[23] **viXra:1612.0415 [pdf]**
*submitted on 2016-12-31 21:01:16*

**Authors:** Richard A Jowsey

**Comments:** 13 Pages.

The fundamental fabric of spacetime is revealed by deep Dimensional Analysis of the Planck Units of mass, energy, and electromagnetism. Using a little-known expression derived by James Clerk Maxwell for the dimensional reduction of mass and charge into units of length and inverse-time (frequency), all of the physical quantities can be expressed in terms of metres and inverse-seconds (Hz). On arranging these quantities into a 2D log-log space/time matrix, simple (but compelling) patterns emerge in the mathematical relationship between fundamental units. The space/time matrix requires five spatial dimensions to accommodate the physical units, two of which are shown to be imaginary spatially-gauged wavelengths, i.e. unobservable dimensions of complex 5+1D spacetime, measured in metres, which exist (mathematically), but are not real.

**Category:** Mathematical Physics

[22] **viXra:1612.0409 [pdf]**
*submitted on 2016-12-31 06:11:07*

**Authors:** Wen Chen

**Comments:** 6 Pages.

This short note proposes a general time-space metric by an extension of the power-function based fractal concept to the structural-function fabric. The structural function can be an arbitrary-function to describe complex metric underlying physical systems. We call such a metric Structal, and the fractal is its special case. This work is inspired by our recent work on the structural derivative, in which the structural function takes into account the significant influence of time-space fabric of a complex system on its physical behaviors, in particular, the ultra-slow diffusion. Based on the structal concept, this communication suggests the structural time-space transformation and introduces the general diffusion model. In addition, the statistics implication of the structal and the structural derivative model is also briefly discussed.

**Category:** Mathematical Physics

[21] **viXra:1612.0357 [pdf]**
*submitted on 2016-12-27 07:30:29*

**Authors:** Renzun Lian

**Comments:** 10 Pages.

As a supplement to the previous Parts I and II, the Surface formulations of the ElectroMagnetic-Power-based Characteristic Mode Theory for the system constructed by Multiple Homogeneous Material bodies (Surf-MHM-EMP-CMT) are established in this Part III. The coupling phenomenon among different bodies is specifically studied, and then a new kind of power-based Characteristic Mode (CM) set, Coupling power CM (CoupCM) set, is developed for characterizing the coupling character.

**Category:** Mathematical Physics

[20] **viXra:1612.0353 [pdf]**
*submitted on 2016-12-27 03:13:34*

**Authors:** Victor L. Mironov

**Comments:** 9 Pages.

In the present paper we develop the description of electromagnetic field in an anisotropic medium using the sedeonic wave equations based on sedeonic potentials and space-time operators.

**Category:** Mathematical Physics

[19] **viXra:1612.0352 [pdf]**
*submitted on 2016-12-27 04:22:39*

**Authors:** Renzun Lian

**Comments:** 13 Pages.

Both the previous Part I and this Part II focus on the linear electromagnetic system constructed by a Single Homogeneous Material body (SHM), and the SHM can be electric and/or magnetic. The studies for the system constructed by Multiple Homogeneous Material bodies (MHM) will be finished in Part III.
It is indispensable for the Surface formulations of the ElectroMagnetic-Power-based SHM Characteristic Mode Theory (Surf-SHM-EMP-CMT) to relate the surface equivalent electric and magnetic currents, and a boundary condition based method for establishing the relation has been provided in the Part I. In this Part II, some further studies for the boundary condition based method are done (such as the revelation for physical essence, the numerical analysis, and the improvement), and a new conservation law based method is given.
As a supplement to the Part I, some new surface formulations for the output power of a SHM are developed in this Part II, and then some new surface formulations for constructing the Output power Characteristic Mode (OutCM) set and some new variational formulations for the scattering problem of a SHM are established.
In addition, the power relation contained in the PMCHWT formulation for a SHM is analyzed. Then, it is clearly revealed that the physical essence of the PMCHWT formulation for the SHM scattering problem is the conservation law of energy; the power character of the CM set derived from the PMCHWT-based CMT is not always identical to the OutCM set derived from the Surf-SHM-EMP-CMT; the PMCHWT-based CMT can be viewed as a special case of the object-oriented EMP-CMT.

**Category:** Mathematical Physics

[18] **viXra:1612.0299 [pdf]**
*submitted on 2016-12-19 12:57:58*

**Authors:** Markos Georgallides

**Comments:** 21 Pages.

Everything in this cosmos , is Done or Becomes , from a Mould where , in Geometry is the Monad , the discrete continuity AB , In Mechanics and Physics is the Recent Acquisition of Material-Geometry where , Material-point is the discrete continuity |{⊕+⊝}| = The Quantum , In Plane is Archimedes number ,π, which is becoming from the Squaring of the circle , In Space ,volume, is the number ³√2 which is becoming from the Duplication of the Cube . In article [STPL] Geometrical Mechanism produces and composite all opposite Spaces and Anti-spaces Points , to Material-points which are the three Breakages {[s²=±(w ̅.r)², [i]= 2(wr)²] of [MFMF] Gravity , under thrust v ̅= c ̅ } , where through it become the Fermions → [ ±v ̅.s²] and Bosons → [v ̅.I = [v ̅.2(w ̅.r)²] = [v ̅.2s²] , i.e. STPL is the Energy-Space Genesis Mechanism .
Big Bang and GR was a temporary solution to the weakness of what men-kind had to answer . Nature cannot be described through infinite concepts as this can happen in Algebra and values , and this because are devoid of any meaning in Objective -Reality , the Physical world which is the Nature . Material Geometry is the Science and the Quantization-Quality of this Cosmos which joints the , infinite dimensionless and meaningless Points , because these have only Position , with those of Nature which are Qualitative Positive - Negative - Zero Points and which have , Positions , Directions and Magnitudes with infinite meanings , which through the Physical laws are the language of them in itself . The Work , as Energy , is the essence of this deep connection of Material-Points , the Space , and through the Conservation-laws is making , Energy-Material-Geometry . Extension of Material-Geometry to Chemical-Sector gives the possibility for new materials in a drained way of thinking .

**Category:** Mathematical Physics

[17] **viXra:1612.0258 [pdf]**
*submitted on 2016-12-15 15:55:23*

**Authors:** M. D. Sheppeard

**Comments:** 15 Pages.

An introduction to Hopf algebras in quantum field theory from the perspective of category theory.

**Category:** Mathematical Physics

[16] **viXra:1612.0229 [pdf]**
*submitted on 2016-12-12 13:34:06*

**Authors:** Algirdas Antano Maknickas

**Comments:** 8 Pages.

It was proposed gravity propulsion method by using asymmetric conical capacitor charged by high voltage. It was used linear approximation of general relativity equations for derivation of gravity field potential of charged conical capacitor and was shown that negative gravity capabilities of conical capacitor depends only on ratio of electric energy and capacitor mass density, where electric energy density depends on applied voltage and geometric parameters of conical capacitor.

**Category:** Mathematical Physics

[15] **viXra:1612.0201 [pdf]**
*replaced on 2017-01-02 09:09:11*

**Authors:** Robert Deloin

**Comments:** 7 Pages. Version 2.

Riemann's hypothesis (1859) is the conjecture stating that:
The real part of every non trivial zero of Riemann's zeta function is 1/2.
The main contribution of this paper is to achieve the proof of Riemann's hypothesis. The key idea is to provide an Hamiltonian operator whose real eigenvalues correspond to the imaginary part of the non trivial zeros of Riemann's zeta function and whose existence, according to Hilbert and Polya, proves Riemann's hypothesis.

**Category:** Mathematical Physics

[14] **viXra:1612.0184 [pdf]**
*submitted on 2016-12-09 20:49:53*

**Authors:** Taha Sochi

**Comments:** 20 Pages.

In this article we present an analytical method for deriving the relationship between the pressure drop and flow rate in laminar flow regimes, and apply it to the flow of power-law fluids through axially-symmetric corrugated tubes. The method, which is general with regards to fluid and tube shape within certain restrictions, can also be used as a foundation for numerical integration where analytical expressions are hard to obtain due to mathematical or practical complexities. Five converging-diverging geometries are used as examples to illustrate the application of this method.

**Category:** Mathematical Physics

[13] **viXra:1612.0182 [pdf]**
*submitted on 2016-12-09 20:55:36*

**Authors:** Taha Sochi

**Comments:** 23 Pages.

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

**Category:** Mathematical Physics

[12] **viXra:1612.0180 [pdf]**
*submitted on 2016-12-09 21:00:49*

**Authors:** Taha Sochi

**Comments:** 29 Pages.

Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration.

**Category:** Mathematical Physics

[11] **viXra:1612.0178 [pdf]**
*submitted on 2016-12-09 21:11:29*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging–diverging tubes for Navier–Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier–Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging–diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging–diverging geometries are used for demonstration, validation and as prototypes for modeling converging–diverging geometries in general.

**Category:** Mathematical Physics

[10] **viXra:1612.0160 [pdf]**
*submitted on 2016-12-09 05:07:35*

**Authors:** Taha Sochi

**Comments:** 22 Pages.

In this paper, we use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile and volumetric flow rate. The theoretical basis of the new variational method, which rests on the use of the Dirichlet principle, also provides theoretical support to the former variational method.

**Category:** Mathematical Physics

[9] **viXra:1612.0157 [pdf]**
*submitted on 2016-12-09 05:12:34*

**Authors:** Taha Sochi

**Comments:** 31 Pages.

We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigations we used the straight circular tube geometry with eight fluid rheological models to demonstrate and establish the variational method, the focus here is on the plane long thin slit geometry using those eight rheological models, namely: Newtonian, power law, Ree-Eyring, Carreau, Cross, Casson, Bingham and Herschel-Bulkley. We demonstrate how the variational principle based on minimizing the total stress in the flow conduit can be used to derive analytical expressions, which are previously derived by other methods, or used in conjunction with numerical procedures to obtain numerical solutions which are virtually identical to the solutions obtained previously from well established methods of fluid dynamics. In this regard, we use the method of Weissenberg-Rabinowitsch-Mooney-Schofield (WRMS), with our adaptation from the circular pipe geometry to the long thin slit geometry, to derive analytical formulae for the eight types of fluid where these derived formulae are used for comparison and validation of the variational formulae and numerical solutions. Although some examples may be of little value, the optimization principle which the variational method is based upon has a significant theoretical value as it reveals the tendency of the flow system to assume a configuration that minimizes the total stress. Our proposal also offers a new methodology to tackle common problems in fluid dynamics and rheology.

**Category:** Mathematical Physics

[8] **viXra:1612.0155 [pdf]**
*submitted on 2016-12-09 05:30:01*

**Authors:** Taha Sochi

**Comments:** 17 Pages.

This article deals with the flow of Newtonian fluids through axially-symmetric corrugated tubes. An analytical method to derive the relation between volumetric flow rate and pressure drop in laminar flow regimes is presented and applied to a number of simple tube geometries of converging-diverging nature. The method is general in terms of fluid and tube shape within the previous restrictions. Moreover, it can be used as a basis for numerical integration where analytical relations cannot be obtained due to mathematical difficulties.

**Category:** Mathematical Physics

[7] **viXra:1612.0154 [pdf]**
*submitted on 2016-12-09 05:32:16*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.

**Category:** Mathematical Physics

[6] **viXra:1612.0153 [pdf]**
*submitted on 2016-12-09 05:34:38*

**Authors:** Taha Sochi

**Comments:** 27 Pages.

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

**Category:** Mathematical Physics

[5] **viXra:1612.0147 [pdf]**
*submitted on 2016-12-09 01:26:02*

**Authors:** Taha Sochi

**Comments:** 20 Pages.

In this paper we investigate the yield condition in the mobilization of yield-stress materials in distensible tubes. We discuss the two possibilities for modeling the yield-stress materials prior to yield: solid-like materials and highly-viscous fluids and identify the logical consequences of these two approaches on the yield condition. As part of this investigation we derive an analytical expression for the pressure field inside a distensible tube with a Newtonian flow using a one-dimensional Navier-Stokes flow model in conjunction with a pressure-area constitutive relation based on elastic tube wall characteristics.

**Category:** Mathematical Physics

[4] **viXra:1612.0143 [pdf]**
*submitted on 2016-12-09 01:42:02*

**Authors:** Taha Sochi

**Comments:** 31 Pages.

A residual-based lubrication method is used in this paper to find the flow rate and pressure field in converging-diverging rigid tubes for the flow of time-independent category of non-Newtonian fluids. Five converging-diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel-Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging-diverging tubes, convergence to analytical solutions found earlier for the flow in converging-diverging tubes of Newtonian fluids as special cases for non-Newtonian, and convergence to analytical solutions found earlier for the flow of power-law fluids in converging-diverging tubes. A brief investigation was also conducted on a sample of diverging-converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically-symmetric converging-diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range.

**Category:** Mathematical Physics

[3] **viXra:1612.0124 [pdf]**
*submitted on 2016-12-07 14:49:20*

**Authors:** Harry Watson

**Comments:** 5 Pages.

A Geometric Model
A family of models in Euclidean space is developed from the following
approximation.
m_p/m_e = 4pi(4pi- 1\pi)(4pi-2/pi) = 1836.15 (1)
where (m_p) and (m_e) are the numeric values for the mass of the proton and the mass of electron, respectively. In particular, we will develop models (1) that agree with the recommended value of the mass ratio of the proton to the electron to six significant figures, (2) that explain the “shape-shifting” behavior of the proton, and (3) that are formed concisely from the sole transcendental number pi. This model is solely geometric, relying on volume as the measure of mass. Claim that inclusion of quantum/relativistic properties enhance the accuracy of the model. The goal is to express the ratio of the proton mass to the electron mass in terms of (1) pure mathematical constants and (2) a quantum corrective factor.
harry.watson@att.net

**Category:** Mathematical Physics

[2] **viXra:1612.0071 [pdf]**
*submitted on 2016-12-06 13:59:21*

**Authors:** Ulrich E. Bruchholz, Horst Eckardt

**Comments:** Pages.

It is demonstrated how to unify all physics on the basis of general relativity. Electrodynamics is revealed to be part of general relativity,
as already seen by Rainich. The properties of elementary particles follow from the equations of the unified theory. The way of calculating these properties is indicated, and successful applications of this method are referenced.
These insights and results have inevitably to be joined with a criticism of contemporary physics.

**Category:** Mathematical Physics

[1] **viXra:1612.0070 [pdf]**
*submitted on 2016-12-06 07:24:24*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 1 Page.

Demonstration of SUSY [super-symmetry]-like electrostatic backgrounds fields of quantum differential topological K-theory.

**Category:** Mathematical Physics