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Volumn 372, Issue 2028, 2014, Pages

On global minimizers of repulsive - Attractive power-law interaction energies

Author keywords

Global discrete minimizers; Interaction energy; Swarming models

Indexed keywords

CONTINUUM PROBLEM; DIRAC DELTA; DISCRETE SETTINGS; FLOCK PATTERNS; GLOBAL DISCRETE MINIMIZERS; GLOBAL MINIMIZERS; INTERACTION ENERGIES; SPATIAL PROFILES;

EID: 84907863231     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2013.0399     Document Type: Article
Times cited : (29)

References (46)
  • 1
    • 1542399709 scopus 로고    scopus 로고
    • Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
    • Carrillo JA, McCann RJ, Villani C. 2003 Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoam. 19, 971-1018. (doi:10.4171/RMI/376)
    • (2003) Rev. Mat. Iberoam. , vol.19 , pp. 971-1018
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 2
    • 32544445429 scopus 로고    scopus 로고
    • Contractions in the 2-Wasserstein length space and thermalization of granular media
    • Carrillo JA, McCann RJ, Villani C. 2006 Contractions in the 2-Wasserstein length space and thermalization of granular media. Arch. Rat. Mech. Anal. 179, 217-263. (doi:10.1007/s00205-005-0386-1)
    • (2006) Arch. Rat. Mech. Anal. , vol.179 , pp. 217-263
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 3
    • 65249090848 scopus 로고    scopus 로고
    • Blowup in multidimensional aggregation equations with mildly singular interaction kernels
    • Bertozzi A, Carrillo JA, Laurent T. 2009 Blowup in multidimensional aggregation equations with mildly singular interaction kernels. Nonlinearity 22, 683-710. (doi:10.1088/0951-7715/22/3/009)
    • (2009) Nonlinearity , vol.22 , pp. 683-710
    • Bertozzi, A.1    Carrillo, J.A.2    Laurent, T.3
  • 4
    • 79551709781 scopus 로고    scopus 로고
    • Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
    • Carrillo JA, Di Francesco M, Figalli A, Laurent T, Slepčev D. 2011 Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Duke Math. J. 156, 229-271. (doi:10.1215/00127094-2010-211)
    • (2011) Duke Math. J. , vol.156 , pp. 229-271
    • Carrillo, J.A.1    Di Francesco, M.2    Figalli, A.3    Laurent, T.4    Slepčev, D.5
  • 5
    • 84857862616 scopus 로고    scopus 로고
    • Aggregation and spreading via the Newtonian potential: The dynamics of patch solutions
    • Bertozzi AL, Laurent T, Léger F. 2012 Aggregation and spreading via the Newtonian potential: the dynamics of patch solutions. Math. Models Methods Appl. Sci. 22, 1140005. (doi:10.1142/S0218202511400057)
    • (2012) Math. Models Methods Appl. Sci. , vol.22 , pp. 1140005
    • Bertozzi, A.L.1    Laurent, T.2    Léger, F.3
  • 6
    • 78651233551 scopus 로고    scopus 로고
    • Stable stationary states of non-local interaction equations
    • Fellner K, Raoul G. 2010 Stable stationary states of non-local interaction equations. Math. Models Methods Appl. Sci. 20, 2267-2291. (doi:10.1142/S0218202510004921)
    • (2010) Math. Models Methods Appl. Sci. , vol.20 , pp. 2267-2291
    • Fellner, K.1    Raoul, G.2
  • 7
    • 79951580992 scopus 로고    scopus 로고
    • Stability of stationary states of non-local equations with singular interaction potentials
    • Fellner K, Raoul G. 2011 Stability of stationary states of non-local equations with singular interaction potentials. Math. Comput. Model. 53, 1436-1450. (doi:10.1016/j.mcm.2010.03.021)
    • (2011) Math. Comput. Model. , vol.53 , pp. 1436-1450
    • Fellner, K.1    Raoul, G.2
  • 8
    • 80053259548 scopus 로고    scopus 로고
    • Swarm dynamics and equilibria for a nonlocal aggregation model
    • Fetecau RC, Huang Y, Kolokolnikov T. 2011 Swarm dynamics and equilibria for a nonlocal aggregation model. Nonlinearity 24, 2681-2716. (doi:10.1088/0951-7715/24/10/002)
    • (2011) Nonlinearity , vol.24 , pp. 2681-2716
    • Fetecau, R.C.1    Huang, Y.2    Kolokolnikov, T.3
  • 9
    • 84885376066 scopus 로고    scopus 로고
    • Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
    • Fetecau RC, Huang Y. 2013 Equilibria of biological aggregations with nonlocal repulsive-attractive interactions. Physica D 260, 49-64. (doi:10.1016/j.physd.2012.11.004)
    • (2013) Physica D , vol.260 , pp. 49-64
    • Fetecau, R.C.1    Huang, Y.2
  • 10
    • 84879250347 scopus 로고    scopus 로고
    • Non-local interaction equations: Stationary states and stability analysis
    • Raoul G. 2012 Non-local interaction equations: stationary states and stability analysis. Diff. Integral Equ. 25, 417-440. See http://projecteuclid.org/euclid.die/1356012673.
    • (2012) Diff. Integral Equ. , vol.25 , pp. 417-440
    • Raoul, G.1
  • 11
    • 84885371603 scopus 로고    scopus 로고
    • Nonlocal interactions by repulsive-attractive potentials: Radial ins/stability
    • Balagué D, Carrillo JA, Laurent T, Raoul G. 2013 Nonlocal interactions by repulsive-attractive potentials: radial ins/stability. Physica D 260, 5-25. (doi:10.1016/j.physd.2012.10.002)
    • (2013) Physica D , vol.260 , pp. 5-25
    • Balagué, D.1    Carrillo, J.A.2    Laurent, T.3    Raoul, G.4
  • 12
    • 84879262358 scopus 로고    scopus 로고
    • Dimensionality of local minimizers of the interaction energy
    • Balagué D, Carrillo JA, Laurent T, Raoul G. 2013 Dimensionality of local minimizers of the interaction energy. Arch. Rat. Mech. Anal. 209, 1055-1088. (doi:10.1007/s00205-013-0644-6)
    • (2013) Arch. Rat. Mech. Anal. , vol.209 , pp. 1055-1088
    • Balagué, D.1    Carrillo, J.A.2    Laurent, T.3    Raoul, G.4
  • 13
    • 79961119434 scopus 로고    scopus 로고
    • Stability of ring patterns arising from 2D particle interactions
    • Kolokolnikov T, Sun H, Uminsky D, Bertozzi A. 2011 Stability of ring patterns arising from 2D particle interactions. Phys. Rev. E 84, 015203. (doi:10.1103/PhysRevE.84.015203)
    • (2011) Phys. Rev. E , vol.84 , pp. 015203
    • Kolokolnikov, T.1    Sun, H.2    Uminsky, D.3    Bertozzi, A.4
  • 14
    • 0032090818 scopus 로고    scopus 로고
    • A non-Maxwellian steady distribution for one-dimensional granular media
    • Benedetto D, Caglioti E, Carrillo JA, Pulvirenti M. 1998 A non-Maxwellian steady distribution for one-dimensional granular media. J. Stat. Phys. 91, 979-990. (doi:10.1023/A:1023032000560)
    • (1998) J. Stat. Phys. , vol.91 , pp. 979-990
    • Benedetto, D.1    Caglioti, E.2    Carrillo, J.A.3    Pulvirenti, M.4
  • 15
    • 3042676199 scopus 로고    scopus 로고
    • Long-time asymptotics of kinetic models of granular flows
    • Li H, Toscani G. 2004 Long-time asymptotics of kinetic models of granular flows. Arch. Rat. Mech. Anal. 172, 407-428. (doi:10.1007/s00205-004-0307-8)
    • (2004) Arch. Rat. Mech. Anal. , vol.172 , pp. 407-428
    • Li, H.1    Toscani, G.2
  • 16
    • 0001508106 scopus 로고    scopus 로고
    • A non-local model for a swarm
    • Mogilner A, Edelstein-Keshet L. 1999 A non-local model for a swarm. J. Math. Biol. 38, 534-570. (doi:10.1007/s002850050158)
    • (1999) J. Math. Biol. , vol.38 , pp. 534-570
    • Mogilner, A.1    Edelstein-Keshet, L.2
  • 17
    • 33644946843 scopus 로고    scopus 로고
    • Self-propelled particles with soft-core interactions: Patterns, stability and collapse
    • D'Orsogna MR, Chuang Y, Bertozzi A, Chayes L. 2006 Self-propelled particles with softcore interactions: patterns, stability and collapse. Phys. Rev. Lett. 96, 104302. (doi:10.1103/PhysRevLett.96.104302)
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 104302
    • D'Orsogna, M.R.1    Chuang, Y.2    Bertozzi, A.3    Chayes, L.4
  • 18
    • 1342268227 scopus 로고    scopus 로고
    • Mutual interactions, potentials, and individual distance in a social aggregation
    • Mogilner A, Edelstein-Keshet L, Bent L, Spiros A. 2003 Mutual interactions, potentials, and individual distance in a social aggregation. J. Math. Biol. 47, 353-389. (doi:10.1007/s00285-003-0209-7)
    • (2003) J. Math. Biol. , vol.47 , pp. 353-389
    • Mogilner, A.1    Edelstein-Keshet, L.2    Bent, L.3    Spiros, A.4
  • 19
    • 84886516210 scopus 로고    scopus 로고
    • Emergent behaviour in multi-particle systems with non-local interactions
    • Kolokolnikov T, Carrillo JA, Bertozzi A, Fetecau R, Lewis M. 2013 Emergent behaviour in multi-particle systems with non-local interactions, Physica D 260, 1-4. (doi:10.1016/j.physd.2013.06.011)
    • (2013) Physica D , vol.260 , pp. 1-4
    • Kolokolnikov, T.1    Carrillo, J.A.2    Bertozzi, A.3    Fetecau, R.4    Lewis, M.5
  • 20
    • 33745787907 scopus 로고    scopus 로고
    • Dynamic pathways for viral capsid assembly
    • Hagan MF, Chandler D. 2006 Dynamic pathways for viral capsid assembly. Biophys. J. 91, 42-54. (doi:10.1529/biophysj.105.076851)
    • (2006) Biophys. J. , vol.91 , pp. 42-54
    • Hagan, M.F.1    Chandler, D.2
  • 21
    • 36449008021 scopus 로고
    • The effect of the range of the potential on the structures of clusters
    • Doye JPK, Wales DJ, Berry RS. 1995 The effect of the range of the potential on the structures of clusters. J. Chem. Phys. 103, 4234-4249. (doi:10.1063/1.470729)
    • (1995) J. Chem. Phys. , vol.103 , pp. 4234-4249
    • Doye, J.P.K.1    Wales, D.J.2    Berry, R.S.3
  • 22
    • 77955910647 scopus 로고    scopus 로고
    • Energy landscapes of clusters bound by short-ranged potentials
    • Wales DJ. 2010 Energy landscapes of clusters bound by short-ranged potentials. ChemPhysChem 11, 2491-2494. (doi:10.1002/cphc.201000233)
    • (2010) ChemPhysChem , vol.11 , pp. 2491-2494
    • Wales, D.J.1
  • 23
    • 28844455500 scopus 로고    scopus 로고
    • Optimized interactions for targeted self-assembly: Application to a honeycomb lattice
    • Rechtsman MC, Stillinger FH, Torquato S. 2005 Optimized interactions for targeted self-assembly: application to a honeycomb lattice. Phys. Rev. Lett. 95, 228301. (doi:10.1103/PhysRevLett.95.228301)
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 228301
    • Rechtsman, M.C.1    Stillinger, F.H.2    Torquato, S.3
  • 25
    • 84879605770 scopus 로고    scopus 로고
    • On soccer balls and linearized inverse statistical mechanics
    • von Brecht J, Uminsky D. 2012 On soccer balls and linearized inverse statistical mechanics. J. Nonlinear Sci. 22, 935-959. (doi:10.1007/s00332-012-9132-7)
    • (2012) J. Nonlinear Sci. , vol.22 , pp. 935-959
    • Von Brecht, J.1    Uminsky, D.2
  • 26
    • 84894906962 scopus 로고    scopus 로고
    • Nonlinear stability of flock solutions in second-order swarming models
    • Carrillo JA, Huang Y, Martin S. 2014 Nonlinear stability of flock solutions in second-order swarming models. Nonlinear Anal. Real World Appl. 17, 332-343. (doi:10.1016/j.nonrwa.2013.12.008)
    • (2014) Nonlinear Anal. Real World Appl. , vol.17 , pp. 332-343
    • Carrillo, J.A.1    Huang, Y.2    Martin, S.3
  • 28
    • 84903935059 scopus 로고    scopus 로고
    • Stability analysis of flock and mill rings for second order models in swarming
    • Albi G, Balagué D, Carrillo JA, von Brecht J. 2014 Stability analysis of flock and mill rings for second order models in swarming. SIAM J. Appl. Math. 74, 794-818. (doi:10.1137/13091779X)
    • (2014) SIAM J. Appl. Math. , vol.74 , pp. 794-818
    • Albi, G.1    Balagué, D.2    Carrillo, J.A.3    Von Brecht, J.4
  • 29
    • 0028554218 scopus 로고
    • The simulation of fish schools in comparison with experimental data
    • Huth A, Wissel C. 1994 The simulation of fish schools in comparison with experimental data. Ecol. Model. 75/76, 135-145. (doi:10.1016/0304-3800(94)90013-2)
    • (1994) Ecol. Model. , vol.75-76 , pp. 135-145
    • Huth, A.1    Wissel, C.2
  • 30
    • 77955434078 scopus 로고    scopus 로고
    • Inferring individual rules from collective behavior
    • Lukeman R, Li YX, Edelstein-Keshet L. 2010 Inferring individual rules from collective behavior. Proc. Natl Acad. Sci. USA 107, 12576-12580. (doi:10.1073/pnas.1001763107)
    • (2010) Proc. Natl Acad. Sci. USA , vol.107 , pp. 12576-12580
    • Lukeman, R.1    Li, Y.X.2    Edelstein-Keshet, L.3
  • 31
    • 34249106048 scopus 로고    scopus 로고
    • Emergent behavior in flocks
    • Cucker F, Smale S. 2007 Emergent behavior in flocks. IEEE Trans. Automat. Control 52, 852-862. (doi:10.1109/TAC.2007.895842)
    • (2007) IEEE Trans. Automat. Control , vol.52 , pp. 852-862
    • Cucker, F.1    Smale, S.2
  • 32
    • 34047112216 scopus 로고    scopus 로고
    • On the mathematics of emergence
    • Cucker F, Smale S. 2007 On the mathematics of emergence. Jpn J. Math. 2, 197-227. (doi:10.1007/s11537-007-0647-x)
    • (2007) Jpn J. Math. , vol.2 , pp. 197-227
    • Cucker, F.1    Smale, S.2
  • 33
    • 34547297895 scopus 로고    scopus 로고
    • Phase and anti-phase boundaries in binary discrete systems: A variational viewpoint
    • Alicandro R, Braides A, Cicalese M. 2006 Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint. Netw. Heterog. Media 1, 85-107. (doi:10.3934/nhm.2006.1.85)
    • (2006) Netw. Heterog. Media , vol.1 , pp. 85-107
    • Alicandro, R.1    Braides, A.2    Cicalese, M.3
  • 34
    • 59449106896 scopus 로고    scopus 로고
    • On the crystallization of 2D hexagonal lattices
    • Weinan E, Li D. 2009 On the crystallization of 2D hexagonal lattices. Commun. Math. Phys. 286, 1099-1140. (doi:10.1007/s00220-008-0586-2)
    • (2009) Commun. Math. Phys. , vol.286 , pp. 1099-1140
    • Weinan, E.1    Li, D.2
  • 35
    • 84858703391 scopus 로고    scopus 로고
    • Minimizing atomic configurations of short range pair potentials in two dimensions: Crystallization in the Wulff shape
    • Au Yeung Y, Friesecke G, Schmidt B. 2012 Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Calc. Var. Partial Diff. Equ. 44, 81-100. (doi:10.1007/s00526-011-0427-6)
    • (2012) Calc. Var. Partial Diff. Equ. , vol.44 , pp. 81-100
    • Au Yeung, Y.1    Friesecke, G.2    Schmidt, B.3
  • 36
    • 29644436437 scopus 로고    scopus 로고
    • A proof of crystallization in two dimensions
    • Theil F. 2006 A proof of crystallization in two dimensions. Commun. Math. Phys. 262, 209-236. (doi:10.1007/s00220-005-1458-7)
    • (2006) Commun. Math. Phys. , vol.262 , pp. 209-236
    • Theil, F.1
  • 40
    • 0000033355 scopus 로고
    • Convergence of random processes and limit theorems in probability theory
    • English translation
    • Prokhorov YV. 1956 Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. 1, 157-214. [English translation] (doi:10.1137/1101016)
    • (1956) Theory Probab. Appl. , vol.1 , pp. 157-214
    • Prokhorov, Y.V.1
  • 41
    • 0000797976 scopus 로고
    • A class of Wasserstein metrics for probability distributions
    • Givens CR, Shortt RM. 1984 A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31, 231-240. (doi:10.1307/mmj/1029003026)
    • (1984) Michigan Math. J. , vol.31 , pp. 231-240
    • Givens, C.R.1    Shortt, R.M.2
  • 42
    • 85067770704 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics, Providence, RI: American Mathematical Society
    • Villani C. 2003 Topics in optimal transportation. Graduate Studies in Mathematics, vol. 58. Providence, RI: American Mathematical Society.
    • (2003) Topics in Optimal Transportation , vol.58
    • Villani, C.1
  • 45
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann RJ. 1997 A convexity principle for interacting gases. Adv. Math. 128, 153-179. (doi:10.1006/aima.1997.1634)
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • McCann, R.J.1
  • 46
    • 84861881074 scopus 로고    scopus 로고
    • A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
    • Carrillo JA, Ferreira LCF, Precioso JC. 2012 A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity. Adv. Math. 231, 306-327. (doi:10.1016/j.aim.2012.03.036)
    • (2012) Adv. Math. , vol.231 , pp. 306-327
    • Carrillo, J.A.1    Ferreira, L.C.F.2    Precioso, J.C.3


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