title: Helical Turing patterns in the Lengyel-Epstein model in thin cylindrical layers.
abstract: 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.
authors.affiliation: Department of Chemical and Biological Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, United Kingdom.
authors.forename: T
authors.initials: T
authors.lastname: Bánsági
authors.affiliation: Department of Chemical and Biological Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, United Kingdom.
authors.forename: A F
authors.initials: AF
authors.lastname: Taylor
mesh_terms: D017606:Chlorine Compounds / Q000737:chemistry*; D007455:Iodine / Q000737:chemistry*; D008314:Malonates / Q000737:chemistry*; D008956:Models, Chemical; D010087:Oxides / Q000737:chemistry*
chemical_list: D017606:Chlorine Compounds; D008314:Malonates; D010087:Oxides; C025109:chlorine dioxide; D007455:Iodine; C030290:malonic acid