| viXra.org > Mathematical Physics > 2207 |
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| viXra.org > Mathematical Physics > 2207 |
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[12] viXra:2207.0179 [pdf] submitted on 2022-07-30 23:36:05
Authors: Shlomy Shitrit
Comments: 233 Pages.
The objective of this work is to develop a highly efficient solver for the Full Potential Equation (FPE) that will be able to compute transonic external and internal flows attaining a (nearly) linear computational complexity. The key innovation of this work is in the solver's efficiency and in the fact that it is achieved by means of adapting and applying the algebraic multi-grid (AMG) approach to solving the problem. The mathematical difficulties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic ow) to hyperbolic (supersonic ow). A pointwise relaxation method when applied directly to the upwind discrete operator, in the supersonic ow regime, is unstable. Resolving this difficulty is the main achievement of this work. A stable pointwise direction independent relaxation was developed for the supersonic and subsonic ow regimes. This stable relaxation is obtained by post-multiplying the original operator by a certain simple first order downwind operator. This new operator is designed in such a way that the pointwise relaxation applied to the product operator becomes stable. A variety of issues regarding the AMG coarsening and construction of transfer operators is addressed in order to achieve the required efficiency for the problems under consideration. An improved coarsening process was developed. Instead of using a fixed threshold parameter in order to select the coarse-grid points, we developed a dynamic threshold parameter as a measure of the strength of connection between the matrix variables. The coarsening by dynamic threshold was shown to be less effective for certain elliptic problems (subsonic flow), but for supersonic flow regime where the operator does not form an M-matrix, we obtained much better performance. In some cases where an irregular grid, shock waves, and extreme nonlinearity are involved, the dynamic threshold is more than necessary in order to achieve convergence. A modified formulation of the interpolation operator is presented. While the standard interpolation is suitable mainly for problems that are characterized by M-matrix form,the proposed formula is more accurate and can be used for more general matrix problems. The proposed interpolation operator includes the choice of negative weights, which is necessary in some cases. In addition, the FMG approach in the context of AMG was developed as a tool to deal with a nonlinear problems... (truncated by viXra Admin to < 400 words).
Category: Mathematical Physics
[11] viXra:2207.0142 [pdf] submitted on 2022-07-24 01:03:37
Authors: Claude Michael Cassano
Comments: 24 Pages.
The Dirac equation is a linear matrix partial differential equation (or 4-vector linear partial differential equation, or system of linear partial differential equations) in non-negative dependent variable(s) (matrix / 4-vector) which also satisfy the generalized Helmholtz / Klein-Gordon Equation.
Category: Mathematical Physics
[10] viXra:2207.0132 [pdf] submitted on 2022-07-22 00:48:10
Authors: Claude Michael Cassano
Comments: 3 Pages. (Note by viXra Admin: This appears to be a repetion of the author's ideas already deposited here - Future repetition will not be accepted. Also, unscholarly remarks blocked by viXra Admin)
The Helmholtzian factorization shows that the heavy leptons and quarks are separated as: (0,0,0,mu2080) heavy leptons satisfying the Dirac factoring, and (mu2081,mu2082,mu2083,0) quarks satisfying the Helmholtzian factoring, as pythagorean quadruples. Investigating pythagorean quadruples leads to one (4,10,28,30) which leads to (1/3,5/6,7/3,5/2) and (2/3,5/3,14/3,5) further leading to the quark mass, color, and charge architecture.
Category: Mathematical Physics
[9] viXra:2207.0116 [pdf] submitted on 2022-07-16 08:34:15
Authors: Michalis Psimopoulos
Comments: 16 Pages.
The partitions of a positive integer can be expressed by a linear recursion formula where the coefficients represent the sum of divisors of their index. In the present paper it is shown that these coefficients can be obtained exactly from a triangular algorithm where its columns are well defined harmonic sequences. As a result, a new relation between partitions and harmonic functions is established.
Category: Mathematical Physics
[8] viXra:2207.0114 [pdf] replaced on 2022-12-08 02:09:23
Authors: Miftachul Hadi
Comments: 3 Pages. In English
We treat the geometrical optics as an Abelian $U(1)$ local gauge theory the same as the Abelian $U(1)$ Maxwell's gauge theory. We propose there exists a knot in a 3-dimensional Euclidean (flat) space of the geometrical optics (the eikonal equation) as a consequence there exists a knot in the Maxwell's theory in a vacuum. We formulate the Chern-Simons integral using an eikonal. We obtain the relation between the knot (the geometric optical helicity, an integer number) and the refractive index.
Category: Mathematical Physics
[7] viXra:2207.0110 [pdf] replaced on 2022-07-22 15:38:33
Authors: Moninder Singh Modgil
Comments: 9 Pages. This is an expanded version of the earlier submission.
Our visual perception places us at the origin of a 3-dimensional cartesian coordinate system. On a cosmological scale, the consciousness (as manifested in the brain) can be approximated as point like. It is proposed that perceptual experiences can be regarded as occurring on a tangent space at the point where the consciousness is located. A differential geometric framework is developed, for consciousness propagating on a curved space-time manifold. Interaction between consciousnesses is discussed at classical and quantum mechanical level. Quantum mechanical experiments such as those of Schrodinger’s cat in Many World Interpretation, are examined in this framework.
Category: Mathematical Physics
[6] viXra:2207.0099 [pdf] submitted on 2022-07-14 00:41:52
Authors: Claude Michael Cassano
Comments: 3 Pages.
Mathematics is shown to be enough to produce the fermion mass architecture and quark mass-color strong force without resort to hypothetical-mythical unobservables, and mere accordance with an imaginative theory and barely in agreement withexperiment.
Category: Mathematical Physics
[5] viXra:2207.0094 [pdf] submitted on 2022-07-13 16:01:03
Authors: Michalis Psimopoulos
Comments: 21 Pages.
We extend in two dimensions the problem of prime numbers by introducing a triangular algorithm which attributes to each prime the number 1 and to each non prime the number 0. It is shown that the positions of the primes within the set of integers are not arbitrary, but are the result of precise combinations of the vertical harmonic sequences forming this algorithm.
Category: Mathematical Physics
[4] viXra:2207.0074 [pdf] replaced on 2023-02-13 03:22:53
Authors: Jaykov Foukzon
Comments: 122 Pages. AIP Conf. Proc. 2872, 060028 (2023) https://doi.org/10.1063/5.0162832
A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator ϕ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^* algebra of bounded observables satisfies all the Haag-Kastler axioms. In particular we prove that the λ(φ^4 )_4 quantum field theory model is Lorentz covariant.
Category: Mathematical Physics
[3] viXra:2207.0047 [pdf] submitted on 2022-07-05 10:32:32
Authors: Aloys J. Sipers, Joh. J. Sauren
Comments: 7 Pages.
In this letter a theorem is stated on the reconstruction of the rotation from stresses with respect to rotated coordinate axes. In most literature a coordinate axis rotation is defined by an angle. Motivated by practical applications, we define the rotation by a unit vector expressed in Cartesian coordinates. An example and an application from the analysis of extreme stresses clarify the theoretical result and demonstrate the practical potential of the theorem.
Category: Mathematical Physics
[2] viXra:2207.0046 [pdf] replaced on 2022-07-11 10:37:21
Authors: Rajeev Kumar
Comments: 5 Pages.
In this paper an alternative derivation of J-integral and its path independence for plane stress using vector calculus has been presented.
Category: Mathematical Physics
[1] viXra:2207.0020 [pdf] submitted on 2022-07-03 08:14:56
Authors: Claude Michael Cassano
Comments: 10 Pages.
Hadrons (mesons and baryons) may be written As Helmholtzian Factorization expressions.
Category: Mathematical Physics
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