Fractal aspects of magneto-thermo-electricity, towards generalised Onsager relations
J. M. Redondo
Departament de Física Aplicada, B5 Campus Nord, Univ. Politécnica de Catalunya, Barcelona 08034, Spain
The success of Onsagerís Linear relationships between Fluxes and Forces in explaining the reversible Thermoelectric effects and in deriving Kelvinís relationships (Onsager 1931) has been extended to include Magneto-Thermo- Electrical effects. Nerst or Nerst-Ettinghausen Effects, among others provide further examples of possible applications in thermal technologies.
The way in which the material structure is built with a controllable multifractal aspect, alternating at many different scales the grains which, either due to intrinsic crystalline anisotropy or due to a selective doping produce power relationships between the interfacial line lengths and the areas in 2D, or between the area of the surface separating subsets of different material properties and the volumes of the respective grains in 3D. The application of these fractal aspects in order to describe fluxes that may be very different when measured at different scales may also be stated in terms of the relationships between fluxes and forces or between fluxes per unit area and gradients perpendicular to that same area.
When basic physical properties that are defined in a very different geometrical way, such as bulk properties or surface properties, the need of integrating over all possible scales arises in order to avoid singularities in the theory. The effect of minimum and maximum grain size clusters and their geometrical self similarity is studied in terms of non-linear relationships and of higher order cumulants for several of the Magneto-Thermo-Electric (Delver 1956) and Thermo-electric Effects