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By Jean-René Chazottes, Bastien Fernandez
This booklet is ready the dynamics of coupled map lattices (CML) and of similar spatially prolonged structures. it is going to be necessary to post-graduate scholars and researchers looking an summary of the cutting-edge and of open difficulties during this sector of nonlinear dynamics. The certain function of this ebook is that it describes the (mathematical) idea of CML and a few comparable platforms and their phenomenology, with a few examples of CML modeling of concrete platforms (from physics and biology). extra accurately, the publication bargains with statistical homes of (weakly) coupled chaotic maps, geometric points of (chaotic) CML, monotonic spatially prolonged platforms, and dynamical types of particular organic systems.
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Extra info for Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems
Sample text
2V r 2 C 4 12 2 V . 15 Measurement of surface tension of solids 43 W In equilibrium ddr D 0; hence, we obtain an equation allowing calculation of the interfacial tension: Â Ã3=2 1 3 1 2 2 V ! 69) contains parameters which could be easily established experimentally with high accuracy, i. , the length of the spinning droplet L, its volume V , and the difference between the densities of the liquids. This method turns out to be extremely suitable for measurement of low interfacial tensions which occur in water/oil systems in the presence of surfactants.
45); "0 is the vacuum permeability, "1 and "2 are dielectric constants of liquid and air respectively, and is the surface tension of the liquid. The experiments reported in [9] confirmed the linear dependence of the drop eccentricity on the value of the applied electric field. It should be stressed that the switch in the direction of the electric field does not change the effect of the droplet deformation, i. , the electric field always stretches the droplet and does not compress it. 15). 13. Experimental set used for study of the deformation of water droplets exposed to an electric field.
Fermi, have shown that the shape of the electrically deformed dielectric droplet could be approximated by a prolate spheroid [13, 35]. "1 C 2"2/ where Req is the radius of the spherical droplet of the same volume [9,13]. 45); "0 is the vacuum permeability, "1 and "2 are dielectric constants of liquid and air respectively, and is the surface tension of the liquid. The experiments reported in [9] confirmed the linear dependence of the drop eccentricity on the value of the applied electric field. It should be stressed that the switch in the direction of the electric field does not change the effect of the droplet deformation, i.