Pattern transient

FIG. 14 Temperature dependence of normalized equilibrium diameters (d/d0) at pHs 3 (open circles) and 10 (shadowed circles) for four polyelectrolyte gels consisting of NIPA and AAc residues (a) Gel I (b) Gel II (c) Gel III (d) Gel IV. PAAc with Mu = 4.5 X 105 was used for the preparation of Gels II and III. Dashed line indicates a discontinuous volume phase transition at a temperature (7 v) at which we observed a transient pattern in both swelling and shrinking processes and thereby were not able to measure d. Such a transient pattern was not observed in the measurements for Gel III at pH 3, suggesting a continuous transition. (From Ref. 28.)... 

Fig. 9.30. Spatial propagation of a sharp Cef front of the type seen in eardiae cells (type 1 wave). Shown are six successive stages of the transient pattern obtained by numerical integration of eqns,(9.11) of the model based on CICR, from which the term Vj/S related to stimulation has been removed and to which the diffusion of cytosolic Ca has been added. In these simulations, the Ca -sensitive Ca pool is assumed to be distributed homogeneously within the cell. The latter is represented as a two-dimensional mesh of 20 x 60 points and diffusion is approximated by finite differences boundary conditions are of the zero-flux type. The terms related to influx from (vq) and into kZ) the extracellular medium only appear in the points located on the borders of the mesh. The diffusion coefficient of is equal to 400 pmVs other parameter...

Fig. 9.31. Spatial propagation of a Ce tide resembling the waves seen in hepa-tocytes, oocytes, or endothelial cells (type 2 wave). The transient pattern is obtained as in fig. 9.30 for parameter values yielding oscillations of a period of the order of 1 min Vq =-1.68 jiM/min, = 93 xM/min, - 500 p,M/min, Kf = 0.66 pM, 2 = 11 -M, k -16.8 min, A , = 1 min other parameter values are as in fig. 9.10. The spatial mesh contains 30 x 30 points (similar results are obtained with a mesh of 60 x 60 points). The black bar in the upper, left part denotes the initial, transient stimulation, which consists in raising locally the level of cytosoUc Ca to 1.5 pM at the left extremity while the rest of the cell is in the resting level of 0.1 pM the scale of Ca concentration extends from 0 (white) to 1.5 pM (black) (Dupont Goldbeter, 1992b, 1994).

In the second group we find pattern forming phenomena based on new instability mechanisms arising from the specific features of liquid crystals, which have no counterpart in isotropic fluids or at least are difficult to assess. Some examples are shear (linear, elliptic, oscillatory, etc.) induced instabilities, transient patterns in electrically or magnetically driven Freedericksz transitions, structures formed in inhomogeneous and/or rotating electric or magnetic fields, electroconvection (EC), etc. [5-7]. 

Instead of irradiating just a single spot, the laser beam may also be moved across the surface, thus forming transient patterns with altered adsorbate composition. Thus, the overall reaction rate may also be affected [38]. Apart from the initiation of reaction waves [39], already moving waves may be "dragged" and thus affected in their movement [40]. 

A. Buka and L. Kramer, Theory of nonlinear transient patterns in the splay Preedericksz transition, Phys. Rev. A 45(8), 5624-5631, (1992). 

Two areas can be identified one with three steady states and another area to be characterized as excitable. At the boundary of the two time regimes transient patterns form in response to a small disturbance. In this unstable region a particularly interesting phenomenon is observed that behaves like cell multiphcation. Patterns occur with concentration profiles of cellular form that grow and rephcate. When these cells exceed a particular dimension, the interior destabilizes (in this case because a necessary concentration gradient is not maintained) and cells divide. 

We have already alluded to three other expected developments the design, by appropriate complcxation of the activator species, of new reactions that give rise to Turing patterns the development of systems that show transient patterns under conveniently obtainable conditions and the generation and analysis of three-... 

Vaegan, Arora, A., Crewther, S.G., and Millar, T.J. 1990. The effect of various anaesthetics on the spatial tuning of two major wave peaks in the transient pattern electroretinogram of the cat evidence for pattern and luminance components. Vis. Res. 30 1401-1407. 

A. Buka, L. Kramer Theory of transient patterns in the splay freedericksz transition of nematics, in S. Kai (ed.) Pattern formation in complex dissipative systems. World Scientific, Kitalqrushu,... 

In some cases, magnetically induced transient twist distortions have been observed in both thermotropic (MBBA [89]) and lyotropic (PBG [90]) systems. In this case, backflow effects are allowed only in a nonlinear regime, for strong distortions. The physical origin of this phenomenon could be the faster response times of modulated structures, as compared with uniform ones. When the equilibrium director distribution is approached, i.e. a relaxation process is over, the transient structures disappear. The emergence and subsequent evolution of the spatial periodicity of the transient structures have been considered theoretically [89,90]. In addition, the pattern kinetics have been studied in detail experimentally [91] on a mixture of a polymer compound with a low-molecular-mass matrix. The polymer considerably increases the rotational viscosity of the substance and reduces the threshold for pattern formation. This indicates the possibility of recording the pattern using a video camera. A typical transient pattern is shown in Fig. 14 [91]. 

Some transient patterns overlapping the Frederiks transition (e.g. as observed by Buka et al. [92]) may be electrohydrody-namic in nature these are discussed in Section 9.4 of this Chapter. 

P.B. Umbanhowar, F. Melo, and H.L. Swinney. Periodic, aperiodic, and transient patterns in vibrated granular layers. Physica A, 249(l-4) l-9,1998. 

---