-
3
-
-
55049122195
-
Parametric approximation of Willmore flow and related geometric evolution equations
-
Barrett JW, Garcke H, Nürnberg (2008) Parametric approximation of Willmore flow and related geometric evolution equations. SIAM J Sci Comput 31: 225-253.
-
(2008)
SIAM J Sci Comput
, vol.31
, pp. 225-253
-
-
Barrett, J.W.1
Garcke, H.2
Nürnberg3
-
4
-
-
33144458232
-
The effect of growth and curvature on pattern formation
-
Barrio RA, Maini PK, Padilla P, Plaza RG, Sánchez-Garduno F (2004) The effect of growth and curvature on pattern formation. J Dyn Diff Equ 4: 1093-1121.
-
(2004)
J Dyn Diff Equ
, vol.4
, pp. 1093-1121
-
-
Barrio, R.A.1
Maini, P.K.2
Padilla, P.3
Plaza, R.G.4
Sánchez-Garduno, F.5
-
5
-
-
73249116154
-
A finite volume method for solving parabolic equations on logically cartesian curved surface meshes
-
Calhoun DA, Helzel C (2009) A finite volume method for solving parabolic equations on logically cartesian curved surface meshes. SIAM J Sci Comput 6: 4066-4099.
-
(2009)
SIAM J Sci Comput
, vol.6
, pp. 4066-4099
-
-
Calhoun, D.A.1
Helzel, C.2
-
6
-
-
0035348998
-
Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
-
Chaplain MAJ, Ganesh M, Graham IG (2001) Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. J Math Biol 42: 387-423.
-
(2001)
J Math Biol
, vol.42
, pp. 387-423
-
-
Chaplain, M.A.J.1
Ganesh, M.2
Graham, I.G.3
-
7
-
-
0036485212
-
Mode doubling and tripling in reation-diffusion patterns on growing domains: a piecewise linear model
-
Crampin EJ, Gaffney EA, Maini PK (2002) Mode doubling and tripling in reation-diffusion patterns on growing domains: a piecewise linear model. J Math Biol 44: 107-128.
-
(2002)
J Math Biol
, vol.44
, pp. 107-128
-
-
Crampin, E.J.1
Gaffney, E.A.2
Maini, P.K.3
-
8
-
-
0032701813
-
Reaction and diffusion on growing domains: scenarios for robust pattern formation
-
Crampin EJ, Gaffney EA, Maini PK (1999) Reaction and diffusion on growing domains: scenarios for robust pattern formation. Bull Math Biol 61: 1093-1120.
-
(1999)
Bull Math Biol
, vol.61
, pp. 1093-1120
-
-
Crampin, E.J.1
Gaffney, E.A.2
Maini, P.K.3
-
9
-
-
19844369196
-
Computation of Geometric PDEs and Mean Curvature Flow
-
Deckelnick KP, Dziuk G, Elliott CM (2005) Computation of Geometric PDEs and Mean Curvature Flow. Acta Numerica 14: 139-232.
-
(2005)
Acta Numerica
, vol.14
, pp. 139-232
-
-
Deckelnick, K.P.1
Dziuk, G.2
Elliott, C.M.3
-
11
-
-
34047103813
-
Finite elements on evolving surfaces
-
Dziuk G, Elliott CM (2007) Finite elements on evolving surfaces. IMA J Num Anal 27: 262-292.
-
(2007)
IMA J Num Anal
, vol.27
, pp. 262-292
-
-
Dziuk, G.1
Elliott, C.M.2
-
12
-
-
34447646892
-
Surface finite elements for parabolic equations
-
Dziuk G, Elliott CM (2007) Surface finite elements for parabolic equations. J Comp Math 25: 430-439.
-
(2007)
J Comp Math
, vol.25
, pp. 430-439
-
-
Dziuk, G.1
Elliott, C.M.2
-
13
-
-
72149102491
-
An Eulerian approach to transport and diffusion on evolving surfaces
-
Dziuk G, Elliott CM (2010) An Eulerian approach to transport and diffusion on evolving surfaces. Comput Vis Sci 13: 17-28.
-
(2010)
Comput Vis Sci
, vol.13
, pp. 17-28
-
-
Dziuk, G.1
Elliott, C.M.2
-
14
-
-
84868381356
-
2 estimates for the evolving surface finite element method
-
(submitted)
-
2 estimates for the evolving surface finite element method. Math Comp (submitted).
-
(2010)
Math Comp
-
-
Dziuk, G.1
Elliott, C.M.2
-
15
-
-
53349164104
-
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method
-
Eilks C, Elliott CM (2008) Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method. J Comp Phys 227: 9727-9741.
-
(2008)
J Comp Phys
, vol.227
, pp. 9727-9741
-
-
Eilks, C.1
Elliott, C.M.2
-
16
-
-
77954144568
-
Modeling and computation of two phase geometric biomembranes using surface finite elements
-
Elliott CM, Stinner B (2010) Modeling and computation of two phase geometric biomembranes using surface finite elements. J Comp Phys 229: 6585-6612.
-
(2010)
J Comp Phys
, vol.229
, pp. 6585-6612
-
-
Elliott, C.M.1
Stinner, B.2
-
17
-
-
79960506297
-
Numerical computation of advection and diffusion on evolving diffuse interfaces
-
Advance Access published on 11 May 2010. doi: 10. 1093/imanum/drq005
-
Elliott CM, Stinner B, Styles VM (2010) Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA J Num Anal. Advance Access published on 11 May 2010. doi: 10. 1093/imanum/drq005.
-
(2010)
IMA J Num Anal.
-
-
Elliott, C.M.1
Stinner, B.2
Styles, V.M.3
-
18
-
-
0015454185
-
A theory of biological pattern formation
-
Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetik 12: 30-39.
-
(1972)
Kybernetik
, vol.12
, pp. 30-39
-
-
Gierer, A.1
Meinhardt, H.2
-
20
-
-
33646143528
-
Fourth order partial differential equations on general geometries
-
Greer J, Bertozzi AL, Sapiro G (2006) Fourth order partial differential equations on general geometries. J Comput Phys 216: 216-246.
-
(2006)
J Comput Phys
, vol.216
, pp. 216-246
-
-
Greer, J.1
Bertozzi, A.L.2
Sapiro, G.3
-
21
-
-
0029163545
-
A reaction-diffusion wave on the skin of the marine anglefish, Pomacanthus
-
Kondo S, Asai R (1995) A reaction-diffusion wave on the skin of the marine anglefish, Pomacanthus. Nature 376: 765-768.
-
(1995)
Nature
, vol.376
, pp. 765-768
-
-
Kondo, S.1
Asai, R.2
-
22
-
-
77954610650
-
A reaction-diffusion model of the human brain development
-
Lefevre J, Mangin J-F (2010) A reaction-diffusion model of the human brain development. PLoS Comput Biol 6: e1000749.
-
(2010)
PLoS Comput Biol
, vol.6
-
-
Lefevre, J.1
Mangin, J.-F.2
-
23
-
-
0141515669
-
A moving grid finite element method applied to a model biological pattern generator
-
Madzvamuse A, Maini PK, Wathen AJ (2003) A moving grid finite element method applied to a model biological pattern generator. J Comp Phys 190: 478-500.
-
(2003)
J Comp Phys
, vol.190
, pp. 478-500
-
-
Madzvamuse, A.1
Maini, P.K.2
Wathen, A.J.3
-
24
-
-
23944439965
-
A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains
-
Madzvamuse A, Wathen AJ, Maini PK (2005) A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains. J Sci Comp 24(2): 247-262.
-
(2005)
J Sci Comp
, vol.24
, Issue.2
, pp. 247-262
-
-
Madzvamuse, A.1
Wathen, A.J.2
Maini, P.K.3
-
25
-
-
33644519990
-
Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
-
Madzvamuse A (2006) Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. J Comput Phys 216: 239-263.
-
(2006)
J Comput Phys
, vol.216
, pp. 239-263
-
-
Madzvamuse, A.1
-
26
-
-
34447283073
-
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
-
Madzvamuse A, Maini P (2007) Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains. J Comput Phys 225: 100-119.
-
(2007)
J Comput Phys
, vol.225
, pp. 100-119
-
-
Madzvamuse, A.1
Maini, P.2
-
27
-
-
72149120586
-
Turing instability conditions for growing domains with divergence free mesh velocity
-
Madzvamuse A (2009) Turing instability conditions for growing domains with divergence free mesh velocity. Nonlinear Anal Theory Methods Appl 12: 2250-2257.
-
(2009)
Nonlinear Anal Theory Methods Appl
, vol.12
, pp. 2250-2257
-
-
Madzvamuse, A.1
-
28
-
-
77952289005
-
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
-
Madzvamuse A, Gaffney EA, Maini PK (2009) Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains. J Math Biol 61: 133-164.
-
(2009)
J Math Biol
, vol.61
, pp. 133-164
-
-
Madzvamuse, A.1
Gaffney, E.A.2
Maini, P.K.3
-
29
-
-
33748737797
-
Spatial pattern formation in chemical and biological systems
-
Maini PK, Painter KJ, Chau HNP (1997) Spatial pattern formation in chemical and biological systems. Faraday Trans 93: 3601-3610.
-
(1997)
Faraday Trans
, vol.93
, pp. 3601-3610
-
-
Maini, P.K.1
Painter, K.J.2
Chau, H.N.P.3
-
31
-
-
33144458232
-
The effect of growth and curvature on pattern formation
-
Plaza RG, Sánchez-Garduño F, Padilla P, Barrio RA, Maini PK (2004) The effect of growth and curvature on pattern formation. J Dynam Diff Eqs 16(4): 1093-11214.
-
(2004)
J Dynam Diff Eqs
, vol.16
, Issue.4
, pp. 1093-11214
-
-
Plaza, R.G.1
Sánchez-Garduño, F.2
Padilla, P.3
Barrio, R.A.4
Maini, P.K.5
-
32
-
-
36849102494
-
Symmetry breaking instabilities in dissipative systems. II
-
Prigogine I, Lefever R (1968) Symmetry breaking instabilities in dissipative systems. II. J Chem Phys 48: 1695-1700.
-
(1968)
J Chem Phys
, vol.48
, pp. 1695-1700
-
-
Prigogine, I.1
Lefever, R.2
-
33
-
-
0018784247
-
Simple chemical reaction systems with limit cycle behaviour
-
Schnakenberg J (1979) Simple chemical reaction systems with limit cycle behaviour. J Theor Biol 81: 389-400.
-
(1979)
J Theor Biol
, vol.81
, pp. 389-400
-
-
Schnakenberg, J.1
-
35
-
-
0002011401
-
The chemical basis of morphogenesis
-
Turing A (1952) The chemical basis of morphogenesis. Phil Trans R Soc Lond B 237: 37-72.
-
(1952)
Phil Trans R Soc Lond B
, vol.237
, pp. 37-72
-
-
Turing, A.1
|