The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to a...The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.展开更多
This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surface...This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine, and cosine. We are building up the general solutions bit for bit according to constant terms that contain the formula of the desired limit cycle, and differentiating them. In Part One, we used only formulas for closed curves where all parts of the formula were of the same degree. In order to use many other formulas for closed curves, the method in this paper is to introduce an additional variable, and we will get an additional ODE. We will choose the part of the formula with the highest degree and multiply the other parts with an extra variable, so that all parts of the formula have the same degree, creating a constant term containing this new formula. We will place it under the fraction line in the solutions, building up the rest of the solutions according to this constant term and differentiating. Keeping this extra variable constant, we will achieve almost the desired result. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions and some surfaces having attractor behavior, where not all parts of the formulas are the same degree. The pictures show the result.展开更多
The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the ra...The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the (GI/G)-expansion method, and the effects of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions are analysed and numerically simulated.展开更多
A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With itera...A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.展开更多
The purpose of this paper is to study cosmological properties of two-dimensional Brans-Dicke gravity model. For massless scatar field, the new cosmological solutions are found by integration of field equation, these s...The purpose of this paper is to study cosmological properties of two-dimensional Brans-Dicke gravity model. For massless scatar field, the new cosmological solutions are found by integration of field equation, these solutions correspond to the inflation solutions with positive cosmological constant. The result of this paper show that the inflation process of universe is controlled by the classical and quantum effect of the scalar field.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T ) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and non...By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.展开更多
In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress di...In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.展开更多
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||po||L∞ is appropriate...We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||po||L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.展开更多
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ...In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.展开更多
In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are est...In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × (n + pr). The algorithm proposed in this paper for the euqation AX - XF = BY does not require the controllability of matrix pair (A, B) and the restriction that A, F do not have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.展开更多
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.展开更多
In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where s...In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.展开更多
A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since i...A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since it involves one less potential function than Blot's solution.展开更多
Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditi...Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.展开更多
In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the bound...In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can't he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.展开更多
The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic an...The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic analysis shows that two solitons undergo elastic collision accompanied by a position shift. Furthermore, our analysis on mixed soliton bound states shows that arbitrary higher-order soliton bound states can take place.展开更多
We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density;their r...We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density;their ratio is less than one and causality condition is obeyed at the centre. The gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb = 2 × 1014g/cm3. Corresponding to K = 0.72 with X = 0.15, the resulting well behaved model has the mass M = 1.94 MΘ with radius rb ? 15.2 km and for K = 2.41 with X = 0.15, the resulting well behaved model has the mass M = 2.26 MΘ with radius rb ? 14.65 km.展开更多
基金supported by the National Natural Sci-ence Foundation of China(11172319)the Chinese Univer-sities Scientific Fund(2011JS046,2013BH008)+2 种基金the Opening Fund of State Key Laboratory of Nonlinear Mechanicsthe Program for New Century Excellent Talents in Univer-sity(NCET-13-0552)the National Science Foundation for Post-doctoral Scientists of China(2013M541086)
文摘The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.
文摘This paper is presenting a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine, and cosine. We are building up the general solutions bit for bit according to constant terms that contain the formula of the desired limit cycle, and differentiating them. In Part One, we used only formulas for closed curves where all parts of the formula were of the same degree. In order to use many other formulas for closed curves, the method in this paper is to introduce an additional variable, and we will get an additional ODE. We will choose the part of the formula with the highest degree and multiply the other parts with an extra variable, so that all parts of the formula have the same degree, creating a constant term containing this new formula. We will place it under the fraction line in the solutions, building up the rest of the solutions according to this constant term and differentiating. Keeping this extra variable constant, we will achieve almost the desired result. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions and some surfaces having attractor behavior, where not all parts of the formulas are the same degree. The pictures show the result.
基金Project supported by the Basic Science and the Front Technology Research Foundation of Henan Province,China(Grant Nos.092300410179 and122102210427)the Doctoral Scientific Research Foundation of Henan University of Science and Technology,China(Grant No.09001204)+1 种基金the Scientific Research Innovation Ability Cultivation Foundation of Henan University of Science and Technology,China(Grant No.011CX011)the Scientific Research Foundation of Henan University of Science and Technology(Grant No.2012QN011)
文摘The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the (GI/G)-expansion method, and the effects of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions are analysed and numerically simulated.
基金Project supported by the National Natural Science Foundation of China (Nos. 10871075 and 10926101)the Natural Science Foundation of Guangdong Province of China(Nos. 9451064201003736 and 9151064201000040)
文摘A class of periodic initial value problems for two-dimensional Newton- Boussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.
基金The Natural Science Foundatin of Sichuan Normal University (No.061k004)
文摘The purpose of this paper is to study cosmological properties of two-dimensional Brans-Dicke gravity model. For massless scatar field, the new cosmological solutions are found by integration of field equation, these solutions correspond to the inflation solutions with positive cosmological constant. The result of this paper show that the inflation process of universe is controlled by the classical and quantum effect of the scalar field.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T ) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
基金Supported by the Develop Programme Foundation of the National Basic research(G1 9990 3 2 80 1 )
文摘By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172211 and 41630633)the National Key Research and Development Project of China(Grant No.2019YFC1509800).
文摘In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.
基金supported by National Natural Science Foundation of China (11001090)the Fundamental Research Funds for the Central Universities(11QZR16)
文摘We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||po||L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675084 and 11435005)the Fund from the Educational Commission of Zhejiang Province,China(Grant No.Y201737177)+1 种基金Ningbo Natural Science Foundation(Grant No.2015A610159)the K C Wong Magna Fund in Ningbo University
文摘In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.
基金This work was supported by the Chinese Outstanding Youth Foundation(No.69925308)Program for Changjiang Scholars and Innovative ResearchTeam in University.
文摘In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × (n + pr). The algorithm proposed in this paper for the euqation AX - XF = BY does not require the controllability of matrix pair (A, B) and the restriction that A, F do not have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.
基金The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
文摘In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.
文摘A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since it involves one less potential function than Blot's solution.
文摘Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.
文摘In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can't he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.
基金Supported by the Global Change Research Program of China under Grant No 2015CB953904the National Natural Science Foundation of China under Grant Nos 11675054 and 11435005the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No ZF1213
文摘The general bright-dark mixed N-soliton solution of the two-dimensional Maccari system is obtained with the KP hierarchy reduction method. The dynamics of single and two solitons are discussed in detail. Asymptotic analysis shows that two solitons undergo elastic collision accompanied by a position shift. Furthermore, our analysis on mixed soliton bound states shows that arbitrary higher-order soliton bound states can take place.
文摘We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge fluid balls with positively finite central pressure, positively finite central density;their ratio is less than one and causality condition is obeyed at the centre. The gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb = 2 × 1014g/cm3. Corresponding to K = 0.72 with X = 0.15, the resulting well behaved model has the mass M = 1.94 MΘ with radius rb ? 15.2 km and for K = 2.41 with X = 0.15, the resulting well behaved model has the mass M = 2.26 MΘ with radius rb ? 14.65 km.