Helical turing patterns in the lengyel-epstein model in thin cylindrical layers

The formation of Turing patterns was investigated in thin cylindrical layers using the Lengyel-Epstein model of the chlorine dioxide-iodine-malonic acid reaction. The influence of the width of the layer W and the diameter D of the inner cylinder on the pattern with intrinsic wavelength l were determined in simulations with initial random noise perturbations to the uniform state for W<l/2 and D~l or lower. We show that the geometric constraints of the reaction domain may result in the formation of helical Turing patterns with parameters that give stripes (b=0.2) or spots (b=0.37) in two dimensions. For b=0.2, the helices were composed of lamellae and defects were likely as the diameter of the cylinder increased. With b=0.37, the helices consisted of semi-cylinders and the orientation of stripes on the outer surface (and hence winding number) increased with increasing diameter until a new stripe appeared.