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Journal articles on the topic 'Polytropie'
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1
Anandaram, M. N. "Emden’s Polytropes: Gas Globes In Hydrostatic Equilibrium." Mapana - Journal of Sciences 12, no. 1 (February 20, 2013): 99–127. http://dx.doi.org/10.12723/mjs.24.9.
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The theory of polytropes dealing with the hydrostatic equilibrium structure of gas globes had its origin in Emden’s publication, Gaskugeln a century ago (1907). This review article has been written for students of physics and astrophysics not only to understand the theory of polytropes as the simplest of stellar models but also computationally solve the Lane-Emden equation for polytropes. Anyone can easily obtain values of normalized temperature, density, pressure and mass distribution as a function of the normalized radius or mass in any polytrope model in tabular form as well as in graphical form using the program code. Explanation of the algorithm to write a code is provided (python script on request). A graphical description of how the polytropic index determines the structure of the polytrope is also given.
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Saad, Abdel-Naby S., Mohamed I. Nouh, Ashraf A. Shaker, and Tarek M. Kamel. "STABILITY ANALYSIS OF RELATIVISTIC POLYTROPES." Revista Mexicana de Astronomía y Astrofísica 57, no. 2 (October 1, 2021): 407–18. http://dx.doi.org/10.22201/ia.01851101p.2021.57.02.13.
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We study the relativistic self-gravitating, hydrostatic spheres with a polytropic equation of state, considering structures with the polytropic indices n=1(0.5)3 and illustrate the results for the relativistic parameters σ=0−0.75. We determine the critical relativistic parameter at which the mass of the polytrope has a maximum value and represents the first mode of radial instability. For n=1(0.5)2.5, stable relativistic polytropes occur for σ less than the critical values 0.42, 0.20, 0.10, and 0.04, respectively, while unstable relativistic polytropes are obtained when σ is greater than the same values. When n=3.0 and σ>0.5, energetically unstable solutions occur. The results of critical values are in full agreement with those evaluated by several authors. Comparisons between analytical and numerical solutions of the given relativistic functions provide a maximum relative error of order 10−3.
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Anandaram, Mandyam N. "On Self-Gravitating Polytropic Cylinders and Slabs." Mapana - Journal of Sciences 18, no. 1 (January 1, 2019): 67–92. http://dx.doi.org/10.12723/mjs.48.5.
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In this review paper the 2-D Lane-Emden equation (LEEq) model of a self-gravitating gas distribution in the form of an infinitely long cylinder shaped polytrope of finite radius is obtained and its basic radial properties are outlined. Similarly reviewed is the derivation of the 1-D LEEq model of an infinitely wide planar polytrope of finite thickness and its basic properties across thickness are discussed. These two polytropes are solved numerically along with the 3-D models for comparison using the 2 nd order Euler-Richardson method (ERM) and their index based parameters are determined. The Python script used in these computations has been shown to be not only fast but is capable of matching fourth order performance. However, these models are found to have finite radii for all polytropic indices unlike the restricted spherical analogs and have astrophysical applications. Distortion due to rotation in polytropic rings has also been computed using ERM.
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Vavrukh, M. V., and D. V. Dzikovskyi. "Method of integral equations in the polytropic theory of stars with axial rotation. I. Polytropes n=0 and n=1." Mathematical Modeling and Computing 8, no. 2 (2021): 338–58. http://dx.doi.org/10.23939/mmc2021.02.338.
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Calculations of characteristics of stars with axial rotation in the frame of polytropic model are based on the solution of mechanical equilibrium equation – differential equation of second order in partial derivatives. Different variants of approximate determinations of integration constants are based on traditional in the theory of stellar surface approximation, namely continuity of gravitational potential in the surface vicinity. We proposed a new approach, in which we used simultaneously differential and integral forms of equilibrium equations. This is a closed system and allows us to define in self-consistent way integration constants, the polytrope surface shape and distribution of matter over volume of a star. With the examples of polytropes n=0 and n=1, we established the existence of two rotation modes (with small and large eccentricities). It is proved that the polytrope surface is the surface of homogeneous rotational ellipsoid for the case n=0. The polytrope characteristics with n=1 in different approximations were calculated as the functions of angular velocity. For the first time it has been calculated the deviation of polytrope surface at fixed value of angular velocity from the surface of associated rotational ellipsoid.
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Nouh, M. I., E. A. Elkholy, and S. H. El-Essawy. "COMPUTING POLYTROPIC AND ISOTHERMAL MODELS USING MONTE CARLO METHOD." Revista Mexicana de Astronomía y Astrofísica 60, no. 1 (April 1, 2024): 3–12. http://dx.doi.org/10.22201/ia.01851101p.2024.60.01.01.
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Polytropic and isothermal gas spheres are crucial in the theory of stellar structure and evolution, galaxy cluster modeling, thermodynamics, and various other physics, chemistry, and engineering disciplines. Based on two Monte Carlo algorithms (MC1 and MC2), we introduce a numerical approach for solving Lane-Emden (LE) equations of the polytropic and isothermal gas spheres. We found that the MC1 and MC2 models agree with each other and also with numerical and analytical models. We tested the compatibility between the MC and the numerical polytropic models by calculating the mass-radius relation and the pressure profile for the polytrope with n=3.
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Novotný, Jan, Zdeněk Stuchlík, and Jan Hladík. "Polytropic spheres modelling dark matter haloes of dwarf galaxies." Astronomy & Astrophysics 647 (March 2021): A29. http://dx.doi.org/10.1051/0004-6361/202039338.
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Context. Dwarf galaxies and their dark matter (DM) haloes have velocity curves of a different character than those in large galaxies. These velocity curves are modelled by a simple pseudo-isothermal model containing only two parameters, which do not give us insight into the physics of the DM halo. Aims. We seek to obtain some insight into the physical conditions in DM haloes of dwarf galaxies by using a simple physically based model of DM haloes. Methods. To treat the diversity of the dwarf galaxy velocity profiles in a unifying framework, we applied polytropic spheres characterised by the polytropic index n and the relativistic parameter σ as a model of dwarf-galaxy DM haloes and matched the velocity of circular geodesics of the polytropes to the velocity curves observed in the dwarf galaxies from the LITTLE THINGS ensemble. Results. We introduce three classes of the LITTLE THINGS dwarf galaxies in relation to the polytrope models due to the different character of the velocity profile. The first class corresponds to polytropes that have n < 1 with linearly increasing velocity along the whole profile, the second class has 1 < n < 2 and the velocity profile becomes flat in the external region, the third class has n > 2, and the velocity profile reaches a maximum and demonstrates a decline in the external region. The σ parameter has to be strongly non-relativistic (σ < 10−8) for all dwarf galaxy models; this parameter varies for the models of each class, but these variations have negligible influence on the character of the velocity profile. Conclusions. Our results indicate a possibility that at least two different kinds of DM are behind the composition of DM haloes. The matches of the observational velocity curves are of the same quality as those obtained by the pseudo-isothermal, core-like models of dwarf galaxy DM haloes.
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Vavrukh, M., and D. Dzikovskyi. "The generalized polytropic model for the Sun-like stars." Mathematical Modeling and Computing 10, no. 1 (2023): 1–9. http://dx.doi.org/10.23939/mmc2023.01.001.
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The Eddington method based on simultaneous consideration of gas and light pressures with a homogeneous сhemical composition of stellar matter was generalized for the case of model with a spatially inhomogeneous chemical composition. As a result, it was obtained the equation of state, which is expressed by a generalized polytrope with index n=3. As an example, it was solved the equilibrium equation for the Sun both using the standard polytropic equation of state and generalized polytrope. The coordinate dependence of the Sun characteristics was calculated within two models. Obtained results are compared with the results of numerical calculations for the Sun based on the system of Schwarzschild equations for the standard model. It was shown that the standard polytropic model is applicable only for the Sun of zero-age. The Sun characteristics calculated with help of generalized equation of state are close to the results of numerical calculations based on Schwarzschild equations. It was concluded that the standard polytropic model is applicable for the stars of zero-age main sequence, and the generalized model – for the stars of finite age, in which thermonuclear reactions have already created a significant spatially inhomogeneity of chemical composition inside of the core.
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Sharif, M., Amal Majid, and M. Shafaqat. "Study of anisotropic polytropes in f (, T) Theory." Physica Scripta 97, no. 3 (February 7, 2022): 035001. http://dx.doi.org/10.1088/1402-4896/ac4f05.
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Abstract This paper examines the general formalism and applications of isotropic as well as anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical and Schwarzschild spacetimes in the interior and exterior regions, respectively. We use two polytropic equations of state to obtain physically viable solutions of the field equations. The hydrostatic equilibrium and Lane-Emden equations are developed for both isotropic as well as anisotropic cases. We study the effects of anisotropic pressure on the stellar structure. Moreover, we graphically inspect the physical behavior of isotropic as well as anisotropic polytropes through energy conditions and stability criterion. Finally, we discuss Tolman mass to explore some characteristics of the models. It is concluded that more viable and stable polytropes are found in this theory as compared to general relativity.
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FERRARI, L., P. C. R. ROSSI, and M. MALHEIRO. "A POLYTROPIC APPROACH TO NEUTRON STARS." International Journal of Modern Physics D 19, no. 08n10 (August 2010): 1569–74. http://dx.doi.org/10.1142/s0218271810017676.
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We analyze here whether polytropic equations of state can be a good approximation for neutron stars. Dividing the matter in the star interior in different regions that can be well-reproduced by different polytropics and imposing the continuity of the pressure among the regions, we obtain the corresponding neutron star mass–radius diagram. A comparison with the results obtained with the polytropic approximation and the exact relativistic mean-field equation of state (EoS) is shown for two compositions of the hadronic matter. We conclude that with more than one polytropic EoS, it is possible to obtain a good fit to neutron stars only if the pressure is written as a power-law in the energy density (or mass density) and not in the baryonic density (the usual polytropic). We also found a correlation between the sound velocity at the star center and its mass. The sound velocity at the interface between the polytropic regions shows a small discontinuity that is greater for the hadronic matter including hyperons.
10
Nazar, H., M. Azam, G. Abbas, Riaz Ahmed, and R. Naeem. "Relativistic polytropic models of charged anisotropic compact objects." Chinese Physics C 47, no. 3 (March 1, 2023): 035109. http://dx.doi.org/10.1088/1674-1137/acae5b.
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Abstract 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 ( ). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state ( ). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., , and . 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
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Hladík, Jan, Camilo Posada, and Zdeněk Stuchlík. "Radial instability of trapping polytropic spheres." International Journal of Modern Physics D 29, no. 05 (March 6, 2020): 2050030. http://dx.doi.org/10.1142/s0218271820500303.
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We complete the stability study of general-relativistic spherically symmetric polytropic perfect fluid spheres, concentrating our attention on 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 [Formula: see text] in the whole range [Formula: see text], and the relativistic parameter [Formula: see text] 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 [Formula: see text]. 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 [Formula: see text]. We found that all the configurations having trapped null geodesics are unstable according to both methods.
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Hopstad, Yngve, and Jan Myrheim. "Rigidly rotating gravitationally bound systems of point particles, compared to polytropes." International Journal of Modern Physics C 31, no. 06 (June 2020): 2050090. http://dx.doi.org/10.1142/s0129183120500904.
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In order to simulate rigidly rotating polytropes, we have simulated systems of [Formula: see text] point particles, with [Formula: see text] up to 1800. Two particles at a distance [Formula: see text] interact by an attractive potential [Formula: see text] and a repulsive potential [Formula: see text]. The repulsion simulates the pressure in a polytropic gas of polytropic index [Formula: see text]. We take the total angular momentum [Formula: see text] to be conserved, but not the total energy [Formula: see text]. The particles are stationary in the rotating coordinate system. The rotational energy is [Formula: see text] where [Formula: see text] is the moment of inertia. Configurations, where the energy [Formula: see text] has a local minimum, are stable. In the continuum limit [Formula: see text], the particles become more and more tightly packed in a finite volume, with the interparticle distances decreasing as [Formula: see text]. We argue that [Formula: see text] is a good parameter for describing the continuum limit. We argue further that the continuum limit is the polytropic gas of index [Formula: see text]. For example, the density profile of the nonrotating gas approaches that computed from the Lane–Emden equation describing the nonrotating polytropic gas. In the case of maximum rotation, the instability occurs by the loss of particles from the equator, which becomes a sharp edge, as predicted by Jeans in his study of rotating polytropes. We describe the minimum energy nonrotating configurations for a number of small values of [Formula: see text].
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Mikheev, Sergey, and Victor Tsvetkov. "Minimum Period of Rotation of Millisecond Pulsars and Pulsar Matter Equations of State." EPJ Web of Conferences 173 (2018): 02015. http://dx.doi.org/10.1051/epjconf/201817302015.
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Based on the findings of our previous studies of fast-rotating Newtonian polytropes, we found the relation between the minimum pulsar rotation period, the value of pulsar central density, and the polytropic index. From this relation we come to the conclusion that the value of minimum central density of a pulsar with a peak period is 2.5088 • 1014 g/cm3.
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Livadiotis, G., D. J. McComas, H. O. Funsten, N. A. Schwadron, J. R. Szalay, and E. Zirnstein. "Thermodynamics of the Inner Heliosheath." Astrophysical Journal Supplement Series 262, no. 2 (October 1, 2022): 53. http://dx.doi.org/10.3847/1538-4365/ac8b88.
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Abstract We derive annual sky maps of the proton temperature in the inner heliosheath (IHS), and track their temporal evolution over the years 2009–2016 of Interstellar Boundary Explorer observations. Other associated thermodynamic parameters also determined are the density, kappa (the parameter that characterizes kappa distributions), temperature rate, polytropic index, and entropy. We exploit the theory of kappa distributions and their connection with polytropes, to (i) express a new polytropic quantity Π that remains invariant along streamlines where temperature and density may vary, (ii) parameterize the proton flux in terms of the Π invariant and kappa, and (iii) derive the temperature and density, respectively, from the slope and intercept of the linear relationship between kappa and logarithm of Π. We find the following thermodynamic characteristics: (1) temperature sky maps and histograms shifted to their lowest values in 2012 and their highest in 2015; (2) temperature negatively correlated with density, reflecting the subisothermal polytropic behavior; (3) temperature positively correlated with kappa, revealing characteristics of the mechanism responsible for generating kappa distributions; (4) processes in IHS are subisothermal tending toward isobaric, consistent with previously published results; (5) linear relationship between kappa and polytropic indices, revealing characteristics of the particle potential energy; and (6) entropy positively correlated with polytropic index, aligned with the underlying theory that entropy increases toward the isothermal state where the kappa distribution reduces to the Maxwell–Boltzmann description.
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Sharif, M., and Sobia Sadiq. "Effects of charge on anisotropic conformally flat polytropes." Canadian Journal of Physics 93, no. 11 (November 2015): 1420–26. http://dx.doi.org/10.1139/cjp-2015-0148.
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In this paper, we study the effects of electromagnetic field on conformally flat spherically symmetric anisotropic matter distribution satisfying two polytropic equations of state. We consider conformally flat condition and evaluate corresponding anisotropy, which is used to study polytropes for the charged compact object. Finally, we study stability of the resulting models using the Tolman mass. It is concluded that only one of the resulting models is physically viable.
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Donkov, S., I. Zh Stefanov, T. V. Veltchev, and R. S. Klessen. "Density profile of a self-gravitating polytropic turbulent fluid in the context of ensembles of molecular clouds." Monthly Notices of the Royal Astronomical Society 505, no. 3 (June 1, 2021): 3655–63. http://dx.doi.org/10.1093/mnras/stab1572.
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ABSTRACT We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid with an equation of state $p_{\rm gas}\propto \rho ^\Gamma$. This is done in the framework of ensembles of molecular clouds represented by single abstract objects as introduced by Donkov et al. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with Γ = 1 to one of ‘hard polytrope’ with exponent Γ > 1. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation reproduces the Bernoulli equation for the proposed model and describes the balance of the kinetic, thermal, and gravitational energy of a fluid element. We propose as well a method to obtain approximate solutions in a power-law form which results in four solutions corresponding to different density profiles, polytropic exponents, and energy balance equations for a fluid element. One of them, a density profile with slope −3 and polytropic exponent Γ = 4/3, matches with observations and numerical works and, in particular, leads to a second power-law tail of the density distribution function in dense, self-gravitating cloud regions.
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Sharif, M., and Arfa Waseem. "Role of σR2 + γRμνTμν model on anisotropic polytropes." International Journal of Modern Physics D 27, no. 16 (December 2018): 1950007. http://dx.doi.org/10.1142/s021827181950007x.
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This paper analyzes the anisotropic stellar evolution governed by polytropic equation-of-state in the framework of [Formula: see text] gravity, where [Formula: see text]. We construct the field equations, hydrostatic equilibrium equation and trace equation to obtain their solutions numerically under the influence of [Formula: see text] gravity model, where [Formula: see text] and [Formula: see text] are arbitrary constants. We examine the dependence of various physical characteristics such as radial/tangential pressure, energy density, anisotropic factor, total mass and surface redshift for specific values of the model parameters. The physical acceptability of the considered model is discussed by verifying the validity of energy conditions, causality condition and adiabatic index. We also study the effects arising due to strong nonminimal matter-curvature coupling on anisotropic polytropes. It is found that the polytropic stars are stable and their maximum mass point lies within the required observational Chandrasekhar limit.
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Albera, Dionigi. "Digressions on Polytropy: An Exploration of Religious Eclecticism in Eurasia." Entangled Religions 9 (April 30, 2019): 139–64. http://dx.doi.org/10.46586/er.v9.2019.139-164.
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The anthropologist Michael Carrithers introduced the notion of polytropy in the field of the study of religion, proposing that this notion (deriving from the Greek poly, ‘many’, and tropos, ‘turning’) may account for the eclecticism and fluidity of South Asian religious life. The exploration effectuated in the article suggests that the notion of polytropy could offer a promising tool for capturing some important features of religiosity in other Asiatic contexts, too, as well as in the Mediterranean. Polytropic trends appear in different religious contexts, from the fuzzy Chinese situation, where religious affiliations are very limited in their scope and relevance, to the South Asian contexts, in which religious orientations coalesce around the multivocal concept of dharma, to the tightly structured Abrahamic religions in the Mediterranean with their strong confessionalism. Polytropy is associated with a practical mode of religiosity and is linked to a particular conception of believing in which the believer tends to multiply the transactions with different supra-mundane partners. This orientation is distinct from religious styles that are based on a discursive and scriptural approach and/or on the cultivation of oneself, which often display a tendency towards unity, coherence and continuity. This permits identifying an opposite pole with respect to polytropy, which I define as monotropy.
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Sharif, M., and Sobia Sadiq. "Study of conformally flat polytropes with tilted congruence." International Journal of Modern Physics D 27, no. 07 (May 2018): 1850063. http://dx.doi.org/10.1142/s0218271818500633.
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This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman–Oppenheimer–Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.
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Fernando Bustos, Oscar. "Lane-Emden equations for Relativistic Anisotropic Polytropes." Journal of Physics: Conference Series 2796, no. 1 (July 1, 2024): 012006. http://dx.doi.org/10.1088/1742-6596/2796/1/012006.
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Abstract In this research work, spherically symmetric compact objects with anisotropic matter are studied within the framework of general relativity. For this purpose, the equation of state of the master polytrope P = Kργ + αρ − β is employed, which prevents the divergence of the tangential velocity at the object’s surface and generalizes the treatment of the equation of state. The corresponding Lane-Emden equation is derived and integrated using an anisotropy function that encompasses conformally flat polytropes and vanishing compactness factor. Furthermore, the physical acceptability conditions of the solutions are analyzed.
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Mosani, Karim, and Gauranga C. Samanta. "Dynamics of general barotropic stellar fluid in the framework of R + 2αT gravity." Modern Physics Letters A 35, no. 12 (January 22, 2020): 2050089. http://dx.doi.org/10.1142/s0217732320500893.
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Gravitational collapse of a spherically symmetric homogeneous perfect barotropic fluid with linear as well as polytropic-type Equation of State (EoS) has been investigated in the framework of a linear model of [Formula: see text] gravity. This modified gravity has the potential to explain the observed cosmic acceleration. The calculations have been done taking the transformed time coordinate [Formula: see text], where [Formula: see text] is the initial density of the fluid. For linear EoS [Formula: see text], the condition for being a true singularity, along with sufficient condition for the formation of apparent horizon covering the singularity has been derived. For a polytrope having the EoS [Formula: see text], the scale factor [Formula: see text] as a function of fluid density [Formula: see text] has been obtained which is then used to study the dynamics of the fluid. Role of the polytropic index [Formula: see text] and the constant of proportionality [Formula: see text] in the dynamics of the fluid is also studied. A new type of exotic matter field having varied dependence of scale factor on the density, and having the potential to give rise to bouncing cosmology, provided it is the dominating fluid in the universe, is obtained in this domain and is investigated. Energy conditions are discussed.
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Hindman, Bradley W., and Rekha Jain. "Overstable Convective Modes in a Polytropic Stellar Atmosphere." Astrophysical Journal 943, no. 2 (February 1, 2023): 127. http://dx.doi.org/10.3847/1538-4357/acaec4.
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Abstract Within the convection zone of a rotating star, the presence of the Coriolis force stabilizes long-wavelength convective modes. These modes, which would have been unstable if the star lacked rotation, are called overstable convective modes or thermal Rossby waves. We demonstrate that the Sun’s rotation rate is sufficiently rapid that the lower half of its convection zone could possess overstable modes. Further, we present an analytic solution for atmospheric waves that reside within a polytropic stratification. We explore in detail the properties of the overstable and unstable wave modes that exist when the polytrope is weakly unstable to convective overturning. Finally, we discuss how the thermal Rossby waves that reside within the convection zone of a star might couple with the prograde branch of the g modes that are trapped within the star’s radiative zone. We suggest that such coupling might enhance the photospheric visibility of a subset of the Sun’s g modes.
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Zhong, Wei, and Cong Yu. "The Critical Core Mass of Rotating Planets." Astrophysical Journal 926, no. 1 (February 1, 2022): 43. http://dx.doi.org/10.3847/1538-4357/ac4261.
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Abstract The gravitational harmonics measured from the Juno and Cassini spacecraft help us specify the internal structure and chemical elements of Jupiter and Saturn, respectively. However, we still do not know much about the impact of rotation on the planetary internal structure as well as on their formation. The centrifugal force induced by the rotation deforms the planetary shape and partially counteracts the gravitational force. Thus, rotation will affect the critical core mass of the exoplanet. Once the atmospheric mass becomes comparable to the critical core mass, the planet will enter the runaway accretion phase and become a gas giant. We have confirmed that the critical core masses of rotating planets depend on the stiffness of the polytrope, the outer boundary conditions, and the thickness of the isothermal layer. The critical core mass with the Bondi boundary condition is determined by the surface properties. The critical core mass of a rotating planet will increase with the core gravity (i.e., the innermost density). For the Hill boundary condition, the soft polytrope shares the same properties as planets with the Bondi boundary condition. Because the total mass for planets with the Hill boundary condition increases with the decrease of the polytropic index, a higher core gravity is required for rotating planets. As a result, the critical core mass in the stiff Hill model sharply increases. The rotational effects become more important when the radiative and convective regions coexist. Further, the critical core mass of planets with the Hill (Bondi) boundary increases noticeably as the radiative layer becomes thinner (thicker).
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Yusha, V. L., A. Yu Gromov, and P. V. Ushakov. "The analysis of influence of temperature conditions of piston long-stroke compressor stage on thermodynamic efficiency of a heat pump." Omsk Scientific Bulletin. Series Aviation-Rocket and Power Engineering 7, no. 1 (2023): 18–25. http://dx.doi.org/10.25206/2588-0373-2023-7-1-18-25.
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A brief overview analysis of the applicability of heat pumps in various branches of engineering and production as one of the most energy-saving technologies is presented. The theoretical cycle of a heat pump based on a piston long-stroke low-speed compressor stage is considered, which allows to realize the compression process in a wide range of the polytrope index. The analysis of the relationship of the integral characteristics and energy efficiency of the heat pump with the temperature regime of the compressor stage when using water vapor as a working fluid is performed. The presented results of the theoretical analysis reflect the nature of the dependence of the thermal power and the transformation coefficient of the heat pump on the polytropy index of the compression process, boiling temperature, steam overheating at suction, the difference in condensation and boiling temperatures.
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Carroll, Bradley W. "Discontinuity Modes in Polytropes." International Astronomical Union Colloquium 111 (1989): 254. http://dx.doi.org/10.1017/s0252921100011623.
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AbstractIn the calculation of linear nonradial oscillation modes in composite polytropes with a small density discontinuity, a discontinuity mode may occur. This mode consists of a wave propagating along the discontinuity interface with a large amplitude that declines exponentially away from the interface. The period P of this mode is well-estimated (to within 10%) bywhere Δρ/<ρ> is the fractional density discontinuity and k is the horizontal wavenumber (c.f. Gabriel and Scuflaire 1980, in Nonradial and Nonlinear Stellar Pulsation, eds. H. Hill and W. Dziembowski, Springer-Verlag). For a 12 solar-mass polytrope with a radius of 4.27 R⊙, a 3% density discontinuity at fractional radius 0.15 produces a discontinuity mode with a period of 7.329 hours. As the density discontinuity increases the period P decreases, resulting in avoided crossings with the normal g-mode spectrum. Between these avoided crossings, the discontinuity mode has an unusually large amplitude at the location of the discontinuity.
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Nicolaou, Georgios, George Livadiotis, and Robert T. Wicks. "On the Calculation of the Effective Polytropic Index in Space Plasmas." Entropy 21, no. 10 (October 12, 2019): 997. http://dx.doi.org/10.3390/e21100997.
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The polytropic index of space plasmas is typically determined from the relationship between the measured plasma density and temperature. In this study, we quantify the errors in the determination of the polytropic index, due to uncertainty in the analyzed measurements. We model the plasma density and temperature measurements for a certain polytropic index, and then, we apply the standard analysis to derive the polytropic index. We explore the accuracy of the derived polytropic index for a range of uncertainties in the modeled density and temperature and repeat for various polytropic indices. Our analysis shows that the uncertainties in the plasma density introduce a systematic error in the determination of the polytropic index which can lead to artificial isothermal relations, while the uncertainties in the plasma temperature increase the statistical error of the calculated polytropic index value. We analyze Wind spacecraft observations of the solar wind protons and we derive the polytropic index in selected intervals over 2002. The derived polytropic index is affected by the plasma measurement uncertainties, in a similar way as predicted by our model. Finally, we suggest a new data-analysis approach, based on a physical constraint, that reduces the amount of erroneous derivations.
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Livadiotis, G., and D. J. McComas. "Connection between Polytropic Index and Heating." Astrophysical Journal 956, no. 2 (October 1, 2023): 88. http://dx.doi.org/10.3847/1538-4357/acf45d.
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Abstract The paper derives the one-to-one connecting relationships between plasma heating and its polytropic index, and addresses the consequences through the transport equation of temperature. Thermodynamic polytropic processes are classified in accordance to their polytropic index, the exponent of the power-law relationship of thermal pressure expressed with respect to density. These processes generalize the adiabatic one, where no heating is exchanged between the system and its environment. We show that, in addition to heating terms, the transport equation of temperature depends on the adiabatic index, instead of a general, nonadiabatic polytropic index, even when the plasma follows nonadiabatic processes. This is because all the information regarding the system's polytropic index is contained in the heating term, even for a nonconstant polytropic index. Moreover, the paper (i) defines the role of the polytropic index in the context of heating; (ii) clarifies the role of the nonadiabatic polytropic index in the transport equation of temperature; (iii) provides an alternative method for deriving the turbulent heating through the comparably simpler polytropic index path; and, finally, (iv) shows a one-component plasma proof-of-concept of this method and discusses the implications of such derived connecting relationships in the solar wind plasma in the heliosphere.
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Evans, Leonard H., Marc Lavignon, Marc Taylor, and A. S. M. Alamgir. "Antigenic Subclasses of Polytropic Murine Leukemia Virus (MLV) Isolates Reflect Three Distinct Groups of Endogenous Polytropic MLV-Related Sequences in NFS/N Mice." Journal of Virology 77, no. 19 (October 1, 2003): 10327–38. http://dx.doi.org/10.1128/jvi.77.19.10327-10338.2003.
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ABSTRACT Polytropic murine leukemia viruses (MLVs) are generated by recombination of ecotropic MLVs with members of a family of endogenous proviruses in mice. Previous studies have indicated that polytropic MLV isolates comprise two mutually exclusive antigenic subclasses, each of which is reactive with one of two monoclonal antibodies termed MAb 516 and Hy 7. A major determinant of the epitopes distinguishing the subclasses mapped to a single amino acid difference in the SU protein. Furthermore, distinctly different populations of the polytropic MLV subclasses are generated upon inoculation of different ecotropic MLVs. Here we have characterized the majority of endogenous polytropic MLV-related proviruses of NFS/N mice. Most of the proviruses contain intact sequences encoding the receptor-binding region of the SU protein and could be distinguished by sequence heterogeneity within that region. We found that the endogenous proviruses comprise two major groups that encode the major determinant for Hy 7 or MAb 516 reactivity. The Hy 7-reactive proviruses correspond to previously identified polytropic proviruses, while the 516-reactive proviruses comprise the modified polytropic proviruses as well as a third group of polytropic MLV-related proviruses that exhibit distinct structural features. Phylogenetic analyses indicate that the latter proviruses reflect features of phylogenetic intermediates linking xenotropic MLVs to the polytropic and modified polytropic proviruses. These studies elucidate the relationships of the antigenic subclasses of polytropic MLVs to their endogenous counterparts, identify a new group of endogenous proviruses, and identify distinguishing characteristics of the proviruses that should facilitate a more precise description of their expression in mice and their participation in recombination to generate recombinant viruses.
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Vavrukh, M. V., and D. V. Dzikovskyi. "Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytropes with indices $n>1$." Mathematical Modeling and Computing 8, no. 3 (2021): 474–85. http://dx.doi.org/10.23939/mmc2021.03.474.
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A new method for finding solutions of the nonlinear equilibrium equations for rotational polytropes was proposed, which is based on a self-consistent description of internal region and periphery using the integral form of equations. Dependencies of geometrical parameters, surface form, mass, moment of inertia and integration constants on angular velocity were calculated for indices $n=2.5$ and $n=3$.
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Evans, Leonard H., Marc Lavignon, Karin Peterson, Kim Hasenkrug, Shelly Robertson, Frank Malik, and Kimmo Virtaneva. "In Vivo Interactions of Ecotropic and Polytropic Murine Leukemia Viruses in Mixed Retrovirus Infections." Journal of Virology 80, no. 10 (May 15, 2006): 4748–57. http://dx.doi.org/10.1128/jvi.80.10.4748-4757.2006.
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ABSTRACT Mixed retrovirus infections are the rule rather than the exception in mice and other species, including humans. Interactions of retroviruses in mixed infections and their effects on disease induction are poorly understood. Upon infection of mice, ecotropic retroviruses recombine with endogenous proviruses to generate polytropic viruses that utilize different cellular receptors. Interactions among the retroviruses of this mixed infection facilitate disease induction. Using mice infected with defined mixtures of the ecotropic Friend murine leukemia virus (F-MuLV) and different polytropic viruses, we demonstrate several dramatic effects of mixed infections. Remarkably, inoculation of F-MuLV with polytropic MuLVs completely suppressed the generation of new recombinant viruses and dramatically altered disease induction. Coinoculation of F-MuLV with one polytropic virus significantly lengthened survival times, while inoculation with another polytropic MuLV induced a rapid and severe neurological disease. In both instances, the level of the polytropic MuLV was increased 100- to 1,000-fold, whereas the ecotropic MuLV level remained unchanged. Surprisingly, nearly all of the polytropic MuLV genomes were packaged within F-MuLV virions (pseudotyped) very soon after infection. At this time, only a fractional percentage of cells in the mouse were infected by either virus, indicating that the coinoculated viruses had infected the same small subpopulation of susceptible cells. The profound amplification of polytropic MuLVs in coinfected mice may be facilitated by pseudotyping or, alternatively, by transactivation of the polytropic virus in the coinfected cells. This study illustrates the complexity of the interactions between components of mixed retrovirus infections and the dramatic effects of these interactions on disease processes.
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Pang, Xuexia, Xiyao Geng, Shiqun Wang, Jinbin Cao, Zechao Deng, Pingguang Duan, Xuechen Li, Pengying Jia, and Longfei Xu. "Spatial Distribution and Low-frequency Disturbance Modulation of Magnetosheath Ion Polytropic Index." Astrophysical Journal 940, no. 2 (November 29, 2022): 120. http://dx.doi.org/10.3847/1538-4357/ac9d2d.
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Abstract We, using the Cluster data from 2001 to 2010, studied spatial distribution of the ion polytropic index in the magnetosheath, and the modulation of polytropic process by the low-frequency disturbances (4–18 mHz). The total of 30,3283 samples is divided into two sorts: quasi-perpendicular and quasi-parallel propagating ones. The median polytropic index increases with spreads narrowing from the bow shock to the magnetopause. The median polytropic indices are basically between isothermal and adiabatic in the inner magnetosheath, and between isothermal and isobaric in the outer magnetosheath. The spatial distributions of the correlation coefficient (CC) between the perturbed ion number density and the parallel magnetic field CC (δn, δB ∥) have a good correlation with those of polytropic index. The quasi-perpendicular disturbances are mostly mirror-like modes (D r ≪ 1) except for some slow-mode disturbances (D r ≥ 1) in the regions near the Sun–Earth line and the inner magnetosheath. The polytropic indices in the inner and middle magnetosheath modulated by mirror-like-mode disturbances are between 0.9 and 1.3. The quasi-parallel propagating low-frequency disturbances are predominantly slow modes in the inner and middle magnetosheath, and Alfvén modes in the outer magnetosheath. For the samples with quasi-parallel propagating disturbances, the polytropic processes are basically between isothermal and isobaric except near the magnetopause. The good correlation between the spatial distributions of polytropic index and low-frequency disturbances indicates that the distribution of the polytropic index in the magnetosheath is modulated by low-frequency disturbances.
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Livadiotis, George. "Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed." Entropy 20, no. 10 (October 17, 2018): 799. http://dx.doi.org/10.3390/e20100799.
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The paper derives the polytropic indices over the last two solar cycles (years 1995–2017) for the solar wind proton plasma near Earth (~1 AU). We use ~92-s datasets of proton plasma moments (speed, density, and temperature), measured from the Solar Wind Experiment instrument onboard Wind spacecraft, to estimate the moving averages of the polytropic index, as well as their weighted means and standard errors as a function of the solar wind speed and the year of measurements. The derived long-term behavior of the polytropic index agrees with the results of other previous methods. In particular, we find that the polytropic index remains quasi-constant with respect to the plasma flow speed, in agreement with earlier analyses of solar wind plasma. It is shown that most of the fluctuations of the polytropic index appear in the fast solar wind. The polytropic index remains quasi-constant, despite the frequent entropic variations. Therefore, on an annual basis, the polytropic index of the solar wind proton plasma near ~1 AU can be considered independent of the plasma flow speed. The estimated all-year weighted mean and its standard error is γ = 1.86 ± 0.09.
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Desta, Ephrem Tesfaye, R. D. Strauss, and N. E. Engelbrecht. "Modeling of the Polytropic Index and Temperature Anisotropy in the Solar Wind." Astrophysical Journal 966, no. 1 (May 1, 2024): 142. http://dx.doi.org/10.3847/1538-4357/ad380e.
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Abstract The polytropic index is a fundamental physical parameter related to the thermodynamic processes present in space and astrophysical plasmas. This paper investigates the theoretical relationship between the polytropic index and the temperature anisotropy for flow parameters relevant to space plasmas. The derivation is based on the Chew–Goldberger–Low double-adiabatic equations of state and the finite Larmor radius correction. On the basis of this, we present the polytropic index relation, taking into account the temperature anisotropy, flow speed, and magnetic field of the plasma. This relation was further analyzed for the limit of the quasi-parallel and quasi-transversal cases. The quasi-transversal limit gives a polytropic index as a function of the anisotropic temperature γ = 1 + 2[2T ⊥ − T ∥]/[2T ⊥ + T ∥]. Using this result, we analyze the polytropic index for the bulk proton parameters derived from Ulysses spacecraft data spanning the interval from 1992 January 1 to 2009 June 30, and we find an average polytropic index of γ ∼ 1.43. This value is close to that of recently published results. However, unlike previous statistical studies, this research computes the polytropic index without relying on power-law fitting, and its variation is now associated with the anisotropic temperature.
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Fahr, H. J., and D. Rucinski. "Heliospheric pick-up ions influencing thermodynamics and dynamics of the distant solar wind." Nonlinear Processes in Geophysics 9, no. 3/4 (August 31, 2002): 377–86. http://dx.doi.org/10.5194/npg-9-377-2002.
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Abstract. Neutral interstellar H-atoms penetrate into the inner heliosphere and upon the event of ionization are converted into pick-up ions (PUIs). The magnetized solar wind flow incorporates these ions into the plasma bulk and enforces their co-motion. By nonlinear interactions with wind-entrained Alfvén waves, these ions are then processed in the comoving velocity space. The complete pick-up process is connected with forces acting back to the original solar wind ion flow, thereby decelerating and heating the solar wind plasma. As we show here, the resulting deceleration cannot be treated as a pure loading effect, but requires adequate consideration of the action of the pressure of PUI-scattered waves operating by the PUI pressure gradient. Hereby, it is important to take into proper account the stochastic acceleration which PUIs suffer from at their convection out of the inner heliosphere by quasi-linear interactions with MHD turbulences. Only then can the presently reported VOYAGER observations of solar wind decelerations and heatings in the outer heliosphere be understood in view of the most likely values of interstellar gas parameters, such as an H-atom density of 0.12 cm-3 . Solar wind protons (SWPs) appear to be globally heated in their motion to larger solar distances. Ascribing the needed heat transfer to the action of suprathermal PUIs, which drive MHD waves that are partly absorbed by SWPs, in order to establish the observed SWP polytropy, we can obtain a quantitative expression for the solar wind proton pressure as a function of solar distance. This expression clearly shows the change from an adiabatic to a quasi-polytropic SWP behaviour with a decreasing polytropic index at increasing distances. This also allows one to calculate the average percentage of initial pick-up energy fed into the thermal proton energy. In a first order evaluation of this expression, we can estimate that about 10% of the initial PUI injection energy is eventually transfered to SWPs independent of the PUI injection rate.
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Sharif, M., and Sobia Sadiq. "Cracking in anisotropic polytropic models." Modern Physics Letters A 33, no. 24 (August 3, 2018): 1850139. http://dx.doi.org/10.1142/s0217732318501390.
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This paper is devoted to examine the cracking of spherically symmetric anisotropic fluid configuration for polytropic equation of state. For this purpose, we formulate the corresponding field equations as well as generalized Tolman–Oppenheimer–Volkoff equation. We introduce density perturbations in matter variables and then construct the force distribution function. In order to examine the occurrence of cracking/overturning, we consider two models corresponding to two values of the polytropic index. It is found that the first model exhibits overturning for the considered values of polytropic constant while the second model neither exhibits cracking nor overturning for larger values of polytropic constant.
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Nicolaou, Georgios, George Livadiotis, and David J. McComas. "The Polytropic Behavior of Solar Wind Protons as Observed by the Ulysses Spacecraft during Solar Minimum." Astrophysical Journal 948, no. 1 (April 28, 2023): 22. http://dx.doi.org/10.3847/1538-4357/acbf33.
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Abstract We analyze proton bulk parameters derived from Ulysses observations and investigate the polytropic behavior of solar wind protons over a wide range of heliocentric distances and latitudes. The large-scale variations of the proton density and temperature over heliocentric distance indicate that plasma protons are governed by subadiabatic processes (polytropic index γ < 5/3), if we assume protons with three effective kinetic degrees of freedom. From the correlation between the small-scale variations of the plasma density and temperature in selected subintervals, we derive a polytropic index γ ∼ 1.4 on average. Further examination shows that the polytropic index does not have an apparent dependence on the solar wind speed. This agrees with the results of previous analyses of solar wind protons at ∼1 au. We find that the polytropic index varies slightly over the range of the heliocentric distances and heliographic latitudes explored by Ulysses. We also show that the homogeneity of the plasma and the accuracy of the polytropic model applied to the data points vary over Ulysses' orbit. We compare our results with the results of previous studies that derive the polytropic index of solar wind ions within the heliosphere using observations from various spacecraft. We finally discuss the implications of our findings in terms of heating mechanisms and the effective degrees of freedom of the plasma protons.
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Jonkobilov, U., U. Rajabov, and S. Jonkobilov. "Experimental study of the polytropic coefficient for hydraulic shock from a decrease in pressure." IOP Conference Series: Earth and Environmental Science 1112, no. 1 (December 1, 2022): 012037. http://dx.doi.org/10.1088/1755-1315/1112/1/012037.
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Abstract The article provides an analysis of scientific papers on the study of a hydraulic shock absorber - an air-hydraulic cap, shows that at present there is no consensus on the choice of the numerical value of the polytropic coefficient n. In practice, during the operation of pumping stations with long pressure pipelines, in the event of a sudden power outage, water hammer often occurs to the motors of the main pumps. To prevent this phenomenon, it is convenient to apply a hydraulic shock absorber. The accuracy of calculating the shock absorber depends on the reliable value of the coefficient n. The correct selection of the numerical value of the polytropic coefficient n provides for determining the optimal dimensions of the proposed hydraulic shock absorber. There are different opinions about the choice of the numerical value of n among scientists. N.E. Zhukovsky, when calculating the hydraulic shock absorber, takes n = 1.41. V.S. Dikarevsky accepts n=1.0. Therefore, the rationale for the correct choice of the numerical value of the polytropic coefficient for calculating the absorber in the case of water hammer is very relevant. The paper presents the results of experimental studies of the polytropic coefficient n in a hydraulic shock absorber from a decrease in pressure. When conducting experiments on the study of the absorber, modern scientific instrumentation was used. At the same time, the obtained results of the experiments confirm that the variability of the value of the polytropic coefficient during hydraulic shock in the cap and the correctness of the recommendation of D.A. Fox. The conducted studies prove that the polytropic coefficient has a strictly polytropic character.
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FERRARI, L., G. ESTRELA, and M. MALHEIRO. "RELATIVISTIC EFFECTS IN POLYTROPIC COMPACT STARS." International Journal of Modern Physics E 16, no. 09 (October 2007): 2834–37. http://dx.doi.org/10.1142/s0218301307008525.
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We solve numerically the two first order differential equations obtained by Tooper for polytropic compact stars. These equations depend on the polytropic index n related to the adiabatic index Γ = 1 + 1/n and on a parameter σ that manifests the relativistic content of the polytropic equation of state (EOS). In this work we investigate the effect of increasing σ for two polytropic EOS: the case of a nonrelativistic Fermi gas (n = 1.5) and the relativistic one (n = 3.0). We show that for large values of σ, where the sound velocity is not small in comparison to the velocity of light, the matter density is more concentrated in the center of the star and as a consequence the star mass also is: this effect is quite strong in the case of the relativistic fermi gas.
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Nicolaou, Georgios, George Livadiotis, and Mihir I. Desai. "Estimating the Polytropic Indices of Plasmas with Partial Temperature Tensor Measurements: Application to Solar Wind Protons at ~1 au." Applied Sciences 11, no. 9 (April 28, 2021): 4019. http://dx.doi.org/10.3390/app11094019.
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We examine the relationships between temperature tensor elements and their connection to the polytropic equation, which describes the relationship between the plasma scalar temperature and density. We investigate the possibility to determine the plasma polytropic index by fitting the fluctuations of temperature either perpendicular or parallel to the magnetic field. Such an application is particularly useful when the full temperature tensor is not available from the observations. We use solar wind proton observations at ~1 au to calculate the correlations between the temperature tensor elements and the scalar temperature. Our analysis also derives the polytropic equation in selected streamlines of solar wind plasma proton observations that exhibit temperature anisotropies related to stream-interaction regions. We compare the polytropic indices derived by fitting fluctuations of the scalar, perpendicular, and parallel temperatures, respectively. We show that the use of the parallel or perpendicular temperature, instead of the scalar temperature, still accurately derives the true, average polytropic index value, but only for a certain level of temperature anisotropy variability within the analyzed streamlines. The use of the perpendicular temperature leads to more accurate calculations, because its correlation with the scalar temperature is less affected by the anisotropy fluctuations.
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Banerjee, Supratik, and Sébastien Galtier. "A Kolmogorov-like exact relation for compressible polytropic turbulence." Journal of Fluid Mechanics 742 (February 21, 2014): 230–42. http://dx.doi.org/10.1017/jfm.2013.657.
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AbstractCompressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term $\mathcal{S}$ which may act as a source or a sink for the mean energy transfer rate. At subsonic scales, we predict dimensionally that the isotropic $k^{-5/3}$ energy spectrum for the density-weighted velocity field ($\rho ^{1/3} \boldsymbol {v}$), previously obtained for isothermal turbulence, is modified by a polytropic contribution, whereas at supersonic scales $\mathcal{S}$ may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.
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GEROYANNIS, V. S., and F. N. VALVI. "A RUNGE–KUTTA–FEHLBERG CODE FOR THE COMPLEX PLANE: COMPARING WITH SIMILAR CODES BY APPLYING TO POLYTROPIC MODELS." International Journal of Modern Physics C 23, no. 05 (May 2012): 1250038. http://dx.doi.org/10.1142/s0129183112500386.
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In this paper, we modify the Runge–Kutta–Fehlberg code of fourth and fifth order with the purpose of solving initial value problems established on ordinary differential equations involving complex-valued functions of one complex variable, which are allowed to have high complexity in their definition, when integration along prescribed complex paths is required. Such initial value problems arise in certain astrophysical issues, like the polytropic models, applied to polytropic stars, and the general-relativistic polytropic models, applied to neutron stars. Comparison with similar codes is made by applying to these models.
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Fahr, H. J. "Solar wind heating by an embedded quasi-isothermal pick-up ion fluid." Annales Geophysicae 20, no. 10 (October 31, 2002): 1509–18. http://dx.doi.org/10.5194/angeo-20-1509-2002.
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Abstract. It is well known that the solar wind plasma consists of primary ions of solar coronal origin and secondary ions of interstellar origin. Interstellar H-atoms penetrate into the inner heliosphere and when ionized there are converted into secondary ions. These are implanted into the magnetized solar wind flow and are essentially enforced to co-move with this flow. By nonlinear interactions with wind-entrained Alfvén waves the latter are processed in the co-moving velocity space. This pick-up process, however, also causes actions back upon the original solar wind flow, leading to a deceleration, as well as a heating of the solar wind plasma. The resulting deceleration is not only due to the loading effect, but also due to the action of the pressure gradient. To calculate the latter, it is important to take into account the stochastic acceleration that suffers at their convection out of the inner heliosphere by the quasi-linear interactions with MHD turbulences. Only then can the presently reported VOYAGER observations of solar wind decelerations and heatings in the outer heliosphere be understood in terms of the current, most likely values of interstellar gas parameters. In a consistent view of the thermodynamics of the solar wind plasma, which is composed of secondary ions and solar wind protons, we also derive that the latter are globally heated at their motion to larger solar distances. The arising heat transfer is due to the action of suprathermal ions which drive MHD waves that are partially absorbed by solar wind protons and thereby establish their observed quasi-polytropy. We obtain a quantitative expression for the solar wind proton pressure as a function of solar distance. This expression clearly shows the change from an adiabatic to a quasi-polytropic behaviour with a decreasing polytropic index at increasing distances, as has been observed by the VOYAGERS. This also allows one to calculate the average percentage of the intitial energy fed into the thermal proton energy. In a first-order evaluation of this expression we can estimate that under stationary flow conditions about 10% of the initial injection energy is eventually transfered to solar wind protons, independent of the actual injection rate. Key words. Interplanetary physics (energetic particles; interstellar gas; solar wind plasma)
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Evans, Leonard H., A. S. M. Alamgir, Nick Owens, Nick Weber, Kimmo Virtaneva, Kent Barbian, Amenah Babar, Frank Malik, and Kyle Rosenke. "Mobilization of Endogenous Retroviruses in Mice after Infection with an Exogenous Retrovirus." Journal of Virology 83, no. 6 (December 30, 2008): 2429–35. http://dx.doi.org/10.1128/jvi.01926-08.
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ABSTRACT Mammalian genomes harbor a large number of retroviral elements acquired as germ line insertions during evolution. Although many of the endogenous retroviruses are defective, several contain one or more intact viral genes that are expressed under certain physiological or pathological conditions. This is true of the endogenous polytropic retroviruses that generate recombinant polytropic murine leukemia viruses (MuLVs). In these recombinants the env gene sequences of exogenous ecotropic MuLVs are replaced with env gene sequences from an endogenous polytropic retrovirus. Although replication-competent endogenous polytropic retroviruses have not been observed, the recombinant polytropic viruses are capable of replicating in numerous species. Recombination occurs during reverse transcription of a virion RNA heterodimer comprised of an RNA transcript from an endogenous polytropic virus and an RNA transcript from an exogenous ecotropic MuLV RNA. It is possible that homodimers corresponding to two full-length endogenous RNA genomes are also packaged. Thus, infection by an exogenous virus may result not only in recombination with endogenous sequences, but also in the mobilization of complete endogenous retrovirus genomes via pseudotyping within exogenous retroviral virions. We report that the infection of mice with an ecotropic virus results in pseudotyping of intact endogenous viruses that have not undergone recombination. The endogenous retroviruses infect and are integrated into target cell genomes and subsequently replicate and spread as pseudotyped viruses. The mobilization of endogenous retroviruses upon infection with an exogenous retrovirus may represent a major interaction of exogenous retroviruses with endogenous retroviruses and may have profound effects on the pathogenicity of retroviral infections.
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Shi, Chen, Marco Velli, Stuart D. Bale, Victor Réville, Milan Maksimović, and Jean-Baptiste Dakeyo. "Acceleration of polytropic solar wind: Parker Solar Probe observation and one-dimensional model." Physics of Plasmas 29, no. 12 (December 2022): 122901. http://dx.doi.org/10.1063/5.0124703.
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The acceleration of the solar coronal plasma to supersonic speeds is one of the most fundamental yet unresolved problems in heliophysics. Despite the success of Parker's pioneering theory on an isothermal solar corona, the realistic solar wind is observed to be non-isothermal, and the decay of its temperature with radial distance usually can be fitted to a polytropic model. In this work, we use Parker Solar Probe data from the first nine encounters to estimate the polytropic index of solar wind protons. The estimated polytropic index varies roughly between 1.25 and 1.5 and depends strongly on solar wind speed, faster solar wind on average displaying a smaller polytropic index. We comprehensively analyze the 1D spherically symmetric solar wind model with the polytropic index [Formula: see text]. We derive a closed algebraic equation set for transonic stellar flows, that is, flows that pass the sound point smoothly. We show that an accelerating wind solution only exists in the parameter space bounded by [Formula: see text] and [Formula: see text], where C0 and Cg are the surface sound speed and one half of the escape velocity of the star, and no stellar wind exists for [Formula: see text]. With realistic solar coronal temperatures, the observed solar wind with [Formula: see text] cannot be explained by the simple polytropic model. We show that mechanisms such as strong heating in the lower corona that leads to a thick isothermal layer around the Sun and large-amplitude Alfvén wave pressure are necessary to remove the constraint in γ and accelerate the solar wind to high speeds.
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Ray, Subharthi, Manuel Malheiro, José P. S. Lemos, and Vilson T. Zanchin. "Charged polytropic compact stars." Brazilian Journal of Physics 34, no. 1a (March 2004): 310–14. http://dx.doi.org/10.1590/s0103-97332004000200038.
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Knight, Randall. "All About Polytropic Processes." Physics Teacher 60, no. 6 (September 2022): 422–24. http://dx.doi.org/10.1119/5.0077026.
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Of all the conceivable ideal-gas processes, almost all introductory physics textbooks as well as more advanced texts on thermodynamics emphasize only four: isochoric, isobaric, isothermal, and adiabatic (isentropic). These are processes in which a state variable—volume, pressure, temperature, or entropy— remains constant. It turns out that these four processes are examples of a more general ideal-gas process, called a polytropic process, in which the specific heat remains constant. Polytropic processes are frequently discussed in engineering thermodynamics but rarely in physics. The goal of this paper is to bring polytropic processes to the attention of physics instructors. These processes have interesting properties (such as, in some cases, negative specific heat), they are easily accessible at the introductory physics level, and they expand the range of examples and problems that can be explored in thermodynamics.
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Chen, Yu-Tung, Niann-Chern Lee, and Ming-Hsien Tu. "Polytropic gas dynamics revisited." Journal of Mathematical Physics 48, no. 7 (July 2007): 072702. http://dx.doi.org/10.1063/1.2748620.
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Theuns, T., and M. David. "Spherically symmetric, polytropic flow." Astrophysical Journal 384 (January 1992): 587. http://dx.doi.org/10.1086/170901.
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Das, Ashok, and Ziemowit Popowicz. "Supersymmetric polytropic gas dynamics." Physics Letters A 296, no. 1 (April 2002): 15–26. http://dx.doi.org/10.1016/s0375-9601(02)00145-7.
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Geroyannis, V. S. "Rotating visco-polytropic models." Astrophysics and Space Science 167, no. 1 (1990): 13–20. http://dx.doi.org/10.1007/bf00642058.
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