By Enrique Tirapegui, Walter Zeller (auth.), Enrique Tirapegui, Walter Zeller (eds.)

This quantity features a number of the lectures given on the 5th foreign Workshop on Instabilities and Nonequilibrium constructions, held in Santiago, Chile, in December 1993. the next basic topics are coated: instabilities and development formation, stochastic results in nonlinear platforms, nonequilibrium statistical mechanics and granular topic. evaluate articles on transitions among spatio-temporal styles and nonlinear wave equations also are incorporated.
Audience: This publication may still attract physicists and mathematicians operating within the parts of nonequilibrium structures, dynamical structures, development formation and partial differential equations. Chemists and biologists attracted to self-organization and statistical mechanics also needs to have an interest, in addition to engineers operating in fluid mechanics and fabrics technology.

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The circulation of v around such a generic singularity is ±411'a. These topological defects are known in the context of superfluidity as "quantum vortices" [5]. Solutions of (14) with cylindrical symmetry can be obtained numerically [20]. The profile of a vortex is shown on Figure 2 (b). The density admits a horizontal asymptote near the core (see Figure 3 (c)) while the velocity diverges as the inverse of the core distance (see Figure 3 (d)). Then the momentum density pv is a regular quantity shown on Figure 4 (f).

Z/(2a)) which corresponds to a fluid moving with the imposed velocity u. Another stationary solution of ARGLE is tPo = JQ/f3(I- (u 2 /4aQ))1/2 which corresponds to a fluid with zero velocity. The linear stability study of tPo can be obtained in term of normal modes using tP = tPo{1 + Uo exp(m + ikx) + Vo exp(l1t - ikx)). We find: :F is given by tP 11 = -Q (1 - ~) 4aQ ak 2 ± u 2 k2 + Q2 (1- ~)2 4aQ ' (18) Note that this stability computation is formally identical to the one leading to the Eckhaus instability of convective rolls [21].

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