Mathematical Physics

1705 Submissions

[20] viXra:1705.0470 [pdf] submitted on 2017-05-31 08:41:13

Line-Surface Formulation of the Electromagnetic-Power-based Characteristic Mode Theory for Metal-Material Combined Objects — Part II

Authors: Renzun Lian
Comments: 20 Pages.

In the Part I of Line-Surface formulation of the ElectroMagnetic-Power-based Characteristic Mode Theory for Metal-Material combined objects (LS-MM-EMP-CMT), the relevant fundamental principle had been established, and some very valuable complements and improvements are done in this Part II. In this Part II, the traditional surface equivalent principle for a homogeneous material body whose boundary is only constructed by a closed surface is generalized to the line-surface equivalent principle of a homogeneous material body whose boundary can include some lines and open surfaces besides a closed surface; a new line-surface formulation of the input/output power operator for metal-material combined objects is given, and the new formulation is more advantageous than the formulation given in Part I; some more detailed formulations for establishing LS-MM-EMP-CMT are explicitly provided here, such as the formulations corresponding to the decompositions for currents and their domains and the formulations corresponding to variable unification. In addition, a new concept intrinsic resonance is introduced in this paper, and then a new Characteristic Mode (CM) set, intrinsic resonant CM set, is introduced into the EMP-CMT family.
Category: Mathematical Physics

[19] viXra:1705.0374 [pdf] replaced on 2017-06-12 02:09:24

Is Mechanics a Proper Approach to Fundamental Physics?

Authors: Zihao Song
Comments: 6 Pages. If one physical quantity can't find where it is originated, it's not a good physical quantity.

Physicists are proposing different mechanics to describe the nature, physical body is measured by intrinsic properties like electric charge, and extrinsic properties being related to space like generalized coordinates or velocities etc., with these properties we can predict what event will happen. We can naturally define the fact of the event and the cause of the event as information, the information grasped by physicist must be originated from something objective, information must have its object container. Intrinsic property information is contained by object itself, but container of extrinsic property information like position is ambiguous, position is a relation based on multiple objects, it's hard to define which one is the information container. With such ambiguity, no mechanics is a complete theory, errors hidden in assumptions are hard to find. Here we show a new theoretical framework with strict information container restriction, on which we can build complete determinism theories to approach grand unification.
Category: Mathematical Physics

[18] viXra:1705.0358 [pdf] submitted on 2017-05-24 13:09:34

Construction of the Lovas-Andai Two-Qubit Function $\tilde{\chi}_2 (\varepsilon )=\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$ Verifies the $\frac{8}{33}$-Hilbert Schmidt Separability Probability Conjecture

Authors: Paul B. Slater
Comments: 35 pages, 26 figures

We investigate relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions''--those recently advanced by Lovas and Andai (arXiv:1610.01410), and those earlier presented by Slater ({\it J. Phys. A} {\bf{40}} [2007] 14279). In the Lovas-Andai framework, the independent variable $\varepsilon \in [0,1]$ is the ratio $\sigma(V)$ of the singular values of the $2 \times 2$ matrix $V=D_2^{1/2} D_1^{-1/2}$ formed from the two $2 \times 2$ diagonal blocks ($D_1, D_2$) of a randomly generated $4 \times 4$ density matrix $D$. In the Slater setting, the independent variable $\mu$ is the diagonal-entry ratio $\sqrt{\frac{d_ {11} d_ {44}}{d_ {22} d_ {33}}}$--with, importantly, $\mu=\varepsilon$ or $\mu=\frac{1}{\varepsilon}$ when both $D_1$ and $D_2$ are themselves diagonal. Lovas and Andai established that their two-rebit function $\tilde{\chi}_1 (\varepsilon )$ ($\approx \varepsilon$) yields the previously conjectured Hilbert-Schmidt separability probability of $\frac{29}{64}$. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we similarly obtain its new (much simpler) two-qubit counterpart, $\tilde{\chi}_2(\varepsilon) =\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$. Verification of the companion conjecture of a Hilbert-Schmidt separability probability of $\frac{8}{33}$ immediately follows in the Lovas-Andai framework. We obtain the formulas for $\tilde{\chi}_1(\varepsilon)$ and $\tilde{\chi}_2(\varepsilon)$ by taking $D_1$ and $D_2$ to be diagonal, allowing us to proceed in lower (7 and 11), rather than the full (9 and 15) dimensions occupied by the convex sets of two-rebit and two-qubit states. The CAD's themselves involve 4 and 8 variables, in addition to $\mu=\varepsilon$. We also investigate extensions of these analyses to rebit-retrit and qubit-qutrit ($6 \times 6$) settings.
Category: Mathematical Physics

[17] viXra:1705.0357 [pdf] submitted on 2017-05-24 16:04:15

A Review of Two Derivations of Maxwell-Dirac Isomorphism and a Few Plausible Extensions

Authors: Victor Christianto
Comments: 5 Pages. this paper has been submitted to MDPI - Mathematics

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.
Category: Mathematical Physics

[16] viXra:1705.0347 [pdf] replaced on 2017-06-19 04:02:19

About Physical Inadequacy of the Three-Dimensional Navier-Stokes Equation for Viscous Incompressible Fluid

Authors: Preobrazhenskiy Andrey
Comments: 13 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.
Category: Mathematical Physics

[15] viXra:1705.0330 [pdf] submitted on 2017-05-22 05:15:16

Nonlinearity, Entropy and Chaos in Music

Authors: Sai Venkatesh Balasubramanian
Comments: 11 Pages.

This article explores the nonlinear aspects underlying music , particularly focusing on melody. By using the concept of scale as the basis, the article explores ways to formulate and study the features and 'feature richness' of a given melody or Raga, and to do this, the Raga scale is represented as a 1-Dimensional array. The Signature graph of a Raga plotted as Interval as a function of Note position, established a graphic visualization of the Raga. The progression and trend of intervals was computed using the Second Level Interval Array. This trend graph reveals the complexity in a Raga structure, through looping, crowded and intricate curves in the graph. Next, the concept of chaos in the context of melody is explored, fundamentally by performing a sensitivity test, which analyzes that given a Raga, and a particular evolution path, how starting at two nearby Swaras results in two entirely different ending Swaras, when sampled after a certain period in time. As a measure of the complexity in a Raga, the entropy, a measure of uncertainty is proposed, and computed using the interval arrays as bases for an occurrence array yielding empirical probabilities. The entropy is seen as a measure of richness, a measure of variety of inter-Swara intervals that a given Raga possesses. One notes that Ragas with high entropy, on account of their interval richness, usually fall under the category of pleasant, appealing and melodious Ragas. These are also the Ragas one finds being employed in film music, clearly owing to their pleasant feel.
Category: Mathematical Physics

[14] viXra:1705.0300 [pdf] replaced on 2017-05-23 08:56:56

Mnozenje Vektora I Struktura 3D Euklidskog Prostora

Authors: Miroslav Josipović
Comments: 80 Pages. geometric algebra

This is the translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.
Category: Mathematical Physics

[13] viXra:1705.0274 [pdf] replaced on 2017-09-17 15:07:54

A Minimalist Derivation of the Theory of Everything

Authors: Alexandre Harvey-Tremblay
Comments: 64 Pages.

In this work, I present a minimalist approach to first-order logic and show how it implies a restriction on any possible Theory of Everything in physics (ToE) of sufficient strength to recover actual laws of physics. The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless impairs it with the following advantage. From an argument originally made by Plato, I argue that each axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal. Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of these sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. On the grounds that any ToE must at the very least recover all maximally irrefutable knowledge, I recover a strong restriction applicable to any possible ToE candidate. Part I is the minimalist derivation of the ToE restriction. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of provable-sentences to that of entropy. Part II is the derivation of the physical laws. I recover, from the master equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy. Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the ToE-restriction should be promoted to a ToE-candidate. This result motivates the ToE claim made in this paper.
Category: Mathematical Physics

[12] viXra:1705.0262 [pdf] replaced on 2017-08-24 03:38:22

On Analysis of a Class of Quadratic Lienard Type Equations Exhibiting Exact Periodic Solutions

Authors: D.K.K. Adjaï, L. H. Koudahoun, J. Akande, Y.J.F. Kpomahou, M. D. Monsia
Comments: 10 pages

This paper exhibits a generalization of the theory of linearizing quadratic Lienard type equa- tions introduced earlier by the authors of the current work and its application to determine the general periodic solutions for the cubic Dung equation and for some equations of Painleve- Gambier classication as illustrative examples. The mathematical equivalence between the cubic Dung equation and the Painleve-Gambier XIX equation has been also highlighted us- ing the present generalized theory.
Category: Mathematical Physics

[11] viXra:1705.0261 [pdf] submitted on 2017-05-18 03:29:03

On the Complex Function Basis of Maxwell Equations

Authors: Zhi Cheng
Comments: 14 Pages. Include Chinese version

In this paper, we propose a concept of vector complex function to prove that the whole world can be reduced to a very simple function f(Z) = F + iG by introducing the knowledge of complex function theories. We can also derive Maxwell equations through the differential and integral analysis of the vector complex function.
Category: Mathematical Physics

[10] viXra:1705.0251 [pdf] submitted on 2017-05-16 19:11:11

Six Easy Pieces in Computational Physics

Authors: Victor Christianto
Comments: 39 Pages. This paper has not been submitted to a journal

The present book consists of 6 papers that I and some colleagues developed throughout the last 3-4 years. The subjects discussed cover wireless energy transmission, soliton model of DNA, cosmology, and also solutions of Navier-Stokes equations both in 2D and 3D. Some additional graphical plots for solution of 3D Navier-Stokes equations are also given. Hopefully the readers will find these papers at least interesting to ponder.
Category: Mathematical Physics

[9] viXra:1705.0212 [pdf] submitted on 2017-05-14 02:26:57

Correcting for Relativity in GPS makes no sense

Authors: Sjaak Uitterdijk
Comments: 3 Pages.

Showing that the Special Theory of Relativity is an untenable theory, many times leads to the reaction that the GPS is so accurate thanks to the STR corrections. This article shows that the supposed relativity errors are by far negligible relative to the errors caused by atmospheric circumstances.
Category: Mathematical Physics

[8] viXra:1705.0203 [pdf] submitted on 2017-05-12 22:53:16

The Relations Between Ancient China’s Taoism And Modern Mathematics & Physics

Authors: ShengYu.Shu
Comments: 62 Pages.

I have mainly analyzed the mathematical meaning of non-classical mathematical theory for three fundamental physics equations - Maxwell’s equations, Dirac’s equations, Einstein’s equations from the quantized core theory of ancient China’s Taoism, and found they have some structures described in the core of the theory of ancient China’s Taoism, especially they all obviously own the yin-yang induction structure. This reveals the relations between the ancient China’s Taoism and modern mathematics and physics in a way, which may help us to understand some problems of the fundamental theory of physics.
Category: Mathematical Physics

[7] viXra:1705.0133 [pdf] submitted on 2017-05-08 07:55:21

The Recursive Future And Past Equation Based On The Ananda-Damayanthi Similarity Measure Considered To Exhaustion (New)

Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Similarity Measure considered to Exhaustion [1].
Category: Mathematical Physics

[6] viXra:1705.0104 [pdf] submitted on 2017-05-04 12:18:15

The Recursive Past Equation Based On The Ananda-Damayanthi Similarity Measure. The Recursive Future Equation Based On The Ananda-Damayanthi Similarity Measure

Authors: Ramesh Chandra Bagadi
Comments: 4 Pages.

In this research investigation, the author has presented a Recursive Past Equation based on the Ananda-Damyanthi Similarity Measure [1]. Also, in this research investigation, the author has presented a Recursive Future Equation based on the Ananda-Damyanthi Similarity Measure [1].
Category: Mathematical Physics

[5] viXra:1705.0095 [pdf] submitted on 2017-05-03 22:01:08

A Detailed Analysis of Geometry Using Two Variables

Authors: John Peel
Comments: 6 Pages. The sets at the end are important

Calculating certain aspects of geometry has been difficult. They have defied analytics. Here I propose a method of analysing shape and space in terms of two variables (n,m).
Category: Mathematical Physics

[4] viXra:1705.0091 [pdf] submitted on 2017-05-04 06:15:57

The Recursive Future Equation (Final)

Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.

The author has presented a Recursive Future Equation
Category: Mathematical Physics

[3] viXra:1705.0035 [pdf] replaced on 2017-05-04 02:31:50

Solving Numerically a System of Coupled Riccati ODEs for Incompressible Non-Stationary 3D Navier-Stokes Equations

Authors: Victor Christianto, Sergey Ershkov
Comments: 11 Pages. This paper is to be submitted to Royal Society Open Access journal. Your comments are welcome.

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of non-stationary incompressible 3D Navier-Stokes equations. Now in this paper, we solve these coupled Riccati ODEs using: a) Maxima and b) Mathematica 11 computer algebra packages. The result seems to deserve further investigation in particular in comparison with rigid body motion, which will be discussed elsewhere.
Category: Mathematical Physics

[2] viXra:1705.0012 [pdf] submitted on 2017-05-01 22:52:24

The Recursive Equation Connecting Future And Past

Authors: Ramesh Chandra Bagadi
Comments: 3 Pages.

In this research manuscript, the author has presented a Recursive Equation Connecting Future And Past
Category: Mathematical Physics

[1] viXra:1705.0011 [pdf] submitted on 2017-05-01 23:45:14

An Introduction to Ontological-Phase Topological Field Theory in Relation to Newton-Einstein G-Duality and Dirac-Majorana Doublet Fusion

Authors: Richard L. Amoroso
Comments: 14 Pages. Version to be published in 10th proceedings honoring mathematical physicist Jean-Pierre Vigier by World Scientific

Ontological-Phase Topological Field Theory (OPTFT) under seminal development to formally describe 3rd regime Unified Field Mechanics (UFM) (classical-Quantum-UFM) is extended to relate the duality of Newton-Einstein gravitation theory by added degrees of freedom in a semi-quantum limit enabling insight into topological Dirac-Majorana doublet fusion supervening the uncertainty principle.
Category: Mathematical Physics