Abstract
Global couplings strongly affect structure formation in spatially extended nonlinear dynamic systems. We review the role of such global constraints on spatiotemporal patterns in reaction-diffusion systems of activator-inhibitor type. Important applications pertain to current filaments and fronts in semiconductors where global couplings are naturally introduced by the resistive circuit environment in which semiconductor devices are generally operated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. S. Mikhailov, Foundations of Synergetics Vol. I,2 ed. (Springer, Berlin, 1994).
F. H. Busse and S. C. Muller, Evolution of spontaneous structures in dissipative continuous systems (Springer, Berlin, 1998).
E. Scholl, Nonequilibrium Phase Transitions in Semiconductors (Springer, Berlin, 1987).
E. Scholl, Nonlinear spatio-temporal dynamics and chaos in semiconductors (Cambridge University Press, Cambridge, 2000), in print.
M. P. Shaw, V. V. Mitin, E. Scholl, and H. L. Grubin, The Physics of Instabilities in Solid State Electron Devices (Plenum Press, New York, 1992).
J. Peinke, J. Parisi, O. Rossler, and R. Stoop, Encounter with Chaos (Springer, Berlin, Heidelberg, 1992).
B. S. Kerner and V. V. Osipov, Autosolitons (Kluwer Academic Publishers, Dordrecht, 1994).
E. Scholl, F.-J. Niedernostheide, J. Parisi, W. Prettl, and H. Purwins, in Evolution of spontaneous structures in dissipative continuous systems, edited by F. H. Busse and S. C. Miiller (Springer, Berlin, 1998), pp. 446–494.
K. Aoki, Nonlinear dynamics and chaos in semiconductors (Institute of Physics Publishing, Bristol, 2000).
Theory of Transport Properties of Semiconductor Nanostructures, Vol. 4 of Electronic Materials Series, edited by E. Scholl (Chapman and Hall, London, 1998).
L. Schimansky-Geier, C. Ziilicke, and E. Scholl, Z. Phys. B 84, 433 (1991).
L. Schimansky-Geier, C. Zulicke, and E. Scholl, Physica A 188, 436 (1992).
A. F. Volkov and S. M. Kogan, Sov. Phys. Usp. 11, 881 (1969).
F. G. Bass, V. S. Bochkov, and Y. G. Gurevich, Soviet Physics JETP 31, 972 (1970), [Zh. Eksp. Teor. Fiz. 58, 1814 (1970)].
A. Alekseev, S. Bose, P. Rodin, and E. Scholl, Phys. Rev. E 57, 2640 (1998).
E. Scholl and D. Drasdo, Z. Phys. B 81, 183 (1990).
R. E. Kunz and E. Scholl, Z. Phys. B 89, 289 (1992).
A. Wacker and E. Scholl, Z. Phys. B 93, 431 (1994).
F.-J. Niedernostheide, H. Schulze, S. Bose, A. Wacker, and E. Scholl, Phys. Rev. E 54, 1253 (1996).
F. Schlogl, Z. Phys. 253, 147 (1972).
G. Schwarz, C. Lehmann, and E. Scholl, Phys. Rev. B 61, 10194 (2000).
J. Hirschinger, W. Eberle, W. Prettl, F.-J. Niedernostheide, and H. Kostial, Phys. Lett. A 236, 249 (1997).
M. Meixner, P. Rodin, E. Scholl, and A. Wacker, Eur. Phys. J. B 13, 157 (2000).
M. Meixner, P. Rodin, and E. Scholl, Phys. Rev. E 58, 2796 (1998).
M. Meixner, P. Rodin, and E. Scholl, Phys. Rev. E 58, 5586 (1998).
Y. Zel’dovich and D. Frank-Kamenetskij, Zh. Eksp. Khim. 12, 100 (1938).
J. B. Gunn, IBM J. Res. Develop. 8, 141 (1964).
L. B. Loeb, Science 148, 1417 (1965).
V. L. Bonch-Bruevich, I. P. Zvyagin, and A. G. Mironov, Domain electrical instabilities in semiconductors (Consultant Bureau, New York, 1975).
P. Pelce, Dynamics of Curved Fronts (Academic Press, San Diego, 1988).
Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1988).
Y. M. Svirezhev, Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology (Nauka, Moscow, 1987), (in Russian).
V. V. Osipov and V. A. Kholodnov, Microelectronica 2, 529 (73), (in Russian).
F.-J. Niedernostheide, M. Ardes, M. Or-Guil, and H.-G. Purwins, Phys. Rev. B 49, 7370 (1994).
A. V. Gorbatyuk and P. B. Rodin, Sol. State El. 35, 1359 (1992).
B. Glavin, V. Kochelap, and V. Mitin, Phys. Rev. B 56, 13346 (1997).
D. Mel’nikov and A. Podlivaev, Semicond. 32, 206 (1998).
A. D. Martin, M. L. F. Lerch, P. E. Simmonds, and L. Eaves, Appl. Phys. Lett. 64, 1248 (1994).
H. Hempel, I. Schebesch, and L. Schimansky-Geier, Eur. Phys. J. B 2,399 (1998).
G. Schwarz, C. Lehmann, A. Reimann, E. Scholl, J. Hirschinger, W. Prettl, and V. Novak, Semicond. Sci. Technol. (2000), (in print).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schöll, E. (2000). Nonlinear Spatiotemporal Patterns in Globally Coupled Reaction-Diffusion Systems. In: Freund, J.A., Pöschel, T. (eds) Stochastic Processes in Physics, Chemistry, and Biology. Lecture Notes in Physics, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45396-2_39
Download citation
DOI: https://doi.org/10.1007/3-540-45396-2_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41074-4
Online ISBN: 978-3-540-45396-3
eBook Packages: Springer Book Archive