@article{balague_carrillo_yao_2014, title={CONFINEMENT FOR REPULSIVE-ATTRACTIVE KERNELS}, volume={19}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2014.19.1227}, abstractNote={We investigate the confinement properties of solutions of the 
aggregation equation with repulsive-attractive potentials. We show 
that solutions remain compactly supported in a large fixed ball 
depending on the initial data and the potential. The arguments 
apply to the functional setting of probability measures with 
mildly singular repulsive-attractive potentials and to the 
functional setting of smooth solutions with a potential being the 
sum of the Newtonian repulsion at the origin and a smooth suitably 
growing at infinity attractive potential.}, number={5}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Balague, Daniel and Carrillo, Jose A. and Yao, Yao}, year={2014}, month={Jul}, pages={1227–1248} }
 @article{albi_balague_carrillo_von brecht_2014, title={STABILITY ANALYSIS OF FLOCK AND MILL RINGS FOR SECOND ORDER MODELS IN SWARMING}, volume={74}, ISSN={["1095-712X"]}, DOI={10.1137/13091779x}, abstractNote={We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. We relate the instability of the flock rings with the instability of the ring solution of the first order model. We observe that repulsive-attractive interactions lead to clustering and fattening instabilities for flock rings that prove analogous to similar instabilities that occur for ring solutions of the first order model. Finally, we numerically explore mill patterns arising from these interactions by varying the asymptotic speed of the system.}, number={3}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Albi, G. and Balague, D. and Carrillo, J. A. and Von Brecht, J.}, year={2014}, pages={794–818} }