Apart that of the people's misunderstanding of what is suggested and how to deal with the averaged (Upper scale) equations along with the Lower scale conventional homogeneous equations, and vice-versa, the many other issues are at stake.

Starting from the main question everybody liked to ask -- So what, what does it mean, if we anyway can not solve these terrible equations and dependencies?

Great, the question was to the point at that time. But now we have many solutions, even the exact analytical solutions.

I had agreed well with this question just at the start many years ago, that is why the many issues of what to do and how to understand and interpret the upper scale phenomena and equations gave the birth to another field than the one traditionally understood under notations used when reading the studies by S.Whitaker, J.Slattery, and W.Gray with their co-authors. While the basic ideas of development of higher scale averaged variables equations are the same, the most of other issues have been determined and treated differently.

One of the first reasons for going at least two-scale at that time was the nature of the fields of large Lower scale physics - as the turbulence, meteorology, urban air pollution modeling, heat and momentum transport in Heat transfer devices as heat exchangers, where one can not abandon or ignore or have unsolved the Lower scale Momentum, Mass, and Heat transport problem.

Well, most of traditional one scale science and engineering do the heat exchangers models and courses up to this time without Lower scale physics and math. They just jump to the Upper scale and try to figure out the "effective" coefficients using the wrong models for that scale physics.

Meanwhile, when we want and need to take the lower scale physics and math correctly, the Upper scale models, equations, solutions and/or characteristics can be sought rigorously and correctly as well - Turbulent Transport Two Scale VAT Governing Equations for Obstructed and Porous Media. Introduction

Among other new directions in HSP-VAT can be mentioned:

1) - the presentation of the HSP-VAT physics and mathematical models as the Two Scale (at least) directly cross-linked Scaleported physical problems;

2) - the True Scaled HSP-VAT models physical Closure;

3) - the HSP-VAT Direct Two-Scale Analytical (mathematical) and Numerical Cross-Linked Modeling and Solutions - Scaleportation;

4) - the HSP-VAT Heterogeneous Experiments fundamentals, basic concepts, definitions, and techniques for a few fields in Fluid mechanics and Thermal Physics;

5) - the HSP-VAT Heterogeneous Optimization basics;

6) - the Non-linear, and Turbulent HSP-VAT physics, models, and simulations have been described, advanced, and took substantial part in the texts;

7) - the fundamentals of Scaleportation between the atomic scale Electromagnetism and Mesoscale Continuum mechanics Electrodynamics.

All issues mentioned above have been advanced for the first time for many physical disciplines -- as those presented in this website -- Acoustics, Electrodynamics, Nanoscale and Atomic scale physics, Biotech and Health science applications, Ferromagnetism, Meteorology and Air Pollution modeling, Optics, Semiconductors, Superconductivity, and few Technologies, etc.

Sorry for this long list.

The exact Two scale first time obtained solutions of common textbooks known problems, see in -

those have been showing the potential for treatment of this new type of physical tasks and at the same time the reality of interconnection of the physical fields acting over the two (at least) scales.

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Of coarse, it became the fashionable topic to use while approaching for funding, that is why so many people suddenly became "multiscaled."

Mathematicians and most of mechanical engineering professionals as well as physicists want to understand the Multiscale approach, the theory as a method of - the calculation procedure, a numerical method, which allows to get rid of multiphase, multibody challenge difficulties when solving the heterogeneous media ONE SCALE problem ? Like the famous Homogenization theory, which is not really the Multiscale theory.

It is strange for someone familiar with the literature on homogenization, but true - read down here the subsection in this section - Comparing with Governing Equations and "Averaging" in Homogenization Theory

which suggests our selective analysis on few main points and issues on derivation of governing equations and their meaning in Homogenization Theory.

Of coarse, technically speaking it might be named the multiscale method when few scales those differentiated one from another just by some coefficient (not by physics) being applied to the same mathematical problem governing equations and to the same physical scale model for each of these scales ? But what is really should be understood under the specific different scale models name in this case - is that it is the MULTIRESOLUTION method.

Meaning, that the same understanding of physical problem and statement is being treated using the different (various) scales for better reflection of the specifics of physics and for easier and better solution of this ONE SCALE HOMOGENEOUS statement problem.

That's it. Nothing more if not HSP-VAT used. Especially, when the task is set about a heterogeneous medium (material).

More than ever, when the problem constituted for a heterogeneous medium or when the scales are different by their peculiar physics - as, for example, the scale of a singular star, planet (or an atom) and the scale of a star nebula (or a piece of solid (or other) state medium). Everybody realizes that the difference is of many orders of magnitude. And the physics on each scale is different. Nevertheless, everything and the physics including are interdependent!

How many physical theories do you know that capable to describe a variety of interdependent via a scale physics phenomena? We are not talking here on one scale traditional physics constructions, of coarse.

So, the next Announcement I would like to do is about the MULTISCALE definition.

Some of the inspired by particle physics and biology notes on Scaleportation are given in -

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There is no personal critique on these pages. If few names appearing more often than the others - that is because those researchers as, for example, S.Torquato or A.Prosperetti studies are outstanding, and they might be of substantial interest for HSP-VAT, if those persons would do the substantial rethinking in terms of the efforts and return on those efforts, and on the prospective outcome. How much of effort and money spent uselessly in the area of Heterogeneous physics (and Engineering) theory, modeling and experiment is unbelievable when compounding the work for government programs, grants, and contracts done in the lab after lab etc., etc. Not only in the universities and government labs, industries are spending even more.

Especially at nowadays, when the Nanotechnology and Multiscaling became the magic words.

Some areas, even when they deserve the attention are out of our time and interests as, for example - the boiling in Thermal Physics. In spite that the theory begins with more or less tedious description of the one bubble produced, not to mention the sufficient morphological features of the surface of boiling. Then, the field is doing well just collecting the experimental data and building heuristic correlations. Because the workers in the field don't know how to combine the multiple bubbles growth in the dense environment. That is the current state of affairs.

Many other disciplines and sub-disciplines are in the same mode, unfortunately.

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It was noticed recently that the "dissident" or better to say "renewing", challenging, unorthodox, pioneering, future physics theories continue sprouting in many areas of physics from the 70s of the last century. Some of them are really vocal and straightly attacking the orthodox "theological" theories of physics mainly, some are rather coward and/or shy.

We are concerning to a variety of them, just because they (according to their authors) try to remodel or renovate based on the one scale concept(s) assumptions, something that is still a Homogeneous theory in orthodox homogeneous physics. As the new concepts claim the intent to improve, often replace the old obsolete orthodox theories. They do this out of the best their objective; nevertheless, it's all made with the one scale Homogeneous description, even when author(s) address the obvious hierarchical, scaled issues.

That is why we need to state -

It is again about the One Scale for All (OSFA) governing equations for the phenomena at the atomic, sub-atomic, continuous, particle physics, heterogeneous, planetary, intergalactic, whatever like for a "Big Bang", etc. scale. That means, so far, people are using the same basic governing equations for any atomic, sub-nuclear and for general relativity (gravitation) models to name a few!

And this is also the obsolete and incorrect concept in physics.