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1.
A. T. Winfree, Science 266, 1003 (1994).
http://dx.doi.org/10.1126/science.7973648
2.
J. P. Keener and J. J. Tyson, Science 239, 1284 (1988).
http://dx.doi.org/10.1126/science.239.4845.1284
3.
M. Cross and P. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
http://dx.doi.org/10.1103/RevModPhys.65.851
4.
P. C. Bressloff and J. M. Newby, Rev. Mod. Phys. 85, 135 (2013).
http://dx.doi.org/10.1103/RevModPhys.85.135
5.
Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995).
6.
M. Bär, M. Eiswirth, H. H. Rotermund, and G. Ertl, Phys. Rev. Lett. 69, 945 (1992).
http://dx.doi.org/10.1103/PhysRevLett.69.945
7.
J. Laplante and T. Erneux, J. Phys. Chem. 96, 4931 (1992).
http://dx.doi.org/10.1021/j100191a038
8.
B. Matkowsky and G. Sivashinsky, SIAM J. Appl. Math. 35, 465 (1978).
http://dx.doi.org/10.1137/0135038
9.
C. Koch and I. Segev, Nat. Neurosci. 3, 1171 (2000).
http://dx.doi.org/10.1038/81444
10.
F. Müller, L. Schimansky-Geier, and D. E. Postnov, Ecol. Complex. 14, 21 (2013).
http://dx.doi.org/10.1016/j.ecocom.2012.11.002
11.
M. A. Dahlem and S. C. Müller, S. Biol. Cybern. 88, 419 (2003).
http://dx.doi.org/10.1007/s00422-003-0405-y
12.
Cardiac Electrophysiology: From Cell to Bedside, 6th ed., edited by D. P. Zipes and J. Jalife (W. B. Saunders, Philadelphia, 2014).
13.
N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and its Applications (Charles Griffin & Company Ltd., 1975).
14.
A. Galione, A. McDougall, W. B. Busa, N. Willmott, I. Gillot, and M. Whitaker, Science 261, 348 (1993).
http://dx.doi.org/10.1126/science.8392748
15.
M. Radszuweit, S. Alonso, H. Engel, and M. Bär, Phys. Rev. Lett. 110, 138102 (2013).
http://dx.doi.org/10.1103/PhysRevLett.110.138102
16.
J. S. Bois, F. Jülicher, and S. W. Grill, Phys. Rev. Lett. 106, 028103 (2011).
http://dx.doi.org/10.1103/PhysRevLett.106.028103
17.
C. Shi, C.-H. Huang, P. N. Devreotes, and P. A. Iglesias, PLoS Comput. Biol. 9, e1003122 (2013).
http://dx.doi.org/10.1371/journal.pcbi.1003122
18.
V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 87, 228301 (2001).
http://dx.doi.org/10.1103/PhysRevLett.87.228301
19.
A. Azhand, J. F. Totz, and H. Engel, Europhys. Lett. 108, 10004 (2014).
http://dx.doi.org/10.1209/0295-5075/108/10004
20.
J. F. Totz, H. Engel, and O. Steinbock, New J. Phys. 17, 093043 (2015).
http://dx.doi.org/10.1088/1367-2630/17/9/093043
21.
E. M. Cherry and F. H. Fenton, J. Theor. Biol. 285, 164 (2011).
http://dx.doi.org/10.1016/j.jtbi.2011.06.039
22.
S. R. Kharche, I. V. Biktasheva, G. Seemann, H. Zhang, and V. N. Biktashev, BioMed Res. Int. 2015, 731386.
http://dx.doi.org/10.1155/2015/731386
23.
M. Yamazaki, S. Mironov, C. Taravant, J. Brec, L. M. Vaquero, K. Bandaru, U. M. R. Avula, H. Honjo, I. Kodama, O. Berenfeld, and J. Kalifa, Cardiovasc. Res. 94, 48 (2012).
http://dx.doi.org/10.1093/cvr/cvr357
24.
J. Pellman, R. C. Lyon, and F. Sheikh, J. Mol. Cell. Cardiol. 48, 461 (2010).
http://dx.doi.org/10.1016/j.yjmcc.2009.09.001
25.
M. Häusser, N. Spruston, and G. J. Stuart, Science 290, 739 (2000).
http://dx.doi.org/10.1126/science.290.5492.739
26.
I. Santamaria-Holek, Z. J. Grzywna, and J. M. Rubí, J. Non-Equilib. Thermodyn. 37, 273 (2012).
http://dx.doi.org/10.1515/jnetdy-2011-0029
27.
A. Ledesma-Durán, S. I. Hernández-Hernández, and I. Santamaría-Holek, J. Phys. Chem. C 120, 7810 (2016).
http://dx.doi.org/10.1021/acs.jpcc.5b12145
28.
K. Suzuki, T. Yoshinobu, and H. Iwasaki, J. Phys. Chem. A 104, 5154 (2000).
http://dx.doi.org/10.1021/jp000009n
29.
C. N. Baroud, F. Okkels, L. Ménétrier, and P. Tabeling, Phys. Rev. E 67, 060104 (2003).
http://dx.doi.org/10.1103/PhysRevE.67.060104
30.
H. Kitahata, K. Fujio, J. Gorecki, S. Nakata, Y. Igarashi, A. Gorecka, and K. Yoshikawa, J. Phys. Chem. A 113, 10405 (2009).
http://dx.doi.org/10.1021/jp903686k
31.
A. Toth, V. Gaspar, and K. Showalter, J. Phys. Chem. 98, 522 (1994).
http://dx.doi.org/10.1021/j100053a029
32.
K. Agladze, S. Thouvenel-Romans, and O. Steinbock, J. Phys. Chem. A 105, 7356 (2001).
http://dx.doi.org/10.1021/jp011294t
33.
B. T. Ginn, B. Steinbock, M. Kahveci, and O. Steinbock, J. Phys. Chem. A 108, 1325 (2004).
http://dx.doi.org/10.1021/jp0358883
34.
O. Steinbock, P. Kettunen, and K. Showalter, J. Phys. Chem. 100, 18970 (1996).
http://dx.doi.org/10.1021/jp961209v
35.
J. Wolff, A. G. Papathanasiou, I. G. Kevrekidis, H. H. Rotermund, and G. Ertl, Science 294, 134 (2001).
http://dx.doi.org/10.1126/science.1063597
36.
S. Martens, J. Löber, and H. Engel, Phys. Rev. E 91, 022902 (2015).
http://dx.doi.org/10.1103/PhysRevE.91.022902
37.
I. V. Biktasheva, H. Dierckx, and V. N. Biktashev, Phys. Rev. Lett. 114, 068302 (2015).
http://dx.doi.org/10.1103/PhysRevLett.114.068302
38.
H. Ke, Z. Zhang, and O. Steinbock, Chaos 25, 064303 (2015).
http://dx.doi.org/10.1063/1.4921718
39.
R. FitzHugh, Biophys. J. 1, 445 (1961).
http://dx.doi.org/10.1016/S0006-3495(61)86902-6
40.
J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 50, 2061 (1962).
http://dx.doi.org/10.1109/JRPROC.1962.288235
41.
A. Hagberg and E. Meron, Nonlinearity 7, 805 (1994).
http://dx.doi.org/10.1088/0951-7715/7/3/006
42.
F. Schlögl, Z. Phys. 253, 147 (1972).
http://dx.doi.org/10.1007/BF01379769
43.
S. Martens, G. Schmid, L. Schimansky-Geier, and P. Hänggi, Phys. Rev. E 83, 051135 (2011).
http://dx.doi.org/10.1103/PhysRevE.83.051135
44.
S. Martens, A. V. Straube, G. Schmid, L. Schimansky-Geier, and P. Hänggi, Phys. Rev. Lett. 110, 010601 (2013).
http://dx.doi.org/10.1103/PhysRevLett.110.010601
45.
R. Zwanzig, J. Phys. Chem. 96, 3926 (1992).
http://dx.doi.org/10.1021/j100189a004
46.
Supposing that the concentration profiles in leading order, u0, equal the product of particle number and the probabilities P(r, t) to find such a given molecule at position r at time t and assuming further that the probabilities P can also be expressed by the conditional probabilities p(ρ|x, t) ∝ 1/Q(x) times the marginal ones p(x, t), one obtains the Fick-Jacobs equation describing the spatial-temporal evolution for p(x, t), .
47.
J. P. Keener, SIAM J. Appl. Math. 61, 317 (2000).
http://dx.doi.org/10.1137/S0036139999350810
48.
J. Löber, M. Bär, and H. Engel, Phys. Rev. E 86, 066210 (2012).
http://dx.doi.org/10.1103/PhysRevE.86.066210
49.
J. Xin, SIAM Rev. 42, 161 (2000).
http://dx.doi.org/10.1137/S0036144599364296
50.
G. Nadin, J. Differ. Equations 249, 1288 (2010).
http://dx.doi.org/10.1016/j.jde.2010.05.007
51.
H. Berestycki, F. Hamel, and N. Nadirashvili, J. Eur. Math. Soc. 7, 173 (2005).
http://dx.doi.org/10.4171/JEMS/26
52.
J. Löber and H. Engel, Phys. Rev. Lett. 112, 148305 (2014).
http://dx.doi.org/10.1103/PhysRevLett.112.148305
53.
I. Dikshtein, A. Neimann, and L. Schimansky-Geier, Phys. Lett. A 246, 259 (1998).
http://dx.doi.org/10.1016/S0375-9601(98)00501-5
54.
G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method, Numerical Methods Series (Wiley, 2012).
55.
M. E. Davis, Numerical Methods and Modeling for Chemical Engineers (Courier Corporation, 2013).
56.
H. Johansen and P. Colella, J. Comput. Phys. 147, 60 (1998).
http://dx.doi.org/10.1006/jcph.1998.5965
57.
A. A. García-Chung, G. Chacón-Acosta, and L. Dagdug, J. Chem. Phys. 142, 064105 (2015).
http://dx.doi.org/10.1063/1.4907553
58.
T. A. Davis, ACM Trans. Math. Software 30, 196 (2004).
http://dx.doi.org/10.1145/992200.992206
59.
P. Grindrod, M. A. Lewis, and J. D. Murray, Proc. R. Soc. A 433, 151 (1991).
http://dx.doi.org/10.1098/rspa.1991.0040
60.
A. S. Verkman, Trends Biochem. Sci. 27, 27 (2002).
http://dx.doi.org/10.1016/S0968-0004(01)02003-5
61.
S. L. Dettmer, U. F. Keyser, and S. Pagliara, Rev. Sci. Instrum. 85, 023708 (2014).
http://dx.doi.org/10.1063/1.4865552
62.
P. S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, and J. M. Rubí, BioSystems 93, 16 (2008).
http://dx.doi.org/10.1016/j.biosystems.2008.03.006
63.
L. Dagdug, M.-V. Vazquez, A. M. Berezhkovskii, V. Y. Zitserman, and S. M. Bezrukov, J. Chem. Phys. 136, 204106 (2012).
http://dx.doi.org/10.1063/1.4720385
64.
P. K. Ghosh, P. Hänggi, F. Marchesoni, S. Martens, F. Nori, L. Schimansky-Geier, and G. Schmid, Phys. Rev. E 85, 011101 (2012).
http://dx.doi.org/10.1103/PhysRevE.85.011101
65.
A. E. Cohen and W. E. Moerner, Proc. Natl. Acad. Sci. U. S. A. 103, 4362 (2006).
http://dx.doi.org/10.1073/pnas.0509976103
66.
I. M. Sokolov, Eur. Phys. J. 31, 1353 (2010).
http://dx.doi.org/10.1088/0143-0807/31/6/005
67.
S. Lifson and J. L. Jackson, J. Chem. Phys. 36, 2410 (1962).
http://dx.doi.org/10.1063/1.1732899
68.
S. Martens, G. Schmid, L. Schimansky-Geier, and P. Hänggi, Chaos 21, 047518 (2011).
http://dx.doi.org/10.1063/1.3658621
69.
S. Martens, J. Chem. Phys. 145, 016101 (2016).
http://dx.doi.org/10.1063/1.4955492
70.
R. Luther, Z. Elektrochem. 12, 596 (1906).
http://dx.doi.org/10.1002/bbpc.19060123208
71.
P. Kalinay and J. K. Percus, Phys. Rev. E 74, 041203 (2006).
http://dx.doi.org/10.1103/PhysRevE.74.041203
72.
K. D. Dorfman and E. Yariv, J. Chem. Phys. 141, 044118 (2014).
http://dx.doi.org/10.1063/1.4890740
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/content/aip/journal/jcp/145/9/10.1063/1.4962173
2016-09-07
2016-09-28

Abstract

We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi-two-dimensional reaction-diffusion equation can be reduced into a one-dimensional reaction-diffusion-advection equation. Assuming a weak perturbation by the advection term and using projection method, in a second step, an equation of motion for traveling waves within such tubes can be derived. Both methods predict properly the nonlinear dependence of the propagation velocity on the ratio of the modulation period of the geometry to the intrinsic width of the front, or pulse. As a main feature, we observe finite intervals of propagation failure of waves induced by the tube’s modulation and derive an analytically tractable condition for their occurrence. For the highly diffusive limit, using the Fick-Jacobs approach, we show that wave velocities within modulated tubes are governed by an effective diffusion coefficient. Furthermore, we discuss the effects of a single bottleneck on the period of pulse trains. We observe period changes by integer fractions dependent on the bottleneck width and the period of the entering pulse train.

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