The Annals of Frontier and Exploratory Science

Two-phase Two-scale (2P2S) Two Coordinate System (2^3PSC) Dynamics of Interaction of Rotating/Spinning Arrays of Particle and/or Bodies. Physics 2

Vladi S. Travkin

Hierarchical Scaled Physics and Technologies (HSPT), Rheinbach, Germany, Denver, CO, USA

INTRODUCTION (in Heterogeneous Classical Mechanics - HtCM)

When Sub-atomic size Particles (SAP) and/or Continuum size Particle (CP) arrays, clouds are in dynamics usually this cloud has already the interactive fields either in steady-state or unsteady changing conditions. Among forces, physical fields that act in between the particles in the aether - the easiest way of interaction, unless we need to include the atoms, molecules of the gas that the SAP cloud might be in, as the most involved and strong interactions we should name the electromagnetic and momentum forces in the Two-phase Two-scale (2P2S) (at least) medium. The spinning particles and aether - 2P2S medium and phenomena in it.

MATH MATH MATH MATH MATH MATH MATH

Various kinds of Sub-atomic and Continuum Media singular and Arrays (Clouds) of Particles, Atoms, Molecules that have usually the interactions of different kinds. In COHP the Interaction of particles and bodies either are taken falsefully via mathematical none-physical One-scale methods, or at Sub-atomic scales just prohibited as the non-existing and taken via Superposition also the One-scale "magnificent" simplification "methods."

If the particles are all of the Continuum media size then we need to develop or have ready the physical models for each particle type phenomena they are at. Meaning inside of a particle - fluid, solid, elastic solid, etc. In Continuum Mechanics of Homogeneous Media there is a great deal of research and the volumes and volumes of written texts, books exist describing these phenomena and models for a particle scale, for each particle - phenomena of EM, heat, mass, elastic, visco-elastic, acoustic, etc. To these particle phase models should be added the aetherodynamics EM and momentum dynamics governing equations.

We also need to remind again that the great, one of the greatest parts of Conventional One-scale (Orthodox) Homogeneous Physics (COHP) of sub-atomic scales is being taught still in the universities and is based on the wrong governing equation of Boltzmann's type [1]. Also it needs to be said - that the Boltzmann's equation base definitions and physical variables are simply the mathematical PMCS (Point-Mass-Charge-Spin) objects.

That just alone means that the acceptance of PMCS objects and pure Mathematical (Statistical) approach and treatment of clouds of SA particles as clouds of points makes all the data regarding Boltzmann's equation related studies very close to be named as just a conjectural Particle Physics (PP) "science."

All these models and GE for Continuum size particles and SAP have been developed for the 2P2S Hierarchical Scaled Physics (HSP) problems [2-59]. While talking about the great part of HSP that takes care about the Two- and Polyphase fluid, gas, suspensions flow and transport of various physical other phenomena, first of all that of heat, energy, and mass transport the great input in this field has been done by S.Whitaker (as well as into other areas of HSP) with his co-authors. Two, three other outstanding pioneers we mention and analyze in some other manuscripts.

In this introductory to general text on HSP theories and methods regarding the 3P transport in the Polyphase Fluid and Mixed Media the results of Whitaker can be analyzed for some reasons of clarity and of general HSP theory. Here we need to make a couple of observations and remarks for students, graduate students.

As a matter of fact, it needs to be said, and we already spoken on that, the methods of GE derivation and results obtained by S.Whitaker are actually of 1.5 scale consideration because after the derivation of the equations on the upper scale - all physics and equations of the lower scale disappear from the discussion and the text completely. We noticed that even in 80 -90s results regarding the Upper Scale GE were the final complete outcomes of a research in works of Whitaker and co-authors. Some analysis of the Upper scale GE is dealt with. Still, the main drawback as of the VA theory developed by Whitaker is that there is no ever the connection, communications, clear ties between the physics and math of physical processes at the Lower and Upper scales.

Still, these connections and interaction over the scales of physics and math are the great reasons why physics and the nature around of us exist at all.

Another great drawback in theory and treatment in studies of Whitaker and most of his followers and other workers in related to VAT, inclined to be seen as of the VAT developments is that workers do not see and understand the models of 2-scale VAT as those that present the real physics on both scales and as such should be treated and sought of their solutions as of the TWO different physics models that, meanwhile, should be solved as the Two physics problems, Two scales problems, but not of only the one Upper scale physics GE and problems described by these GE. These Two scale problems are genuinely connected.

Also, they don't understand that in this way, in these kinds of mathematical statements the two mistakes at least are being done.

One is that the problem became stated without correctness and strong mathematics. With the kind of frivolous mathematical outcomes.

And the second error is that the solutions of problems on the Upper scale only are sought as of a variety of different physics statement, and some solutions and results are lost in this way of "solution" search.

We need not teach on these basics of HSP in this abstract, by the way.

Some more detail should be cared of for the mathematical models and special coordinate systems for mathematical simulation of particles' physics themselves and of intermedium of the aether processes.

Any size particle can have easier communication algorithms and more straightforward mathematical methods developed when each particle (or body in Heterogeneous Classical Mechanics [28-30,55-59]) has its own coordinate system to tackle the simulation methods, algorithms separately for that particle.

Communication between physical and mathematical models and GE for each of two (if any only) scale Top-Down or Bottom-Up is the task of the Hierarchical Mathematics [53-58] and it is much more tedeous and complicated thing than COHP physicists could tackle in modeling and simulation of COHP problems. Remember, that in COHP the problems are all of the One-scale and much simpler in mathematics than in HSP.

When L.Euler was developing the areas, fields in Classical Mechanics for Modeling of Rigid Bodies dynamics he imagined a single body dynamics without the 2-nd material, mostly gaseous or fluid matter surrounding the particle (body) and without any interaction of even the aether with that single particle or body.

We need here to remind again - that up to the 1950-1970s there was no understanding and physics and mathematics of Heterogeneous Media [2-7,60-64] (only partial list of references). Then, up to 1980 there were not much of developments. While in the 1980s was conceived and commenced the Hierarchical Mathematics and Hierarchical Scaled Physics (HSP) for working with Heterogeneous Media in the post WSAM theorem era [2-59], with long time delay in publications. Many studies are unpublished up to now.

Nevertheless, the idea of using two coordinate systems for modeling of dynamics of a single rigid (elastic, visco-elastic, etc.) or fluid particle or body as well as fluids has been used and in 3P dynamics of Continuum Particle (CP) Arrays as well as for SAP clouds dynamics. The two (at least) scale HSP for CP and SAP arrays 3P Dynamics consists of many more the instruments in its formulation, modeling and simulation of particles arrays of any kind than just the Euler's equations for rigid particles and HSP ones for clouds of rigid particles in an aether as a One-phase medium [2-59].

We deliver some models and simulation techniques for Reciprocal Top-Down Bottom-Up (TD-BU) 3P dynamics of CP and SAP arrays in a mode that is appealing for studies. That field is the only credible one at present for numerous technical applications regarding the Many Body Problems (MBP) of this kind [20-35,53-59].

Remembering, that all of the above said is actually about and for famous Many Body Problems solution.

Key words: Key words: Multiscale; Polyscale; Polyscale modeling; Heterogeneous media; WSAM theorem; Averaging theories; Polyscale physics; Two-phase Two-scale dynamics; Homogeneous Electrodynamics; Heterogeneous electrodynamics; Sub-Atomic modeling; Particles modeling; Elementary particles dynamics; Collective interaction; HSP-VAT; Scaleportation; Many Body Problems (MBP).

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The following article will describe and explain in more or less simple text and mathematics the scaled subjects regarding the 3P Hierarchical Physics and Mathematics modeling and simulation phenomena for the Polyscale electromagnetic particles/bodies and atoms, molecules in the clouds of them and with collective interactions. Well, and not only Particles of Sub-atomic and Atomic scales, but and Continuum size - oh yes, and of Nano-size particles and Bodies of larger scales. General methods:

Travkin, V.S., "Two-phase Two-scale (2P2S) Two Coordinate System (2^3PSC) Dynamics of Interaction of Rotating/Spinning Arrays of Particle and/or Bodies. Physics 2," ** http://travkin-hspt.com/classmechht/2p2s2cdyninterpart/2p2s2cdyninterpart.htm

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Some of the relevant HS physics and mathematics outcomes, methods, and derivation procedures can be found in this Hierarchical Scaled Physics disciplines - http://travkin-hspt.com/index.htm, some other references on Physics 2 sciences and in closely narrated materials. =================================================================================================

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"Two-phase Two-scale (2P2S) Two Coordinate System (2^3PSC) Dynamics of Interaction of Rotating/Spinning Arrays of Particle and/or Bodies. Physics 2."

This is not relatively the Well Known problem in physics, meanwhile, within the COHP it has been even formulated wrongly - read our analysis and texts on Conventional Homogeneous One-phase Physics disciplines great Imbalances. Nevertheless, this kind of problems are the Gatekeeper problems in 2nd Physics and for COHP - and they can not be advanced, solved within the Homogeneous One-Scale physics and mathematics and/or specifically particle physics.

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