-
1
-
-
1542399709
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
24
-
-
84857874283
-
Predicting pattern formation in particle interactions
-
von Brecht J, Uminsky D, Kolokolnikov T, Bertozzi A. 2012 Predicting pattern formation in particle interactions. Math. Models Methods Appl. Sci. 22, 1140002. (doi:10.1142/S0218202511400021)
-
(2012)
Math. Models Methods Appl. Sci.
, vol.22
, pp. 1140002
-
-
Von Brecht, J.1
Uminsky, D.2
Kolokolnikov, T.3
Bertozzi, A.4
-
25
-
-
84879605770
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
37
-
-
80055013696
-
Confinement in nonlocal interaction equations
-
Carrillo JA, Di Francesco M, Figalli A, Laurent T, Slepčev D. 2012 Confinement in nonlocal interaction equations. Nonlinear Anal. 75, 550-558. (doi:10.1016/j.na.2011.08.057)
-
(2012)
Nonlinear Anal.
, vol.75
, pp. 550-558
-
-
Carrillo, J.A.1
Di Francesco, M.2
Figalli, A.3
Laurent, T.4
Slepčev, D.5
-
40
-
-
0000033355
-
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
-
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
-
-
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
-
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
-
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
|