A simple axion model is proposed in the scenario of large extra dimensions where gravity scale is as low as 1 TeV. To obtain an intermediate-scale decay constant of the axion, the axion is assumed to live in a sub-spacetime (brane) of the whole bulk. In this model there appear Kaluza-Klein modes of the axion which have stronger interaction than those of the graviton. The axion brane plays a role of absorber of the graviton Kaluza-Klein modes. Because of these reasons phenomenology and cosmology of the axion become highly non-trivial.We discuss various cosmological constraints as well as astrophysical ones and show that the model is viable for certain choices of the dimensionality of the axion brane. The structure of the model proposed here provides a viable realization of the fat brane idea to relax otherwise very severe cosmological constraints.

This paper describes a method of designing the fan filter with a steep cutoff characteristic, using McClellan transformation. The conventional design by McClellan transformation has a problem in that the cutoff region of the fan filter is broad due to the restriction to a lower order of the subfilter employed. From such a viewpoint, this paper proposes a systematic design method for the subfilter with arbitrary order. First, it is pointed out that the ideal response of the subfilter can be represented in a functional form. Then the error function is defined in regard to the ideal response, and the design is shown for the subfilter where the filter coefficients minimize the error function. Finally, a design example is discussed, and it is shown that a fan filter with a steeper cutoff characteristic than in the conventional method can be designed by the proposed method.