Ferromagnetism of an all-carbon composite composed of a carbon nanowire nside a single-walled carbon nanotube

Using the first-principles spin density functional approach, we have studied magnetism of a new type of all-carbon nanomaterials, i.e., the carbon nanowires inserted into the single-walled carbon nanotubes. It is found that if the 1D carbon nanowire density is not too higher, the ferromagnetic ground state will be more stable than the antiferromagnetic one, which is caused by weak coupling between the 1D carbon nanowire and the single-walled carbon nanotube. Also, both dimerization of the carbon nanowire and carbon vacancy on the tube-wall are found to enhance the magnetic moment of the composite.Comment: 3 figure

On Regularity of Abnormal Subriemannian Geodesics

We prove the smoothness of abnormal minimizers of subriemannian manifolds of step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4 admit no strictly abnormal minimizers. For any subriemannian manifolds of step less than 7, we show all abnormal minimizers have no corner type singularities, which partly generalize the main result of Leonardi-Monti.Comment: This paper has been withdrawn by the author due to a crucial computation error in (F_t^1)_sta