Rotating spiral pattern

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. 

In this talk, attention will be drawn to the ease by which spatio-temporal patterns observed in the Belousov-Zhabotinskii reagent can be understood by the use of PC models. My specific purposes are (1) to show that PC systems are present in model chemical networks which have been proposed for the BZ reagent (2) to expound and analyze the simpler mathematical reaction-diffusion systems which are of PC type, and finally (3) to show that expanding ring and rotating spiral patterns can be understood within this context. 

FIG. 21-29 Table feeder. The sldrt is raised in a spiral pattern for increased capacity in the direction of rotation. Couitesy of Chemical Engineering.)... 

Dry gas seals are in the positive seal class and have the same basic design features as mechanical face seals with one significant difference. The dry gas seal has shallow grooves cut in the rotating seal face located part way across the face. The grooves may be in a spiral pattern the exact location and pattern vary from one manufacturer to another. Lubrication and separation is effected by a microscopically thin film of gas. This implies some finite amount of leakage, which is quite small but must be accounted for in the design. 

S. Jabubith, H. H. Rotermund, W. Engel, A. von Oertzen, G. Ertl. Spatio-temporal concentration patterns in a surface reaction Propagation of standing waves, rotating spirals and turbulence. Phys Rev Lett 65 3013-3016, 1990. 

The principal features of the spiral structure are believed to be maintained by a pattern of density waves. This pattern rotates about the galactic center like a rigid body with an angular velocity that is lower than that of most of the material. Thus, the material of the Galaxy (i.e. both stars and gas) flows through the pattern and as it enters the density wave, the gas is strongly compressed. There are also less important elements of the spiral pattern that rotate with the material these are called material arms, as against density-wave ... 

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. 

Figure 6. Four examples of spatio-temporal pattern formation in our simulations (A) cellular structures, (B) target patterns, (C) a double rotating spiral, (D) turbulent patterns.

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. 

Our attention is focused on the properties of periodic trains formed by kinks or traveling Bloch walls. Our analysis reveals that, depending on the parameters of the oscillatory medium and the spatial period of a train, it can undergo a reversal of its propagation direction [19]. We show how this phenomenon can be used to design traps for traveling kinks and Bloch walls. Furthermore, we find that a new kind of patterns - twisted rotated spiral waves - exist in oscillatory media under the conditions of front propagation reversal. 

It is generally immaterial which phase, solid or fluid, is assumed to be at rest, and it is the relative velocity between the two that is important. An exception to this is met in some situations when the fluid stream has been previously influenced by solid walls and is in turbulent flow. The scale and intensity of turbulence then may be important parameters in the process. In wind tunnels, for example, where the solid shape is at rest and the stream of air is in motion, turbulence may give different forces on the solid than if the solid were moving at the same relative velocity through a quiescent and turbulence-free mass of air. Objects in free fall through a continuous medium may move in spiral patterns or rotate about their axis or both again the forces acting on them are not the same as when they are held stationary and the fluid is passed over them. 

Additionally, reactant concentrations can form surface patterns in a variety of shapes such as concentric circles or rotating spirals. Simulation of such spatio-temporal behavior based on atomistic elementary reaction rate parameter provides a sensitive test for macroscopic rate simulations. Here we report dynamic Monte Carlo simulationsof spatio-temporal patterns and kinetic oscillations. 

On large grids, another form of self-organization, yielding-temporal pattern formation becomes possible. Wave fronts in the form of pulsing concentrical circles as well as rotating spiral structures can occur. Such patterns have been observed experimentally on Pt(l 10). 

Monte Carlo simulations show that, during a simulation, due to stochastic fluctuations, synchronized kinetic oscillations spontaneously change into spatio-temporal patterns with steady state kinetic behavior, and vice versa. Also, rotating spirals can change into pulse generators and vice versa. 

Spiral-defect chaos in Rayleigh-Benard convection. The most remarkable phenomenon that needs an extension of the Swift-Hohenberg model for its explanation, is the development of spiral-defect chaos in Rayleigh-Benard convection [56], [6], which involves rotating spirals, target patterns, dislocations etc. The origin of this complicated behavior is the creation of a two-dimensional mean flow... 

The true nature of Shapley s disc became clear with the discovery of Lindblad and Oort in 1926 that stars in the Milky Way are moving in a pattern, consistent with rotation of the Galaxy, like the solar system, around a central attracting mass. It was confirmed much later (1952) that the Milky Way indeed has a rotating spiral structure. 

In these dryers, the product to be dried is metered and continuously fed onto the top plate. A vertical rotating shaft provided with radial arms and self-aligning plows conveys the product in a spiral pattern across stationary plates. The plates are heated by a liquid medium or steam. Small plates with internal rims and large plates with external rims are arranged in an alternating sequence (Figure 47.2). 

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