Polytropic Model Research Articles

Irreversible Performance Characteristics of Air Standard Otto Cycles with Polytropic Processes

In this study, the standard Otto cycle is reconsidered, leading to the replacement of its reversible adiabatic processes by polytropic processes. Two models were proposed, the sub-k polytropic model and the super-k polytropic model, in order to account for the losses encountered in the real Otto engine. The performance characteristics of the Otto engine were presented via plots of power vs. efficiency curves. The results, based on the two models, predict a slightly higher than 30% reduction in the net power output. The results also show that the efficiency of the real Otto engine lies at approximately 70% of the efficiency obtained from the standard Otto cycle. The current study’s value is generally educational, and may also serve as guidance for engineers performing detailed simulations or conducting expensive experiments in the field.

Third-Order Corrections and Mass-Shedding Limit of Rotating Neutron Stars Computed By a Complex-Plane Strategy

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.

Kaluza-Klein cosmology with polytropic gas dark energy

The compact Kaluza-Klein cosmology in which polytropic gas dark energy is interacting with dark matter has been studied. The equation of state parameter and the equation of evolution of the polytropic gas dark energy has been evaluated. It has been observed that the polytropic gas model can describe the matter-dominated universe [Ω Λ → 0] in the far past and the dark-energy-dominated universe [Ω Λ → 1] at the late time. It has been also observed that (in the context of this interacting polytropic model), the transition from decelerated expansion (q > 0) to accelerated expansion (q < 0) takes place sooner for larger value of c and also by increasing the interaction parameter α.

STATIONARY WAVE ASSOCIATED WITH AN INFLOW PROBLEM IN THE HALF LINE FOR VISCOUS HEAT-CONDUCTIVE GAS

We study the large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half space. We consider an inflow problem where the gas enter into the region through the boundary, and we show that a corresponding stationary solution is time-asymptotically stable in both the subsonic and transonic cases. The proof of asymptotic stability is based on a priori estimates of the perturbation from the stationary solution, which are derived by a standard energy method, provided the boundary strength and the initial perturbation in a certain Sobolev space are sufficiently small.

POLYTROPIC MODEL FITS TO THE GLOBULAR CLUSTER NGC 2419 IN MODIFIED NEWTONIAN DYNAMICS

We present an analysis of the globular cluster NGC 2419, using a polytropic model in Modified Newtonian Dynamics (MOND) to reproduce recently published high quality data of the structure and kinematics of the system. We show that a specific MOND polytropic model of NGC 2419 suggested by a previous study can be completely ruled out by the data. Furthermore, the highest likelihood fit polytrope in MOND is a substantially worse model (by a factor of approximately 5000) than a Newtonian Michie model studied in an earlier contribution by Ibata et al. (2011). We conclude that the structure and dynamics of NGC 2419 favor Newtonian dynamics and do indeed challenge the MOND theory.

STARLESS CLOUD CORE L1517B IN ENVELOPE EXPANSION WITH CORE COLLAPSE

Various spectral emission lines from star-forming molecular cloud core L1517B manifest red asymmetric double-peaked profiles with stronger red peaks and weaker blue peaks, in contrast to the oft-observed blue-skewed molecular spectral line profiles with blue peaks stronger than red peaks. Invoking a spherically symmetric general polytropic hydrodynamic shock model for the envelope expansion with core collapse (EECC) phase, we show the radial flow velocity, mass density and temperature structures of self-similar evolution for L1517B in a dynamically consistent manner. By prescribing simple radial profiles of abundance distribution for pertinent molecules, we perform molecular excitation and radiative transfer calculations using the publicly available RATRAN code set for the spherically symmetric case. Our computational results show that the EECC model reproduces molecular spectral line profiles in sensible agreement with observational data of IRAM, FCRAO and Effelsberg 100 m telescopes for L1517B. We also report spatially resolved observations of optically thick line HCO+(1-0) using the Purple Mountain Observatory (PMO) 13.7 m telescope at Delingha in China and the relevant fitting results. Hyperfine line structures of NH3 and N2H+ transitions are also fitted to consistently reveal the dynamics of central core collapse. As a consistent model check, radial profiles of 1.2 mm and 0.85 mm dust continua observed by IRAM 30 m telescope and SCUBA, respectively, are also fitted numerically using the same EECC model that produces the molecular line profiles. L1517B is likely undergoing an EECC shock phase. For future observational tests, we also predict several molecular line profiles with spatial distributions, radial profile of sub-millimeter continuum at wavelength 0.45mm, as well as the radial profiles of the column density and visual extinction for L1517B.

Structures and oscillations of rotationally and tidally distorted polytropic models of stars in the presence of the Coriolis force

The problems of equilibrium structures and periods of oscillations of rotationally and/or tidally distorted polytropic models of stars in binary systems have been studied previously. In the studies, only the effects of gravitational and centrifugal forces while obtaining the Roche equipotential of such stars were considered. The Coriolis force were not considered. In the present study, we have included the effects of the Coriolis force also. The objective of this study is to investigate as to how the inclusion of the Coriolis force in the Roche equipotential affects the equilibrium structures and periods of oscillations of rotationally and/or tidally distorted stars. The results of our study show that the Coriolis force has no appreciable effect on the equilibrium structures and periods of small oscillations of polytropic models of stars in binary systems. The present study also confirms the earlier conclusions that uniform rotation decreases the eigenfrequencies of various modes of oscillation.

MAGNETIZED ROTATING NEUTRON STARS SIMULATED BY GENERAL-RELATIVISTIC POLYTROPIC MODELS: THE NUMERICAL TREATMENT

We compute general-relativistic polytropic models of magnetized rotating neutron stars, assuming that magnetic field and rotation can be treated as decoupled perturbations acting on the nondistorted configuration. Concerning the magnetic field, we develop and apply a numerical method for solving the relativistic Grad–Shafranov equation as a nonhomogeneous Sturm–Liouville problem with nonstandard boundary conditions. We present significant geometrical and physical characteristics of six models, four of which are models of maximum mass. We find negative ellipticities owing to a magnetic field with both toroidal and poloidal components; thus the corresponding configurations have prolate shape. We also compute models of magnetized rotating neutron stars with almost spherical shape due to the counterbalancing of the rotational effect (tending to yield oblate configurations) and the magnetic effect (tending in turn to derive prolate configurations). In this work such models are simply called "equalizers." We emphasize on numerical results related to magnetars, i.e. ultramagnetized neutron stars with relatively long rotation periods.

F-Mode Instability in Relativistic Neutron Stars

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ℓ=m=4 mode) of the order of 10(3)-10(4) s near the Kepler frequency Ω(K) while the instability is active above ∼0.92 Ω(K) and for temperatures ∼(10(9)-2×10(10)) K, characteristic of newborn neutron stars.

Latest cosmological constraints on Cardassian expansion models including the updated gamma-ray bursts

We constrain the Cardassian expansion models from the latest observations, including the updated Gamma-ray bursts (GRBs), which are calibrated using a cosmology independent method from the Union2 compilation of type Ia supernovae (SNe Ia). By combining the GRB data with the joint observations from the Union2 SNe Ia set, along with the results from the Cosmic Microwave Background radiation observation from the seven-year Wilkinson Microwave Anisotropy Probe and the baryonic acoustic oscillation observation galaxy sample from the spectroscopic Sloan Digital Sky Survey Data Release, we find significant constraints on the model parameters of the original Cardassian model ΩM0 = 0.282+0.015−0.014, n = 0.03+0.05−0.05; and n = −0.16+0.25−3.26, β = 0.76+0.34−0.58 of the modified polytropic Cardassian model, which are consistent with the ΛCDM model in a 1-σ confidence region. From the reconstruction of the deceleration parameter q(z) in Cardassian models, we obtain the transition redshift zT = 0.73 ± 0.04 for the original Cardassian model and zT = 0.68 ± 0.04 for the modified polytropic Cardassian model.

A polytropic model for the solar wind

The solar wind fills the heliosphere and is the background medium in which coronal mass ejections propagate. A realistic modelling of the solar wind is therefore essential for space weather research and for reliable predictions. Although the solar wind is highly anisotropic, magnetohydrodynamic (MHD) models are able to reproduce the global, average solar wind characteristics rather well. The modern computer power makes it possible to perform full three dimensional (3D) simulations in domains extending beyond the Earth’s orbit, to include observationally driven boundary conditions, and to implement even more realistic physics in the equations. In general, MHD models for the solar wind often make use of additional source and sink terms in order to mimic the observed solar wind parameters and/or they hide the not-explicitly modelled physical processes in a reduced or variable adiabatic index. Even the models that try to take as much as possible physics into account, still need additional source terms and fine tuning of the parameters in order to produce realistic results. In this paper we present a new and simple polytropic model for the solar wind, incorporating data from the ACE spacecraft to set the model parameters. This approach allows to reproduce the different types of solar wind, where the simulated plasma variables are in good correspondence with the observed solar wind plasma near 1 AU.

Effects of Pressure Drops on the Performance Characteristics of Air Standard Otto Cycle

The effects of pressure drops on the performance characteristics of the air standard Otto cycle are reported. The pressure drops are assumed as constant values independent of the engine size. It has been shown that the pressure drops to about 60% of the maximum pressure in the ideal cycle (Curto-Risso et al., 2008). Three different models are studied: constant pressure model, reversible adiabatic expansion model and polytropic expansion model. The findings of this study show that, at this level of pressure drop, the maximum efficiency of the Otto cycle is reduced by 15% approximately based on the constant pressure model. The combined effect of pressure drop with other modes of irreversibility, for example, internal irreversibility and heat leaks, could reduce the maximum efficiency into very low values (approximately 30%). The reversible adiabatic model predicts reduction of 13% in efficiency at 40% pressure drop levels but at the price of zero power production. On the other hand, the polytropic expansion model predicts 40% reduction in efficiency for the same level of pressure drop (40%). All three models show that the power output is very sensitive to pressure drop.

Notes on the stability threshold for radially anisotropic polytropes

We discuss some contradictions found in the literature concerning the problem of stability of collisionless spherical stellar systems which are the simplest anisotropic generalization of the well-known polytrope models. Their distribution function $F(E,L)$ is a product of power-low functions of the energy $E$ and the angular momentum $L$, i.e. $F\propto L^{-s}(-E)^q$. On the one hand, calculation of the growth rates in the framework of linear stability theory and N-body simulations show that these systems become stable when the parameter $s$ characterizing the velocity anisotropy of the stellar distribution is lower than some finite threshold value, $s<s_\textrm{crit}$. On the other hand Palmer & Papaloizou (1987) showed that the instability remained up to the isotropic limit $s=0$. Using our method of determining the eigenmodes for stellar systems, we show that the growth rates in weakly radially-anisotropic systems are indeed positive, but decrease exponentially as the parameter $s$ approaches zero, i.e. $\gamma\propto \exp(-s_{\ast}/s)$. In fact, for the systems with finite lifetime this means stability.

Collapse of differentially rotating neutron stars and cosmic censorship

We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum $J/{M}^{2}$, where $J$ and $M$ are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with $J/{M}^{2}&lt;1$, i.e. ``sub-Kerr'' models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves resemble those seen for uniformly rotating stars, although with an overall decrease in the efficiency of gravitational-wave emission. For stellar models with $J/{M}^{2}&gt;1$, i.e. ``supra-Kerr'' models, on the other hand, we were not able to find models that are dynamically unstable and all of the computed supra-Kerr models were found to be far from the stability threshold. For these models a gravitational collapse is possible only after a very severe and artificial reduction of the pressure, which then leads to a torus developing nonaxisymmetric instabilities and eventually contracting to a stable axisymmetric stellar configuration. While this does not exclude the possibility that a naked singularity can be produced by the collapse of a differentially rotating star, it also suggests that cosmic censorship is not violated and that generic conditions for a supra-Kerr progenitor do not lead to a naked singularity.

Modelling and identification of industrial pneumatic drive system

A model and an identification method appropriate for typical industrial, open-loop controlled, pneumatic systems are presented in this paper. The development of the mathematical model takes into consideration nonlinear flow through extended pneumatic circuits, direction dependent friction, dead volume in cylinder chamber, fittings and piping, leakage between actuator chambers, time delays due to valve switching and long lengths of tubing, polytropic temperature model and heat transfer. The identification method is evolved with a view to apply in industrial environments and takes careful consideration of flow characteristics of both charge and exhaust elements of the circuit. Model validation is presented for a standard double-acting asymmetric cylinder with different payloads. The results of the residual analysis indicate an improved system model in comparison to the published literature. The approach presented should therefore be useful in simulation-based design and analysis of pneumatic systems. It is also applicable in the development of servo-pneumatic systems.

Thermodynamic origin of the Cardassian universe

In the Cadassian universe, one can explain the acceleration of the universe without introducing a dark energy component. However, it is hard to get the dynamical equations of this model from the action principle. Recently, works on the relation between thermodynamics and gravity indicate that gravity force may not be a fundamental force. In this paper, we shall study the thermodynamics of the Cardassian universe, and it might be the origin of this cosmological model. We find that the corresponding entropy obeys ordinary area law when the area of the trapping horizon is small, and it becomes a constant when the area is going to be large in the original and modified polytropic Cardassian models, while it has a maximum value in the exponential one. It seems that the Cardassian universe only contains finite information according to the holographic principle, which states that all the information in the bulk should be encoded on the boundary of the bulk.

A polytropic approach to semi-relativistic isothermal gas spheres at arbitrary temperature

We use standard polynomial expansion technique to show the existence of a relation between polytropic model and the description of gas spheres at finite temperature. A numerical analysis is made concerning the obtained perturbative parameters. It is shown that there is a correspondence between polytropic and gas sphere thermal models for fermions and bosons. For instance, the polytropic index $n$ displays evident correlation with temperature and chemical potential.

Cosmological Implications of Interacting Polytropic Gas Dark Energy Model in Non-flat Universe

The polytropic gas model is investigated as an interacting dark energy scenario. The cosmological implications of the model including the evolution of EoS parameter w Λ, energy density ΩΛ and deceleration parameter q are investigated. We show that, depending on the parameter of model, the interacting polytropic gas can behave as a quintessence or phantom dark energy. In this model, the phantom divide is crossed from below to up. The evolution of q in the context of polytropic gas dark energy model represents the decelerated phase at the early time and accelerated phase later. The singularity of this model is also discussed. Eventually, we establish the correspondence between interacting polytropic gas model with tachyon, K-essence and dilaton scalar fields. The potential and the dynamics of these scalar field models are reconstructed according to the evolution of interacting polytropic gas.

The structure and evolution of quasi-stars

The existence of bright quasars at high redshifts implies that supermassive black holes were able to form in the early Universe. Though a number of mechanisms to achieve this have been proposed, none yet stands out. A recent suggestion is the formation of quasi-stars, initially stellar-mass black holes accreting from hydrostatic giant-like envelopes of gas, formed from the monolithic collapse of pre-galactic gas clouds. In this work, we modify the Cambridge STARS stellar evolution package to construct detailed models of the evolution of these objects. We find that, in all of our models, the black hole inside the envelope is able to reach slightly more than one-tenth of the total mass of the system before hydrostatic equilibrium breaks down. This breakdown occurs after a few million years of evolution. We show that the mechanism which causes the hydrostatic evolution to end is present in polytropic models. We also show that the solutions are highly sensitive to the size of the inner boundary radius and that no physical solutions exist if the inner boundary is chosen to be less than about 0.3 of the Bondi radius.

On the effects of rotation on acoustic stellar pulsations: validity domains of perturbative methods and close frequency pairs

Pulsation frequencies of acoustic modes are calculated for realistic rotating stellar models using both a perturbative and a two-dimensional approach. A comparison between the two yields validity domains which are similar to those previously obtained in Reese, Lignieres and Rieutord (2006) for polytropic models. One can also construct validity domains based on polynomial fits to the frequencies from the two-dimensional approach, and these also turn out to be similar, thus further confirming the agreement between the perturbative and two-dimensional approach at low rotation rates. Furthermore, as was previously shown in Espinosa, Perez Hernandez and Roca Cortes (2004), adjacent frequencies in multiplets come close together, thus forming pairs. This phenomena, exclusive to two-dimensional calculations, is shown to be an unlikely explanation of the close frequency pairs observed in delta Scuti stars. A systematic search for all close frequency pairs in the calculated spectrum is also carried out. The number of close frequency pairs is shown to agree with what is expected based on a Poisson distribution, but does not match the number or distribution of close pairs in stars like FG Vir. Furthermore, a lack of close frequency pairs appears at low rotation rates, where frequency multiplets do not overlap. Delta Scuti stars currently reported as having close frequency pairs do not fall in this interval.