[17] **viXra:1610.0386 [pdf]**
*submitted on 2016-10-31 23:23:00*

**Authors:** Renzun Lian

**Comments:** 12 Pages.

An ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Metal-Material combined objects (MM-EMP-CMT) was built by expressing the various electromagnetic powers as the functions of the line current on metal line, the surface current on metal surface, the surface current on the boundary of metal volume, and the total field in material volume, so it can be simply called as the Line-Surface-Volume formulation for the MM-EMP-CMT (LSV-MM-EMP-CMT). As a companion to the LSV-MM-EMP-CMT, a Line-Surface formulation for the MM-EMP-CMT (LS-MM-EMP-CMT) is established in this paper by expressing the various powers as the functions of the line and surface currents on metal part and the surface equivalent current on the boundary of material part.
The physical essence of LS-MM-EMP-CMT is the same as LSV-MM-EMP-CMT, i.e., to construct the various power-based Characteristic Mode (CM) sets for metal-material combined objects, but the LS-MM-EMP-CMT is more advantageous than the LSV-MM-EMP-CMT in some aspects. For example, the former saves computational resources; the former avoids to calculate the modal scattering field in source region; the field-based definitions for the impedance and admittance of metal-material combined electromagnetic systems can be easily introduced into the former.

**Category:** Mathematical Physics

[16] **viXra:1610.0354 [pdf]**
*submitted on 2016-10-29 07:32:58*

**Authors:** Renzun Lian

**Comments:** 8 Pages.

As a companion to the ElectroMagnetic-Power-based Characteristic Mode Theory (EMP-CMT) for PEC systems (PEC-EMP-CMT) and the EMP-CMT for Material bodies (Mat-EMP-CMT), an EMP-CMT for Metal-Material combined objects (MM-EMP-CMT) is established in this paper, and then some power-based Characteristic Mode (CM) sets are constructed for depicting the inherent power characteristics of metal-material combined objects. The MM-EMP-CMT is valuable for analyzing and designing the metal-material combined electromagnetic structures, such as the microstrip antennas and the Dielectric Resonant Antennas (DRAs) mounted on metal platforms etc. In addition, a variational formulation for the scattering problem of metal-material combined objects is provided based on the conservation law of energy.

**Category:** Mathematical Physics

[15] **viXra:1610.0345 [pdf]**
*submitted on 2016-10-28 22:26:32*

**Authors:** Renzun Lian

**Comments:** 13 Pages.

Recently, a volume formulation of the ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Material bodies (Mat-EMP-CMT) is built by expressing various electromagnetic powers as the functions of the total fields in material bodies, so it can be simply called as Vol-Mat-EMP-CMT. As a companion to the Vol-Mat-EMP-CMT, several Surface formulations of the Mat-EMP-CMT (Surf-Mat-EMP-CMT) are established in this paper by expressing various electromagnetic powers as the functions of the surface equivalent sources on the boundaries of material bodies.
The physical essence of Surf-Mat-EMP-CMT is the same as the Vol-Mat-EMP-CMT, i.e., to construct the various power-based Characteristic Mode (CM) sets for material bodies, but the former is more advantageous than the latter in some aspects. For example, the former saves computational resources; the former avoids to compute the modal scattering field in source region; the field-based definitions for the impedance and admittance of material bodies can be easily introduced into the former.

**Category:** Mathematical Physics

[14] **viXra:1610.0340 [pdf]**
*submitted on 2016-10-28 05:21:45*

**Authors:** Renzun Lian

**Comments:** 15 Pages.

In this paper, an ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Material bodies (Mat-EMP-CMT) is provided. The Mat-EMP-CMT is valid for the inhomogeneous and lossy material bodies, and it is applicable to the bodies which are placed in complex electromagnetic environments.
Under the Mat-EMP-CMT framework, a series of power-based Characteristic Mode (CM) sets are constructed, and they have abilities to depict the inherent power characteristics of material bodies from different aspects. All power-based CM sets are independent of the external electromagnetic environment and excitation.
Among the various power-based CM sets constructed in Mat-EMP-CMT, only the Input power CM (InpCM) set has the same physical essence as the CM set constructed in Mat-VIE-CMT (the Volume Integral Equation based CMT for Material bodies), and the other CM sets are completely new. However, the power characteristic of the InpCM set is more physically reasonable than the CM set derived from Mat-VIE-CMT.
In addition, not only radiative CMs and real characteristic currents but also non-radiative CMs and complex characteristic currents can be constructed under the Mat-EMP-CMT framework; the traditional characteristic quantity, Modal Significance (MS), is generalized, and some new characteristic and non-characteristic quantities are introduced to depict the modal characteristics from different aspects; a variational formulation for the scattering problem of material scatterer is established based on the conservation law of energy.

**Category:** Mathematical Physics

[13] **viXra:1610.0337 [pdf]**
*replaced on 2016-11-20 13:13:40*

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

Il sera démontré dans cet article que la masse noire est une conséquence nécessaire de la mécanique relativiste. Cette démonstration fait abstraction des forces de la physique et est donc une explication purement mécanique. La relation de Tully-Fisher sera déduite naturellement, sans appel à une quelconque nouvelle physique, et il est par conséquent possible de dériver cette loi sans modifier la gravitation de Newton ou la relativité générale. De plus, une prédiction théorique sur une nouvelle forme de décalage de fréquence sera effectuée permettant de réfuter ou de confirmer cette théorie.

**Category:** Mathematical Physics

[12] **viXra:1610.0332 [pdf]**
*submitted on 2016-10-28 04:20:20*

**Authors:** Renzun Lian

**Comments:** 17 Pages.

In this paper, an ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for PEC systems (PEC-EMP-CMT) is built. The PEC-EMP-CMT is valid for the PEC systems which are surrounded by any electromagnetic environment, and it can construct the complex characteristic currents and non-radiative Characteristic Modes (CMs).
In this paper, some traditional concepts, such as the system input impedance and modal input impedance etc., are redefined; the traditional characteristic quantity, Modal Significance (MS), is generalized; a series of new power-based CM sets are introduced.
It is proven in this paper that various power-based CM sets of a certain objective PEC structure are independent of the external environment and excitation; the non-radiative space constituted by all non-radiative modes is identical to the interior resonance space constituted by all interior resonant modes of closed PEC structures, and the non-radiative CMs constitute a basis of the space. Based on above these, the normal Eigen-Mode Theory (EMT) for closed PEC structures is classified into the PEC-EMP-CMT framework.
In addition, a variational formulation for the external scattering problem of PEC structures is provided in this paper, based on the conservation law of energy.

**Category:** Mathematical Physics

[11] **viXra:1610.0315 [pdf]**
*submitted on 2016-10-26 08:43:06*

**Authors:** M.E.Hassani

**Comments:** 6 Pages; 4 References.

In the present paper, the Schwarzschild’s original solution (1916) is scrutinized and proven to be logically, mathematically and physically not only wrong but basically meaningless because the ʻeasy trickʼ used by Schwarzschild violated the fundamental concepts of analytic geometry (rectangular coordinates), trigonometry (triangles) and dimensional analysis (consistency and homogeneity). It seems that Schwarzschild had systematically and deliberately violated these fundamental concepts in order to avoid/break an unavoidable/unbreakable impasse (the determinant ≠ 1). Then he had mathematically cheated to have the determinant =1 in an anti-mathematical manner since he was not attached to his initial claim, viz., ‒ x1, x2, x3 and x, y, z are rectangular coordinates ‒ Thus, as scientists we should not forget one very important thing, namely, mathematics is not only an exact science, but it is the language of Science itself.

**Category:** Mathematical Physics

[10] **viXra:1610.0231 [pdf]**
*submitted on 2016-10-19 15:07:45*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 83 Pages.

This manuscript encompasses our published and unpublished topological results in physics. Topology, the mathematical branch that assesses objects and their properties preserved through deformations, stretching and twisting, allows the investigation of the most general physical systems features. In particular, the Borsuk-Ulam Theorem (BUT) states that, if a single point projects to a higher spatial dimension, it gives rise to two antipodal points with matching description. Physical counterparts of BUT and its variants allow an inquiry of physical problems. The opportunity to treat systems as topological structures makes BUT a universal principle underlying natural phenomena.

**Category:** Mathematical Physics

[9] **viXra:1610.0221 [pdf]**
*submitted on 2016-10-19 03:43:29*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 8 Pages.

The Borsuk-Ulam Theorem (BUT) states that a single point, if embedded in one spatial dimension higher, gives rise to two antipodal points with matching descriptions and similar features. Novel BUT variants allow the assessment of countless physical systems, from entropies to quantum entanglement. We argue that BUT, cast in a quantitative fashion which has the potential of being operationalized, is a universal principle underlying a number of natural phenomena.

**Category:** Mathematical Physics

[8] **viXra:1610.0198 [pdf]**
*submitted on 2016-10-17 11:30:45*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from the generic method. This is an advantage as compared to some traditional methods which only produce some of these quantities. The method is also superior to the numerical meshing techniques which may be used for resolving the flow in these systems. The method is particularly useful when analytical solutions are not available or when the available analytical solutions do not yield all the flow parameters.

**Category:** Mathematical Physics

[7] **viXra:1610.0196 [pdf]**
*submitted on 2016-10-17 11:34:00*

**Authors:** Taha Sochi

**Comments:** 16 Pages.

We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well established for the case of a one-dimensional flow through simply connected regions, specifically tubes of circular uniform cross sections and plane thin slits. If it can also be established for the more general case of generalized Newtonian flow through non-circular or multiply connected geometries, such as the two-dimensional flow through conduits of rectangular or elliptical cross sections or the flow through annular circular pipes, then analytical or semi-analytical or highly accurate numerical solutions; regarding stress, rate of strain, velocity profile and volumetric flow rate; for these geometries can be obtained from the stress function, which can be easily obtained from the Newtonian case, in combination with the constitutive rheological relation for the particular non-Newtonian fluid, as done previously for the case of the one-dimensional flow through simply connected regions.

**Category:** Mathematical Physics

[6] **viXra:1610.0195 [pdf]**
*submitted on 2016-10-17 11:36:50*

**Authors:** Taha Sochi

**Comments:** 9 Pages.

In this article we challenge the claim that the previously proposed variational method to obtain flow solutions for generalized Newtonian fluids in circular tubes and plane slits is exact only for power law fluids. We also defend the theoretical foundation and formalism of the method which is based on minimizing the total stress through the application of the Euler-Lagrange principle.

**Category:** Mathematical Physics

[5] **viXra:1610.0194 [pdf]**
*submitted on 2016-10-17 11:51:12*

**Authors:** Taha Sochi

**Comments:** 43 Pages.

In this article, the extensional flow and viscosity and the converging-diverging geometry were examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shearthinning, elasticity and thixotropic time-dependency, was used for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm, originally proposed by Philippe Tardy, that employs this model to simulate steadystate time-dependent flow was implemented in a non-Newtonian flow simulation code using pore-scale modeling and the initial results were analyzed. The findings are encouraging for further future development.

**Category:** Mathematical Physics

[4] **viXra:1610.0193 [pdf]**
*submitted on 2016-10-17 11:53:33*

**Authors:** Taha Sochi

**Comments:** 27 Pages.

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modeling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modeling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modeling strategies are required to tackle this problem in the future.

**Category:** Mathematical Physics

[3] **viXra:1610.0078 [pdf]**
*submitted on 2016-10-06 18:16:19*

**Authors:** Vito R. D'Angelo

**Comments:** 2 Pages.

In the spirit of the Pythagorean school of thought, that everything in the universe can be reduced to pure numbers; utilizing the Rydberg constant, arguably the most precise value in physics, an attempt is made to bring to fruition the aforementioned tenet. The relationships of seven well known constants are utilized within the context of four equations.

**Category:** Mathematical Physics

[2] **viXra:1610.0059 [pdf]**
*submitted on 2016-10-05 01:38:20*

**Authors:** Claude Michael Cassano

**Comments:** 9 Pages.

Elementary Linear Algebra theory handles transformations between sets of n-square matrix vector bases of M-dimensions well. Considering n-square & m-square matrices of M-dimensions, further theory and techniques, shown here, may be applied to yield results; including relationships between spin matrices and components.

**Category:** Mathematical Physics

[1] **viXra:1610.0027 [pdf]**
*submitted on 2016-10-03 07:39:34*

**Authors:** Ricardo Gil

**Comments:** 1 Page.

In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. The purpose of this paper is to suggest that the lowest state in a system is the entanglement which’s gravity for the Entanglement State is calculated by 2.99E12 x 1G / 9.8 m/s2 = 305102040846 G= 1/30510204086 G = 3.277592E-12 G X 1E-32m= 3.277 E-44 at 1/8.96 E20 Joules /Kg=1.11E-21 Joules/Kg energy state.

**Category:** Mathematical Physics