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Journal articles on the topic 'Reaction-diffusion waves'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Sherratt, Jonathan A. "Irregular wakes in reaction-diffusion waves." Physica D: Nonlinear Phenomena 70, no. 4 (1994): 370–82. http://dx.doi.org/10.1016/0167-2789(94)90072-8.

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2

McDermott, Sean, Anthony J. Mulholland, and Jagannathan Gomatam. "Knotted reaction—diffusion waves." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2028 (2002): 2947–66. http://dx.doi.org/10.1098/rspa.2002.0997.

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3

Volpert, V., and S. Petrovskii. "Reaction–diffusion waves in biology." Physics of Life Reviews 6, no. 4 (2009): 267–310. http://dx.doi.org/10.1016/j.plrev.2009.10.002.

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4

Clavin, P. "Flames and Reaction-Diffusion Waves (Abstract)." Materials Science Forum 155-156 (May 1994): 445–46. http://dx.doi.org/10.4028/www.scientific.net/msf.155-156.445.

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5

Bland, J. A., and J. Smoller. "Shock Waves and Reaction-Diffusion Equations." Mathematical Gazette 69, no. 447 (1985): 70. http://dx.doi.org/10.2307/3616482.

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6

Keyfitz, Barbara Lee, and Joel Smoller. "Shock Waves and Reaction-Diffusion Equations." American Mathematical Monthly 93, no. 4 (1986): 315. http://dx.doi.org/10.2307/2323701.

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7

Galochkina, Tatiana, Anass Bouchnita, Polina Kurbatova, and Vitaly Volpert. "Reaction-diffusion waves of blood coagulation." Mathematical Biosciences 288 (June 2017): 130–39. http://dx.doi.org/10.1016/j.mbs.2017.03.008.

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8

Abe, Yotaro, and Ryo Yoshida. "Dancing Waves in Reaction−Diffusion Systems." Journal of Physical Chemistry A 109, no. 17 (2005): 3773–76. http://dx.doi.org/10.1021/jp050075v.

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9

Saxena, R. K., A. M. Mathai, and H. J. Haubold. "Reaction-Diffusion Systems and Nonlinear Waves." Astrophysics and Space Science 305, no. 3 (2006): 297–303. http://dx.doi.org/10.1007/s10509-006-9190-0.

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10

Apreutesei, Narcisa, and Vitaly Volpert. "Reaction-diffusion waves with nonlinear boundary conditions." Networks & Heterogeneous Media 8, no. 1 (2013): 23–35. http://dx.doi.org/10.3934/nhm.2013.8.23.

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11

Panfilov, A. V., H. Dierckx, and V. Volpert. "(INVITED) Reaction–diffusion waves in cardiovascular diseases." Physica D: Nonlinear Phenomena 399 (December 2019): 1–34. http://dx.doi.org/10.1016/j.physd.2019.04.001.

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12

Crooks, Elaine C. M., and John F. Toland. "Travelling waves for reaction-diffusion-convection systems." Topological Methods in Nonlinear Analysis 11, no. 1 (1998): 19. http://dx.doi.org/10.12775/tmna.1998.002.

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13

Koga, S. "Obliquely Colliding Waves in Reaction-Diffusion Systems." Progress of Theoretical Physics 74, no. 5 (1985): 1022–32. http://dx.doi.org/10.1143/ptp.74.1022.

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14

Steele, Aaron J., Mark Tinsley, and Kenneth Showalter. "Collective behavior of stabilized reaction-diffusion waves." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 2 (2008): 026108. http://dx.doi.org/10.1063/1.2900386.

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15

Johnson, Barry R., Stephen K. Scott, and Annette F. Taylor. "Reaction-diffusion waves Homogeneous and inhomogeneous effects." Journal of the Chemical Society, Faraday Transactions 93, no. 20 (1997): 3733–36. http://dx.doi.org/10.1039/a704616b.

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16

Tamemoto, Naoki, and Hiroshi Noguchi. "Reaction-diffusion waves coupled with membrane curvature." Soft Matter 17, no. 27 (2021): 6589–96. http://dx.doi.org/10.1039/d1sm00540e.

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Reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature.

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17

SHERRATT, JONATHAN A. "TRANSITION WAVES THAT LEAVE BEHIND REGULAR OR IRREGULAR SPATIOTEMPORAL OSCILLATIONS IN A SYSTEM OF THREE REACTION–DIFFUSION EQUATIONS." International Journal of Bifurcation and Chaos 03, no. 05 (1993): 1269–79. http://dx.doi.org/10.1142/s021812749300101x.

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Transition waves are widespread in the biological and chemical sciences, and have often been successfully modelled using reaction–diffusion systems. I consider a particular system of three reaction–diffusion equations, and I show that transition waves can destabilise as the kinetic ordinary differential equations pass through a Hopf bifurcation, giving rise to either regular or irregular spatiotemporal oscillations behind the advancing transition wave front. In the case of regular oscillations, I show that these are periodic plane waves that are induced by the way in which the transition wave

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18

Sherratt, Jonathan A., and Matthew J. Smith. "Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models." Journal of The Royal Society Interface 5, no. 22 (2008): 483–505. http://dx.doi.org/10.1098/rsif.2007.1327.

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Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction–diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves oc

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19

Belk, M., B. Kazmierczak, and V. Volpert. "Existence of reaction-diffusion-convection waves in unbounded strips." International Journal of Mathematics and Mathematical Sciences 2005, no. 2 (2005): 169–93. http://dx.doi.org/10.1155/ijmms.2005.169.

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Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unbounded domains.

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20

Merkin, J. H., and M. A. Sadiq. "Reaction-diffusion travelling waves in the acidic nitrate-ferroin reaction." Journal of Mathematical Chemistry 17, no. 3 (1995): 357–75. http://dx.doi.org/10.1007/bf01165755.

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21

DELLNITZ, MICHAEL, MARTIN GOLUBITSKY, ANDREAS HOHMANN, and IAN STEWART. "SPIRALS IN SCALAR REACTION–DIFFUSION EQUATIONS." International Journal of Bifurcation and Chaos 05, no. 06 (1995): 1487–501. http://dx.doi.org/10.1142/s0218127495001149.

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Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral" boundary conditions (ur = muθ). Spiral boundary conditions are motivated by assuming that a solution is infin

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22

HORSTHEMKE, WERNER. "EXTERNAL NOISE AND FRONT PROPAGATION IN REACTION-TRANSPORT SYSTEMS WITH INERTIA: THE MEAN SPEED OF FISHER WAVES." Fluctuation and Noise Letters 02, no. 04 (2002): R109—R124. http://dx.doi.org/10.1142/s0219477502000932.

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We review the effect of spatiotemporal noise, white in time and colored in space, on front propagation in systems of reacting and dispersing particles, where the particle motion displays inertia or persistence. We discuss the three main approaches that have been developed to describe transport with inertia, namely hyperbolic reaction-diffusion equations, reaction-Cattaneo systems or reaction-telegraph equations, and reaction random walks. We focus on the mean speed of Fisher waves in these systems and study in particular reaction random walks, which are the most natural generalization of react

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23

Needham, D. J., and A. N. Barnes. "Reaction-diffusion and phase waves occurring in a class of scalar reaction-diffusion equations." Nonlinearity 12, no. 1 (1999): 41–58. http://dx.doi.org/10.1088/0951-7715/12/1/004.

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24

Bramburger, Jason J., and David Goluskin. "Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (2020): 20200450. http://dx.doi.org/10.1098/rspa.2020.0450.

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Many monostable reaction–diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present methods for finding upper and lower bounds on minimum wave speed. They rely on constructing trapping boundaries for dynamical systems whose heteroclinic connections correspond to the travelling waves. Simple versions of this approach can be carried out analytically but often give overly conservative bounds on minimum wave speed. When the reaction–diffusion e

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25

ABDULBAKE, JANAN, ANTHONY J. MULHOLLAND, and JAGANNATHAN GOMATAM. "A RENORMALIZATION APPROACH TO REACTION-DIFFUSION PROCESSES ON FRACTALS." Fractals 11, no. 04 (2003): 315–30. http://dx.doi.org/10.1142/s0218348x03002191.

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Of fundamental importance to wave propagation in a wide range of physical phenomena is the structural geometry of the supporting medium. Recently, there have been several investigations on wave propagation in fractal media. We present here a renormalization approach to the study of reaction-diffusion (RD) wave propagation on finitely ramified fractal structures. In particular we will study a Rinzel-Keller (RK) type model, supporting travelling waves on a Sierpinski gasket (SG), lattice.

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26

Regenauer-Lieb, Klaus, Manman Hu, Christoph Schrank, et al. "Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes." Solid Earth 12, no. 8 (2021): 1829–49. http://dx.doi.org/10.5194/se-12-1829-2021.

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Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction–diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion wav

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27

Xu, Tianyuan, Shanming Ji, Ming Mei, and Jingxue Yin. "Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion." Journal of Differential Equations 265, no. 9 (2018): 4442–85. http://dx.doi.org/10.1016/j.jde.2018.06.008.

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28

Watt, S. D., and R. O. Weber. "Reaction waves and non-constant diffusivities." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 37, no. 4 (1996): 458–73. http://dx.doi.org/10.1017/s0334270000010808.

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AbstractA reaction-diffusion equation with non-constant diffusivity,ut = (D(x, t)ux)x + F(u),is studied for D(x, t) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t) are given. For D(x, t) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.

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29

Alfaro, Matthieu, Jérôme Coville, and Gaël Raoul. "Bistable travelling waves for nonlocal reaction diffusion equations." Discrete & Continuous Dynamical Systems - A 34, no. 5 (2014): 1775–91. http://dx.doi.org/10.3934/dcds.2014.34.1775.

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30

Matsuoka, C., K. Shimodoi, T. Iizuka, and T. Hasegawa. "Reflection of active waves in reaction-diffusion media." Physics Letters A 243, no. 1-2 (1998): 47–51. http://dx.doi.org/10.1016/s0375-9601(98)00172-8.

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31

Galochkina, T., M. Marion, and V. Volpert. "Initiation of reaction–diffusion waves of blood coagulation." Physica D: Nonlinear Phenomena 376-377 (August 2018): 160–70. http://dx.doi.org/10.1016/j.physd.2017.11.006.

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32

Keyfitz, Barbara Lee. "Shock Waves and Reaction-Diffusion Equations.By Joel Smoller." American Mathematical Monthly 93, no. 4 (1986): 315–18. http://dx.doi.org/10.1080/00029890.1986.11971816.

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33

Yamada, Hiroyasu, Chihiro Matsuoka, and Akira Yoshimori. "Refraction of active waves in reaction—diffusion media." Physics Letters A 210, no. 3 (1996): 189–94. http://dx.doi.org/10.1016/s0375-9601(96)80008-9.

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34

Wu, Ezi, and Yanbin Tang. "Random perturbations of reaction–diffusion waves in biology." Wave Motion 49, no. 7 (2012): 632–37. http://dx.doi.org/10.1016/j.wavemoti.2012.04.004.

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35

Kneer, Frederike, Eckehard Schöll, and Markus A. Dahlem. "Nucleation of reaction-diffusion waves on curved surfaces." New Journal of Physics 16, no. 5 (2014): 053010. http://dx.doi.org/10.1088/1367-2630/16/5/053010.

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36

Kazmierczak, B., and V. Volpert. "Travelling Waves in Partially Degenerate Reaction-Diffusion Systems." Mathematical Modelling of Natural Phenomena 2, no. 2 (2007): 106–25. http://dx.doi.org/10.1051/mmnp:2008021.

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37

Yu-Fang, Liu, Wu Yan-Ning, Xu Hou-Ju, and Sun Jin-Feng. "Spiral and Antispiral Waves in Reaction-Diffusion Systems." Communications in Theoretical Physics 42, no. 4 (2004): 637–40. http://dx.doi.org/10.1088/0253-6102/42/4/637.

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38

Kosek, Juraj, and Miloš Marek. "Collision-Stable Waves in Excitable Reaction-Diffusion Systems." Physical Review Letters 74, no. 11 (1995): 2134–37. http://dx.doi.org/10.1103/physrevlett.74.2134.

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39

Vanag, V. K., and I. R. Epstein. "Segmented spiral waves in a reaction-diffusion system." Proceedings of the National Academy of Sciences 100, no. 25 (2003): 14635–38. http://dx.doi.org/10.1073/pnas.2534816100.

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40

de Pablo, Arturo, and Ariel Sánchez. "Global Travelling Waves in Reaction–Convection–Diffusion Equations." Journal of Differential Equations 165, no. 2 (2000): 377–413. http://dx.doi.org/10.1006/jdeq.2000.3781.

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41

Scheel, Arnd. "Bifurcation to Spiral Waves in Reaction-Diffusion Systems." SIAM Journal on Mathematical Analysis 29, no. 6 (1998): 1399–418. http://dx.doi.org/10.1137/s0036141097318948.

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42

Lansdell, Benjamin, Kevin Ford, and J. Nathan Kutz. "A Reaction-Diffusion Model of Cholinergic Retinal Waves." PLoS Computational Biology 10, no. 12 (2014): e1003953. http://dx.doi.org/10.1371/journal.pcbi.1003953.

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43

Rossi, Federico, Marcello A. Budroni, Nadia Marchettini, and Jorge Carballido-Landeira. "Segmented waves in a reaction-diffusion-convection system." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 3 (2012): 037109. http://dx.doi.org/10.1063/1.4752194.

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44

Strunin, D. V., A. G. Strunina, E. N. Rumanov, and A. G. Merzhanov. "Chaotic reaction waves with fast diffusion of activator." Physics Letters A 192, no. 5-6 (1994): 361–63. http://dx.doi.org/10.1016/0375-9601(94)90219-4.

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45

Lü, GuangYing, and MingXin Wang. "Stability of planar waves in reaction-diffusion system." Science China Mathematics 54, no. 7 (2011): 1403–19. http://dx.doi.org/10.1007/s11425-011-4210-0.

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46

Huang, Wenzhang. "Traveling Waves for a Biological Reaction-Diffusion Model." Journal of Dynamics and Differential Equations 16, no. 3 (2004): 745–65. http://dx.doi.org/10.1007/s10884-004-6115-x.

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47

Gomatam, Jagannathan, and Peter Grindrod. "Three-dimensional waves in excitable reaction-diffusion systems." Journal of Mathematical Biology 25, no. 6 (1987): 611–22. http://dx.doi.org/10.1007/bf00275497.

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48

Erneux, Thomas, and Grégoire Nicolis. "Propagating waves in discrete bistable reaction-diffusion systems." Physica D: Nonlinear Phenomena 67, no. 1-3 (1993): 237–44. http://dx.doi.org/10.1016/0167-2789(93)90208-i.

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49

Caffarelli, L., A. Mellet, and Y. Sire. "Traveling waves for a boundary reaction–diffusion equation." Advances in Mathematics 230, no. 2 (2012): 433–57. http://dx.doi.org/10.1016/j.aim.2012.01.020.

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50

Dovzhenko, A. Yu, and É. N. Rumanov. "Behavior of reaction-diffusion waves with fast activator diffusion near propagation threshold." Journal of Experimental and Theoretical Physics 98, no. 2 (2004): 359–65. http://dx.doi.org/10.1134/1.1675905.

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