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 the 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 the 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, for example, models and courses up to this time without the Lower scale physics and math. That is no sense to write down it because communications between both scales physics in Conventional Orthodox Homogeneous Physics (COHP) of XVIII - XX are occurring via adjustable coefficients that have being sought via Homogeneous experiments. No correct theories for this in COHP. The way of thinking is just jump to the Upper scale and try to figure out the "effective" coefficients with using the wrong Homogeneous models for that scale physics.

Meanwhile, when we want and need to take the lower (and both) scale physics and math correctly, the Upper scale models, equations, solutions and/or characteristics can be sought rigorously and correctly as well.

Firstly it was done by me in the USSR in ~1982- 1984, see some information on that in Turbulent Transport Two Scale VAT Governing Equations for Obstructed and Porous Media. Introduction

Meanwhile, it is an appropriate place in this sub-section for telling some of the history of HSP-VAT application to the HEs theory and not only, modeling, and simulation. The matter is and about the authorship and Intellectual Properties (IP) that had been gained outside of some employment (UCLA) and the US.

As the response to the keynote talk by I.Catton in 2010 - "Conjugate Heat Transfer Within a Heterogeneous Hierarchical Structure" title of his keynote lecture at (IHTC-14) International Heat Transfer Conference, August 8 - 13, 2010, Washington D.C., USA, (http://www.asmeconferences.org/IHTC14/Keynotes.cfm) we need to say some otherwise statements.

In his talk there are wordings - "In 1985, he began his work on Volume Averaging Theory (VAT) as a basis for dealing with transport in heterogeneous hierarchical media. This work culminated in a lengthy paper in Advances in Heat Transfer in 2001. This work has continued and now forms the basis for optimization of heat sinks and heat exchangers."

First of all - Prof. I.Catton could not start the VAT in 1985, as long as I came to the US in 1990, and that was me who named this discipline approximately in 1992-1994 as the VAT (Volume Averaging Theory). Sorry, but I need to disclose this, and this is not in a single case when people liked to get attention via using my IP and publications.

Before that nobody, neither professors S.Whitaker, J.C.Slattery, W.Gray, nor I.Catton ever used the mathematics, physical concepts for heterogeneous (two scale at least) description of physical problems as the scaled ones, two scale at least, for heterogeneous media, for nonlinear fields, for turbulence, biology, medicine, other sciences, etc., etc.

Not talking on the coining of the field as the VAT (HSP-VAT now).

I.Catton used to deal with the heat exchangers (HE) modeling for many years (and for Nuclear Power industry as well) before me, but never came to the ideas of connecting HE theory, modeling and design to the HSP-VAT, or VAT in the 90s.

Heat Exchangers are the two or more scale thermal and fluid mechanics physics devices.

That was me, who brought all of that on HEs and other fields to the MAE department of UCLA in 1991 and later on performed the theories, mathematical modeling and simulation specifically for HEs in 1998-2002. Using students and collaborators from many countries actually.

See on this in all my - "Fundamentals ......"

especially in "Fundamentals of Hierarchical Scaled Physics (HSP-VAT) Description of Transport and Phenomena in Heterogeneous and Scaled Media"

as well as in this "Heat Exchangers, and in a few other sub-sections.

Regarding the "start" in 1985 - that was the start of porous media research by I.Catton in a completely conventional orthodox way - the one scale homogeneous Darcy-Forchheimer type modeling governing equations, the papers on the topic Catton published with his active grad student J.Georgiadis in those few years before my arrival.

And only my active participation starting in 1991 (Georgiadis left to those days) turned table to the HSP-VAT agenda. I was writing during all the consecutive 11 years to the DOE and DOD, DARPA, corporate research quarters the proposals in the fields of Ht Fluid Mechanics, Ht Thermal Physics, that were the natural fields for the areas of interest at MAE, as well as for other physical sciences that only I had brought in as the Hierarchical, Heterogeneous (Hr, Ht) fields to the department, as the solid state, composites via HSP-VAT, electrodynamics, magnetism, acoustics, medicine, etc., etc. Have copies of those texts and scripts, if anyone would like to look at.

I.Catton for nearly three years learned the basics to understand and participate in this new for him science. Before my work at MAE of UCLA, he spoke to Whitaker for a few occasions, and left the field unconvinced of its usefulness.

He told me himself on that - "too much of math and what is the goal, the purpose?"

It took, as I said, nearly 3 years before I.Catton had acquired the basics of VAT (HSP-VAT) and began believing in that science (HSP-VAT), and consecutively our program manager of that time at DOE (O.Manly).

And especially, this is my guess, as he witnessed through the years the first of this kind the 2 scale exact solutions in Ht Fluid Mechanics and Thermal Physics which I had developed.

Some even with collaborators from other countries - as Dr. V.Kushch, Dr. Y.Gordienko, Prof. E.Sergievsky, and other personalities, paying to them myself, not via or by UCLA in the 90s.

I.Catton knows about that.

Some of these developments are in the websites, this one - web-1:

and in Russian - web-3: "http://www.travkin-hspt.narod.ru"

And finally for this short history remark, that was me, who wrote the full text of chapter in the book - Travkin, V.S. and Catton, I. Transport phenomena in heterogeneous media based on volume averaging theory// Advances in Heat Transfer, New York, Academic Press, Vol. 34, pp.1-144, (2001). I.Catton was the minor contributor, co-author. He even rejected acceptance of the compensation from the Avademic Press publishing house, because he knew who was the author. We were in good relationship at that time 98-2000, so he gave me his half-part payment. And I'd acknowledged this.

At present times, it would be more modest of I.Catton and fair to write that he "had participated and supported the science of HSP-VAT," but not "started" or "invented," and that he was co-authoring the texts along the major contributor.

Establishment usually attributes all the benefits to themselves in similar situations. Well, with my state of affairs - I am too big fish for that kind of tricks with authorship. Nevertheless, we know the situation in general in the US universities, when the position determines the "major" contributor. This rule is not always truthful, specifically when the lower compensation person having done so many things in the field, that others can not compete.

It is true also, that I.Catton was following my advices in directions from the 90s - 2002, in the HSP-VAT Optimization of HEs, etc. We have many papers written by me. Yes, there are some grad students, other collaborators, but the theory, texts, ideology, mathematics, physical models all were developed by myself with their and I.Catton participations.

Many fields, along with solved problems in HSP-VAT have been done by me and my collaborators in the 80s, before arriving to the US and continue developing HSP-VAT (in physics and math) and its applications far beyond the mechanical engineering at MAE of UCLA as, for example, in meteorology, spinning, atomic, particle, and nuclear physics, biophysics, biology, medicine, for many technologies, etc. Along the area of Heat Exchangers scaled transport as well.

It is interesting - What S.Whitaker, a real one of pioneers since 60s, thinks now on that? In the 90s he told me - that nobody in his department of Chemical Engineering at UC, Davis even understood what he was suggesting and studying. And this is about the really good application field for HSP-VAT such as the chemical reactors modeling and design?

Now, as I wrote here in this website also in the place - "Global Financial Opportunities in Multiscale Technologies. Introduction", other sub-sections,

some people seems, who is somehow familiar with the science of HSP-VAT and publishing close to HSP-VAT, are declaring themselves as the "founders"! And it's a fun to read, but is not true.

It will be enough just to read and compare the bibliography of mine and other major players in local-non-local physics since the 1980s, including internet publications of exclusive texts, materials, web appearances, papers written in Russian as well. The few papers of 80s and 90s after being laid down side by side will tell to specialist and to a student who is the founder of HSP-VAT (VAT). And who suggested to apply, had developed the theories, models and simulated in the HS physics, its applications modeling and design.

This is the 3-rd stage of recognition according to great names of XIX-XX centuries, when specialists around are in a hurry to join the bandwagon. And it is Great. Something interesting is coming out unending and more essential.

Prof. A.Nakayama is also suggesting his name as of the person who developed the VAT. Well, we can state that he participated in 90s, is participating now in the one scale half-homogeneous modeling in porous media, started to work in medicine, but had never even written the properly SCALED mathematical statements.

I would upload to the sub-section - "How not to Scale-Down...or -Up.. ..Analysis of Current Studies on Scaled, Collective Phenomena in Biology Fields Presented as the One-Scale Concepts," the analysis of A.Nakayama and his co-authors VAT statements.

Right now in these notes here written for the first time the state of the history on the subject of HSP-VAT (VAT).

We continue these historical notes with the priorities remark on the larger scope things - that among other new directions in HSP-VAT, biology and medicine can be mentioned the following ones that were developed by me. With some ideological, technical and still principal support by Prof. I.Catton, other collaborators. With the help of my associates from a few countries:

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.

Well, and I am not sorry for this long list, with regard of other researchers claims. This should be announced, this is like agreements in business - if not stated, recorded, then workers and adversaries around do that for themselves.

The exact Two scale first time obtained by me solutions of common textbooks known problems that cannot be sold in Homogeneous One-Scale statements, but being presented to students as the solutions, can be seen in -

These exact solutions have been demonstrating the potential for treatment of this new type of physics tasks - the two and more scales interconnected strictly problems, and at the same time the reality of interconnection (Scaleportation) of the physical fields acting over the two (at least) scales.

It is important to note for a public who is not proficient enough in mathematics, that in mathematics the things that just once had been proven are valid and continue to be official, "legally binding" for all similar problems. That means the volume of research, studies that has been gained throughout >40 years in physics of Continuum Heterogeneous media is official, valid, and "legally binding" in all other areas of physics and technologies. Including and sub-atomic fields in physics.

This said, it is not precluding the great need in HSP research in the sub-atomic physics.

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The interest and realization of universal mathematics principles of polyscale science made the HSP-VAT successfully being applied in the last ~20 years of development, no UCLA involvements, to the subatomic physics fields: particle physics -

nuclear physics -

biophysics of mostly sub-atomic scale fundamentals -

HS physics of mostly sub-atomic scale fundamentals -

as well to the new polyscale energy devices with the COP>1 and demonstrated a pretty good level of success.

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Of course, 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 course, 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 Homogeneous concept in physics.