-
2
-
-
65249090848
-
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
-
A. L. Bertozzi, J. A. Carrillo, and T. Laurent, Blow-up in multidimensional aggregation equations with mildly singular interaction kernels, Nonlinearity, 22 (2009), pp. 683-710.
-
(2009)
Nonlinearity
, vol.22
, pp. 683-710
-
-
Bertozzi, A.L.1
Carrillo, J.A.2
Laurent, T.3
-
3
-
-
34547507325
-
Finite-time blow-up of solutions of an aggregation equation in rn
-
A. L. Bertozzi and T. Laurent, Finite-time blow-up of solutions of an aggregation equation in Rn, Comm. Math. Phys., 274 (2007), pp. 717-735.
-
(2007)
Comm. Math. Phys.
, vol.274
, pp. 717-735
-
-
Bertozzi, A.L.1
Laurent, T.2
-
4
-
-
84885343269
-
The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels
-
A. L. Bertozzi and T. Laurent, The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels, Chinese Ann. Math. Ser. B, 30 (2009), pp. 463-482.
-
(2009)
Chinese Ann. Math. Ser. B
, vol.30
, pp. 463-482
-
-
Bertozzi, A.L.1
Laurent, T.2
-
5
-
-
0003112033
-
Helmholtz and taylor instability
-
American Mathematical Society, Providence, RI
-
G. Birkhoff, Helmholtz and Taylor instability, in Proceedings of the Symposium on Applied Mathematics, vol. 13, American Mathematical Society, Providence, RI, 1962, pp. 55-76.
-
(1962)
Proceedings of the Symposium on Applied Mathematics
, vol.13
, pp. 55-76
-
-
Birkhoff, G.1
-
6
-
-
0033163978
-
Diffusion, attraction and collapse
-
M. P. Brenner, P. Constantin, L. P. Kadanoff, A. Schenkel, and S. C. Venkataramani, Diffusion, attraction and collapse, Nonlinearity, 12 (1999), pp. 1071-1098.
-
(1999)
Nonlinearity
, vol.12
, pp. 1071-1098
-
-
Brenner, M.P.1
Constantin, P.2
Kadanoff, L.P.3
Schenkel, A.4
Venkataramani, S.C.5
-
7
-
-
0001528484
-
Convergence of the vortex method for vortex sheets
-
R. E. Caflisch and J. S. Lowengrub, Convergence of the vortex method for vortex sheets, SIAM J. Numer. Anal., 26 (1989), pp. 1060-1080.
-
(1989)
SIAM J. Numer. Anal.
, vol.26
, pp. 1060-1080
-
-
Caflisch, R.E.1
Lowengrub, J.S.2
-
8
-
-
0030488510
-
A mean-field model of superconducting vortices
-
S. J. Chapman, J. Rubinstein, and M. Schatzman, A mean-field model of superconducting vortices, European J. Appl. Math., 7 (1996), pp. 97-111.
-
(1996)
European J. Appl. Math.
, vol.7
, pp. 97-111
-
-
Chapman, S.J.1
Rubinstein, J.2
Schatzman, M.3
-
9
-
-
0002223508
-
On the critical dissipative quasi-geostrophic equation
-
P. Constantin, D. Cordoba, and J. Wu, On the critical dissipative quasi-geostrophic equation, Indiana Univ. Math. J., 50 (2001), pp. 97-107.
-
(2001)
Indiana Univ. Math. J.
, vol.50
, pp. 97-107
-
-
Constantin, P.1
Cordoba, D.2
Wu, J.3
-
10
-
-
0043172071
-
Formation of strong fronts in the 2-d quasigeostrophic thermal active scalar
-
P. Constantin, A. J. Majda, and E. Tabak, Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar, Nonlinearity, 7 (1994), pp. 1495-1533.
-
(1994)
Nonlinearity
, vol.7
, pp. 1495-1533
-
-
Constantin, P.1
Majda, A.J.2
Tabak, E.3
-
11
-
-
0033419179
-
Behavior of solutions of 2d quasi-geostrophic equations
-
P. Constantin and J. Wu, Behavior of solutions of 2D quasi-geostrophic equations, SIAM J. Math. Anal., 30 (1999), pp. 937-948.
-
(1999)
SIAM J. Math. Anal.
, vol.30
, pp. 937-948
-
-
Constantin, P.1
Wu, J.2
-
12
-
-
0242511186
-
Existence of weak solutions to some vortex density models
-
Q. Du and P. Zhang, Existence of weak solutions to some vortex density models, SIAM J. Math. Anal., 34 (2003), pp. 1279-1299.
-
(2003)
SIAM J. Math. Anal.
, vol.34
, pp. 1279-1299
-
-
Du, Q.1
Zhang, P.2
-
13
-
-
0036647967
-
A vortex particle method for two-dimensional compressible flow
-
J. D. Eldredge, T. Colonius, and A. Leonard, A vortex particle method for two-dimensional compressible flow, J. Comput. Phys., 179 (2002), pp. 371-399.
-
(2002)
J. Comput. Phys.
, vol.179
, pp. 371-399
-
-
Eldredge, J.D.1
Colonius, T.2
Leonard, A.3
-
14
-
-
0039420344
-
Dynamics of vortex liquids in ginzburg-landau theories with applications to superconductivity
-
E. Weinan, Dynamics of vortex liquids in Ginzburg-Landau theories with applications to superconductivity, Phys. Rev. B, 50 (1994), pp. 1126-1135.
-
(1994)
Phys. Rev. B
, vol.50
, pp. 1126-1135
-
-
Weinan, E.1
-
15
-
-
70450159983
-
Azimuthal instability of a vortex ring computed by a vortex sheet panel method
-
H. Feng, L. Kaganovskiy, and R. Krasny, Azimuthal instability of a vortex ring computed by a vortex sheet panel method, Fluid Dynam. Res., 41 (2009), p. 051405, 16.
-
(2009)
Fluid Dynam. Res.
, vol.41
, Issue.16
, pp. 051405
-
-
Feng, H.1
Kaganovskiy, L.2
Krasny, R.3
-
16
-
-
0028976264
-
Surface quasigeostrophic dynamics
-
I. M. Held, R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, Surface quasigeostrophic dynamics, J. Fluid Mech., 282 (1995), pp. 1-20.
-
(1995)
J. Fluid Mech.
, vol.282
, pp. 1-20
-
-
Held, I.M.1
Pierrehumbert, R.T.2
Garner, S.T.3
Swanson, K.L.4
-
17
-
-
0030334089
-
Chemotactic collapse for the keller-segel model
-
M. A. Herrero and J. J. L. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol., 35 (1996), pp. 177-194.
-
(1996)
J. Math. Biol.
, vol.35
, pp. 177-194
-
-
Herrero, M.A.1
Velázquez, J.J.L.2
-
18
-
-
0026137905
-
Convergence of a point vortex method for vortex sheets
-
T. Y. Hou, J. Lowengrub, and R. Krasny, Convergence of a point vortex method for vortex sheets, SIAM J. Numer. Anal., 28 (1991), pp. 308-320.
-
(1991)
SIAM J. Numer. Anal.
, vol.28
, pp. 308-320
-
-
Hou, T.Y.1
Lowengrub, J.2
Krasny, R.3
-
19
-
-
77956257904
-
Self-similar blowup solutions to an aggregation equation in rn
-
Y. Huang and A. L. Bertozzi, Self-similar blowup solutions to an aggregation equation in Rn, SIAM J. Appl. Math., 70 (2010), pp. 2582-2603.
-
(2010)
SIAM J. Appl. Math.
, vol.70
, pp. 2582-2603
-
-
Huang, Y.1
Bertozzi, A.L.2
-
20
-
-
84861616334
-
Asymptotics of blowup solutions for the aggregation equation
-
(to appear)
-
Y. Huang and A. L. Bertozzi, Asymptotics of blowup solutions for the aggregation equation, DCDS, (to appear).
-
DCDS
-
-
Huang, Y.1
Bertozzi, A.L.2
-
21
-
-
79961119434
-
Stability of ring patterns arising from two-dimensional particle interactions
-
T. Kolokolnikov, H. Sun, D. Uminsky, and A. L. Bertozzi, Stability of ring patterns arising from two-dimensional particle interactions, Phys. Rev. E, 84 (2011), 015203.
-
(2011)
Phys. Rev. E
, vol.84
, pp. 015203
-
-
Kolokolnikov, T.1
Sun, H.2
Uminsky, D.3
Bertozzi, A.L.4
-
22
-
-
36048971185
-
Desingularization of periodic vortex sheet roll-up
-
R. Krasny, Desingularization of periodic vortex sheet roll-up, J. Comput. Phys., 65 (1986), pp. 292-313.
-
(1986)
J. Comput. Phys.
, vol.65
, pp. 292-313
-
-
Krasny, R.1
-
23
-
-
0023451072
-
Computation of vortex sheet roll-up in the treffitz plane
-
R. Krasny, Computation of vortex sheet roll-up in the Treffitz plane, J. Fluid Mech., 184 (1987), pp. 123-155.
-
(1987)
J. Fluid Mech.
, vol.184
, pp. 123-155
-
-
Krasny, R.1
-
24
-
-
0040309074
-
Vortex methods for flow simulation
-
A. Leonard, Vortex methods for flow simulation, J. Comput. Phys., 37 (1980), pp. 289-335.
-
(1980)
J. Comput. Phys.
, vol.37
, pp. 289-335
-
-
Leonard, A.1
-
25
-
-
0034387188
-
On the hydrodynamic limit of ginzburg-landau vortices
-
F. Lin and P. Zhang, On the hydrodynamic limit of Ginzburg-Landau vortices, Discrete Contin. Dyn. Syst., 6 (2000), pp. 121-142.
-
(2000)
Discrete Contin. Dyn. Syst.
, vol.6
, pp. 121-142
-
-
Lin, F.1
Zhang, P.2
-
27
-
-
18844433317
-
Global solutions to vortex density equations arising from supconductivity
-
N. Masmoudi and P. Zhang, Global solutions to vortex density equations arising from supconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), pp. 441-458.
-
(2005)
Ann. Inst. H. Poincaré Anal. Non Linéaire
, vol.22
, pp. 441-458
-
-
Masmoudi, N.1
Zhang, P.2
-
28
-
-
0033515748
-
Complexity, pattern, and evolutionary trade-offs in animal aggregation
-
J. K. Parrish and L. Edelstein-Keshet, Complexity, pattern, and evolutionary trade-offs in animal aggregation, Science, 284 (1999), pp. 99-101.
-
(1999)
Science
, vol.284
, pp. 99-101
-
-
Parrish, J.K.1
Edelstein-Keshet, L.2
-
29
-
-
0010817242
-
A study of the vortex sheet method and its rate of convergence
-
E. G. Puckett, A study of the vortex sheet method and its rate of convergence, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 298-327.
-
(1989)
SIAM J. Sci. Statist. Comput.
, vol.10
, pp. 298-327
-
-
Puckett, E.G.1
-
30
-
-
0001308278
-
Self-organized vortex state in two-dimensional dictyostelium dynamics
-
W.-J. Rappel, A. Nicol, A. Sarkissian, H. Levine, and W. F. Loomis, Self-organized vortex state in two-dimensional dictyostelium dynamics, Phys. Rev. Lett., 83 (1999), pp. 1247-1250.
-
(1999)
Phys. Rev. Lett.
, vol.83
, pp. 1247-1250
-
-
Rappel, W.-J.1
Nicol, A.2
Sarkissian, A.3
Levine, H.4
Loomis, W.F.5
-
31
-
-
77949425067
-
From generation to chaotic motion of a ring configuration of vortex structures on a sphere
-
T. Sakajo, From generation to chaotic motion of a ring configuration of vortex structures on a sphere, Theoret. Computational Fluid Dynam., 24 (2010), pp. 151-156.
-
(2010)
Theoret. Computational Fluid Dynam.
, vol.24
, pp. 151-156
-
-
Sakajo, T.1
-
32
-
-
0005464952
-
A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation, amer
-
T. C. Schneirla, A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation, Amer. Museum Novitates, 1253 (1944), pp. 1-26.
-
(1944)
Museum Novitates
, vol.1253
, pp. 1-26
-
-
Schneirla, T.C.1
-
33
-
-
0026809542
-
A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method
-
M. J. Shelley, A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method, J. Fluid Mechan., 244 (1992), pp. 493-526.
-
(1992)
J. Fluid Mechan.
, vol.244
, pp. 493-526
-
-
Shelley, M.J.1
-
34
-
-
0036592410
-
Surface quasigeostrophic turbulence: The study of an active scalar
-
J. Sukhatme and R. T. Pierrehumbert, Surface quasigeostrophic turbulence: The study of an active scalar, Chaos, 12 (2002), pp. 439-450.
-
(2002)
Chaos
, vol.12
, pp. 439-450
-
-
Sukhatme, J.1
Pierrehumbert, R.T.2
-
35
-
-
0038247451
-
Finite time analyticity for the two-and three-dimensional kelvin-helmholtz instability
-
C. Sulem, P.-L. Sulem, C. Bardos, and U. Frisch, Finite time analyticity for the two-and three-dimensional Kelvin-Helmholtz instability, Comm. Math. Phys., 80 (1981), pp. 485-516.
-
(1981)
Comm. Math. Phys.
, vol.80
, pp. 485-516
-
-
Sulem, C.1
Sulem, P.-L.2
Bardos, C.3
Frisch, U.4
-
36
-
-
16244371027
-
Swarming patterns in a two-dimensional kinematic model for biological groups
-
C. M. Topaz and A. L. Bertozzi, Swarming patterns in a two-dimensional kinematic model for biological groups, SIAM J. Appl. Math., 65 (2004), pp. 152-174.
-
(2004)
SIAM J. Appl. Math.
, vol.65
, pp. 152-174
-
-
Topaz, C.M.1
Bertozzi, A.L.2
-
37
-
-
0036588873
-
Stability of some mechanisms of chemotactic aggregation
-
J. J. L. Velázquez, Stability of some mechanisms of chemotactic aggregation, SIAM J. Appl. Math., 62 (2002), pp. 1581-1633.
-
(2002)
SIAM J. Appl. Math.
, vol.62
, pp. 1581-1633
-
-
Velázquez, J.J.L.1
-
38
-
-
84857874283
-
Predicting pattern formation in particle interactions
-
to appear
-
J. von Brecht, D. Uminsky, T. Kolokolnikov, and A. L. Bertozzi, Predicting pattern formation in particle interactions, Math. Models Methods Appl. Sci., to appear.
-
Math. Models Methods Appl. Sci
-
-
Von Brecht, J.1
Uminsky, D.2
Kolokolnikov, T.3
Bertozzi, A.L.4
-
39
-
-
84879605770
-
On soccer balls and linearized inverses statistical mechanics
-
to appear
-
J. von Brecht and D. Uminsky, On soccer balls and linearized inverses statistical mechanics, J. Nonlinear Sci., to appear.
-
J. Nonlinear Sci
-
-
Von Brecht, J.1
Uminsky, D.2
|