We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approach.

Using the Dirac theory of constraints, the reduction procedure for the field degrees of freedom, the number of which is restricted by the equations of motion and topological conditions, is proposed. Such a procedure is applied to the Chern-Simons gravity generalized by the inclusion of a source, in the case when the space has a torus topology. The splitting of the discrete levels of time due to the presence of additional interaction is observed.

In systems of phthalocyanine particles dispersed in polymer, the effects of pigment particle size, electric property of the polymer and addition of fine γ-alumina particles on photocarrier generation efficiency have been studied. With smaller pigment particle size and higher dielectric constant of the polymer, the photocurrent increased. Addition of γ-alumina particles also caused a considerable increase in the photocurrent. It seemed that photocarrier generation occurred at the surface of the pigment particles and adsorbed oxygen played an important role in the process.

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Organic photoconductors using 2-[p-di(p-tolyl)aminostyryl]-4-methylthiazole, which is a newly developed material with high hole mobility, as a charge-transport material and τ-type metal-free phthalocyanine as a charge-generation material, have been examined. The photoconductors showed an excellent photoresponse, but had a high residual potential. In order to ascertain the reason for this, the variation of the xerographic gain with the thickness of the charge-transport layer and the electric field was measured. The results suggested that a large energy barrier between 2-[p-di(p-tolyl)aminostyryl]-4-methylthiazole and τ-type metal-free phthalocyanine induced a large decrease in the xerographic gain at a low electric field, which caused a high residual potential.