Patterns target

FIG. IS Series of snapshot configurations obtained using lattices of side L = 1024 during the stationary regime of the HS model. (A) Cellular structures, (B) target patterns, (C) double spirals and (D) turbulence. (From Ref. 15.)... 

Other travelling waveforms include target patterns, fronts, or pulses as expanding and concentric circles and which may be broken to form spirals (which may also arise apparently spontaneously under some conditions) as shown in Fig. 1.17. 

Fig. 1.17. Different forms of travelling wavefronts (a) travelling wavefront (propagating down tube) in iodate-arsenous acid reaction with excess iodate (b) travelling wavefront or pulse in iodate-arsenous acid reaction with excess arsenite (c) target patterns in Belousov-Zhabotinskii...

In an N-NDR model Christoph et al. [35, 37] found stable target patterns coexisting with the pulse solution for values of the external voltage for which the stationary state is also unstable with respect to homogeneous perturbations. In contrast, the asymmetric target patterns and the more complex motions observed during H2 oxidation on Pt ring electrodes (cf. Fig. 56) have not yet been reproduced in simulations. 

H)N-NDR systems DL activator accelerated waves, inhomogeneous (BF unstable) oscillations stationary domains, standing waves, anti-phase oscillations with n = 1 pulses, target patterns, clusters enhanced acceleration of potential fronts, mainly homogenizing effect cluster formation in the oscillatory region... 

Uncertainty expresses the doubt associated with the accuracy of any single measurement. Accuracy establishes how close in agreement a measurement is with the accepted value. The precision of a measurement is the degree to which successive measurements agree with each other (the average deviation is minimized). Error is the difference between a value obtained experimentally and the standard value accepted by the scientific community. Consider the bull s-eye target patterns in Figure 3.1. 

Under conditions where the front generation is slow, i.e. in the second regime of section 3.2.2, spatio-temporal pattern formation is observed in several forms. Target patterns, rotating spirals and turbulent structures are the observed forms. When turbulent patterns are present, sometimes small fragments of reaction fronts exhibit solitonic behavior. Figure 6 shows the four main forms of pattern formation that we have observed in our simulations. 

Rotating spiral patterns can be formed when target patterns break down due to interference with other reaction fronts, or due to interference with themselves across the boundary conditions. They can also be formed spontaneously, when a new reaction front starts rotating around a core. We have not been able to determine the microscopic mechanism that causes a reaction front to start rotating. 

Breakdown of patterns, both spirals and target patterns, can lead to the... 

The main application that was discussed was a microscopic model for the oxidation of CO, catalyzed by a Pt(lOO) single crystal surface. The simulations show kinetic oscillations as well as spatio-temporal pattern formation in the form of target patterns, rotating spirals and turbulent patterns. Finally, mean-field simulations of the same model were compared with the Monte Carlo simulations. When diffusion is fast and the simulation grids are small, the results of Monte Carlo simulations approach those of the mean-field simulations. 

J. J. Tyson and P. C. Fife. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys., 73 2224, 1980. 

Study of the BZ reaction in a thin unstirred layer of reacting solution demonstrates that concentric waves ("target patterns") or spiral waves are developed. The reacting solution is normally spread out as a thin film with a few millimeters thickness in a Petri dish (diameter ca. 10 cm). After a certain time blue oxidation fronts which propagate on the red background (reduced ferroin) develop. 

The design of the blast includes the types, quantity and distribution of explosive placed in each drill hole. Before the design of the blast is finalised, an accurate survey of the profile of the quarry face and detailed logs of the drill holes are required to identify how the blast deviates fi-om the target pattern so that corrections to the standard design can be made. 

Fig. 5.46. Spatial patterns obtained in the three-variable model for cAMP signalling governed by eqns (5.12) supplemented with a term for the diffusion of extracellular cAMP. (a) Concentric (target) patterns, (b) Spiral patterns. The square area of 1 cm is represented by a mesh of 160 x 160 points in (a) and 100 X 100 points in (b). In (a) a pacemaker, represented by four points at the...

Tyson, J.J., K.A. Alexander, V.S. Manoranjan J.D. Murray. 1989. Spiral waves of cyclic AMP in a model of slime mold aggregation. Physica 34D 193-207. Tyson, J.J. P.C. Fife. 1980. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys. 73 2224-37. 

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