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We consider the nonstationary shear flow of a compressible viscous and heat-conducting micropolar fluid between two parallel plates that present solid thermoinsulated walls, whereby the lower plate is fixed and the upper one is moving irrotationally. We assume that the fluid is perfect and polytropic in the thermodynamical sense, as well as that the initial density and temperature are strictly positive.We take smooth initial functions and analyze the corresponding problem with non- homogeneous boundary data for velocity and homogeneous boundary data for microrotation and heat flux. In this work we give the overview of the current progress in mathematical analysis of the described problem with particular emphasis on the existence theorems and the uniqueness of the solution.

We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of General Relativity and from their metric $f(R)$ counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need not to. We illustrate the relevance of these conditions by considering the properties of stellar surfaces in polytropic models, showing that the range of equations of state with potentially pathological effects is shifted beyond the domain of physical interest. This confirms, in particular, that neutron stars and white dwarfs can be safely modelled within the Palatini $f(R)$ framework., 7 pages; some additions in conclusions and references' list. Version accepted for publication on Class. Quant. Grav

Explaining the initial mass function (IMF) of stars is a long-standing problem in astrophysics. The number of complex mechanisms involved in the process of star cluster formation, such as turbulence, magnetic fields and stellar feedback, make understanding and modeling the IMF a challenging task. In this paper, we aim to assert the importance of stellar heating feedback in the star cluster formation process and its effect on the shape of the IMF. We use an analytical sub-grid model to implement the radiative feedback in fully three-dimensional magnetohydrodynamical (MHD) simulations of star cluster formation, with the ultimate objective of obtaining numerical convergence on the IMF. We compare a set of MHD adaptive-mesh-refinement (AMR) simulations with three different implementations of the heating of the gas: 1) a polytropic equation of state (EOS), 2) a spherically symmetric stellar heating feedback, and 3) our newly developed polar heating model that takes into account the geometry of the accretion disc and the resulting shielding of stellar radiation by dust. For each of the three heating models, we analyse the distribution of stellar masses formed in ten molecular cloud simulations with different realizations of the turbulence to obtain a statistically representative IMF. We conclude that stellar heating feedback has a profound influence on the number of stars formed and plays a crucial role in controlling the IMF. We find that the simulations with the polar heating model achieve the best convergence on the observed IMF., Comment: 10 pages, 5 figures, 1 table; added references, published in MNRAS

In this manuscript, new classes of polytropic models have been developed by using polytropic equation of state (PEoS) for spherically symmetric gravitating sources in isotropic coordinates. The inner fluid configuration is charged anisotropic and models are developed for different values of polytropic index $$n=1,~\frac{1}{2},~2,~\frac{2}{3}$$. Mass and radii of eight stars 4U 1820-30, Cen X-3, EXO 1785-248, SMC X-4, LMC X-4, SAX J1808.4-3658, 4U 1538-52 and Her X-1 have been regained with the help of developed models. The stability of models is discussed by using speed of sound technique and graphical analysis of model parameters. It is concluded that all models are well behaved and physically acceptable.

We study compact mixed configurations with a nontrivial wormholelike spacetime topology supported by a complex ghost scalar field with a quartic self-interaction and a polytropic fluid. The latter is modeled by a relativistic barotropic equation of state that can approximately describe more or less realistic matter. For such systems, we find regular asymptotically flat equilibrium solutions describing localized configurations in which the fluid is concentrated in a finite-size region. The solutions obtained describe double-throat wormholes which are located outside the fluid (one can say that the fluid is hidden inside the region between the throats). Also, we consider the dependence of the total mass of the system on the central density of the fluid and demonstrate the existence of critical values of the central density at which the mass diverges. In this case all regular solutions possessing finite masses lie in the region between these critical values, and this region also contains a discontinuity in magnitudes of the central density where only physically unacceptable oscillating solutions do exist. Is shown that for some values of the central density of the fluid there can exist solutions describing systems whose fluid density and pressure maxima lie not at the center. This results in the fact that such systems possess two equators (local maxima of the metric function) resided symmetrically with respect to the center.

In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass-radius relations, moments of inertia and other results of interest are obtained and compared with the ones for non-rotating stars.

Several earlier studies have attempted to estimate some of the thermodynamic properties of Coronal Mass Ejections (CMEs) either very close to the Sun or at 1 AU. In the present study, we attempt to extrapolate the internal thermodynamic properties of 2010 April 3 flux rope CME from near the Sun to 1 AU. For this purpose, we use the flux rope internal state (FRIS) model which is constrained by the kinematics of the CME. The kinematics of the CME is estimated using the \textit{STEREO}/COR and HI observations in combination with drag based model (DBM) of CME propagation. Using the FRIS model, we focus on estimating the polytropic index of the CME plasma, heating/cooling rate, entropy changing rate, Lorentz force and thermal pressure force acting inside the CME. Our study finds that the polytropic index of the selected CME ranges between 1.7 to 1.9. This implies that the CME is in the heat-releasing state (i.e., entropy loss) throughout its journey from the Sun to Earth. The hindering role of Lorentz force and contributing role of thermal pressure force in governing the expansion of the CME is also identified. On comparing the estimated properties of the CME flux rope from the FRIS model with the in situ observations of the CME taken at 1 AU, we find relevant discrepancies between the results predicted by the model and the observations. We outline the approximations made in our study of probing the internal state of the CME during its heliospheric evolution and discuss the possible causes of the observed discrepancies.

In this paper, we prove that the kappa distribution is the stationary solution of the Vlasov–Poisson system in an inhomogeneous plasma under the polytropic equation of state and an assumption restricting the local velocity distribution to a specific mathematical form. The profiles of density, temperature, and electric potential are obtained theoretically. The kappa index can be determined if the initial state is known. In order to verify the theory, particle-in-cell simulations are made and the results show excellent agreement with the theoretical predictions for density, temperature, and velocity distributions of electrons. It is shown that the electron velocity distribution of spatially inhomogeneous plasma evolves from an initial Maxwellian to the final kappa distribution. It is also found that the value of kappa index in the final stationary state depends on the initial state of plasma.

Short gamma-ray bursts are thought to result from the mergers of two neutron stars or a neutron star and stellar mass black hole. The final stages of the merger are generally accompanied by the production of one or more tidal "tails" of ejecta, which fall back onto the remnant-disc system at late times. Using the results of a linear stability analysis, we show that if the material comprising these tails is modeled as adiabatic and the effective adiabatic index satisfies $\gamma \ge 5/3$, then the tails are gravitationally unstable and collapse to form small-scale knots. We analytically estimate the properties of these knots, including their spacing along the tidal tail and the total number produced, and their effect on the mass return rate to the merger remnant. We perform hydrodynamical simulations of the disruption of a polytropic (with the polytropic and adiabatic indices $\gamma$ equal), $\gamma =2$ neutron star by a black hole, and find agreement between the predictions of the linear stability analysis and the distribution of knots that collapse out of the instability. The return of these knots to the black hole induces variability in the fallback rate, which can manifest as variability in the lightcurve of the GRB and -- depending on how rapidly the instability operates -- the prompt emission. The late-time variability induced by the return of these knots is also consistent with the extended emission observed in some GRBs., Comment: Small corrections, additional references included to reflect ApJL published version

In this work we study how the small contribution of the inner crust to the total equation of state (EoS) of a neutron star affects its mass-radius relation, focusing on the canonical mass of 1.4$M_\odot$. We build empirical EoS of the kind - $p = K\epsilon^{\gamma} + b$ - in the range of 0.003 fm$^{-3}~, Comment: letter, Published version

We consider nonstationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid which is in the thermodynamical sense perfect and polytropic. In the first part of the work we present corresponding initial-boundary value problems whereby we allow non-homogeneous boundary conditions for velocity, microrotation or temperature. In the second part of the work we present existence results for described problems under the additional assumption that the initial density and initial temperature are strictly positive.

Various theoretical arguments motivate an expectation of a phase transition in matter at extreme densities above nuclear density, accompanied by hopes that gravitational wave observations may reveal the properties of such a transition. Instead of adopting a particular theory, we consider here a generic form of first order phase transition using a piecewise polytropic equation of state, and evolve both isolated neutron stars and neutron star binaries, including unequal mass binaries and, in some cases, magnetic field, looking at dynamical effects. Of particular interest are effects that may be observable either via gravitational waves or electromagnetic observations., Comment: 10 pages, 12 figures; Updated with accepted version which includes updates to the text, a new figure, and rearrangement of certain existing figures

The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state and consequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of the field variables, called hyperbolicity region. The goal of this paper is first to determine the differential system with 14 fields for a rarefied polyatomic polytropic gas, approximated at the second-order in the non-equilibrium variables. Then, we investigate and compare the hyperbolicity property of the first-order and second-order systems. In particular, we analyze the role played by the dynamic pressure and the molecular degrees of freedom. Finally, we also show that in the monatomic singular limit the quadratic theory for a polyatomic gas converges to the corresponding quadratic theory for a monatomic gas.

We combine different measurements of the polytropic index of the proton plasma in the heliosphere: i) near-adiabatic index in the inner heliosphere ~1AU, ii) subadiabatic indices in the outer heliosphere ~20-40AU, and iii) near-zero indices in the inner heliosheath. These observations are unified by a single theoretical model of the polytropic index throughout its radial extent in the heliosphere; the corresponding fitting reveals the decreasing trend of the polytropic index with increasing heliocentric distance R. We anticipate that with increasing R, (i) the Debye length and mean-free-path decreases; (ii) the Landau damping is less effective, transferring thus less wave energy to particles; and (iii) the collisionality degree increases, indicating that the proton plasma in the inner heliosheath might be collisionless., Comment: 5 pages, 1 figure; to appear in RNAAS

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a computational approach to solve the problems related to fractional Lane-Emden differential equations based on neural networks. Such a solution will help solve the fractional polytropic gas spheres problems which have different applications in physics, astrophysics, engineering, and several real-life issues. We used Artificial Neural Network (ANN) framework in its feedforward back propagation learning scheme. The efficiency and accuracy of the presented algorithm are checked by testing it on four fractional Lane-Emden equations and compared with the exact solutions for the polytopic indices n=0,1,5 and those of the series expansions for the polytropic index n=3. The results we obtained prove that using the ANN method is feasible, accurate, and may outperform other methods., Comment: 29 pages, 11 pages, 5 tables

We present equilibrium sequences of rotating relativistic stars, constructed with a new rotation law that was proposed by Uryu et al. (2017). We choose rotational parameters motivated by simulations of binary neutron star merger remnants, but otherwise adopt a cold, relativistic N=1 polytropic EOS, in order to perform a detailed comparison to published equilibrium sequences that used the Komatsu, Eriguchi and Hachisu (1989) rotation law. We find a small influence of the choice of rotation law on the mass of the equilibrium models and a somewhat larger influence on their radius. The versatility of the new rotation law allows us to construct models that have a similar rotational profile and axis ratio as observed for merger remnants, while at the same time being quasi-spherical. More specifically, we construct equilibrium sequence variations with different degrees of differential rotation and identify type A and type C solutions, similar to the corresponding types in the classification of Ansorg, Gondek-Rosinska and Villain (2009). While our models are highly accurate solutions of the fully general relativistic structure equations, we demonstrate that for models relevant to merger remnants the IWM-CFC approximation still maintains an acceptable accuracy., Comment: [v1]:14 pages, 10 figures, [v2]: 18 pages, 12 figures (extra results added), [v3]: typos corrected, accepted for publication in MNRAS

We complete the stability study of general relativistic spherically symmetric polytropic perfect fluid spheres, concentrating attention to the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm-Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5, and the relativistic parameter {\sigma} given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter {\sigma}. For the dynamical approach we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of {\sigma}. We found that all the configurations having trapped null geodesics are unstable according to both methods., Comment: 20 pages, 18 figures. Accepted manuscript to appear in IJMPD

A tidal disruption event (TDE) occurs when a star passes too close to a supermassive black hole and gets torn apart by its gravitational tidal field. After the disruption, the stellar debris form an expanding gaseous stream. The morphology and evolution of this stream is particularly interesting as it ultimately determines the observational properties of the event itself. In this work we perform 3D hydrodynamical simulations of the TDE of a star modelled as a polytropic sphere of index {\gamma} = 5/3, and study the gravitational stability of the resulting gas stream. We provide an analytical solution for the evolution of the stream in the bound, unbound and marginally bound case, that allows us to describe the stream properties and analyse the time-scales of the physical processes involved, applying a formalism developed in star formation context. Our results are that, when fragmentation occurs, it is fueled by the failure of pressure in supporting the gas against its self-gravity. We also show that a stability criterion that includes also the stream gas pressure proves to be far more accurate than one that only considers the black hole tidal forces, giving analytical predictions of the time evolution of the various forces associated to the stream. Our results point out that fragmentation occurs on timescales longer compared with the observational windows of these events and is thus not expected to give rise to significant observational features., Comment: 12 pages,15 figures, accepted for publication in MNRAS

We study self-gravitating stars in the bootstrapped Newtonian picture for polytropic equations of state. We consider stars that span a wide range of compactness values. Both matter density and pressure are sources of the gravitational potential. Numerical solutions show that the density profiles can be well approximated by Gaussian functions. Later we assume Gaussian density profiles to investigate the interplay between the compactness of the source, the width of the Gaussian density profile and the polytropic index. We also dedicate a section to comparing the pressure and density profiles of the bootstrapped Newtonian stars to the corresponding General Relativistic solutions. We also point out that no Buchdahl limit is found, which means that the pressure can in principle support a star of arbitrarily large compactness. In fact, we find solutions representing polytropic stars with compactness above the Buchdhal limit., 21 pages, 10 figures

The star rotation will undoubtedly affect the star's characteristics described by the hydrostatic equilibrium equation. The centrifugal force distorts the star's shape and modifies its equilibrium structure. The choice of the gravity model such as Eddington inspired Born Infeld theory of gravity will also affect the geometry properties of stars. In this case, it will change the corresponding Poisson's equations. So it is desirable to see the modification of hydrostatic equation of states of the non-relativistic rotating stellar object within Eddington inspired Born Infeld theory of gravity. Lane-Emden equations have been used to describe the mass-density distribution in the stars of polytropic equation state of the stars with and without rotation [4]. In this paper, we would like to derive analytically and numerically the modified Lame-Emden equations for rotating non-relativistic stars within Eddington inspired Born Infeld theory of gravity. In this study Eddington inspired Born Infeld theory of gravity will give contribution to make the differences in the geometry and mass of the star.

Hydro-pneumatic suspension models built on the ideal-gas (IG) state equation or the traditional Benedict–Webb–Rubin (BWR) real-gas (RG) model cannot accurately predict the variation of gas pressure during suspension movement because the influence of gas hysteresis is ignored. This leads to incorrectly reflecting the properties of suspension and limiting the effect of control methods on the actual suspension system. In this study, the RG multivariate index model considering gas hysteresis is identified and applied. Based on this model, the output force of the suspension cylinder is deduced. Then, the general motion-force models of full-vehicle suspension are derived by applying a vector method based on a six suspension cylinders’ test platform. Further, the stiffness and damping property formulas under different working conditions are discussed. The model’s accuracy was verified through sinusoidal excitation tests on a full-vehicle test platform under different frequencies and amplitudes. The maximum discrepancy of gas pressure between prediction results and test data was 0.9%; whereas the maximum discrepancy of roll moment was 0.85%. The results indicate that the full-vehicle suspension models can accurately reflect the influence of gas hysteresis on the performance of a full-vehicle suspension system and be applied in confidence.

This paper is concerned with the stabilizing effect of the power law inflation on relativistic Eulerian fluids. We prove the global stability of the background solutions to the relativistic fluids including the isothermal gases and generalized Chaplygin gases by the method of conformal transformation when the initial data is a small perturbation to the background solution. We also prove the blowup phenomena of the relativistic Euler fluids including the isothermal gases and polytropic gases when the initial data satisfies suitable assumptions.

The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.

Shock revival in core-collapse supernovae (CCSNe) may be due to the neutrino mechanism. While it is known that in a neutrino-powered CCSN, explosion begins when the neutrino luminosity of the proto-neutron star exceeds a critical value, the physics of this condition in time-dependent, multidimensional simulations are not fully understood. \citet{Pejcha2012} found that an `antesonic condition' exists for time-steady spherically symmetric models, potentially giving a physical explanation for the critical curve observed in simulations. In this paper, we extend that analysis to time-dependent, spherically symmetric polytropic models. We verify the critical antesonic condition in our simulations, showing that models exceeding it drive transonic winds whereas models below it exhibit steady accretion. In addition, we find that (1) high spatial resolution is needed for accurate determination of the antesonic ratio and shock radius at the critical curve, and that low resolution simulations systematically underpredict these quantities, making explosion more difficult at lower resolution; (2) there is an important physical connection between the critical mass accretion rate at explosion and the mass loss rate of the post-explosion wind: the two are directly proportional at criticality, implying that, at criticality, the wind kinetic power is tied directly to the accretion power; (3) the value of the post-shock adiabatic index $\Gamma$ has a large effect on the length and time scales of the post-bounce evolution of the explosion larger values of $\Gamma$ result in a longer transition from the accretion to wind phases., Comment: 13 pages, 10 figures; corrected typos in arXiv metadata; updated to final published version

This paper contributes to modeling and supervision of multi-stage centrifugal compressors coping with real-gas processes and steady to highly transient operating conditions. A novel dynamic model is derived, and the incorporation of the generic Lee-Kesler-Pl\"ocker real-gas equation of state and its derivatives is presented. The model allows for embedding arbitrarily shaped performance maps, based on state-of-the-art polytropic change-of-state compressor characteristics. As the validity of these maps is a key issue for simulation and model-based monitoring, performance maps are treated as time-variant, and their shape is to be identified and monitored during operation. The proposed real-time map estimation scheme comprises an Unscented Kalman Filter and a newly proposed algorithm, referred to as Recursive Map Estimation. The combination yields a novel parameter and state estimator, which is expected to be superior if some parameters are characterized by a distinct operating point dependency. Two additional time-variant parameters are provided for monitoring: The first indicates the level of confidence in the local estimate, and the second points to drastic performance map alterations, which may be further exploited in fault detection. A modified reference simulation of a two-stage supercritical carbon dioxide compressor with known state trajectories, performance maps, and alterations demonstrates the successful application of the entire monitoring scheme, and serves for a discussion of the results., Comment: to be published in Journal of Process Control, Volume 85

In this paper, we study the asymptotic behavior of solution to the initial boundary value problem for the two-fluid non-isentropic Navier–Stokes–Poisson system in a half line ( 0 , ∞ ) . We consider an inflow problem where the gas enter into the region through the boundary for general gases including ideal polytropic gas. On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we show the existence of the stationary solutions with the aid of the center manifold theory, and then we give the rigorous proof of the stability theorem on the stationary solutions under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system. Note that it is the first result for the stability of nonlinear waves on the inflow problem of the Navier–Stokes–Poisson system.

For Euler equations describing a steady motion of an ideal polytropic gas, we consider the problem of a flow around a body with known surface in the class of twice continuously differentiable functions. We use approaches of the geometric method developed by the authors. In the first part of the paper, the problem of a flow around a given body is solved in a special class of flows for which the continuity equation holds identically. We show that the class of solutions is nonempty and obtain one exact solution. In the second part of the paper, we consider the general case of stationary flows of an ideal polytropic gas. The Euler equations are reduced to a system of ordinary differential equations, for which we obtain an exact solution for a given pressure on the body. Examples illustrating the properties of the obtained exact solutions are considered. It is shown that such solutions make it possible to find points of a smooth surface of a body where blowups or strong or weak discontinuities occur.

Very accurate second-order thermal models have been developed for the thermal simulation of Stirling engines in recent years. One of the last ones is the comprehensive polytropic model of Stirling engine called the CPMS model. The accuracy of the CPMS model was found to be sufficient for the nominal operation of a prototype Stirling engine known as the GPU-3 engine. Nevertheless, the accuracy of the CPMS model was drastically reduced at high rotational speeds of the engine. In this paper, power loss and pressure change due to the inertial force of the crank system were integrated into the CPMS thermal model in order to compensate inaccuracy of the CPMS model at high rotational speeds. Moreover, the effect of rotational speed on the gas temperature in heater and cooler was also incorporated. A precise model for evaluating the mechanical friction loss was also employed and compared with the simple frictional model of the simple frictional model used in the CPMS. The model was examined on the GPU-3 engine, and it was found that it has superior accuracy compared to the previous thermal model over the entire working regime of the GPU-3 engine.

A method is proposed for determining equilibrium structures and various physical parameters of differentially rotating polytropic models of stars, taking into account the effect of mass variation inside the star and on its equipotential surfaces. The law of differential rotation has been assumed to be the form of ω 2 ( s ) = b 1 + b 2 s 2 + b 3 s 4 . The proposed method utilizes the averaging approach of Kippenhahn and Thomas and concepts of Roche-equipotential to incorporate the effects of differential rotation on the equilibrium structures of polytropic stellar models. Mathematical expressions of determining the equipotential surfaces, volume, surface area and other physical parameters are also obtained under the effects of mass variation inside the stars. Some significant conclusions are also drawn.

The Lie algebras admitted by the dynamics equations of self-gravitating gas for an arbitrary equation of state and a polytropic gas are calculated. A spherically symmetric submodel is constructed for the case of a polytropic gas. The Lie algebras and the optimal system of subalgebras for a spherically symmetric submodel are computed. An invariant solution describing the steady motion is obtained.

The increasing demands for more accurate dynamic measurements of pressure in different industrial and scientific applications require the use of sensors with suitable dynamic characteristics. This paper discusses a development of a piston-in-cylinder primary standard for dynamic calibration of pressure sensors. The time-varying pressure generated by a piston-in-cylinder pressure generator can be traceable to measurements of the static pressure and length at the highest and the lowest pulsation frequencies, where the process can be considered as adiabatic and isothermal, respectively. The main limitation of such a dynamic pressure calibrator to provide SI-traceable dynamic calibrations in the transition frequency range of polytropic pulsations is the fact that the value of the polytropic index depends on the degree to which the heat transfers to the surroundings during the generation of the time-varying pressure. In order to investigate the polytropic index, which defines the ratio of the amplitude of the generated relative pressure change to the amplitude of the relative volume change of the gas in the piston-in-cylinder calibrator, the analytical solution in the frequency domain is presented. The analytical solution was derived on the basis of the lumped physical-mathematical model for the gas in the cylinder chamber of the piston-in-cylinder dynamic pressure calibrator. The experimentally obtained polytropic index for the built piston-in-cylinder calibrator confirms the results obtained from the analytical solution. The paper ends with an estimation of the measurement uncertainty related to the polytropic corrections and the time-varying pressure amplitude generated by the developed piston-in-cylinder calibrator.

We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small. The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.

We consider the initial-boundary value problem governing unsteady polytropic motions of viscous compressible multifluids. We prove the existence and uniqueness of a strong solution to the problem. Bibliography: 11 titles.

An inappropriate choice of isentropic efficiencies for the sizing of the component parts of monophasic ejectors is one of the greatest sources of error in their design. The present study shows that the replacement of isentropic efficiencies with polytropic efficiencies within 1D ejector models provides more accurate results. Polytropic efficiencies access more precisely the effects of the pressure ratio variation on the irreversibilities of the acceleration and deceleration processes. It is demonstrated that the deviation in the constant area duct length, calculated by using an isentropic efficiency from the real length is three times greater than the one calculated by using a polytropic efficiency. The polytropic efficiencies are extracted from the CFD modeling of two types of ejectors, a constant area mixing (CAM) ejector and a constant pressure mixing (CPM) ejector. A 1D thermodynamic model for CAM and CPM ejectors, based on the polytropic efficiency concept, is proposed and validated against experimental data. Parametric studies based on this model were completed. They reveal that the variation in polytropic efficiency of the primary nozzle has the most important impact on the constant area duct length. New empirical correlations to estimate the polytropic efficiencies are also provided.

We investigate and explore self-similar dynamic radial collapses of relativistic degenerate stellar cores (RDSCs) and radiation pressure dominated stellar interiors (RPDSIs) of spherical symmetry by invoking a conventional polytropic (CP) equation of state (EoS) with a constant polytropic index γ = 4 / 3 and by allowing free-fall non-zero RDSC or RPDSI surface mass density and pressure due to their sustained physical contact with the outer surrounding stellar envelopes also in contraction. Irrespective of the physical triggering mechanisms (including, e.g., photodissociation, electron-positron pair instability, general relativistic instability etc.) for initiating such a self-similar dynamically collapsing RDSC or RPDSI embedded within a massive star, a very massive star (VMS) or a supermassive star (SMS) in contraction and by comparing with the Schwarzschild radii associated with their corresponding RDSC/RPDSI masses, the emergence of central black holes in a wide mass range appears inevitable during such RDSC/RPDSI dynamic collapses inside massive stars, VMSs, and SMSs, respectively. Radial pulsations of progenitor cores or during a stellar core collapse may well leave imprints onto collapsing RDSCs/RPDSIs towards their self-similar dynamic evolution. Massive neutron stars may form during dynamic collapses of RDSC inside massive stars in contraction under proper conditions.

Viscosity driven bar mode secular instabilities of rapidly rotating neutron stars are studied using LORENE/Nrotstar code. These instabilities set a more rigorous limit to the rotation frequency of neutron star than the Kepler frequency/mass shedding limit. The procedure employed in the code comprises of perturbing an axisymmetric and stationary configuration of a neutron star and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. Symmetry breaking point was found out for Polytropic as well as 10 realistic Equations of states (EOS) from the CompOSE database. The concept of piecewise polytropic EOSs has been used to comprehend the rotational instability of Realistic EOSs and validated with 19 different Realistic EOSs from CompOSE. The possibility of detecting quasi-periodic gravitational waves from viscosity driven instability with ground based LIGO/VIRGO interferometers is also discussed very briefly., 12 pages, 17 figures, MNRAS (in press)

Euler equations of compressible gas dynamics, coupled with a source term due to the gravitational fields, often appear in many interesting astrophysical and atmospheric applications. In this paper, we design high order finite difference weighted essentially non-oscillatory (WENO) methods for the Euler equations under static gravitation fields, which are well-balanced for known steady state solutions. We simplify the well-balanced WENO methods designed in Xing and Shu (2013) for the isothermal equilibrium, and then extend them to more general steady state solutions which include both isothermal and polytropic equilibria. One- and two-dimensional numerical examples are provided at the end to test the performance of the proposed WENO methods and verify these properties numerically.

CO2 two-phase ejectors are used as expansion work recovery components in refrigeration or heat pump systems. A new thermodynamic model is developed for both single choking and double choking conditions to design such ejectors and investigate their performances. This model, based on the homogeneous equilibrium model (HEM), solves the conservation equations using real fluid properties rather than ideal gas assumptions. The irreversibilities due to friction in the nozzles and the diffuser are accounted for by polytropic efficiencies. The performance of a two-phase ejector is predicted for a fixed ejector geometry and given inlet operating specifications at off-design conditions. The model can also evaluate the ejector dimensions for given inlet and outlet operating conditions (on-design). The results are compared and validated against published experimental data. The effects of the irreversibilities on the ejector dimensions are investigated in detail.

The calculation of polytropic efficiencies is a very important task, especially during the development of new compression units, like compressor impellers, stages and stage groups. Such calculations are also crucial for the determination of the performance of a whole compressor. As processors and computational capacities have substantially been improved in the last years, the need for a new, rigorous, robust, accurate and at the same time standardized method merged, regarding the computation of the polytropic efficiencies, especially based on thermodynamics of real gases. The proposed method is based on the rigorous definition of the polytropic efficiency. The input consists of pressure and temperature values at the end points of the compression path (suction and discharge), for a given working fluid. The average relative error for the studied cases was 0.536 %. Thus, this high-accuracy method is proposed for efficiency calculations related with turbocompressors and their compression units, especially when they are operating at high power levels, for example in jet engines and high-power plants.

Starting from a two-velocity version of a recently derived six-moment closure of the kinetic Boltzmann description of a polyatomic gas, based on a discrete structure of internal energy levels, the classical shock wave problem is analyzed in some detail. Explicit analytical results are achieved under a simplifying assumption equivalent to the standard approximation of polytropic gases, to which this paper is generally restricted. In particular, existence of smooth solutions, occurrence of jumps in the kinetic and excitation temperatures, and possible temperature overshooting are emphasized.

Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies., Comment: 20 pages

In this paper, we study the existence of global entropy solutions for the Cauchy problem of system of polytropic gas dynamics in a divergent nozzle with a friction (1.1) with bounded L ∞ initial data (1.2).

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 AT, 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.

For an improved understanding of the in-cylinder processes in internal combustion (IC) engines, advanced diagnostics are needed to measure the thermodynamic state of the in-cylinder fluid. This is essential to validate numerical simulations which aim at predicting the in-cylinder processes during motored engine operation. Here, knowledge of the in-cylinder temperature is essential, as it strongly influences in-cylinder gas viscosity as well as the in-cylinder mass and thus the peak pressure. This work presents temperature measurements at 2.3 ∘CA resolution of a motored, optically accessible engine by applying tunable diode laser absorption spectroscopy (TDLAS) to in-cylinder water vapor. The temperature was investigated in different heights along the cylinder axis for variations of intake temperature and engine speed. Temperature uncertainties of ± 2.3 K were achieved at various cycle phases, and the absolute temperatures are verified using thermodynamic calculations of simultaneously measured water vapor concentration. The measured temperature dependency is compared to isentropic and polytropic changes of state, the incylinder gas mass is calculated and an estimation of the heat transfer to the walls is given. Based on the in-cylinder mass, different numerical simulations of the engine found in literature are compared.

The polytropic coefficient is an important variable for determining errors in pressure and volume measurements and for apparent heat release calculation in engine combustion analysis. For commercial gasoline-fueled spark ignition engines and diesel-fueled compression ignition engines exist a wide understanding about the thermodynamic models and values of polytropic coefficient, however, in other technologies, in which gaseous fuels are used, the pressure treatment strategies and heat transfer models should be adjusted to allow a better calculation of polytropic coefficient. This paper presents a study on the effects of fuel composition, spark timing, and engine load on polytropic coefficient determination in an air cooled spark ignition engine with high compression ratio (15.5:1), which it was fueled with natural gas, biogas, and propane-syngas blend. The experimental results suggests that during compression an appropriate crank angle interval for polytropic coefficient estimation is between 50 and 30 cra...

The entrapped air pockets in a pressurized water supply pipe may produce a significant transient pressure, resulting in pipe deformation or even pipe rupture. This article focuses on the maximum pressure of entrapped air pockets in a rapid filling pipe and its influencing factors. In this paper, the rigid water column theory and the ideal gas equation are applied to the air vessel-pressured pipe–air pocket system, and the theoretical formula representing the relationship between the maximum air pressure (MAP) and air comprehensive coefficient is presented. In addition, a numerical model of the system is established by the method of characteristics. The rapid filling process is simulated according to the experimental setup and the results are in good agreement with the experimental data. The influence of the air comprehensive coefficient on the MAP is also studied. Both the theoretical formula and numerical simulation show that the smaller air comprehensive coefficient will result in larger MAP (i.e., the MAP decreases with the increase of the polytropic exponent and initial air pressure, and increases with the increase of the initial air length).

In this paper, we revisit the singular Non-Newton polytropic filtration equation, which was studied extensively in the recent years. However, all the studies are mostly concerned with subcritical initial energy, i.e., \begin{document} $E(u_0) , where \begin{document} $E(u_0)$ \end{document} is the initial energy and \begin{document} $d$ \end{document} is the mountain-pass level. The main purpose of this paper is to study the behaviors of the solution with \begin{document} $E(u_0)≥d$ \end{document} by potential well method and some differential inequality techniques.