Students should be aware and have to give some thoughts regarding their undergraduate, graduate, and post-doctoral education based on the information - which is the University and Institution able to teach, practice, and develop applications based on the correct fundamental courses for Heterogeneous Matters, Media, Devices and True Multiscaling in the following fundamental disciplines:

1) Particle Physics;

2) Particle Physics 2;

3) Nuclear Physics Structured;

4 Electrodynamics;

5) Electrodynamics 2;

6) Atomic Physics;

7) Ferromagnetism;

8) Continuum Mechanics;

9) Heat Transfer;

10) Mass Transfer;

11) Thermal Physics;

12) Fluid Mechanics ;

13) Electrostatics ;

14) Acoustics;

15) Environmental Engineering;

16) Air Pollution (Urban and Modeling);

17) Agro-Meteorology;

18) Nanotechnologies;

19) Optics;

20) Materials Science;

21) Semiconductors;

22) Superconductivity;

23) Composite Engineering;

24) Experimental Science for Heterogeneous Matter;

25) Optimization in Heterogeneous Media;

26) Biology 3P (Polyscale-Polyphase-Polyphysics);

27) Biology Multiscale Applications;

28) Biotech many Fields;

29) Health Sciences; etc., etc.

In all these courses should be included and Taught the following topics or some parts of those and of the technical problems of the Two-scale (at least) nature:

1) Elements of Heterogeneous Physics and Mathematics;

2) Elements of 2P Particle Physics;

3) What are the Nuclei in Elements;

4) What is the Electromagnetism of Atoms and Particles;

5) What is the Interaction and Aether in Physics;

6) Conductivity, Diffusivity, Electrical Permittivity of the Two Scale Media with Globular Inclusions, for Spheres This Problem Have Been Solved Exactly. Lecturers Must Know or at Least be Able to Describe and Discuss How This Problem Was Solved, and What are Implications.

7) Conductivity, Diffusivity, Electrical Permittivity of the Two Scale Media with Straight Rods (Bars) Second Phase of Inclusions. For Morphologies with Dilute Random or Functionally Dependent Diameters This Problem Have Been Solved Exactly.

8) Conductivity, Diffusivity, Electrical Permittivity of the Two Scale Media with Two Phase Layered Morphology. For Morphologies with Linear Statements This Problem Have Been Solved Exactly.

9) Momentum transport, Conductivity, Diffusivity, Electrical Permittivity of the Two Scale Media with Straight Pores of the Second Phase. Flow regimes might be of three types (laminar, creeping, and turbulent), that other methods can not apprehend. For Morphologies with Dilute Random or Functionally Dependent Diameters these problems have been solved.

10) Momentum transport, Conductivity, Diffusivity, Electrical Permittivity of the Two Scale Media with Straight Slits of the Second Phase. Flow regimes might be of three types (laminar, creeping, and turbulent), that other methods can not apprehend.

11) Fundamentals of Experimental Science for Heterogeneous Media and Devices.

12) Few Two-scale problems in Wave Mechanics - as in Acoustics, Electrodynamics, Elasticity. Few of them have been solved also exactly on both scales.

There is the great need to introduce this teaching first of all in the areas (professions) of nanotechs, medicine and life sciences, biotechs, and energy related technologies.

Why "should be taught these problems" ?

Simply because these are the basic principal classical problems usually taught in any coursework set that necessary for disciplines in technical, biotech and physical sciences specialties and the only known today Scaled, Hierarchical problems solved completely on both scale spaces, as well as the only known experiences with experimental techniques developed for scaled, heterogeneous devices two-scale experiments.

The methods, "theories" of other nature taught in the Universities mostly are simply imitating the Multiscaling as a methodology, that's it. Professors just verbally combine the descriptions of different scale problems in physics, chemistry, biology and telling the students - That's what you need to know and remember. Couple of coefficients and you've got the "mathematical" (but not a physical connection). It hardly reflects the real physical dependencies in heterogeneous, scaled media and the tools in need to model those.

For example, which is taken from the widely used undergraduate textbook on physics by Halliday et al. (2005) (textbook used and for biology students teaching), we can find in it the basic general rule for the heat (mass) transfer through the multilayer wall - "Conduction Through a Composite Slab...." in p. 494 as the formula (18-37)

which is for unit surface in SI units can be presented as

with the effective bulk medium coefficient of conductivity

is the heat flux through the multilayer wall with fixed external surfaces temperatures - the hot wall's surface and is the cold one, and volume fraction of the i-th phase..

Authors of this example problem - which is the Two-scale problem, do not tell the students that the formula hides the insufficiencies in the solution for mean heat flux (heat rate), for example, as following:

1) that this is the two-scale actually problem;

2) the Upper (the second) scale solutions are not achievable in brackets of homogeneous physics. There are no definitions and mathematics (at least correct ones) for that in homogeneous physics;

3) the steady-state mean heat flux and the effective conductivity coefficient and of the transient problem ones are different by their definitions and scaled mathematics involved, not by only fact that those problems are different by time derivative and temperature depending on time;

4) the dependencies outlined in homogeneous physics solutions are incorrect if being applied with the exact fields for the lower scale solutions as, for example, the homogeneous formula gives the averaged difference temperatures (averaged gradients) that are not equal to the difference (gradient) of averaged temperatures

in spite that in homogeneous physics they should be equal (here is the phase averaged temperature). Why is that? There is no correct answer in the homogeneous thermal physics for that.

Also, there is inequality one scale homogeneous physics can not explain

in spite that the homogeneous thermal physics formula is correct (here is the intrinsic phase averaged temperature, and is the phase fraction).

5) that for the linear problem there are the two physical mechanisms involved in field's transport - 1) is the INTRAPHASE, in each phase transport; and 2) is the INTERFACE transport each with their respective phase effective coefficients. These transport means and phase effective coefficients are not known in the one-scale homogeneous physics transport;

6) they don't tell the students that with this formula the transient problem can not be solved;

7) that there is no solution for this problem of mean heat flux (heat rate) in the transient formulated problem. The solution is achievable only via the two-scale physical and mathematical statement.

8) the formulae (18-37) and are invalid for transient heat transfer, for example, when one of the boundary temperatures is changing during the time period. In spite that in this case the difference in temperatures is still known, the heat rate ( mean heat flux) can not be found via this formula and/or this method;

9) it might be impossible to design the optimal heat transfer or heat protection multilayer coating while study only the one scale Homogeneous statements. There is no one optimally designed yet - and that is the result of the more than hundred years effort!? That is why it can be stated the optimal design is unachievable when the one-scale thermal physics theory used.

Halliday, D., Resnick, R., and Walker, J., Fundamentals of Physics, 7th Ed., J. Wiley & Sons Int., (2005)

In various pages of this and other our sites spread multiple examples of such "teaching".

We start explaining and talking on this in -

• Are there any other Methods and Theories available? http://travkin-hspt.com/fundament/04.htm

Even if lecturers, professors don't know how these solutions were obtained and What is the HSP-VAT at all. Nevertheless, to be honest with students they need to tell to students that this is it. This kind of knowledge and solutions exist and this knowledge should be taught to students if Universities (or any other educational Institution) adhere to their policies of "state of the art" education.

This will be an advanced education for many fields that Universities are struggling to add the specialties for and stay in the markets.

We can estimate some of educational Institutions, Universities and give a researched summary on their abilities to teach or even to simply concern the subjects of Scaling, Multiscaling, etc. etc. physics' content and advancements.

We paid extraordinary attention to lecturing in our courses on the few scaled problems that were solved even exactly some years ago, actually from 94-95. These two scale connected solutions, the solutions that explain hidden in textbooks incorrectness's and inconsistencies - are supposed to overturn the many physical disciplines lecture courses. The main features of these solutions and consequences are known since 1994-95. Through the years I also disseminated them to many professionals lecturing in the universities, and particularly in fields demanding already for many years the usage of words - "local," "nonlocal," "heterogeneous," "multiscale," "averaged," "two scale," etc.

The content of this course below is by no means follows the usual university traditional teaching of the multi-phase transport and processes in technologies and/or physics, and presenting them as they are like the one scale and GO theorem based disciplines.

On the other hand, this course and others portrayed in this website are not quite similar to some courses with elements of linear and half-linear HSP-VAT taught in few US universities, because we had taken the basis for them as rendered with critical features and detail in

Fundamentals of Hierarchical Scaled Description
in Physics and Technologies

That is why the outcomes and much of teaching materials and results and problems, are different in many parts and instances.

Course Outline:

Elements of Heterogeneous Media Transport - Local, Non-Local and Multiscale Theories

Instructor: Travkin, V.S.
http://travkin-hspt.com

Objectives of the Course:

The objective of this course is to provide the students with elements of transport of energy, mass and momentum in heterogeneous systems - based on hierarchical multiscale phenomena description theory (Hierarchical Scaled Physics Volume Averaging Theory - HSP-VAT). At present time the HSP-VAT is the only theory which suggests the correct physical and mathematical description and connection of processes on different scales of hierarchical media, materials, and/or fields.

Tentative outline:

First starting with the review of theories used for the description and problem statements in multiphase flow and heat and mass transport the course content will guide students through the basic physics and mathematics of collective phenomena. Among other major topics that will be covered are the heat transport in heterogeneous media such as composites, in addition to topics concerning experiments in heterogeneous media.

The basics of the multiscale field phenomenological and stochastic transport governing equations will be described and their application to thermal physics and fluid mechanics will be emphasized while comparing with known conventional problem formulations and mathematical statements. The pure analysis of classical problems of momentum and heat transport in heterogeneous media will be demonstrated with the hands on participation of students in various methodologies.

The major engineering issues of estimation of effective characteristics and coefficients will be emphasized in the course with applications in thermal science. Specific topics include effective conductivity coefficients, heat exchanger modeling methodologies and design, porous media fluid flow, permeability and flow regimes, experiments over composites and their data reduction.

Required Textbooks: none

Required Lecture Notes, Texts: few printed papers by Travkin, V.S. and

1. Travkin, V. S., "Particle Physics - Heterogeneous Polyscale Collectively Interactive," http://www.travkin-hspt.com/parphys/index.htm

2. Travkin, V. S., "Electrodynamics 2 - Elements 3P (Polyphase-Polyscale-Polyphysics)," http://travkin-hspt.com/eldyn2/index.htm

3. Travkin, V. S. and Bolotina, N.N., "Quantum Chemistry, Physical Chemistry, Molecular Dynamics Simulation, DFT (Density Functional Theory), and Coarse-Graining Techniques Applied in Structural, Cellular Biology, Polymer Science and Implication for Scaleportation," Journal of Alternative Energy and Ecology, No. 2, pp. 58-75, (2011a)

4. Travkin, V.S. and Catton, I., Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory, in Advances in Heat Transfer, New York, Academic Press, Vol. 34., pp.1-144, (2001)

Recommended Textbooks:

Kaviany, M., Principles of Heat Transfer in Porous Media, 2nd. edition, Springer, (1995).

Slattery, J.C., Momentum, Energy and Mass Transfer in Continua, Krieger, Malabar, (1980).

Whitaker, S., "Volume Averaging of Transport Equations", Chap. 1, in Fluid Transport in Porous Media, Computational Mechanics Publications, Southampton, UK, (1997).

• In Russian
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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: Tï¿½ï¿½ï¿½ï¿½ï¿½ï¿½, ï¿½.ï¿½.

http://travkin-hspt.com

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ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: ï¿½ï¿½ï¿½

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½: ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½, ï¿½.ï¿½. and

Travkin, V.S. and Catton, I., Chap. 1, "TRANSPORT PHENOMENA IN HETEROGENEOUS MEDIA BASED ON VOLUME AVERAGING THEORY", in Advances in Heat Transfer, Vol. 34, pp.1-144, (2001).

ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½:

Kaviany, M., Principles of Heat Transfer in Porous Media, 2nd. edition, Springer, (1995).

Slattery, J.C., Momentum, Energy and Mass Transfer in Continua, Krieger, Malabar, (1980).

Whitaker, S., "Volume Averaging of Transport Equations", Chap. 1, in Fluid Transport in Porous Media, Computational Mechanics Publications, Southampton, UK, (1997).

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