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| viXra.org > Classical Physics > 2611 |
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[2] viXra:2611.0032 [pdf] submitted on 2026-11-11 10:23:30
Authors: Bernard Riley
Comments: 10 pages, 6 figures
The values of pairs of related physical quantities are shown to arise in the judgement of one person, the first cogniser, in the union of observation and concept. An expression of each value is observed and, using an original method, its numerical value is mapped, by a mathematical function deemed appropriate, to an explanatory rational number that both indicates the significance of the physical quantity and establishes its value. If the physical quantity is considered to be significant the explanatory number will take a rational value of low denomination. If the quantity is considered to be of great significance the explanatory number will take a special integer or half-integer value. Having been explained with sound judgement, the value of the physical quantity is what anyone will experience on observation. By the use of two mapping functions, the numerical values of significant quantities deemed to be paired are mapped to closely coincident special integers or half-integers. Mathematical relationships established between the values of quantities reflect the thinking of the observer. Fundamental particle and atomic quantities are judged in Planck units. Astronomical and cosmological quantities are judged in SI units.
Category: Classical Physics
[1] viXra:2611.0007 [pdf] submitted on 2026-11-02 15:40:09
Authors: Shisheng Wang
Comments: 18 Pages.
A multicomponent, multiphase fluid can be modelled as either a homogeneous mixture flow field or separated flow fields. The key concept is that fluid flows will be considered as continuum fields through suitable volumetric "average" procedures, so that the differential calculus tools can be used. For a homogeneous mixture flow field, the mixture is treated as a single system (single-phase flow). Starting from the mixture momentum density 1-form per unit volume, taking the exterior derivative of this 1-form yields a field strength tensor in a differential 2-form. The interior product (contraction) of this 2-form with the tangent velocity yields the dynamic equation of the homogeneous mixture flow, E u20d7+Ω u20d7×V u20d7=0 (or expressed as a differential 1-form of eq. (20)). It is equivalent to the Euler-Lagrange equation, but the gradient of kinetic energy doesn’t equal zero for continuum fields, in contrast to the classical Euler-Lagrange equation for a discrete isolated particle. For separated flow fields, different components travel at their own velocities; there exists a velocity difference between components, and each component is treated as an individual system to consider the interactions between different components. The homogeneous mixture dynamic equation turns into two equations for separated flow fields. The two equations become tightly entangled. This shows there are very complicated interaction forces between the two flows.
Category: Classical Physics
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