Unified Field Equations Research Articles

On the reflection of thermoelastic waves under an exact heat conduction model with a delay and temperature-dependent elastic parameters

The present work aims at describing the reflection of thermoelastic waves under a recently proposed thermoelasticity theory by Quintanilla [Some solutions for a family of exact phase-lag heat conduction problems. Mech Res Commun. 2011;38:355–360.]. Here the author has highlighted the condition for well-posedness by treating the three-phase-lag heat conduction theory differently and extended the results to obtain an alternative thermoelasticity theory with a single-delay term. In the present work, we formulate a mathematical model under this new theory to investigate the reflection of thermoelastic waves at the boundary of an elastic medium. The work is discussed for an isotropic medium with temperature-dependent elastic parameters. Unified field equations for Quintanilla's theory along with three other theories, namely, classical thermoelasticity theory, Lord-Shulman theory and Green-Naghdi theory, are considered for the analysis. The three waves, i.e. elastic-mode longitudinal wave, thermal-mode wave and transverse wave are found, among which only the first two are observed to be coupled. The amplitude ratio and phase velocity for various waves are obtained for incident longitudinal and incident transverse wave cases. The results are presented graphically for various angles of incidence and temperature dependence index parameter. Some important observations are highlighted and comparison between the considered theories is presented.

Superunification Theory: The Shortest Way to The Unified Field Equations

This continues previous articles on the unified theory published in this journal and intends to discuss the general principles of the theory, again. The Final theory, if any, shall necessarily be the most original scheme grounded upon certain postulates intuitively clear to us. The universal system of mathematical harmony begins with the

Dark-matter-like solutions to Einstein’s unified field equations

Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we interpret it more modestly as an alternative to Einstein-Maxwell theory, approximating the coupling between the electromagnetic field and spacetime curvature in the macroscopic classical regime. Previously it was shown that the Lorentz force can be derived from this theory, albeit with deviation on the scale of a universal length constant $\ell$. Here we assume that $\ell$ is of galactic scale and show that the modified coupling of the electromagnetic field with charged particles allows a non-Maxwellian equilibrium of non-neutral plasma. The resulting electromagnetic field is "dark" in the sense that its modified Lorentz force on the plasma vanishes, yet through its modified coupling to the gravitational field it engenders a nonvanishing, effective mass density. We obtain a solution for which this mass density asymptotes approximately to that of the pseudo-isothermal model of dark matter. The resulting gravitational field produces radial acceleration, in the context of a post-Minkowskian approximation, which is negligible at small radius but yields a flat rotation curve at large radius. We further exhibit a family of such solutions which, like the pseudo-isothermal model, has a free parameter to set the mass scale (in this case related to the charge density) and a free parameter to set the length scale (in this case an integer multiple of $\ell$). Moreover, these solutions are members of a larger family with more general angular and radial dependence. They thus show promise as approximations of generalized pseudo-isothermal models, which in turn are known to fit a wide range of mass density profiles for galaxies and clusters.

Consciousness: A Non-reductive Study Based on a Non-coding RNA Gene

We ascribe the insurmountable problems posed by central issues in cognitive neuroscience as to how a physical brain engenders meaning and how meaning is represented, to the conventional reductionist approach to consciousness. While neurobiology is ontologically necessary for processing multisensory information, it is not epistemologically sufficient to engender meaning in a conscious experience, as well as, representation of meaning, before it is expressed linguistically. We postulate a field of epistemic faculty of consciousness to emerge nonreductively by virtue of a non-coding RNA gene (human accelerated region 1F, HAR1F) found to be responsible for development of cerebral cortex, to regulate two cognitive functions simultaneously: One, to integrate multisensory information as a source of meaning based on the assumption that each sensory input carries a specific semantic potential; and two, to represent meaning in a semantically coextensive fashion, independent of a natural language. A unified cognitive field equation of consciousness is formulated to mathematically describe emergence of meaning and its representation. A principle of meaning-energy equivalence is derived as a basis of exploration of mind, free will, and self.

Unified field equations coupling four forces and principle of interaction dynamics

The main objective of this article is to postulate a principle of interaction dynamics (PID) and to derive field equations coupling the four fundamental interactions based on first principles. PID is a least action principle subject to div$_A$-free constraints for the variational element with $A$ being gauge potentials. The Lagrangian action is uniquely determined by 1) the principle of general relativity, 2) the $U(1)$, $SU(2)$ and $SU(3)$ gauge invariances, 3) the Lorentz invariance, and 4) the principle of representation invariance (PRI), introduced in [11]. The unified field equations are then derived using PID. The field model spontaneously breaks the gauge symmetries, and gives rise to a new mass generation mechanism.The unified field model introduces a natural duality between the mediators and their dual mediators, and can be easily decoupled to study each individual interaction when other interactions are negligible. The unified field model, together with PRI and PID applied to individual interactions, provides clear explanations and solutions to a number of outstanding challenges in physics and cosmology, including e.g. the dark energy and dark matter phenomena, the quark confinement, asymptotic freedom, short-range nature of both strong and weak interactions, decay mechanism of sub-atomic particles, baryon asymmetry, and the solar neutrino problem.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method (FEM)-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air (THMA) behavior of geomaterial and using finite element-finite difference (FE-FD) scheme for soil–water–air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste (HLRW), are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. (2007), is simulated in the framework of soil–water–air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz (2006) is simulated in the same framework under the conditions of variable temperature but constant air pressure.

A SOLUTION OF EINSTEIN'S FIELD EQUATIONS FOR THE THIRD CLASS IN X4

The main goal in the present paper is to obtain a solution of Einstein`s unified field equations for the third class in .

Generalized plane gravitational waves of non-symmetric unified field theories in plane symmetry

In this paper we investigated the plane wave solutions of both the weak and strong non-symmetric unified field equations of Einstein and Bonner in a generalized plane symmetric space-time in the sense of Taub [Ann. Math. 53, 472 (1951)] for plane gravitational waves. We show that the plane wave solutions of Einstein and Bonner field equations exist in plane symmetry.

TLM Extension to Electromagnetic Field Analysis of Anisotropic and Dispersive Media: A Unified Field Equation

The transmission-line matrix (TLM) method, in time domain, is extended to account for the presence of anisotropic and dispersive media in electromagnetic structures or devices. The model is thoroughly constructed by using Maxwell's equations that make it a unified general TLM formulation. Numerical results are compared with experimental measurements; hence, in the case of ferrite-based structures, validating the model and showing the accuracy of the approach.

The Spinning and Curving of Spacetime: The Electromagnetic and Gravitational Fields in the Evans Field Theory

The unification of the gravitational and electromagnetic fields achieved geometrically in the generally covariant unified field theory of Evans implies that electromagnetism is the spinning of spacetime and gravitation is the curving of spacetime. The homogeneous unified field equation of Evans is a balance of spacetime spin and curvature and governs the influence of electromagnetism on gravitation using the first Bianchi identity of differential geometry. The second Bianchi identity of differential geometry is shown to lead to the conservation law of the Evans unified field, and also to a generalization of the Einstein field equation for the unified field. Rigorous mathematical proofs are given in appendices of the four equations of differential geometry which are the cornerstones of the Evans unified field theory: the first and second Maurer-Cartan structure relations and the first and second Bianchi identities. As an example of the theory, the origin of wavenumber and frequency is traced to elements of the torsion tensor of spinning spacetime.

Curvature tensors unified field equations on SEXn

We study the curvature tensors and field equations in then-dimensional SE manifold SEXn. We obtain several basic properties of the vectorsSλ andUλ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

The Einstein-Maxwell field equations, II

In order to arrive at more general results solving Einstein-Maxwell's equations our investigation is centered around an electromagnetic spin tensor, which must be chosen in such a way that conservation laws still hold. This notion of the combined tensor is of course closely linked with the unified field equations. We shall avoid in this way the problem of the form of the matter tensor and neglect non-linear gravitational terms in the Ricci tensor. Then, the field equations have as solutionsh ij=h ij (P) +h ij (h) , whereh ij (P) are particular solutions, which are obtained by direct calculations andh ij (h) are solutions of □h ij (h) =0. The quantitiesh ij (P) are purely electromagnetic in nature, whileh ij (h) may represent purely gravitational terms. The results obtained complete the ones which have been published already in the preceeding paper (Dionysiou, 1980a; which will hereafter be referred to as Paper I).

On plane wave solutions of non-symmetric field equations of unified theories of Einstein, Bonnor and Schrödinger

Various attempts have been made to obtain wave solutions of nonsymmetric unified field equations of Einstein, Bonnor and Schrödinver in different space-times. Lal and Ali, Lal and Khare, Lal and Singh have obtained wave solutions of these field equations in different space-times under certain restrictions. In this paper plane wave solutions of both the weak and strong, nonsymmetric unified field equations of Einstein, Bonnor and Schrödinger have been investigated in a space which is more general than Pandey and Rao plane wave metric. It has been shown that the plane wave solutions of Einstein and Bonnor's equations exist but Schrödinger's field equations have no solution in this space-time.

?Anomalous? refractive index dispersion curves?a relativistic interpretation

The Einstein field equations (R μσ =0) are seen as possible candidates for a set of unified field equations. Three solutions of these field equations are used for a new interpretation and reformulation of the refractive index of an isotropic material medium. The new formulation explains the basic features of “anomalous” refractive index dispersion curves. It also predicts that the refractive index is a function of the angle of incidence when the plane in which the measurement is made is not tangential to the surface of the spherical gravitating mass, thereby providing a suitable test for the theory and hence of general relativity.

On the strength of Einstein's unified field equations

Einstein's concept of the “strength” of a system of field equations, which has been related in a simple way to the amount of initial data required for the system, is examined for his last unified field theory. The apparently surprising weakness of this system is traced to the high order of the associated electromagnetic field equations. These equations allow the existence of purely electric longitudinal waves, in spite of the absence of any “photon mass.”

Nonexistence theorem for a unified field theory in plane symmetry

We show that the unified field equations used recently by Moffat et al. do not have a solution in plane symmetry with a constant magnetic field in the $x$ direction. This is in contrast to the Einstein-Maxwell equations which have a solution only for a constant magnetic field in the $x$ direction for plane symmetry.

Complementary aspects of gravitation and electromagnetism

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge.

A model unified field equation

The classical solutions of a unified field theory in a two-dimensional space-time are considered. This system, a model of interacting mesons and baryons, illustrates how the particle can be built from a wave-packet of mesons and how reciprocally the meson appears as a tightly bound combination of particle and antiparticle.

The General Static Spherically Symmetric Solution of the "Weak" Unified Field Equations

In 1947 Einstein and Strauss (2) proposed a unified field theory based on a four-dimensional manifold characterized by a nonsymmetric tensor gij and a non-symmetric connection , where(1)Using a variational principle in which gij and are independently varied, the above authors obtain the equivalent of the following field equations:(2a)(2b)In these equations a comma denotes partial differentiation with respect to the co-ordinates of the manifold, Wij is the Ricci tensor formed from and the notationfor the symmetric and skew-symmetric parts of geometric objects Q is employed.

A simple unified field equation and hypothesis by

A unified field equation of force, that is, F u = m e 2 c 3/ ha e 2 = m e 2 c 4 ϵ o / e 2 a e = 0.5 m e 3 C 5/ E R h = hcS e 2/ M b 2 m e 2 = hc/ L m 2 = mr o 3 ω o 2 ω e 2/ ω p 2 B a 2 = mr e ω e 3 ω n 3/ ωp 2 B a 2 = G/ μb 2 = 1.23163 × 10 23 g cm/sec 4 gauss 2 = 3.981 × 10 8 dynes has been developed from well-known physical quantities such as electronic mass ( m e ) ; the light velocity constant ( c) ; the angular momentum constant ( h = h/27 π) ; the electronic fine structure constant ( a e ) ; the dielectric constant ( ϵ o = 1.0) ; the electronic charge ( e) ; the Rydberg energy ( E R ) ; electronic spin ( h/2); the Bohr magneton ( M b ) ; the electron's “classical radius” ( L m ); the Earth's mass ( m) ; the moon's average orbital radius ( r e ) and angular velocity ( ω o ) ; the rotating Earth's angular velocity (ω e), radius ( r e ), polar magnetic intensity ( B a ), angular velocity of nutation ( ω n ), angular velocity of precession ( w p ) ; the gravitation constant ( G) ; and a proposed proportionality constant of terrestrial and stellar magnetism ( μ b = r e B a / mω e = 7.359 × 10 −16 cm sec gauss/g = 1.2943 × 10 −8 cm/g, where one gauss unit is considered equal to 1.7589 × 10 7/sec). The fact that hcμ b 2/GL m 2 is equal to 1.000 suggests that μ b and L m are, respectively, universal constants of macroscopic and submicroscopic particle magnetism, and that the equation F u prescribes a single universal physical law governing the action-reaction of all particles and fields, whether astronomic or submicroscopic in character.