A Primer of Swarm Equilibria

2011 ◽  
Vol 10 (1) ◽  
pp. 212-250 ◽  
Author(s):  
Andrew J. Bernoff ◽  
Chad M. Topaz
Keyword(s):  
Swarm Equilibria

scholarly journals Nonlocal Aggregation Models: A Primer of Swarm Equilibria

SIAM Review ◽  
2013 ◽  
Vol 55 (4) ◽  
pp. 709-747 ◽  
Author(s):  
Andrew J. Bernoff ◽  
Chad M. Topaz
Keyword(s):  
Swarm Equilibria

scholarly journals Equilibria of an aggregation model with linear diffusion in domains with boundaries

2020 ◽  
Vol 30 (04) ◽  
pp. 805-845
Author(s):  
Daniel Messenger ◽  
Razvan C. Fetecau
Keyword(s):  
Critical Points ◽  
Energy Minimization ◽  
Domain Boundary ◽  
Energy Functional ◽  
Linear Diffusion ◽  
Sharp Condition ◽  
Global Minimizers ◽  
Swarm Equilibria ◽  
External Forces ◽  
Domain I

We investigate the effect of linear diffusion and interactions with the domain boundary on swarm equilibria by analyzing critical points of the associated energy functional. Through this process we uncover two properties of energy minimization that depend explicitly on the spatial domain: (i) unboundedness from below of the energy due to an imbalance between diffusive and aggregative forces depends explicitly on a certain volume filling property of the domain, and (ii) metastable mass translation occurs in domains without sufficient symmetry. From the first property, we present a sharp condition for existence (respectively non-existence) of global minimizers in a large class of domains, analogous to results in free space, and from the second property, we identify that external forces are necessary to confine the swarm and grant existence of global minimizers in general domains. We also introduce a numerical method for computing critical points of the energy and give examples to motivate further research.

scholarly journals Swarm Equilibria in Domains with Boundaries

2017 ◽  
Vol 16 (3) ◽  
pp. 1260-1308 ◽  
Author(s):  
R. C. Fetecau ◽  
M. Kovacic
Keyword(s):  
Swarm Equilibria
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