with . All the other settings are the same as Fig. 2.
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pone-0022123-g005: (Color online) The distance distribution with increasing .Here, the particle number and . (a) “Liquid-like” pattern with , (b) “Crystal-like” pattern with , (c) Intermediate pattern with . All the other settings are the same as Fig. 2.

Mentions: To facilitate our investigation, we assume there are totally connections in the proximity net of the group, and then define and () as the Euclidean distance of the -th link and the distance between the geometric center of each cluster and the middle point of -th link. With these definitions, we study the density's variation from inside to outside of each cluster by exhibiting the distribution of along with increasing as shown in Fig. 5. Apparently, it is shown in Fig. 5(a) that rises with increasing , implying that the particles will become sparse from the kernel to the surface of each cluster, and hence this case corresponds to the liquid-like pattern. By contrast, Fig. 5(b) is self-consistent with the crystal-like pattern, where are independent of since the distance between each particle pair remains constant. Per the intermediate phase, Fig. 5(c) shows a mixture of crystal-like and liquid-like pattern, in which the neighboring distances 's also rise slightly with increasing . Nevertheless, the standard variance of is much larger than those of the crystal-like and liquid-like phases, which well explains the irregular features of the “partially melted” phase.


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) The distance  distribution with increasing .Here, the particle number  and . (a) “Liquid-like” pattern with , (b) “Crystal-like” pattern with , (c) Intermediate pattern with . 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-g005: (Color online) The distance distribution with increasing .Here, the particle number and . (a) “Liquid-like” pattern with , (b) “Crystal-like” pattern with , (c) Intermediate pattern with . All the other settings are the same as Fig. 2.
Mentions: To facilitate our investigation, we assume there are totally connections in the proximity net of the group, and then define and () as the Euclidean distance of the -th link and the distance between the geometric center of each cluster and the middle point of -th link. With these definitions, we study the density's variation from inside to outside of each cluster by exhibiting the distribution of along with increasing as shown in Fig. 5. Apparently, it is shown in Fig. 5(a) that rises with increasing , implying that the particles will become sparse from the kernel to the surface of each cluster, and hence this case corresponds to the liquid-like pattern. By contrast, Fig. 5(b) is self-consistent with the crystal-like pattern, where are independent of since the distance between each particle pair remains constant. Per the intermediate phase, Fig. 5(c) shows a mixture of crystal-like and liquid-like pattern, in which the neighboring distances 's also rise slightly with increasing . Nevertheless, the standard variance of is much larger than those of the crystal-like and liquid-like phases, which well explains the irregular features of the “partially melted” phase.

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