In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obt...In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.展开更多
The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized ...The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.展开更多
The modified Chaplygin gas (MCG) as an interacting model of holographic dark energy in which dark energy and dark matter are coupled together is investigated in this paper. Concretely, by studying the evolutions of re...The modified Chaplygin gas (MCG) as an interacting model of holographic dark energy in which dark energy and dark matter are coupled together is investigated in this paper. Concretely, by studying the evolutions of related cosmological quantities such as density parameter Ω, equation of state w, deceleration parameter q and transition redshift zT, we find the evolution of the universe is from deceleration to acceleration, their present values are consistent with the latest observations, and the equation of state of holographic dark energy can cross the phantom divide w = -1. Furthermore, we put emphasis upon the geometrical diagnostics for our model, i.e., the statefinder and Om diagnostics. By illustrating the evolutionary trajectories in r - s, r - q, w -w and Om planes, we find that the holographic constant c and the coupling constant b play very important roles in the holographic dark energy (HDE) model. In addition, we also plot the LCDM horizontal lines in Om diagrams, and show the discrimination between the HDE and LCDM models.展开更多
In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,wh...In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.展开更多
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial ve...In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.展开更多
The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and t...The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.展开更多
In this paper,we investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas and the pure Chaplygin gas,which are the set of all rarefaction waves,shock waves,contact discont...In this paper,we investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas and the pure Chaplygin gas,which are the set of all rarefaction waves,shock waves,contact discontinuity andδ-shock waves.Under some appropriate conditions,by studing the limiting behavior,we find that the Riemann solutions of modified Chaplygin gas is the same as pure Chaplygin gas including theδ-shock waves.展开更多
In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial ...In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.展开更多
We study the generalized Riemann problem of the Chapman-Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we construct uniquely the solution of the generalized Riem...We study the generalized Riemann problem of the Chapman-Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we construct uniquely the solution of the generalized Riemann problem under the global entropy conditions. We find that although there is no combustion wave of the corresponding Riemann solution, the combustion wave may occur after perturbation which reveals the instability of the unburnt gas.展开更多
We use the latest data to investigate observational constraints on the new generalized Chaplygin gas （NGCG） model. Using the Markov Chain Monte Carlo method, we constrain the NGCG model with type Ia supernovae from ...We use the latest data to investigate observational constraints on the new generalized Chaplygin gas （NGCG） model. Using the Markov Chain Monte Carlo method, we constrain the NGCG model with type Ia supernovae from the Union2 set （557 data）, the usual baryonic acoustic oscillation （BAO） observation from the spectroscopic Sloan Digital Sky Survey data release 7 galaxy sample, the cosmic mi- crowave background observation from the 7-year Wilkinson Microwave Anisotropy Probe results, newly revised data on H（z）, as well as a value of θBAO （Z = 0.55） = （3.90° ±0.38°） for the angular BAO scale. The constraint results for the NGCG model are ωX=-1.0510＋0.1563-0.1685（1σ）＋0.2226-0.2398（2σ）,η=1.0117＋0.0469-0.0502（1σ）＋0.0693-0.0716（2σ）and ΩX=0.7297＋0.0229-0.0276（1σ）＋0.0329-0.0402（2σ）, which give a rather stringent constraint. From the results, we can see that a phantom model is slightly favored and the proba- bility that energy transfers from dark matter to dark energy is a little larger than the inverse.展开更多
The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, t...The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.展开更多
Using recently observed data： the Constitution dataset of type supernovae Ia （SNIa）, the observational Hubble data （OHD）, the measurement results of baryon acoustic oscillation （BAO） from the Sloan Digital Sky ...Using recently observed data： the Constitution dataset of type supernovae Ia （SNIa）, the observational Hubble data （OHD）, the measurement results of baryon acoustic oscillation （BAO） from the Sloan Digital Sky Survey （SDSS） and the Two Degree Field Galaxy Redshift Survey （2dFGRS）, and the current cosmic microwave background （CMB） data from the five-year Wilkinson Microwave Anisotropy Probe （WMAP）, we apply the Markov Chain Monte Carlo method to investigate the observational constraints on the generalized Chaplygin gas （GCG） model as the unification of dark matter and dark energy. For this unified model, the constraints on GCG mixture are discussed by considering the different expressions of current matter density or considering constraints as being independent of the matter quantity Ωm.展开更多
This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condit...This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condition on metric potential . Also to obtain deterministic models we have considered physically reasonable relations like , and the equation of state for generalized Chaplygin gas given by . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behaviour of the models has been discussed.展开更多
In this paper, we suggest that a toy model of our universe is based on FRW bulk viscous cosmology in presence of modified Chaplygin gas. We obtain modified Friedman equations due to bulk viscosity and Chaplygin gas an...In this paper, we suggest that a toy model of our universe is based on FRW bulk viscous cosmology in presence of modified Chaplygin gas. We obtain modified Friedman equations due to bulk viscosity and Chaplygin gas and calculate time-dependent energy density for the special case of flat space.展开更多
In this paper, bulk viscous Bianchi type V cosmological model with generalized Chaplygin gas, dynamical gravitational and cosmological constants has been investigated. We are assuming the condition on metric potential...In this paper, bulk viscous Bianchi type V cosmological model with generalized Chaplygin gas, dynamical gravitational and cosmological constants has been investigated. We are assuming the condition on metric potential . To obtain deterministic model, we have considered physically plausible relations like , and the generalized Chaplygin gas is described by equation of state . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behavior of the models has been discussed.展开更多
In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability ...In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.展开更多
In this paper, we have studied the generalized chaplygin gas of interacting dark energy to ob-tain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological mode...In this paper, we have studied the generalized chaplygin gas of interacting dark energy to ob-tain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological model. For negative value of B in equation of state of generalized chaplygin gas, we see that γ effΛ<-1 , that corresponds to a universe dominated by phantom dark energy.展开更多
We consider the most general static spherically symmetric black hole metric. The accretion of the fluid flow around the Van der Waal's black hole is investigated and we calculate the fluid's four-velocity, the...We consider the most general static spherically symmetric black hole metric. The accretion of the fluid flow around the Van der Waal's black hole is investigated and we calculate the fluid's four-velocity, the critical point and the speed of sound during the accretion process. We also analyze the nature of the universe's density and the mass of the black hole during accretion of the fluid flow. The density of the fluid flow is also taken into account. We observe that the mass is related to redshift. We compare the accreting power of the Van der Waal's black hole with Schwarzschild black hole for different accreting fluid.展开更多
In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypot...In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypothesis that the initial data are of sufficiently small total variation, we prove that the difference between the solutions to these two systems can be bounded by the cube of the total variation of the initial perturbation.展开更多
The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementar...The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.展开更多
基金supported by National Natural Science Foundation of China (10871199)
文摘In this article, we study the Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtain the global existence of generalized solutions that explicitly exhibit four kinds of different structures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(Grant No.KYLX16-0414)
文摘The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No. 10875056)the Scientific Research Foundation of the Higher Education Institute of Liaoning Province, China (Grant Nos.2007T087 and 2009R35)
文摘The modified Chaplygin gas (MCG) as an interacting model of holographic dark energy in which dark energy and dark matter are coupled together is investigated in this paper. Concretely, by studying the evolutions of related cosmological quantities such as density parameter Ω, equation of state w, deceleration parameter q and transition redshift zT, we find the evolution of the universe is from deceleration to acceleration, their present values are consistent with the latest observations, and the equation of state of holographic dark energy can cross the phantom divide w = -1. Furthermore, we put emphasis upon the geometrical diagnostics for our model, i.e., the statefinder and Om diagnostics. By illustrating the evolutionary trajectories in r - s, r - q, w -w and Om planes, we find that the holographic constant c and the coupling constant b play very important roles in the holographic dark energy (HDE) model. In addition, we also plot the LCDM horizontal lines in Om diagrams, and show the discrimination between the HDE and LCDM models.
基金supported in part by National Natural Science Foundation of China(Grant No. 11031001)the Doctorial Foundation of National Educational Ministry (Grant No. 20090071110002)Tianyuan Fund of Mathematics (Grant No. 11126181)
文摘In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.
基金supported by National Natural Science Foundation of China (Grant No.10671124)
文摘In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
文摘The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.
基金Academic Discipline Project of Shanghai Dianji University(Grant No.16JCXK02)。
文摘In this paper,we investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas and the pure Chaplygin gas,which are the set of all rarefaction waves,shock waves,contact discontinuity andδ-shock waves.Under some appropriate conditions,by studing the limiting behavior,we find that the Riemann solutions of modified Chaplygin gas is the same as pure Chaplygin gas including theδ-shock waves.
基金Project supported by the Natural Science Foundation of China (Grant No.10671120)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe.
文摘We study the generalized Riemann problem of the Chapman-Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we construct uniquely the solution of the generalized Riemann problem under the global entropy conditions. We find that although there is no combustion wave of the corresponding Riemann solution, the combustion wave may occur after perturbation which reveals the instability of the unburnt gas.
基金supported by the National Natural Science Foundation of China under the Distinguished Young Scholar program(Grant No. 10825313)the National Basic Research Program of China (973 program,Grant No. 2012CB821804)the Fundamental Research Funds for the Central Universities and Scientific Research Foundation of Beijing Normal University
文摘We use the latest data to investigate observational constraints on the new generalized Chaplygin gas （NGCG） model. Using the Markov Chain Monte Carlo method, we constrain the NGCG model with type Ia supernovae from the Union2 set （557 data）, the usual baryonic acoustic oscillation （BAO） observation from the spectroscopic Sloan Digital Sky Survey data release 7 galaxy sample, the cosmic mi- crowave background observation from the 7-year Wilkinson Microwave Anisotropy Probe results, newly revised data on H（z）, as well as a value of θBAO （Z = 0.55） = （3.90° ±0.38°） for the angular BAO scale. The constraint results for the NGCG model are ωX=-1.0510＋0.1563-0.1685（1σ）＋0.2226-0.2398（2σ）,η=1.0117＋0.0469-0.0502（1σ）＋0.0693-0.0716（2σ）and ΩX=0.7297＋0.0229-0.0276（1σ）＋0.0329-0.0402（2σ）, which give a rather stringent constraint. From the results, we can see that a phantom model is slightly favored and the proba- bility that energy transfers from dark matter to dark energy is a little larger than the inverse.
基金Project supported by the National Natural Science Foundation of China(No.11371240)the Scientific Research Innovation Project of Shanghai Municipal Education Commission(No.11ZZ84)the grant of "The First-Class Discipline of Universities in Shanghai"
文摘The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10875056 and 10703001)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20070141034)
文摘Using recently observed data： the Constitution dataset of type supernovae Ia （SNIa）, the observational Hubble data （OHD）, the measurement results of baryon acoustic oscillation （BAO） from the Sloan Digital Sky Survey （SDSS） and the Two Degree Field Galaxy Redshift Survey （2dFGRS）, and the current cosmic microwave background （CMB） data from the five-year Wilkinson Microwave Anisotropy Probe （WMAP）, we apply the Markov Chain Monte Carlo method to investigate the observational constraints on the generalized Chaplygin gas （GCG） model as the unification of dark matter and dark energy. For this unified model, the constraints on GCG mixture are discussed by considering the different expressions of current matter density or considering constraints as being independent of the matter quantity Ωm.
文摘This paper is devoted to studying the generalized Chaplygin gas models in Bianchi type III space- time geometry with time varying bulk viscosity, cosmological and gravitational constants. We are considering the condition on metric potential . Also to obtain deterministic models we have considered physically reasonable relations like , and the equation of state for generalized Chaplygin gas given by . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behaviour of the models has been discussed.
文摘In this paper, we suggest that a toy model of our universe is based on FRW bulk viscous cosmology in presence of modified Chaplygin gas. We obtain modified Friedman equations due to bulk viscosity and Chaplygin gas and calculate time-dependent energy density for the special case of flat space.
文摘In this paper, bulk viscous Bianchi type V cosmological model with generalized Chaplygin gas, dynamical gravitational and cosmological constants has been investigated. We are assuming the condition on metric potential . To obtain deterministic model, we have considered physically plausible relations like , and the generalized Chaplygin gas is described by equation of state . A new set of exact solutions of Einstein’s field equations has been obtained in Eckart theory, truncated theory and full causal theory. Physical behavior of the models has been discussed.
文摘In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.
文摘In this paper, we have studied the generalized chaplygin gas of interacting dark energy to ob-tain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological model. For negative value of B in equation of state of generalized chaplygin gas, we see that γ effΛ<-1 , that corresponds to a universe dominated by phantom dark energy.
基金supported by the project grant of Goverment of West Bengal,Department of Higher Education,Science and Technology and Biotechnology(File No:–ST/P/S&T/16G–19/2017)Goverment of West Bengal,Department of Higher Education,Science and Technology and Biotechnology for non-NET fellowship
文摘We consider the most general static spherically symmetric black hole metric. The accretion of the fluid flow around the Van der Waal's black hole is investigated and we calculate the fluid's four-velocity, the critical point and the speed of sound during the accretion process. We also analyze the nature of the universe's density and the mass of the black hole during accretion of the fluid flow. The density of the fluid flow is also taken into account. We observe that the mass is related to redshift. We compare the accreting power of the Van der Waal's black hole with Schwarzschild black hole for different accreting fluid.
基金Supported by the TianYuan Special Funds of the National Natural Science Foundation of China(Grant No.11226171)Discipline construction of equipment manufacturing system optimization calculation(Grant No.13XKJC01)
文摘In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypothesis that the initial data are of sufficiently small total variation, we prove that the difference between the solutions to these two systems can be bounded by the cube of the total variation of the initial perturbation.
文摘The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.
