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Transport properties of highly porous fiber structures are investigated. The fibers are assumed to be thin, but long, so that the number of interfiber connections along each fiber is large. We show that the effective conductivity of such structures can be found from the correlation length of the two-point correlation function of the local conductivities. The correlation function in the most interesting cases can be estimated from two-dimensional (2D) images of the structures. This means that the three-dimensional conductivity problem can be considered using 2D digital images of the structure. We apply this approach to analyze the parameters that determine the thermal conductivity of fiber structures.

Thermal conductivity of porous media is considered. The model permits regular power-series expansion of the expression for thermal conductivity as a function of porosity. The coefficients of the expansion depend on two-site correlation function of local thermal conductivities, which can be calculated from the microscopy image of the structure. Thermal conductivities of some model two-dimensional structures as well as a real porous yttria-stabilized zirconia film are calculated and discussed.

The envelope function approach for the electric and magnetic fields of the light wave in the photonic crystals has been used to investigate the propagation of light in disordered photonic crystals and its reflection or refraction at the boundary. We showed that small long-range distortion of the crystal lattice can explain peculiarities of the transmittance spectrum of the polystyrene colloid film we have grown.

The temperature dependence of the thermal conductivity of porous, nanostructured alumina has been measured. It is shown that this dependence can be described with a single parameter, the value of which depends on the intergrain boundary structure and is independent of the grain size and porosity.