Limits...
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).

Show MeSH
The particle density  with  and particle number  varying from  to .
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3140480&req=5

pone-0022123-g009: The particle density with and particle number varying from to .

Mentions: To study the distinct features of the different aggregation patterns, we hereby demonstrate the density and average distance index along with increasing parameter of Eq. (3) in Figs. 9 and 10, respectively. It is apparent from Fig. 9 that the particle density remains at a quite low level below 1.6 in the crystal-like pattern and then rises abruptly to the high lever over 2.3 representing the liquid-like pattern. Moreover, the intermediate range of is so narrow that highlighting a clear pattern transition from the crystal-like pattern to the liquid-like one. Remarkably, in the crystal-like pattern as shown in Fig. 10, all pairwise distances remain constant roughly at . However, beyond a threshold of , an evident declination of index appears from about to around roughly at , corresponding to the transient intermediate phase (see Fig. 4(c)) between liquid-like (see Fig. 4(a)) and crystal-like (see Fig. 4(b)) phases. Afterwards, the index reaches a low level corresponding to the liquid-like pattern. Significantly, this intermediate region in Fig. 10 nicely matches the one of evolvement at Fig. 9, which strongly supports the existence of the transition from the crystal-like pattern to the liquid-like one.


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

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

The particle density  with  and particle number  varying from  to .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0022123-g009: The particle density with and particle number varying from to .
Mentions: To study the distinct features of the different aggregation patterns, we hereby demonstrate the density and average distance index along with increasing parameter of Eq. (3) in Figs. 9 and 10, respectively. It is apparent from Fig. 9 that the particle density remains at a quite low level below 1.6 in the crystal-like pattern and then rises abruptly to the high lever over 2.3 representing the liquid-like pattern. Moreover, the intermediate range of is so narrow that highlighting a clear pattern transition from the crystal-like pattern to the liquid-like one. Remarkably, in the crystal-like pattern as shown in Fig. 10, all pairwise distances remain constant roughly at . However, beyond a threshold of , an evident declination of index appears from about to around roughly at , corresponding to the transient intermediate phase (see Fig. 4(c)) between liquid-like (see Fig. 4(a)) and crystal-like (see Fig. 4(b)) phases. Afterwards, the index reaches a low level corresponding to the liquid-like pattern. Significantly, this intermediate region in Fig. 10 nicely matches the one of evolvement at Fig. 9, which strongly supports the existence of the transition from the crystal-like pattern to the liquid-like one.

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