Flexoelectricity in Nematics Confined to Cylindrical Geometry

External fields act on the order parameter, the tensor which is describing the local order of molecules, driving the liquid crystal cells to their final configuration. The external actions can be an applied magnetic or electric field or the confinement created by the walls of the cell. Here we consider a nematic liquid crystal confined in a cylindrical cell. Besides elasticity, electric field and confinement, we consider the flexoelectricity too. Given the free energy density of the nematic, the corresponding Euler-Lagrange equation is solved numerically. A phase diagram of the director configuration according to the flexoelectricity of the material is obtained