1) Principle - Recognition of the fact - that at any scale the Continuum description material substance is the Polyphase Polyscale Heterogeneous medium. From some of the continuum scales and Top-Down to one of the atomic scale.
2) Principle - Recognition of the fact - that the structure and the specific "phase" content in a Continuum Homogeneous or Heterogeneous Medium are the fundamental facts controlling the function of the medium along with the environmental (boundary) conditions.
3) Principle - Recognition or knowledge of the fact that - in this consideration the polyphase, polyscale studying of the subject - the Homogeneous and/or Heterogeneous medium's sample, for example, is the most accurate and revealing way of obtaining the facts, conclusions. This was and is one of the main methods (the reductionism with the inseparable up-scale the holism approach) to study the nature by physical and biophysical methods so far for many centuries.
4) Principle - Recognition or knowledge of the fact - that for studying the polyphase matters, media the only correct way is to use the discovered in 60s - 80s methods, theorems of Hierarchical physics and mathematics: Hierarchical Scaled Physics - Volume Averaging Theory, those specifically were created and tuned throughout the last 40+ years for polyphase polyscale physical, biological matters. Of many other methods suggested for the Heterogeneous media theorizing, modeling and understanding, up to this time there is no one more fundamental and/or correct.
We won't discuss or comment on numerous schemes suggested for heterogeneous, physical, biological polyphase media, as the mixture theory, for example, because they openly use an inadequate or truly simplified physical and mathematical description of the problem. We also published numerous analytical texts in hard copy and the web publications on this issue.
This fact is not objected or disputed by any professional, openly at least, for the last >30 years. The complexity and educational policies are preventing professionals to acquire and employ the tools of HSP-VAT.
One of the examples, is the use of Gauss-Ostrogradsky (GO) theorem for deduction of governing equations for near 200 years in physics and other sciences. This theorem is valid only for a Homogeneous matter, that most of professionals even do not know and acknowledge. In hierarchical mathematics there are many like theorems for the same purposes that have been developed and used during the last 40 something years.
Hierarchical Polyphase Polyscale Concepts for Heterogeneous Continuum Mechanics and Modeling of its Problems
1) There is no physical phenomena, process, act that at the determined scale is not of the Volumetric character or is not consciously or sub-consciously understood and/or modeled with the Averaged phenomena of the sub-scale. Any point-like experiment or method, theory is about for accepting at first the premise that the point is formed by/after somehow averaging of the forces/movements/reactions etc. of the below scale physics. Mostly it is done implicitly, even sub-consciously, but this premise is present. The Top-Down sequence of physical phenomena is more accurate down to the sub-atomic scale particles, an aether in between the particles and some pertained to them phenomena.
2) Any Heterogeneous media (Ht), materials sample is in reality a two scale, at least, physical entity that have continuous (meso-scale might be and often is not already continuous, but having cracks, discontinuous surfaces, dislocations and other imperfect solid state features) transport, physical field processes of a physical volumetric (averaged at some point) character.
3) It is not correct to study, model and make valuable definitive conclusions about this medium physical functions when using only the one scale physical phenomenon(a) in a medium taken into account. Contemporary experimental physics, biology, medical investigations lack of ground and fundamental science, while applying the theoretical schemes of one scale nature that were suggested in physics many decades ago. Chemistry is itself of low understanding of integrative molecular mechanisms in a medium molecular sample etc.
4) The scale models constitute the separate spatial and temporal physical and mathematical models describing the functions of transport on the scale dependent phenomena in such media.
5) Scale dependent physical, mathematical models are inherently communicative Up-and-Down the scales in heterogeneous media. The scale communication of physical properties of Ht medium has been named as a scaleportation of properties and characteristics in HSP-VAT.
6) It is possible to commute the physical models and medium's properties at the neighboring scales in Heterogeneous materials with mathematical strictness using methods developed in HSP-VAT.
7) Each scale developed Homogeneous models in a Ht medium based on Homogeneous presentation of this scale physical definitions and the field's governing equations can be connected more or less mathematically strictly to the neighboring next Up-scale or Down-scale models only (most strictly) via using the interscale mechanisms of HSP-VAT.
8) The polyscale depiction of Ht medium's function (elasticity, thermal, mass, momentum, wave mechanics, visco-elasticity, plasticity, etc.) models is the only correct approach for theoretical modeling and simulation, for experiments data reduction when the subject of analysis, theory, model, experiment is the polyscale physically object with the nature prescribed polyscaling of function.
9) Any Homogeneous physical substance, medium, materials sample is in reality also of the two scale, at least, the physical entity that have molecular, atomic, sub-atomic and continuous description of transport, physical field processes of a physical volumetric character. The averaging and scaleportation of molecular (atomic) scale transport and phenomena Up- to the Continuum (one of the continuum) scale phenomena and Down- to the molecular, atomic scale, should be used with application of correct Hierarchical mathematics of discontinuous "broken" physical fields.
10) At present, in the last approximately 27-29 years all the main physical fields, definitions and homogeneous governing equations have been reformulated and upgraded using methods of HSP-VAT for acting in the heterogeneous subject matters, for Heterogeneous media of solids, solids and fluids, polyfluids, particles in fluid, scaled fluids, elasticity of solid and soft solid media, mass, heat, momentum, electromagnetism describing phenomena, wave mechanics, acoustical fields. That is now making available the polyscaling in the description and modeling the most obvious and important transport phenomena in a Continuum Mechanics media.
11) Advancements in the last 25 years in Hierarchical Scaled Physics - Volume Averaging Theory allowed to surpass inadequate, incomplete one scale homogeneous theories for averaging (mixing), "bulk" representing theories in almost every field of physics and biology. Now we can formulate the true polyscale Dynamics theories and models for Ht medium, including and meso-scale medium objects and relevant processes, polyscale by nature in a Ht Continuum Mechanics medium.
12) None of the concepts written above is on the lists of "advanced" programs formulated in the 90s-2000s years (and in "new" formulations of disciplines) in academic, university, government programs. And that is a signal of misleading development in the contemporary conventional Homogeneous (Heterogeneous methods, theory is not known) Continuum Mechanics.
P.S. Starting from the 2011 year of proposal applications cycle, any proposal that would have content reminding these concepts will be considered as of some plagiarized nature, if not describing and mentioning the origins of these present sources, published texts and names.
Any information displayed here is the propriatary information in the area of "Concepts: HSP-VAT Conceptual Vision and Methods in Application to Continuum Mechanics."
This is also the group of well known problems - still can not be resolved within the Homogeneous One-Scale Continuum Mechanics, etc.
