-
1
-
-
0019188958
-
Biased random walk models for chemotaxis and related diffusion approximations
-
W. Alt Biased random walk models for chemotaxis and related diffusion approximations J. Math. Biol. 9 1980 147 177
-
(1980)
J. Math. Biol.
, vol.9
, pp. 147-177
-
-
Alt, W.1
-
2
-
-
0032170064
-
Continuous and discrete mathematical models of tumor-induced angiogenesis
-
A.R.A. Anderson M.A.J. Chaplain Continuous and discrete mathematical models of tumor-induced angiogenesis Bull. Math. Biol. 60 1998 857 900
-
(1998)
Bull. Math. Biol.
, vol.60
, pp. 857-900
-
-
Anderson, A.R.A.1
Chaplain, M.A.J.2
-
3
-
-
0001517703
-
Encephalitis periaxialis concentrica
-
J. Baló Encephalitis periaxialis concentrica Arch. Neurol. Psychiatr. 19 1928 242 264
-
(1928)
Arch. Neurol. Psychiatr.
, vol.19
, pp. 242-264
-
-
Baló, J.1
-
4
-
-
1642281535
-
Relapsing and remitting multiple sclerosis: Pathology of the newly forming lesion
-
M.H. Barnett J.W. Prineas Relapsing and remitting multiple sclerosis: Pathology of the newly forming lesion Ann. Neurol. 55 2004 458 468
-
(2004)
Ann. Neurol.
, vol.55
, pp. 458-468
-
-
Barnett, M.H.1
Prineas, J.W.2
-
6
-
-
0000531920
-
Existence and nonexistence of solutions for a model of gravitational interaction of particles
-
P. Biler T. Nadzieja Existence and nonexistence of solutions for a model of gravitational interaction of particles Colloq. Math. 66 1994 319 334
-
(1994)
Colloq. Math.
, vol.66
, pp. 319-334
-
-
Biler, P.1
Nadzieja, T.2
-
7
-
-
0031897383
-
Physical mechanisms for chemotactic pattern formation by bacteria
-
M.P. Brenner L.S. Levitov E.O. Budrene Physical mechanisms for chemotactic pattern formation by bacteria Biophys. J. 74 1998 1677 1693
-
(1998)
Biophys. J.
, vol.74
, pp. 1677-1693
-
-
Brenner, M.P.1
Levitov, L.S.2
Budrene, E.O.3
-
8
-
-
0029023398
-
Dynamics of formation of symmetrical patterns by chemotactic bacteria
-
E.O. Budrene H.C. Berg Dynamics of formation of symmetrical patterns by chemotactic bacteria Nature 376 1995 49 53
-
(1995)
Nature
, vol.376
, pp. 49-53
-
-
Budrene, E.O.1
Berg, H.C.2
-
9
-
-
0842281982
-
Modeling solid tumour growth using the theory of mixtures
-
H.M. Byrne L. Preziosi Modeling solid tumour growth using the theory of mixtures Math. Med. Biol. 20 2004 341 366
-
(2004)
Math. Med. Biol.
, vol.20
, pp. 341-366
-
-
Byrne, H.M.1
Preziosi, L.2
-
10
-
-
33746377577
-
Volume effects in the Keller–Segel model: Energy estimates preventing blow-up
-
V. Calvez J.A. Carrillo Volume effects in the Keller–Segel model: Energy estimates preventing blow-up J. Math. Pures Appl. 86 2006 155 175
-
(2006)
J. Math. Pures Appl.
, vol.86
, pp. 155-175
-
-
Calvez, V.1
Carrillo, J.A.2
-
11
-
-
85120137337
-
-
V. Calvez, Y. Dolak-Struss, Asymptotic Behavior of a two-dimensional Keller–Segel model with and without density control, To appear in Proceedings of the sixth ECMTB, Dresden, 2005
-
-
-
-
12
-
-
33750903512
-
A Lyapunov function for a two-chemical version of the chemotaxis model
-
V. Calvez B. Perthame A Lyapunov function for a two-chemical version of the chemotaxis model BIT Num. Math. 46 2006 S85 S97
-
(2006)
BIT Num. Math.
, vol.46
, pp. S85-S97
-
-
Calvez, V.1
Perthame, B.2
-
13
-
-
85120100359
-
-
V. Calvez, B. Perthame, M. Sharifi tabar, Modified Keller–Segel system and critical mass for the log interaction kernel, ENS, 2006, Preprint
-
-
-
-
16
-
-
0032831010
-
Serial magnetic resonance imaging in patients with Baló’s concentric sclerosis: Natural history of lesion development
-
C.J. Chen N.S. Chu C.S. Lu C.Y. Sung Serial magnetic resonance imaging in patients with Baló’s concentric sclerosis: Natural history of lesion development Ann. Neurol. 46 1999 651 656
-
(1999)
Ann. Neurol.
, vol.46
, pp. 651-656
-
-
Chen, C.J.1
Chu, N.S.2
Lu, C.S.3
Sung, C.Y.4
-
17
-
-
26844499863
-
Global solutions of some chemotaxis and angiogenesis systems in high space dimensions
-
L. Corrias B. Perthame H. Zaag Global solutions of some chemotaxis and angiogenesis systems in high space dimensions Milan J. Math. 72 2004 1 28
-
(2004)
Milan J. Math.
, vol.72
, pp. 1-28
-
-
Corrias, L.1
Perthame, B.2
Zaag, H.3
-
18
-
-
0028574098
-
Mathematical modelling of corneal epithelium wound healing
-
P.D. Dale P.K. Maini J.A. Sherratt Mathematical modelling of corneal epithelium wound healing Math. Biosci. 124 1994 127 147
-
(1994)
Math. Biosci.
, vol.124
, pp. 127-147
-
-
Dale, P.D.1
Maini, P.K.2
Sherratt, J.A.3
-
19
-
-
0000416519
-
Patterns produced by precipitation at a moving reaction front
-
G.T. Dee Patterns produced by precipitation at a moving reaction front Phys. Rev. Lett. 57 1986 275 278
-
(1986)
Phys. Rev. Lett.
, vol.57
, pp. 275-278
-
-
Dee, G.T.1
-
20
-
-
33644610345
-
The Keller–Segel model with logistic sensitivity function and small diffusivity
-
Y. Dolak C. Schmeiser The Keller–Segel model with logistic sensitivity function and small diffusivity SIAM J. Appl. Math. 66 2005 595 615
-
(2005)
SIAM J. Appl. Math.
, vol.66
, pp. 595-615
-
-
Dolak, Y.1
Schmeiser, C.2
-
22
-
-
33749243493
-
A finite volume scheme for the Patlak–Keller–Segel chemotaxis model
-
F. Filbet A finite volume scheme for the Patlak–Keller–Segel chemotaxis model Numer. Math. 2006
-
(2006)
Numer. Math.
-
-
Filbet, F.1
-
24
-
-
36749107694
-
Mechanism of chemical instability for periodic precipitation phenomena
-
M. Flicker J. Ross Mechanism of chemical instability for periodic precipitation phenomena J. Chem. Phys. 60 1974 3458 3465
-
(1974)
J. Chem. Phys.
, vol.60
, pp. 3458-3465
-
-
Flicker, M.1
Ross, J.2
-
25
-
-
0032445844
-
Global behavior of a reaction–diffusion system modelling chemotaxis
-
H. Gajewski K. Zacharias Global behavior of a reaction–diffusion system modelling chemotaxis Math. Nachr. 195 1998 77 114
-
(1998)
Math. Nachr.
, vol.195
, pp. 77-114
-
-
Gajewski, H.1
Zacharias, K.2
-
26
-
-
85088493164
-
Percolation, morphogenesis, and Burgers dynamics in blood vessels formation
-
A. Gamba D. Ambrosi A. Coniglio A. de Candia S. Di Talia E. Giraudo G. Serini L. Preziosi F. Bussolino Percolation, morphogenesis, and Burgers dynamics in blood vessels formation Phys. Rev. Lett. 90 2003 118101–4
-
(2003)
Phys. Rev. Lett.
, vol.90
-
-
Gamba, A.1
Ambrosi, D.2
Coniglio, A.3
de Candia, A.4
Di Talia, S.5
Giraudo, E.6
Serini, G.7
Preziosi, L.8
Bussolino, F.9
-
28
-
-
0000534296
-
Über die konzentrische Sklerose und die physicalisch-chemischen Faktoren bei der Ausbreitung von Entmarkungsprozessen
-
J. Hallervorden H. Spatz Über die konzentrische Sklerose und die physicalisch-chemischen Faktoren bei der Ausbreitung von Entmarkungsprozessen Arch. Psychiat. Nervenkr. 98 1933 641 701
-
(1933)
Arch. Psychiat. Nervenkr.
, vol.98
, pp. 641-701
-
-
Hallervorden, J.1
Spatz, H.2
-
29
-
-
0004008653
-
Crystals in Gels and Liesegang Rings
-
H.K. Henisch Crystals in Gels and Liesegang Rings 1986 Cambridge University Press Cambridge pp. 137–152
-
(1986)
-
-
Henisch, H.K.1
-
30
-
-
85120137612
-
-
D. Hilhorst, R. Van der Hout, M. Mimura, I. Ohnishi, Personal communication
-
-
-
-
31
-
-
0001404830
-
Global existence for a parabolic chemotaxis model with prevention of overcrowding
-
T. Hillen K.J. Painter Global existence for a parabolic chemotaxis model with prevention of overcrowding Adv. Appl. Math. 26 2001 280 301
-
(2001)
Adv. Appl. Math.
, vol.26
, pp. 280-301
-
-
Hillen, T.1
Painter, K.J.2
-
32
-
-
0028987613
-
Dictyostelium discoideum: Cellular self-organisation in an excitable medium
-
T. Höfer J.A. Sherratt P.K. Maini Dictyostelium discoideum: Cellular self-organisation in an excitable medium Proc. R. Soc. Lond. B 259 1995 249 257
-
(1995)
Proc. R. Soc. Lond. B
, vol.259
, pp. 249-257
-
-
Höfer, T.1
Sherratt, J.A.2
Maini, P.K.3
-
33
-
-
4744373150
-
From 1970 until present: The Keller–Segel model in chemotaxis and its consequences. Part I
-
D. Horstmann From 1970 until present: The Keller–Segel model in chemotaxis and its consequences. Part I Jahresbericht der DMV 105 2003 103 165
-
(2003)
Jahresbericht der DMV
, vol.105
, pp. 103-165
-
-
Horstmann, D.1
-
34
-
-
84966208077
-
On explosions of solutions to a system of partial differential equations modelling chemotaxis
-
W. Jäger S. Luckhaus On explosions of solutions to a system of partial differential equations modelling chemotaxis Trans. Amer. Math. Soc. 329 1992 819 824
-
(1992)
Trans. Amer. Math. Soc.
, vol.329
, pp. 819-824
-
-
Jäger, W.1
Luckhaus, S.2
-
35
-
-
11144326950
-
Comparative analysis of the development of swarming communities of Bacillus subtilis 168 and a natural wild type: Critical effects of surfactin and the composition of the medium
-
D. Julkowska M. Obuchowski I.B. Holland S.J. Séror Comparative analysis of the development of swarming communities of Bacillus subtilis 168 and a natural wild type: Critical effects of surfactin and the composition of the medium J. Bacteriol. 187 2005 65 76
-
(2005)
J. Bacteriol.
, vol.187
, pp. 65-76
-
-
Julkowska, D.1
Obuchowski, M.2
Holland, I.B.3
Séror, S.J.4
-
36
-
-
0014748565
-
Initiation of slime mold aggregation viewed as an instability
-
E.F. Keller L.A. Segel Initiation of slime mold aggregation viewed as an instability J. Theoret. Biol. 26 1970 399 415
-
(1970)
J. Theoret. Biol.
, vol.26
, pp. 399-415
-
-
Keller, E.F.1
Segel, L.A.2
-
37
-
-
0038046529
-
Recurrent precipitation and Liesegang rings
-
J.B. Keller S.I. Rubinow Recurrent precipitation and Liesegang rings J. Chem. Phys. 74 1981 5000 5007
-
(1981)
J. Chem. Phys.
, vol.74
, pp. 5000-5007
-
-
Keller, J.B.1
Rubinow, S.I.2
-
38
-
-
85120099911
-
-
H. Khonsari, V. Calvez, The origins of concentric demyelination: Self-organization in the human brain, Plos ONE (2007), doi:10.1371/journal.pone.0000150
-
-
-
-
39
-
-
15844396394
-
Preventing blow-up in a chemotaxis model
-
R. Kowalczyk Preventing blow-up in a chemotaxis model J. Math. Anal. Appl. 305 2005 566 588
-
(2005)
J. Math. Anal. Appl.
, vol.305
, pp. 566-588
-
-
Kowalczyk, R.1
-
40
-
-
0029731281
-
Morphological instabilities in pattern formation by precipitation and crystallization processes
-
H.J. Krug H. Brandstädter K.H. Jacob Morphological instabilities in pattern formation by precipitation and crystallization processes Geol. Rundsch. 85 1996 19 28
-
(1996)
Geol. Rundsch.
, vol.85
, pp. 19-28
-
-
Krug, H.J.1
Brandstädter, H.2
Jacob, K.H.3
-
41
-
-
23844506444
-
Multiple sclerosis pathology: Evolution of pathogenic concepts
-
H. Lassmann Multiple sclerosis pathology: Evolution of pathogenic concepts Brain Pathol. 15 2005 217 222
-
(2005)
Brain Pathol.
, vol.15
, pp. 217-222
-
-
Lassmann, H.1
-
42
-
-
0002293719
-
Nucleation and colloidal growth in concentration gradients (Liesegang rings)
-
R.E. Liesegang Nucleation and colloidal growth in concentration gradients (Liesegang rings) Photogr. Archiv. 21 1986 221
-
(1986)
Photogr. Archiv.
, vol.21
, pp. 221
-
-
Liesegang, R.E.1
-
44
-
-
16644400591
-
Mathematical modeling of tumor-induced angiogenesis
-
N.V. Mantzaris S. Webb H.G. Othmer Mathematical modeling of tumor-induced angiogenesis J. Math. Biol. 49 2004 111 187
-
(2004)
J. Math. Biol.
, vol.49
, pp. 111-187
-
-
Mantzaris, N.V.1
Webb, S.2
Othmer, H.G.3
-
45
-
-
0012470921
-
Mathematical Biology II. Spatial Models and Biomedical Applications
-
J.D. Murray Mathematical Biology II. Spatial Models and Biomedical Applications 3rd ed. 2003 Springer-Verlag New York
-
(2003)
-
-
Murray, J.D.1
-
46
-
-
0000911252
-
Blow-up of radially symmetric solutions to a chemotaxis system
-
T. Nagai Blow-up of radially symmetric solutions to a chemotaxis system Adv. Math. Sci. Appl. 5 1995 581 601
-
(1995)
Adv. Math. Sci. Appl.
, vol.5
, pp. 581-601
-
-
Nagai, T.1
-
47
-
-
19744380563
-
Resting microglial cells are highly dynamic surveillants of brain parenchyma in vivo
-
A. Nimmerjahn F. Kirchhoff F. Helmchen Resting microglial cells are highly dynamic surveillants of brain parenchyma in vivo Science 308 2005 1314 1318
-
(2005)
Science
, vol.308
, pp. 1314-1318
-
-
Nimmerjahn, A.1
Kirchhoff, F.2
Helmchen, F.3
-
48
-
-
85120130324
-
-
Oberwolfach Report 24, Mathematical Biology, Mathematisches Forschungsinstitut Oberwolfach, 2006
-
-
-
-
49
-
-
0004037179
-
Lehrbuch der allgemeinen Chemie
-
W. Ostwald Lehrbuch der allgemeinen Chemie 1897 Engelman Leipzig
-
(1897)
-
-
Ostwald, W.1
-
50
-
-
0033545988
-
Stripe formation in juvenile Pomacanthus explained by a generalised Turing mechanism with chemotaxis
-
K.J. Painter P.K. Maini H.G. Othmer Stripe formation in juvenile Pomacanthus explained by a generalised Turing mechanism with chemotaxis Proc. Natl. Acad. Sci. 96 1999 5549 5554
-
(1999)
Proc. Natl. Acad. Sci.
, vol.96
, pp. 5549-5554
-
-
Painter, K.J.1
Maini, P.K.2
Othmer, H.G.3
-
51
-
-
4944248574
-
Volume-filling and quorum-sensing in models for chemosensitive movement
-
K.J. Painter T. Hillen Volume-filling and quorum-sensing in models for chemosensitive movement Canad. Appl. Math. Q. 10 2002 501 543
-
(2002)
Canad. Appl. Math. Q.
, vol.10
, pp. 501-543
-
-
Painter, K.J.1
Hillen, T.2
-
52
-
-
51249193541
-
Random walk with persistence and external bias
-
C.S. Patlak Random walk with persistence and external bias Bull. Math. Biophys. 15 1953 311 338
-
(1953)
Bull. Math. Biophys.
, vol.15
, pp. 311-338
-
-
Patlak, C.S.1
-
53
-
-
84867975891
-
PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
-
B. Perthame PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic Appl. Math. 49 2004 539 564
-
(2004)
Appl. Math.
, vol.49
, pp. 539-564
-
-
Perthame, B.1
-
54
-
-
85120110218
-
-
L. Preziosi Cancer Modelling and Simulation 2003 Chapman Hall/CRC Press
-
(2003)
-
-
-
55
-
-
84916389355
-
Gummel, Large signal analysis of a Silicon Read diode oscillator
-
D. Scharfetter Gummel, Large signal analysis of a Silicon Read diode oscillator IEEE Trans. Electron. Dev. 16 1969
-
(1969)
IEEE Trans. Electron. Dev.
, vol.16
-
-
Scharfetter, D.1
-
56
-
-
18744394057
-
Tissue preconditioning may explain concentric lesions in Baló’s type of multiple sclerosis
-
C. Stadelmann S. Ludwin T. Tabira A. Guseo C.F. Lucchinetti L. Leel-Ossy A.T. Ordinario W. Brück H. Lassmann Tissue preconditioning may explain concentric lesions in Baló’s type of multiple sclerosis Brain 128 2005 979 987
-
(2005)
Brain
, vol.128
, pp. 979-987
-
-
Stadelmann, C.1
Ludwin, S.2
Tabira, T.3
Guseo, A.4
Lucchinetti, C.F.5
Leel-Ossy, L.6
Ordinario, A.T.7
Brück, W.8
Lassmann, H.9
-
57
-
-
0029959555
-
The molecular biology of axon guidance
-
M. Tessier-Lavigne C.S. Goodman The molecular biology of axon guidance Science 274 1996 1123 1133
-
(1996)
Science
, vol.274
, pp. 1123-1133
-
-
Tessier-Lavigne, M.1
Goodman, C.S.2
-
59
-
-
0033112265
-
Model and analysis of chemotactic bacterial patterns in a liquid medium
-
R. Tyson S.R. Lubkin J.D. Murray Model and analysis of chemotactic bacterial patterns in a liquid medium J. Math. Biol. 38 1999 359 375
-
(1999)
J. Math. Biol.
, vol.38
, pp. 359-375
-
-
Tyson, R.1
Lubkin, S.R.2
Murray, J.D.3
-
60
-
-
0001743254
-
Nucleation and colloidal growth in concentration gradients (Liesegang rings)
-
G. Venzl J. Ross Nucleation and colloidal growth in concentration gradients (Liesegang rings) J. Chem. Phys. 77 1982 1302 1307
-
(1982)
J. Chem. Phys.
, vol.77
, pp. 1302-1307
-
-
Venzl, G.1
Ross, J.2
-
61
-
-
17144417771
-
Diffusion abnormality in Baló’s concentric sclerosis: Clues for the pathogenesis
-
H. Wiendl R. Weissert U. Herrlinger H. Krapf W. Kuker Diffusion abnormality in Baló’s concentric sclerosis: Clues for the pathogenesis Eur. Neurol. 53 2005 42 44
-
(2005)
Eur. Neurol.
, vol.53
, pp. 42-44
-
-
Wiendl, H.1
Weissert, R.2
Herrlinger, U.3
Krapf, H.4
Kuker, W.5
-
62
-
-
33646266962
-
Long-time behaviour of solutions to a chemotaxis model with volume-filling effect
-
D. Wrzosek Long-time behaviour of solutions to a chemotaxis model with volume-filling effect Proc. Roy. Soc. Edinburgh Sect. A 136 2006 431 444
-
(2006)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.136
, pp. 431-444
-
-
Wrzosek, D.1
-
63
-
-
0036746709
-
Cell movement patterns during gastrulation in the chick are controlled by positive and negative chemotaxis mediated by FGF4 and FGF8
-
X. Yang D. Dormann A.E. Munsterberg C.J. Weijer Cell movement patterns during gastrulation in the chick are controlled by positive and negative chemotaxis mediated by FGF4 and FGF8 Dev. Cell 3 2002 425 437
-
(2002)
Dev. Cell
, vol.3
, pp. 425-437
-
-
Yang, X.1
Dormann, D.2
Munsterberg, A.E.3
Weijer, C.J.4
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