EFFECTS OF POLYTROPIC EXPONENT ON DATA PROCESSING METHODS USED IN CONSTANT VOLUME DISCHARGE

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.

Stability Analysis of the Viscous Polytropic Dark Energy Model in Einstein Cosmology

The viscous polytropic gas model as one model of dark energy is hot-spot and keystone to the modern cosmology. We study the evolution of the viscous polytropic dark energy model interacting with the dark matter in the Einstein cosmology. Setting the autonomous dynamical system for the interacting viscous polytropic dark energy with dark matter and using the phase space analysis method to investigate the dynamical evolution and its critical stability, we find that the viscosity property of the dark energy creates a benefit for the stable critical dynamical evolution of the interaction model between dark matter and dark energy in the flat Friedmann-Robertson-Walker universe and the viscosity of dark energy will soften the coincidence problem just like the interacting dark energy model.

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

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）.

A New Differential Quadrature Methodology Based on Bernstein Polynomials for Solving the Equations Governing the Unsteady Flow of a Polytropic Gas

Aims of this paper are to improve ADI differential quadrature method （ADI-DQM） based on Bernstein polynomials and add a new application to the differential quadrature method. By using the new methodology, the numerical solutions of the governing equations of unsteady two-dimensional flow of a polytropic gas are investigated. The numerical results reveal that the new technique is very effective and gives high accuracy, good convergence and reasonable stability.

Gravitationally Quantized Orbits in the Solar System: Computations Based on the Global Polytropic Model

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.

Quasi-Radial Modes of Pulsating Neutron Stars: Numerical Results for General-Relativistic Rigidly Rotating Polytropic Models

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.

The Intrinsic Beauty of Polytropic Spheres in Reduced Variables

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=nth=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 .

Study of Polytropic Exponent Based on High Pressure Switching Expansion Reduction

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).

Case study of small scale polytropic index in the central plasma sheet

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.

Thermodynamic performance of Dual-Miller cycle(DMC) with polytropic processes based on power output, thermal efficiency and ecological function

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.

HARNACK ESTIMATES FOR WEAK SOLUTIONS OF EQUATIONS OF NON-NEWTONIAN POLYTROPIC FILTRATION

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.

BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS OF VISCOUS POLYTROPIC GAS EQUATIONS

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.

Spatial distribution of ion polytropic index joint-modulated by temperature anisotropy and MHD disturbances in the southern high latitude magnetosheath

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.

The Strong Solution for the Viscous Polytropic Fluids with Non-Newtonian Potential

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.

Relativistic polytropic models of charged anisotropic compact objects

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.

BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS OF VISCOUS POLYTROPIC GAS EQUATIONS

A piston problem of viscous polytropic 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.

Properties of the phase diagram from the Nambu-Jona-Lasino model with a scalar-vector interaction

We investigated the properties of the phase diagram of high-order susceptibilities,speed of sound,and polytropic index based on an extended Nambu-Jona-Lasinio model with an eight-quark scalar-vector interaction.Non-monotonic behavior was observed in all these quantities around the phase transition boundary,which also revealed the properties of the critical point.Further,this study indicated that the chiral phase transition boundary and critical point could vary depending on the scalarvector coupling constant G_(SV).At finite densities and temperatures,the negative G_(SV)term exhibited attractive interactions,which enhanced the critical point temperature and reduced the chemical potential.The G_(SV)term also affected the properties of the high-order susceptibilities,speed of sound,and polytropic index near the critical point.The non-monotonic(peak or dip)structures of these quantities shifted to a low baryon chemical potential(and high temperature)with a negative G_(SV).G_(SV)also changed the amplitude and range of the nonmonotonic regions.Therefore,the scalar-vector interaction was useful for locating the phase boundary and critical point in QCD phase diagram by comparing the experimental data.The study of the non-monotonic behavior of high-order susceptibilities,speed of sound,and polytropic index is of great interest,and further observations related to high-order susceptibilities,speed of sound,and polytropic index being found and applied to the search for critical points in heavy-ion collisions and the study of compact stars are eagerly awaited.

Stiffness Characteristics of a Basic Nonlinear Air Spring Model

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.

Polytropic gas cosmology and late-time acceleration

The accelerated expansion of the Universe has sparked significant interest in the mysterious concept of dark energy within cosmology.Various theories have been proposed to explain dark energy,and many models have been developed to understand its origins and properties.This research explores cosmic expansion using the Polytropic Gas(PG)approach,which combines Dark Matter(DM)and Dark Energy(DE)into a single mysterious fluid.We used the principles of general relativity and built our model within the homogeneous and isotropic framework of Friedmann-Lemaître-Robertson-Walker(FLRW)spacetime.We revised the Original Polytropic Gas(OPG)model to expand its applicability beyond the OPG,to theΛCDM model.Our model's parameters were carefully adjusted to reflect key cosmological features of the variable PG approach.To validate our model,we performed a Markov chain Monte Carlo analysis using recent Supernova data from the Pantheon+survey,36 observational data points,162 Gamma-Ray Bursts,and 24 binned Quasars distance modulus data.The AIC and BIC criteria indicate that our model is slightly preferred over theΛCDM model based on observational data.We also tested our model with data,Supernova,Gamma-Ray Bursts,and Quasars and found that it exhibits a transition from a quintessential to phantom regime.The Polytropic dark fluid model(PDFM)is a promising candidate that effectively addresses the interplay between cosmic acceleration and dark energy.

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

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.