In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic f...In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.展开更多
The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the rese...The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.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
We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conser...We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.展开更多
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the for...The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.展开更多
By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions ...By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.展开更多
In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes...In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.展开更多
We have investigated the general relativistic field equations for neutron stars.We find that there are solutions for the equilibriummass distribution without a maximum mass limit.The solutions correspond to stars with...We have investigated the general relativistic field equations for neutron stars.We find that there are solutions for the equilibriummass distribution without a maximum mass limit.The solutions correspond to stars with a void inside their centers.In thesesolutions,the mass density and pressure increase first from zero at the inner radius to a peak and then decrease to zero at the outerradius.With the change of the void boundary,the mass and particle number of the star can approach infinity.Neutron stars withlarge masses can remain stable and do not collapse into black holes.展开更多
With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carrie...With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.展开更多
In this paper, a new class of solutions of the vacuum Einstein＇s field equa- tions with cosmological constant is obtained. This class of solutions possesses the naked physical singularity. The norm of the Riemann cur...In this paper, a new class of solutions of the vacuum Einstein＇s field equa- tions with cosmological constant is obtained. This class of solutions possesses the naked physical singularity. The norm of the Riemann curvature tensor of this class of solutions takes infinity at some points and the solutions do not have any event horizon around the singularity.展开更多
The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on varia...The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.展开更多
According to special relativity,the relationship of electromagnetic conversion in a linear moving vacuum and the relationship formula between the magnetic vector potential/scalar potential and the LEM(Longitudinal Ele...According to special relativity,the relationship of electromagnetic conversion in a linear moving vacuum and the relationship formula between the magnetic vector potential/scalar potential and the LEM(Longitudinal Electromagnetic)waves,it is inferred that the spherical vacuum space we are in undergoes outward helical motion at the speed of light following the right-hand screw rule,accompanied by a radial space expansion motion far less than the speed of light.Based on this space basis,we derive a unified field equation indicating that the gravitational field might be equivalent to the acceleration field of the radial expansion motion of our vacuum space,the strong nuclear force field presumably is generated by the light-rotation angular velocity of our space,the weak nuclear force field is most probably produced by its radial expansion motion and the electromagnetic field is undoubtedly produced by the radial linear motion of our space at the speed of light.We have also demonstrated both theoretically and experimentally that the LEM waves can generate artificial gravitational fields,and the LEM waves are the material basis of the unified field theory.Essentially,on Earth,time is the result of the relativistic length contraction effect caused by the radial space expansion speed,which leads to the rate of change of distance in the radial dimension on the unit radial space expansion speed.Moreover,based on the length contraction effect in special relativity,the time and space generated by the outward helical motion of space at the speed of light can be expressed as zero.This indicates that such motion not only does not affect the seemingly perpetually stationary space that we can constantly perceive but also enables the gravitational field formula to remain unchanged in our space.They constitute the spatio-temporal basis of the unified field theory.Based on our unified field theory,we have also discussed some forward-looking perspectives,such as motion at the speed of light,anti-gravitation fields,and interstellar travel.展开更多
In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connect...In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connected finite graphs by Grigor'yan,Lin and Yang.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
We have examined an isotropic and homogeneous cosmological model in f(R,T^(φ))gravity,where R represents the Ricci scalar and T^(φ)exhibits the energy momentum tensor's trace.We examine the stability criteria by...We have examined an isotropic and homogeneous cosmological model in f(R,T^(φ))gravity,where R represents the Ricci scalar and T^(φ)exhibits the energy momentum tensor's trace.We examine the stability criteria by performing the dynamical system analysis for our model f(R,T^(φ))=R+2(a T^(φ)+b),where a and b are the constants.We derive a set of autonomous equations and find their solutions by assuming a flat potential V0.We assess the equilibrium points from these equations and find the eigenvalues.We analyze the physical interpretation of the phase space for this system.We obtain three stable equilibrium points.We also examine the interaction between the scalar field and dark energy,represented by Q=ψH_(ρde)and determine the equilibrium points for this interaction.We identify four stable equilibrium points for this interaction.We calculate the values of the physical parameters for both scenarios at each equilibrium point,indicating the Universe's accelerated expansion.展开更多
The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. ...The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. What the spin of a particle really tells us is what the particle looks like from different directions, in other words it is nothing more than a geometrical property. The motivation for this work stems from the fact that geometry has always played a fundamental role in physics, macroscopic and microscopic, relativistic and non-relativistic. Our belief is that if a GUT （Grand Unified Theory） is to be established at all, then geometry must be the common thread connecting all the different aspects of the already known theories. We propose a new way to visualize the concept of four-dimensional space-time in simple geometrical terms. It is observed that our time frame becomes curved, just as the space-frame, in the presence of a massive gravitating body. Specifically, in the event horizon of a black hole, where time seems to grind to a halt for external observers, the time frame appears to curve in on itself, forming an imaginary loop. This results in extreme time dilation, due to the strong gravitational field. Finally we adopt a descriptive view of a GUT called Quantum Necklace GUT which attempts to connect gravity together the other three fundamental forces of nature, namely the strong, weak and electromagnetic interactions.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
In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of s...In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.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
The distributions of the electrical potential and field have been given from Maxwells field equations.The results show that there exists very strong electric field intensity on the tip of the nanotube,and the intensit...The distributions of the electrical potential and field have been given from Maxwells field equations.The results show that there exists very strong electric field intensity on the tip of the nanotube,and the intensity decays rapidly as the distance increases away from the tip. The strong electric field intensity on the tip is consistent with the low threshold voltage under the electric field emission from a nanotube. The calculation also revealed that the higher the aspect ratio is,the stronger the electric field intensity on the tip of the nanotube will be,if the distance and voltage between the cathode and the anode do not change, which predicts the lower threshold voltage under the field emission.展开更多
文摘In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.
文摘The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.
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We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.
文摘The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
文摘By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.
基金supported by National Natural Science Foundation of China (Grant No.10971190) and the Qiu-Shi Professor Fellowship from Zhejiang University,China
文摘In this paper we construct a new time-periodic solution of the vacuum Einstein's field equations, this solution possesses physical singularities, i.e., the norm of the solution's Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "time-periodic physical singularity". By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this universal model.
基金supported by the National Natural Science Foundation of China (Grant No. 10974107)
文摘We have investigated the general relativistic field equations for neutron stars.We find that there are solutions for the equilibriummass distribution without a maximum mass limit.The solutions correspond to stars with a void inside their centers.In thesesolutions,the mass density and pressure increase first from zero at the inner radius to a peak and then decrease to zero at the outerradius.With the change of the void boundary,the mass and particle number of the star can approach infinity.Neutron stars withlarge masses can remain stable and do not collapse into black holes.
文摘With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.
基金supported by National Natural Science Foundation of China(Grant No.11101085)Natural Science Foundation of Fujian Province(Grant No.2015J0101)
文摘In this paper, a new class of solutions of the vacuum Einstein＇s field equa- tions with cosmological constant is obtained. This class of solutions possesses the naked physical singularity. The norm of the Riemann curvature tensor of this class of solutions takes infinity at some points and the solutions do not have any event horizon around the singularity.
基金funded by the Major National Scientific Research Plan(2013CB733305,2012CB957703)the National Natural Science Foundation of China(41174066,41131067,41374087,41431070)
文摘The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.
文摘According to special relativity,the relationship of electromagnetic conversion in a linear moving vacuum and the relationship formula between the magnetic vector potential/scalar potential and the LEM(Longitudinal Electromagnetic)waves,it is inferred that the spherical vacuum space we are in undergoes outward helical motion at the speed of light following the right-hand screw rule,accompanied by a radial space expansion motion far less than the speed of light.Based on this space basis,we derive a unified field equation indicating that the gravitational field might be equivalent to the acceleration field of the radial expansion motion of our vacuum space,the strong nuclear force field presumably is generated by the light-rotation angular velocity of our space,the weak nuclear force field is most probably produced by its radial expansion motion and the electromagnetic field is undoubtedly produced by the radial linear motion of our space at the speed of light.We have also demonstrated both theoretically and experimentally that the LEM waves can generate artificial gravitational fields,and the LEM waves are the material basis of the unified field theory.Essentially,on Earth,time is the result of the relativistic length contraction effect caused by the radial space expansion speed,which leads to the rate of change of distance in the radial dimension on the unit radial space expansion speed.Moreover,based on the length contraction effect in special relativity,the time and space generated by the outward helical motion of space at the speed of light can be expressed as zero.This indicates that such motion not only does not affect the seemingly perpetually stationary space that we can constantly perceive but also enables the gravitational field formula to remain unchanged in our space.They constitute the spatio-temporal basis of the unified field theory.Based on our unified field theory,we have also discussed some forward-looking perspectives,such as motion at the speed of light,anti-gravitation fields,and interstellar travel.
基金partially supported by the National Science Foundation of China(Grant No.11401575 and 11721101).
文摘In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connected finite graphs by Grigor'yan,Lin and Yang.
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.
基金funded by Researchers Supporting Project No.RSPD2025R733,King Saud University,Riyadh,Saudi Arabia。
文摘We have examined an isotropic and homogeneous cosmological model in f(R,T^(φ))gravity,where R represents the Ricci scalar and T^(φ)exhibits the energy momentum tensor's trace.We examine the stability criteria by performing the dynamical system analysis for our model f(R,T^(φ))=R+2(a T^(φ)+b),where a and b are the constants.We derive a set of autonomous equations and find their solutions by assuming a flat potential V0.We assess the equilibrium points from these equations and find the eigenvalues.We analyze the physical interpretation of the phase space for this system.We obtain three stable equilibrium points.We also examine the interaction between the scalar field and dark energy,represented by Q=ψH_(ρde)and determine the equilibrium points for this interaction.We identify four stable equilibrium points for this interaction.We calculate the values of the physical parameters for both scenarios at each equilibrium point,indicating the Universe's accelerated expansion.
文摘The consequence of the wave-particle duality is a pointer to the fact that everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin. What the spin of a particle really tells us is what the particle looks like from different directions, in other words it is nothing more than a geometrical property. The motivation for this work stems from the fact that geometry has always played a fundamental role in physics, macroscopic and microscopic, relativistic and non-relativistic. Our belief is that if a GUT （Grand Unified Theory） is to be established at all, then geometry must be the common thread connecting all the different aspects of the already known theories. We propose a new way to visualize the concept of four-dimensional space-time in simple geometrical terms. It is observed that our time frame becomes curved, just as the space-frame, in the presence of a massive gravitating body. Specifically, in the event horizon of a black hole, where time seems to grind to a halt for external observers, the time frame appears to curve in on itself, forming an imaginary loop. This results in extreme time dilation, due to the strong gravitational field. Finally we adopt a descriptive view of a GUT called Quantum Necklace GUT which attempts to connect gravity together the other three fundamental forces of nature, namely the strong, weak and electromagnetic interactions.
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In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
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The distributions of the electrical potential and field have been given from Maxwells field equations.The results show that there exists very strong electric field intensity on the tip of the nanotube,and the intensity decays rapidly as the distance increases away from the tip. The strong electric field intensity on the tip is consistent with the low threshold voltage under the electric field emission from a nanotube. The calculation also revealed that the higher the aspect ratio is,the stronger the electric field intensity on the tip of the nanotube will be,if the distance and voltage between the cathode and the anode do not change, which predicts the lower threshold voltage under the field emission.
