In this area of physics we also have been concerned about Experimental basics for Heterogeneous Media. Here we also had the recognition that the experiments and their analysis for homogeneous and heterogeneous media should be modeled differently. The basic studies in the field of heterogeneous scaled electrodynamics field transport brought the understandings of the theoretical basis for experimental set-ups for heterogeneous, hierarchical media. Many years ago I was firmly agreed upon that the scale of measurements and of the modeling must correspond one to another:
This obvious and simple principle is violated in Homogeneous physics when what is clearly a two scale physical problem is described on the upper (measurement) scale with the same kind homogeneous mathematics as is used for the lower really Homogeneous scale. Substitution of the effective coefficients into models of this type is the primary question that must be dealt with.
Following the basics of HSP-VAT in 90th and beginning of 2000th the full two-scale electrostatics and electrodynamics governing equations were obtained and used to achieve understanding and modeling of the possible mechanisms that play a role in shaping the effective ( and measured and modeled) various coefficients of electrical permittivity, conductivities in superlattices, globular heterogeneous media, 2D one direction capillary media, cross-characteristics, etc. Some of these results have been published in our work, some are in this website -
some are waiting a proper publication.
We obtained after 2002 the analytical and numerical solutions of the following classical two-scale problems that have not been solved for many decades by other methods and by this we have proven the interscale dependencies of these physical fields
The contribution into understanding of surficial and phase related phenomena and their inclusion into experimental and consequently simulation procedures on the upper scale, as well as the problem of interaction of charge carriers transport on both scales has been achieved.
Now we can state that the path to the physically and mathematically correct procedures, methods of design and Scaled Optimization of Heterogeneous Multiphysics structures and devices as - superlattices, composites, etc. has been opened.
It does not mean that everything is straight and just simple to go. Vise versa, everything is much more complicated well, just because the number of phenomena and their experimental and modeling characteristics are much larger. Well, we DO WANTED THESE or THOSE features to be involved, because we know or knew that they can bring some new advantage. Right? Then we need to agree that the price for convenience and progress comes with the complications because of that progress. Societies did want this.
That is why they (societies) need to pay. Like they pay for the ITER, even not knowing that science so far is able to deliver? Isn't it?