The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivat...The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).展开更多
In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori's, we solve the Einstein's equations with the energy-momentum tensors for ele...In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori's, we solve the Einstein's equations with the energy-momentum tensors for electromagnetic field, and construct the time-machine solutions, which solve the time machine problem in electromagnetic field.展开更多
In this paper some properties of a symmetric tensor field T(X,Y) = g(A(X), Y) on a Riemannian manifold (M, g) without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij+bξiξj are given. ...In this paper some properties of a symmetric tensor field T(X,Y) = g(A(X), Y) on a Riemannian manifold (M, g) without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij+bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.展开更多
The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of E...The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R<sup>2</sup>, |Ric|<sup>2</sup>, where the Ricci tensor Ric = R<sub>αβ</sub>dx<sup>α</sup>dx<sup>β</sup> is inserted in some formulas which are of geometrical or physical importance, such as;Raychaudhuri equation and Tolman’s formula.展开更多
Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (Hc2) of H3S (critical temperature, Tc ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtai...Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (Hc2) of H3S (critical temperature, Tc ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtained by Talantsev (2019) in an approach based on an ingenious mix of the Ginzberg-Landau (GL), the Werthamer, Helfand and Hohenberg (WHH), and the Gor’kov, etc., theories which have individually been employed for the same purpose for a long time. Up to the lowest temperature (TL) in each of these data-sets, similarly accurate fits have also been obtained by Malik and Varma (2023) in a radically different approach based on the Bethe-Salpeter equation (BSE) supplemented by the Matsubara and the Landau quantization prescriptions. For T TL, however, while the (GL, WHH, etc.)-based approach leads to Hc2(0) ≈ 100 T, the BSE-based approach leads to about twice this value even at 1 K. In this paper, a fit to one of the said data-sets is obtained for the first time via a thermodynamic approach which, up to TL, is as good as those obtained via the earlier approaches. While this is interesting per se, another significant result of this paper is that for T TL it corroborates the result of the BSE-based approach.展开更多
In this paper, we consider the Post Einstein Planetary equation of motion. We succeeded in offering a solution using second approximation method, in which we obtained eight exact mathematical solutions that rebel amaz...In this paper, we consider the Post Einstein Planetary equation of motion. We succeeded in offering a solution using second approximation method, in which we obtained eight exact mathematical solutions that rebel amazing theoretical results. To the order of C<sup>-2</sup>, two of these exact solutions are reduced to the approximate solutions from the method of successive approximations.展开更多
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitra...This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.展开更多
A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge fie...A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.展开更多
For explicitly time depending mass density which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approxim...For explicitly time depending mass density which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related assumptions. As a consequence, it is shown that several features already known in Electrodynamics (Poynting vector, density of energy, tensor stress, and radiation) are totally reproduced for gravitational field.展开更多
The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out: they...The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, reslpetivcly. The definitions of the divergence and the curl of a 2D surface flux of a tensor arc obtained. Maxwell's equations, namely, the constraction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field (or its composition). By the feature of central field (or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces) axe presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.展开更多
When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit ...When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.展开更多
In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showe...In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.展开更多
According to Hypersphere World-Universe Model, dark matter particles DIRACs are magnetic dipoles consisting of two Dirac’s monopoles. We conclude that DIRACs are the subject of Maxwell’s equations. So-called “auxil...According to Hypersphere World-Universe Model, dark matter particles DIRACs are magnetic dipoles consisting of two Dirac’s monopoles. We conclude that DIRACs are the subject of Maxwell’s equations. So-called “auxiliary” magnetic field intensity H is indeed current density of magnetic dipoles. The developed approach to magnetic field can explain a wealth of discovered phenomena in Cosmic Magnetism: a dark magnetic field, the large-scale structure of the Milky Way’s magnetic field, and other magnetic phenomena which are only partly related to objects visible in other spectral ranges.展开更多
Recent decades have seen rapid advances in the field of electrical engineering, such that our environment has become a sea of electrical and magnetic signals, raising questions about the possible effects of low-freque...Recent decades have seen rapid advances in the field of electrical engineering, such that our environment has become a sea of electrical and magnetic signals, raising questions about the possible effects of low-frequency electromagnetic fields on the environment and which are capable of modifying and destroying our ecosystem. Particular interest was given in this article due to a massive influx of population living near high voltage lines. The analysis and simulation of the influence of low frequency electromagnetic fields on living beings in the vicinity of high voltage sources 132 kV and 220 kV in urban areas in DR Congo is the subject of our research with a view to estimating the level of exposure of humans to low frequency electromagnetic fields. To carry out our research, we used the classic method of analyzing the field produced near a high voltage line based on Maxwell’s image theory, the Maxwell-Gauss theorem and Maxwell-Ampère theorem to model and quantify low-frequency electromagnetic fields in the vicinity of high-voltage lines. The 2D FDTD numerical formulation was developed from telegraphers’ equations and allowed us to obtain models of current and voltage induced by electromagnetic fields on living beings below and near HV lines. The different simulations carried out on the proposed models illustrate the effects of the electrical and geometric parameters of the pylons on the distribution of the electromagnetic field in the vicinity of the HV lines. The results obtained were compared to the safety limits recommended by the standards.展开更多
In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichart...In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz's inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal展开更多
Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S)...Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.展开更多
Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S report...Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S<sub>1</sub> = {T<sub>c</sub>, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of H<sub>c</sub><sub>2</sub>(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for H<sub>c</sub><sub>2</sub>(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of H<sub>c</sub><sub>2</sub>(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S<sub>2</sub> = {μ, m*, interaction parameter λ<sub>m</sub>, Landau index N<sub>L</sub>}, which is altogether different from S<sub>1</sub>.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
Based on theoretical system of current Maxwell’s equations, the Maxwell’s equations for LEM waves concealed in full current law and Faraday’s law of electromagnetic induction (Faraday’s law) are proposed. Then, ta...Based on theoretical system of current Maxwell’s equations, the Maxwell’s equations for LEM waves concealed in full current law and Faraday’s law of electromagnetic induction (Faraday’s law) are proposed. Then, taking them as the fundamental equations, the wave equation and energy equation of LEM waves are established, and a new electromagnetic wave propagation mode based on the mutual induction of scalar electromagnetic fields/vortex magneto-electric fields, which was overlooked in current Maxwell’s equations, are put forward. Moreover, through theoretical derivation based on vacuum LEM waves, the Maxwell’s equations of the gravitational field generated by vacuum LEM waves, the wave equations of the electromagnetic scalar potential/magnetic vector potential and the constraint equation governing the wave phase-velocities between LEM/TEM waves are discovered. Finally, on the basis of these theoretical research results, the electromagnetic properties of vacuum LEM waves are analyzed in detail, encompassing the speed of light, harmless penetrability to the human body, absorption and stable storage by water, the possibility of generating artificial gravitational fields, and the capability of extracting free energy. This reveals the medical functional mechanism of LEM waves and establishes a solid theoretical basis for the application of LEM waves in the fields of medicine and energy.展开更多
文摘The introduction of a new concept of space-energy duality serves to extend the applicability of the Einstein field equation in the context of a 4-index framework. The utilization of the Weyl tensor enables the derivation of Einstein’s equations in the 4-index format. Additionally, a two-index field equation is presented, comprising a conventional Einstein field equation and a trace-free Einstein equation. Notably, the cosmological constant is associated with a novel concept that facilitates the encoding of space and energy information, thereby enabling the recognition of mutual interactions between space and energy in the presence of gravitational forces, as dictated by Einstein’s field equations (EFE) and Trace-Free Einstein Equation (TFE).
基金Supported by the Start-up Fund of Fuzhou University under Grant No.0460022346
文摘In this paper we investigate the time-machine problem in the electromagnetic field. Based on a metric which is a more general form of Ori's, we solve the Einstein's equations with the energy-momentum tensors for electromagnetic field, and construct the time-machine solutions, which solve the time machine problem in electromagnetic field.
基金The Grant-in-Aid for Scientific Research from Nanjing University of ScienceTechnology (AB41409) the NNSF (19771048) of China partly.
文摘In this paper some properties of a symmetric tensor field T(X,Y) = g(A(X), Y) on a Riemannian manifold (M, g) without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij+bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.
文摘The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R<sup>2</sup>, |Ric|<sup>2</sup>, where the Ricci tensor Ric = R<sub>αβ</sub>dx<sup>α</sup>dx<sup>β</sup> is inserted in some formulas which are of geometrical or physical importance, such as;Raychaudhuri equation and Tolman’s formula.
文摘Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (Hc2) of H3S (critical temperature, Tc ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtained by Talantsev (2019) in an approach based on an ingenious mix of the Ginzberg-Landau (GL), the Werthamer, Helfand and Hohenberg (WHH), and the Gor’kov, etc., theories which have individually been employed for the same purpose for a long time. Up to the lowest temperature (TL) in each of these data-sets, similarly accurate fits have also been obtained by Malik and Varma (2023) in a radically different approach based on the Bethe-Salpeter equation (BSE) supplemented by the Matsubara and the Landau quantization prescriptions. For T TL, however, while the (GL, WHH, etc.)-based approach leads to Hc2(0) ≈ 100 T, the BSE-based approach leads to about twice this value even at 1 K. In this paper, a fit to one of the said data-sets is obtained for the first time via a thermodynamic approach which, up to TL, is as good as those obtained via the earlier approaches. While this is interesting per se, another significant result of this paper is that for T TL it corroborates the result of the BSE-based approach.
文摘In this paper, we consider the Post Einstein Planetary equation of motion. We succeeded in offering a solution using second approximation method, in which we obtained eight exact mathematical solutions that rebel amazing theoretical results. To the order of C<sup>-2</sup>, two of these exact solutions are reduced to the approximate solutions from the method of successive approximations.
文摘This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.
文摘A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
文摘For explicitly time depending mass density which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related assumptions. As a consequence, it is shown that several features already known in Electrodynamics (Poynting vector, density of energy, tensor stress, and radiation) are totally reproduced for gravitational field.
文摘The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, reslpetivcly. The definitions of the divergence and the curl of a 2D surface flux of a tensor arc obtained. Maxwell's equations, namely, the constraction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field (or its composition). By the feature of central field (or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces) axe presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.
文摘When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.
文摘In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.
文摘According to Hypersphere World-Universe Model, dark matter particles DIRACs are magnetic dipoles consisting of two Dirac’s monopoles. We conclude that DIRACs are the subject of Maxwell’s equations. So-called “auxiliary” magnetic field intensity H is indeed current density of magnetic dipoles. The developed approach to magnetic field can explain a wealth of discovered phenomena in Cosmic Magnetism: a dark magnetic field, the large-scale structure of the Milky Way’s magnetic field, and other magnetic phenomena which are only partly related to objects visible in other spectral ranges.
文摘Recent decades have seen rapid advances in the field of electrical engineering, such that our environment has become a sea of electrical and magnetic signals, raising questions about the possible effects of low-frequency electromagnetic fields on the environment and which are capable of modifying and destroying our ecosystem. Particular interest was given in this article due to a massive influx of population living near high voltage lines. The analysis and simulation of the influence of low frequency electromagnetic fields on living beings in the vicinity of high voltage sources 132 kV and 220 kV in urban areas in DR Congo is the subject of our research with a view to estimating the level of exposure of humans to low frequency electromagnetic fields. To carry out our research, we used the classic method of analyzing the field produced near a high voltage line based on Maxwell’s image theory, the Maxwell-Gauss theorem and Maxwell-Ampère theorem to model and quantify low-frequency electromagnetic fields in the vicinity of high-voltage lines. The 2D FDTD numerical formulation was developed from telegraphers’ equations and allowed us to obtain models of current and voltage induced by electromagnetic fields on living beings below and near HV lines. The different simulations carried out on the proposed models illustrate the effects of the electrical and geometric parameters of the pylons on the distribution of the electromagnetic field in the vicinity of the HV lines. The results obtained were compared to the safety limits recommended by the standards.
基金Supported by the National Natural Science Foundation of China the Doctoral Foundation of NEM of China
文摘In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz's inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal
文摘Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.
文摘Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S<sub>1</sub> = {T<sub>c</sub>, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of H<sub>c</sub><sub>2</sub>(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for H<sub>c</sub><sub>2</sub>(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of H<sub>c</sub><sub>2</sub>(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S<sub>2</sub> = {μ, m*, interaction parameter λ<sub>m</sub>, Landau index N<sub>L</sub>}, which is altogether different from S<sub>1</sub>.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
文摘Based on theoretical system of current Maxwell’s equations, the Maxwell’s equations for LEM waves concealed in full current law and Faraday’s law of electromagnetic induction (Faraday’s law) are proposed. Then, taking them as the fundamental equations, the wave equation and energy equation of LEM waves are established, and a new electromagnetic wave propagation mode based on the mutual induction of scalar electromagnetic fields/vortex magneto-electric fields, which was overlooked in current Maxwell’s equations, are put forward. Moreover, through theoretical derivation based on vacuum LEM waves, the Maxwell’s equations of the gravitational field generated by vacuum LEM waves, the wave equations of the electromagnetic scalar potential/magnetic vector potential and the constraint equation governing the wave phase-velocities between LEM/TEM waves are discovered. Finally, on the basis of these theoretical research results, the electromagnetic properties of vacuum LEM waves are analyzed in detail, encompassing the speed of light, harmless penetrability to the human body, absorption and stable storage by water, the possibility of generating artificial gravitational fields, and the capability of extracting free energy. This reveals the medical functional mechanism of LEM waves and establishes a solid theoretical basis for the application of LEM waves in the fields of medicine and energy.