Abstract
In this paper, we have studied the chiral lipid bilayers with the tilted fluid phase where the orientation of the molecular tilt varies as a function of the cylindrical coordinates. The rigorous solution of the equation related to the orientation of the long molecular axis is obtained, which describes the property of the tubules with a modulation in the tilt. When the angle of the molecular director is independent of the cylindrical coordinates θ, z, the patterns formed by chiral molecules can be degenerated to the right-handed helix, the left-handed helix, the straight lines, and the circles. The curvature and torsion of the corresponding curves are given explicitly, which denotes the winding of the molecules around the cylinder. We find also that the angle between the director of the molecule and the local normal direction of the cylinder increases if the radius of the cylinder reduces when the tilted angle ϕ from the equator of the cylinder is uniform.
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