This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced...This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced with two polytropic processes in order to more accurately reflect the practical working performance. The heat transfer loss is taken into account. The expressions of power output, thermal efficiency, entropy generation rate(EGR) and ecological function are addressed using finite-time thermodynamic theory. Through numerical calculations, the influences of compression ratio, cut-off ratio and polytropic exponent on the performance are thermodynamically analyzed. The model can be simplified to other cycle models under specific conditions, which means the results have an certain universality and may be helpful in the design of practical heat engines. It is shown that the entropy generation minimization does not always lead to the best system performance.展开更多
This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic p...This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.展开更多
This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn i...This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ(4) H(i) (i = 1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i) (i = 1.2.4) is established.展开更多
In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components....In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components. Three data processing principles are first introduced, and then the discharge pressure data obtained from the measured solenoid valve are processed to obtain the sonic conductance with three methods: the partial polytropic exponent method, the complete polytropic exponent method and the adiabatic method. By comparison of the obtained results it indicates that the complete polytropic exponent method is the most accurate. However, the partial polytropic exponent method is of a high applicable value, because it is easy and simple to measure and the obtained results are relatively accurate.展开更多
Munitions contain casings that consume explosive energy.The blast load(e.g.,peak overpressure and maximum impulse)intensity generated by ammunition explosion will be lower than that generated by a bare charge with equ...Munitions contain casings that consume explosive energy.The blast load(e.g.,peak overpressure and maximum impulse)intensity generated by ammunition explosion will be lower than that generated by a bare charge with equal mass.To evaluate the blast load of a cased charge under different conditions,the equivalent bare mass needs to be calculated.However,the accuracy of existing correlations strongly depends on the empirical determination of relevant controlling parameters and lacks theoretical clarification.In this paper,new correlations are proposed based on a more rigorous theoretical derivation,considering both the mechanical behaviors of the casing’s material and the change of the polytropic exponent during the expansion process of the explosion products.The controlling parameters are attributed to the rupture radius ratio and the polytropic exponent of detonation products expansion to casing rupture state.The reasonability is validated by both comprehensive numerical simulations with dynamic mechanical constitutive model and theoretical derivations.The results calculated by the new correlation show better agreement with the experimental results than those calculated by previous correlations,and the results difference is explained in more consistency with the thermos-physical properties of the charge and mechanical behaviors of casing material.Furthermore,the correlation of the cased-to-bare impulse ratio is also theoretically improved,providing a more accurate theoretical basis for both the equivalent bare mass and impulse evaluation for a cased charge.展开更多
In this paper,we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity(GR).To obt...In this paper,we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity(GR).To obtain these solutions,we employed the Finch-Skea spacetime,along with a generalized polytropic equation of state( EoS).We constructed various models of generalized polytropes by assuming different values of the polytropic index,i.e.,η=1/2,2/3,1,and 2.Next,numerous physical characteristics of these considered models were studied via graphical analysis,and they were found to obey all the essential conditions for astrophysical compact objects.Furthermore,such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear,quadratic,and polytropic EoS.展开更多
We reach a thermodynamic interpretation of the CODET model and its accurate electron density and temperature prediction, grounded on the physics of hydro magnetism in global equilibrium. The thermodynamic interpretati...We reach a thermodynamic interpretation of the CODET model and its accurate electron density and temperature prediction, grounded on the physics of hydro magnetism in global equilibrium. The thermodynamic interpretation finds consistency with the model of a magneto-matter medium possessing a 3-D Langmuir structure. That medium is diamagnetic in the context of ideal magnetohydrodynamic (MHD). It is shown that this magneto-matter has unusual characteristics consistent with assuming that the low quiescent solar corona possesses a nature-state, non yet studied. It is further noticed that this is wholly consistent with the CODET model prediction of a polytropic anomalous index for the electron gas of the Sun’s corona. Constitutive properties are derived from this novel state of nature, like magnetic permeability properties and non-dispersive acoustic speed. This non-dispersive acoustic speed is also expected to predict the observed equilibration time for the 1.1 to 1.3R<sub>⊙</sub> quiescent corona during the solar minimum from 2008 to 2009.展开更多
A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,the...A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.展开更多
Switching expansion reduction(SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics.The experiments indicate that the simulation model well predicts the actual chara...Switching expansion reduction(SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics.The experiments indicate that the simulation model well predicts the actual characteristics.The heat transfers and polytropic exponents of the air in expansion tank and supply tanks of SER have been studied on the basis of the experiments and the simulation model.Through the mathematical reasoning in this paper,the polytropic exponent can be calculated by the air mass,heat,and work exchanges of the pneumatic container.For the air in a constant volume tank,when the heat-absorption is large enough to raise air temperature in discharging process,the polytropic exponent is less than 1;when the air is experiencing a discharging and heat-releasing process,the polytropic exponent exceeds the specific heat ratio(the value of 1.4).展开更多
The concept of reduced variables is revisited with regard to van der Waals’ theory and an application is made to polytropic spheres, where the reduced radial coordinate is , R radius, and the reduced density is , cen...The concept of reduced variables is revisited with regard to van der Waals’ theory and an application is made to polytropic spheres, where the reduced radial coordinate is , R radius, and the reduced density is , central density. Reduced density profiles are plotted for several polytropic indexes within the range, 0≤n≤5, disclosing two noticeable features. First, any point of coordinates, (w, v), 0≤w≤1, 0≤v≤1, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at n=n<sub>th</sub>=0.888715. Reduced pressure profiles,, central pressure, Lane-Emden fucntions, , and polytropic curves, q=q(v), are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction,. The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range, 1/2≤n≤5 .展开更多
The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence...The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.展开更多
In this paper, we have made an investigation on a stellar model with Kramer’s Opacity and negligible abundance of heavy elements. We have determined the structure of a star with mass , i.e. the physical variables lik...In this paper, we have made an investigation on a stellar model with Kramer’s Opacity and negligible abundance of heavy elements. We have determined the structure of a star with mass , i.e. the physical variables like pressure, density, temperature and luminosity at different interior points of the star. We have discussed about some equations of structure, mechanism of energy production in a star and energy transports in stellar interior in a star and then we have solved radiative envelope and convective core by the matching or fitting point method and Runge-Kutta method by C Programming language. In future, it will help us to know about the characteristics of new stars.展开更多
In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlo...In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743).展开更多
In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of ~10 km and mass between ~1.4 and 3.2 solar mas...In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of ~10 km and mass between ~1.4 and 3.2 solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.展开更多
The so-called “global polytropic model” is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet’s system of statellites (like the Jovian system), described by the Lane-Emden diff...The so-called “global polytropic model” is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet’s system of statellites (like the Jovian system), described by the Lane-Emden differential equation. A polytropic sphere of polytropic index?n?and radius?R1?represents the central component?S1?(Sun or planet) of a polytropic configuration with further components the polytropic spherical shells?S2,?S3,?..., defined by the pairs of radi (R1,?R2), (R2,?R3),?..., respectively.?R1,?R2,?R3,?..., are the roots of the real part Re(θ) of the complex Lane-Emden function?θ. Each polytropic shell is assumed to be an appropriate place for a planet, or a planet’s satellite, to be “born” and “live”. This scenario has been studied numerically for the cases of the solar and the Jovian systems. In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code DCRKF54 (modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane along complex paths). We include in our numerical study some trans-Neptunian objects.展开更多
Thermal characteristic of cavitation has great influence on the process of occurrence,development and collapse of bubble in hydraulic system. By choosing the stage of bubble growth as the research object,combining wit...Thermal characteristic of cavitation has great influence on the process of occurrence,development and collapse of bubble in hydraulic system. By choosing the stage of bubble growth as the research object,combining with the characteristic of the process of bubble occurrence and development in hydraulic system, and ignoring the impact of thermal radiation,the heat transfer situation of bubble growth was analyzed under appropriate assumptions of thermodynamic conditions in the bubble generation and development process. The mathematical expression of the temperature change of bubble was deduced using thermodynamic principle. Through combining the expression with classic Rayleigh-Plesset Equation,numerical calculation was carried out and the temperature variation over time( or bubble radius) was obtained. The influences of convective heat transfer coefficient of bubble and polytropic exponent on the thermodynamic process of bubble were analyzed. Finally,the thermal characteristic of bubble growth after cavitation occurrence was summarized.展开更多
We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations,...We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations, required within the framework of Hartle’s perturbation method, in the complex plane. We give emphasis on computing corrections up to third order in the angular velocity, and the mass-shedding limit. We also compute the angular momentum, moment of inertia, rotational kinetic energy, and gravitational potential energy of the models considered.展开更多
An intrinsic Harnack estimate and some sup-estimates are established for nonnegative weak solutions of equations of non-Newtonian polytropic filtration ut -div(|Dum |p-2Dum) =0, m(p- 1) < 1, m>0, p> 1.
Using the Cluster data from 2001 to 2010, we studied spatial distribution of effective ion polytropic index in the southern high latitude magnetosheath, and joint-modulation of ion polytropic index by temperature anis...Using the Cluster data from 2001 to 2010, we studied spatial distribution of effective ion polytropic index in the southern high latitude magnetosheath, and joint-modulation of ion polytropic index by temperature anisotropy and MHD disturbances. The magnetosheath ions generally experience various polytropic processes with different polytropic index. The median polytropic indexes of magnetosheath ions in the GSE X-Y plane decrease toward the bow shock. Near the magnetopause, the median polytropic indexes are basically between isothermal and adiabatic except in the duskside flank close to the terminator. The analysis of correlation coefficient of perturbed ion number density with parallel magnetic field CC_δnδB_‖ and ion temperature anisotropy parameter A_T, indicates that the dominant MHD disturbance near magnetopause is slow mode with larger ion temperature anisotropy, and there are various modes of MHD disturbances with insignificant ion temperature anisotropy near the bow shock.The polytropic index modulated by slow mode disturbances is generally larger than that modulated by fast mode disturbances, and the larger ion temperature anisotropy, the larger polytropic index. The median polytropic indexes modulated jointly by slow mode disturbances and the strong ion temperature anisotropy can be larger than 1.0, while those modulated by fast mode disturbances and weak temperature anisotropy can be even possibly close to zero. Moreover, because of pronounced dusk-favored asymmetry of ion temperature anisotropy, the median polytropic index in the dawnside flank of the magnetosheath near the terminator is smaller than that in the duskside flank of the magnetosheath. The good correspondence between the distributions of median polytropic indexes and ion temperature anisotropy and MHD disturbances indicates that the ion temperature anisotropy and MHD disturbances determine the distribution of the polytropic index in the magnetosheath.展开更多
This paper studies the effective polytropic index in the central plasma sheet (CPS) by using the method of Kartalev et al. (2006), which adopts the denoising technique of Haar wavelet to identify the homogeneous M...This paper studies the effective polytropic index in the central plasma sheet (CPS) by using the method of Kartalev et al. (2006), which adopts the denoising technique of Haar wavelet to identify the homogeneous MHD Bernoulli integral (MBI) and has been frequently used to study the polytropic relation in the solar wind. We chose the quiet CPS crossing by Cluster C1 during the interval 08:51:00-09:19:00 UT on 03 August 2001. In the central plasma sheet, thermal pressure energy per unit mass is the most important part in MBI, and kinetic energy of fluid motion and electromagnetic energy per unit mass are less important. In the MBI, there are many peaks, which correspond to isothermal or near isothermal processes. The interval lengths of homogenous MBI regions are generally less than 1 min. The polytropic indexes are calculated by linearly fitting the data of lnp and Inn within a 16 s window, which is shifted forward by 8 s step length. Those polytropic indexes with IRI ≥0.8 (R is the correlation coefficient between lnp and inn) and p-value≤0.1 in the homogeneous regions are almost all in the range of [0, 1]. The mean and median effective polytropic indexes with high R and low p-value in homogeneous regions are 0.34 and 0.32 respectively, which are much different from the polytropic index obtained by traditional method (αtrad=-0.15). This result indicates that the CPS is not uniform even during quiet time and the blanket applications of polytropic law to plasma sheet may return misleading value of polytropic index. The polytropic indexes in homogeneous regions with a high correlation coefficient basically have good regression significance and are thus credible. These results are very important to understand the energy transport in magnetotail in the MHD frame.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51576207)
文摘This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced with two polytropic processes in order to more accurately reflect the practical working performance. The heat transfer loss is taken into account. The expressions of power output, thermal efficiency, entropy generation rate(EGR) and ecological function are addressed using finite-time thermodynamic theory. Through numerical calculations, the influences of compression ratio, cut-off ratio and polytropic exponent on the performance are thermodynamically analyzed. The model can be simplified to other cycle models under specific conditions, which means the results have an certain universality and may be helpful in the design of practical heat engines. It is shown that the entropy generation minimization does not always lead to the best system performance.
文摘This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.
基金supported in part by the NSF of China (10571024,10871040)the grant of Prominent Youth of Henan Province of China (0412000100)
文摘This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ(4) H(i) (i = 1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i) (i = 1.2.4) is established.
文摘In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components. Three data processing principles are first introduced, and then the discharge pressure data obtained from the measured solenoid valve are processed to obtain the sonic conductance with three methods: the partial polytropic exponent method, the complete polytropic exponent method and the adiabatic method. By comparison of the obtained results it indicates that the complete polytropic exponent method is the most accurate. However, the partial polytropic exponent method is of a high applicable value, because it is easy and simple to measure and the obtained results are relatively accurate.
文摘Munitions contain casings that consume explosive energy.The blast load(e.g.,peak overpressure and maximum impulse)intensity generated by ammunition explosion will be lower than that generated by a bare charge with equal mass.To evaluate the blast load of a cased charge under different conditions,the equivalent bare mass needs to be calculated.However,the accuracy of existing correlations strongly depends on the empirical determination of relevant controlling parameters and lacks theoretical clarification.In this paper,new correlations are proposed based on a more rigorous theoretical derivation,considering both the mechanical behaviors of the casing’s material and the change of the polytropic exponent during the expansion process of the explosion products.The controlling parameters are attributed to the rupture radius ratio and the polytropic exponent of detonation products expansion to casing rupture state.The reasonability is validated by both comprehensive numerical simulations with dynamic mechanical constitutive model and theoretical derivations.The results calculated by the new correlation show better agreement with the experimental results than those calculated by previous correlations,and the results difference is explained in more consistency with the thermos-physical properties of the charge and mechanical behaviors of casing material.Furthermore,the correlation of the cased-to-bare impulse ratio is also theoretically improved,providing a more accurate theoretical basis for both the equivalent bare mass and impulse evaluation for a cased charge.
文摘In this paper,we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity(GR).To obtain these solutions,we employed the Finch-Skea spacetime,along with a generalized polytropic equation of state( EoS).We constructed various models of generalized polytropes by assuming different values of the polytropic index,i.e.,η=1/2,2/3,1,and 2.Next,numerous physical characteristics of these considered models were studied via graphical analysis,and they were found to obey all the essential conditions for astrophysical compact objects.Furthermore,such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear,quadratic,and polytropic EoS.
文摘We reach a thermodynamic interpretation of the CODET model and its accurate electron density and temperature prediction, grounded on the physics of hydro magnetism in global equilibrium. The thermodynamic interpretation finds consistency with the model of a magneto-matter medium possessing a 3-D Langmuir structure. That medium is diamagnetic in the context of ideal magnetohydrodynamic (MHD). It is shown that this magneto-matter has unusual characteristics consistent with assuming that the low quiescent solar corona possesses a nature-state, non yet studied. It is further noticed that this is wholly consistent with the CODET model prediction of a polytropic anomalous index for the electron gas of the Sun’s corona. Constitutive properties are derived from this novel state of nature, like magnetic permeability properties and non-dispersive acoustic speed. This non-dispersive acoustic speed is also expected to predict the observed equilibration time for the 1.1 to 1.3R<sub>⊙</sub> quiescent corona during the solar minimum from 2008 to 2009.
文摘A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.
基金supported by the National Natural Science Foundation of China (No.50575202)
文摘Switching expansion reduction(SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics.The experiments indicate that the simulation model well predicts the actual characteristics.The heat transfers and polytropic exponents of the air in expansion tank and supply tanks of SER have been studied on the basis of the experiments and the simulation model.Through the mathematical reasoning in this paper,the polytropic exponent can be calculated by the air mass,heat,and work exchanges of the pneumatic container.For the air in a constant volume tank,when the heat-absorption is large enough to raise air temperature in discharging process,the polytropic exponent is less than 1;when the air is experiencing a discharging and heat-releasing process,the polytropic exponent exceeds the specific heat ratio(the value of 1.4).
文摘The concept of reduced variables is revisited with regard to van der Waals’ theory and an application is made to polytropic spheres, where the reduced radial coordinate is , R radius, and the reduced density is , central density. Reduced density profiles are plotted for several polytropic indexes within the range, 0≤n≤5, disclosing two noticeable features. First, any point of coordinates, (w, v), 0≤w≤1, 0≤v≤1, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at n=n<sub>th</sub>=0.888715. Reduced pressure profiles,, central pressure, Lane-Emden fucntions, , and polytropic curves, q=q(v), are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction,. The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range, 1/2≤n≤5 .
文摘The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.
文摘In this paper, we have made an investigation on a stellar model with Kramer’s Opacity and negligible abundance of heavy elements. We have determined the structure of a star with mass , i.e. the physical variables like pressure, density, temperature and luminosity at different interior points of the star. We have discussed about some equations of structure, mechanism of energy production in a star and energy transports in stellar interior in a star and then we have solved radiative envelope and convective core by the matching or fitting point method and Runge-Kutta method by C Programming language. In future, it will help us to know about the characteristics of new stars.
基金supported by NSFC(11271154,11401252)Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education,the 985 program of Jilin University+1 种基金Fundamental Research Funds of Jilin University(450060501179)supported by Graduate Innovation Fund of Jilin University(2014084)
文摘In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743).
文摘In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of ~10 km and mass between ~1.4 and 3.2 solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.
文摘The so-called “global polytropic model” is based on the assumption of hydrostatic equilibrium for the solar system, or for a planet’s system of statellites (like the Jovian system), described by the Lane-Emden differential equation. A polytropic sphere of polytropic index?n?and radius?R1?represents the central component?S1?(Sun or planet) of a polytropic configuration with further components the polytropic spherical shells?S2,?S3,?..., defined by the pairs of radi (R1,?R2), (R2,?R3),?..., respectively.?R1,?R2,?R3,?..., are the roots of the real part Re(θ) of the complex Lane-Emden function?θ. Each polytropic shell is assumed to be an appropriate place for a planet, or a planet’s satellite, to be “born” and “live”. This scenario has been studied numerically for the cases of the solar and the Jovian systems. In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code DCRKF54 (modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane along complex paths). We include in our numerical study some trans-Neptunian objects.
基金National Natural Science Foundation of China(No.51275123)
文摘Thermal characteristic of cavitation has great influence on the process of occurrence,development and collapse of bubble in hydraulic system. By choosing the stage of bubble growth as the research object,combining with the characteristic of the process of bubble occurrence and development in hydraulic system, and ignoring the impact of thermal radiation,the heat transfer situation of bubble growth was analyzed under appropriate assumptions of thermodynamic conditions in the bubble generation and development process. The mathematical expression of the temperature change of bubble was deduced using thermodynamic principle. Through combining the expression with classic Rayleigh-Plesset Equation,numerical calculation was carried out and the temperature variation over time( or bubble radius) was obtained. The influences of convective heat transfer coefficient of bubble and polytropic exponent on the thermodynamic process of bubble were analyzed. Finally,the thermal characteristic of bubble growth after cavitation occurrence was summarized.
文摘We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations, required within the framework of Hartle’s perturbation method, in the complex plane. We give emphasis on computing corrections up to third order in the angular velocity, and the mass-shedding limit. We also compute the angular momentum, moment of inertia, rotational kinetic energy, and gravitational potential energy of the models considered.
基金Project supported by the National Natural Science Foundation of China (No.19771069).
文摘An intrinsic Harnack estimate and some sup-estimates are established for nonnegative weak solutions of equations of non-Newtonian polytropic filtration ut -div(|Dum |p-2Dum) =0, m(p- 1) < 1, m>0, p> 1.
基金supported by the National Natural Science Foundation of China(Grant Nos.41431071,41504127,and 41474124)
文摘Using the Cluster data from 2001 to 2010, we studied spatial distribution of effective ion polytropic index in the southern high latitude magnetosheath, and joint-modulation of ion polytropic index by temperature anisotropy and MHD disturbances. The magnetosheath ions generally experience various polytropic processes with different polytropic index. The median polytropic indexes of magnetosheath ions in the GSE X-Y plane decrease toward the bow shock. Near the magnetopause, the median polytropic indexes are basically between isothermal and adiabatic except in the duskside flank close to the terminator. The analysis of correlation coefficient of perturbed ion number density with parallel magnetic field CC_δnδB_‖ and ion temperature anisotropy parameter A_T, indicates that the dominant MHD disturbance near magnetopause is slow mode with larger ion temperature anisotropy, and there are various modes of MHD disturbances with insignificant ion temperature anisotropy near the bow shock.The polytropic index modulated by slow mode disturbances is generally larger than that modulated by fast mode disturbances, and the larger ion temperature anisotropy, the larger polytropic index. The median polytropic indexes modulated jointly by slow mode disturbances and the strong ion temperature anisotropy can be larger than 1.0, while those modulated by fast mode disturbances and weak temperature anisotropy can be even possibly close to zero. Moreover, because of pronounced dusk-favored asymmetry of ion temperature anisotropy, the median polytropic index in the dawnside flank of the magnetosheath near the terminator is smaller than that in the duskside flank of the magnetosheath. The good correspondence between the distributions of median polytropic indexes and ion temperature anisotropy and MHD disturbances indicates that the ion temperature anisotropy and MHD disturbances determine the distribution of the polytropic index in the magnetosheath.
基金supported by the National Natural Science Foundation of China(Grant Nos.41431071,41174141,41474124)the National Basic Research Program of China(Grant No.2011CB811404)
文摘This paper studies the effective polytropic index in the central plasma sheet (CPS) by using the method of Kartalev et al. (2006), which adopts the denoising technique of Haar wavelet to identify the homogeneous MHD Bernoulli integral (MBI) and has been frequently used to study the polytropic relation in the solar wind. We chose the quiet CPS crossing by Cluster C1 during the interval 08:51:00-09:19:00 UT on 03 August 2001. In the central plasma sheet, thermal pressure energy per unit mass is the most important part in MBI, and kinetic energy of fluid motion and electromagnetic energy per unit mass are less important. In the MBI, there are many peaks, which correspond to isothermal or near isothermal processes. The interval lengths of homogenous MBI regions are generally less than 1 min. The polytropic indexes are calculated by linearly fitting the data of lnp and Inn within a 16 s window, which is shifted forward by 8 s step length. Those polytropic indexes with IRI ≥0.8 (R is the correlation coefficient between lnp and inn) and p-value≤0.1 in the homogeneous regions are almost all in the range of [0, 1]. The mean and median effective polytropic indexes with high R and low p-value in homogeneous regions are 0.34 and 0.32 respectively, which are much different from the polytropic index obtained by traditional method (αtrad=-0.15). This result indicates that the CPS is not uniform even during quiet time and the blanket applications of polytropic law to plasma sheet may return misleading value of polytropic index. The polytropic indexes in homogeneous regions with a high correlation coefficient basically have good regression significance and are thus credible. These results are very important to understand the energy transport in magnetotail in the MHD frame.