Polytropic Model Research Articles

Evaluation of heat transfer enhancement effect at the hot/cold end of a Stirling engine using performance improvement factor

The driving force of a Stirling engine comes from the heating expansion and cooling compression of working medium. The enhancement of heat transfer capacity of the hot/cold end is the key to improve the Stirling engine performance, while how to objectively evaluate the heat transfer enhancement effect is a precondition. Herein, a polytropic model of a Stirling engine thermal cycle process was firstly established. A method for evaluating the heat transfer enhancement performance under oscillating flow was proposed based on the efficiency and power improvement of a Stirling engine. This method was further used to evaluate the heat transfer enhancement effect of a novel four-leaf helical heating tube under oscillating flow, the efficiency and power improvement factor of which was reached 13.5 % and 6.1 %, respectively. The results show that the efficiency and power improvement evaluation criterion was more comprehensive and intuitive in evaluating the heat transfer enhancement performance under oscillating flow compared with the conventional evaluation indictor like performance evaluation criterion and equivalent tube length and tube number criterion.

The operationally ready full 3D magnetohydrodynamic model from the Sun to Earth: COCONUT+Icarus

Context. Solar wind modelling has become a crucial area of study due to the increased dependence of modern society on technology, navigation, and power systems. Accurate space weather forecasts can predict upcoming threats to Earth’s geospace and allow for harmful socioeconomic impacts to be mitigated. Coronal and heliospheric models must be as realistic as possible to achieve successful predictions. In this study, we examine a novel full magnetohydrodynamic (MHD) chain from the Sun to Earth. Aims. The goal of this study is to demonstrate the capabilities of the full MHD modelling chain from the Sun to Earth by finalising the implementation of the full MHD coronal model into the COolfluid COroNa UnsTructured (COCONUT) model and coupling it to the MHD heliospheric model Icarus. The resulting coronal model has significant advantages compared to the pre-existing polytropic alternative, as it includes more physics and allows for a more realistic modelling of bi-modal wind, which is crucial for heliospheric studies. In particular, we examine different empirical formulations for the heating terms in the MHD equations to determine an optimal one that would be able to mimic a realistic solar wind configuration most accurately. Methods. New heating source terms were implemented into the MHD equations of the pre-existing polytropic COCONUT model. A realistic specific heat ratio was applied. In this study, only thermal conduction, radiative losses, and approximated coronal heating function were considered in the energy equation. Multiple approximated heating profiles were examined to see the effect on the solar wind. The output of the coronal model was used to onset the 3D MHD heliospheric model Icarus. A minimum solar activity case was chosen as the first test case for the full MHD model. The numerically simulated data in the corona and the heliosphere were compared to observational products. First, we compared the density data to the available tomography data near the Sun and then the modelled solar wind time series in Icarus was compared to OMNI 1-min data at 1 AU. Results. A range of approximated heating profiles were used in the full MHD coronal model to obtain a realistic solar wind configuration. The bi-modal solar wind was obtained for the corona when introducing heating that is dependent upon the magnetic field. The modelled density profiles are in agreement with the tomography data. The modelled wind in the heliosphere is in reasonable agreement with observations. Overall, the density is overestimated, whereas the speed at 1 AU is more similar to OMNI 1-min data. The general profile of the magnetic field components is modelled well, but its magnitude is underestimated. Conclusions. We present a first attempt to obtain the full MHD chain from the Sun to Earth with COCONUT and Icarus. The coronal model has been upgraded to a full MHD model for a realistic bi-modal solar wind configuration. The approximated heating functions have modelled the wind reasonably well, but simple approximations are not enough to obtain a realistic density-speed balance or realistic features in the low corona and farther, near the outer boundary. The full MHD model was computed in 1.06 h on 180 cores of the Genius cluster of the Vlaams Supercomputing Center, which is only 1.8 times longer than the polytropic simulation. The extended model gives the opportunity to experiment with different heating formulations and improves the approximated function to model the real solar wind more accurately.

The motion of twisted particles in a stellar gravitational field

Abstract In this work, we explore the motion of a twisted particle possessing intrinsic orbital angular momentum (OAM) as it traverses a weak stellar gravitational field, which we approximate using a polytropic model. We disregard the spin characteristic of the twisted particle, modeling it as a massless complex twisted scalar wave packet to simplify its interaction with gravitational fields. Building on this simplification, we determine the trajectory of this twisted particle by using the center of its energy density and investigate the gravitational birefringence induced by its OAM. In a weak field approximation, we find the gravitational birefringence-OAM relationship parallels that with spin, as described by the Mathisson-Papapetrou-Dixon equations. This indicates that the gravitational birefringence induced by OAM can potentially exceed that induced by spin by several orders of magnitude, significantly enhancing its detectability. To broaden our analysis, we introduce a nonminimal coupling term, $\lambda R|\phi|^2$, into the Lagrangian, resulting in the modified expression $\mathcal{L}=-\frac{1}{2}\nabla _\rho\phi\nabla^\rho\phi^*-\frac{1}{2}\lambda R|\phi|^2$. This adjustment is necessitated by the quantization of the scalar field in curved spacetime. We then explore the effects of this term on the motion of the twisted particle. Our findings show that the trajectory of the twisted particle under nonminimal coupling ($\lambda\neq 0$) differs from that in the minimal coupling scenario ($\lambda=0$). Specifically, for a positive nonminimal coupling constant $\lambda$, the trajectory of the twisted particle is expected to deviate away from the stellar center, compared to the minimal coupling scenario.

Adiabatic Mass Loss in Binary Stars. IV. Low- and Intermediate-mass Helium Binary Stars

The unstable mass transfer situation in binary systems will asymptotically cause the adiabatic expansion of the donor star and finally lead to the common envelope phase. This process could happen in helium binary systems once the helium donor star fills its Roche-lobe. We have calculated the adiabatic mass-loss model of naked helium stars with a mass range of 0.35 M ⊙–10 M ⊙, and every mass sequence evolved from the helium-zero-age main sequence to the cooling track of white dwarf or carbon ignition. In consideration of the influence of stellar wind, massive helium stars are not considered in this paper. Comparing the stellar radius with the evolution of the Roche-lobe under the assumption of conservative mass transfer, we give the critical mass ratio q crit = M He/M accretor as the binary stability criteria of low- and intermediate-mass helium binary stars. On the helium main sequence, the result shows 1.0 < q crit < 2.6, which is more unstable than the classical result of polytropic model q crit = 3. After the early helium Hertzsprung Gap, the q crit quickly increases even larger than 10 (more stable compared with the widely used result of q crit = 4), which is dominated by the expansion of the radiative envelope. Our result could be useful for these quick mass transfer binary systems such as AM CVns, ultra-compact X-ray binaries, and helium novae, and it could guide the binary population synthesis for the formation of special objects such as type Ia supernova and gravitational wave sources.

Polytropic gas cosmology and late-time acceleration

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

Compact stars with non-uniform relativistic polytrope

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman–Oppenheimer–Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation.

Godunov-type scheme for air–water transient pipe flow considering variable heat transfer and laboratorial validation

A robust comprehensive energy dissipation model is developed to investigate the rapid filling process of a T-shaped bifurcated pipeline with entrapped air pocket, while an experimental system is designed to validate the numerical model. In this work, a self-adapting heat transfer model is proposed to describe the energy exchange during transient event, fully considering the heat transfer of entrapped air pocket and hydraulic losses caused by steady friction and unsteady friction in the section of the filling water column. Importantly, the related heat transfer coefficient is variable and determined by mechanism formula of media characteristics, which is obviously different from the constant heat transfer coefficient in conventional model relying on the trial-and-error method and experimental data. Moreover, the second-order Godunov-type scheme is introduced to solve the governing equations of filling water column, while a virtual plug approach is proposed to track the air–water interface. The resulting predictions are compared to those obtained via a conventional empirical polytropic model and constant coefficient heat transfer model, and to experimental data. The proposed model accurately reproduces the experimental pressure oscillations. The results display that when an air pocket content exceeds a certain threshold (>1.7%), the comprehensive model using forced convection can reproduce the pressure fluctuations. When the air content is lower (<0.9%), the comprehensive model using natural convection can simulate pressure changes more accurately. The conventional empirical polytropic model underestimates the pressure damping. The constant coefficient heat transfer model previously cannot be employed if there is no experimental data to calibrate the constant coefficient, but now the constant coefficient can be obtained from the results of the proposed model. Significantly, the comprehensive model can directly and accurately simulate the energy dissipation during the rapid filling process.

Annular structures in perturbed low mass disc-shaped gaseous nebulae: general, standard and polytropic models

We study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas-perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation’s frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to slowly rotating thin gaseous discs of negligible relative mass, submitted to small radial periodic perturbations.

Realistic compact objects in the f(R, T) gravity in the background of polytropic and barotropic gas models

The f(R, T) gravity in the background of the polytropic and barotropic fluid has been investigated in this work. We have selected the TOV equation to determine the internal spacetime of a spherically symmetric galactic object. With the use of the Einstein equation, we have selected KB-spacetime to calculate the mass, compactness, and surface redshift of a spherically symmetric body. Explicit conditions for model parameters have been constructed for the boundary conditions of the interior and exterior spacetime, and the Schwarzschild solution has been employed in the modified f(R, T) gravity theory to evaluate different matching criteria. An increasing pattern in compactness with respect to the different radii is evident in the graphical representation of the compactness evolution for each of the individual star models. After selecting a non-vacuum field equation for higher order curvature, we reformulated f(R, T) for R and T. As a result, the tangential pressure, radial pressure, and matter density have all been calculated. According to the study, as the radius goes to infinity, the tangential and radial pressures display asymptotic flatness and converge to zero. Polytropic and barotropic gas EoS have been adopted since the star model confronts the presence of an isotropic fluid backdrop. It has been noted that in a polytropic background, density and pressure increase with distance from the star’s core, but in a barotropic background, the pressure exhibits an ascending pattern as a function of radius.

COMPUTING POLYTROPIC AND ISOTHERMAL MODELS USING MONTE CARLO METHOD

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.

The calculation of normal stars structure within the generalized polytropic model

The calculation of normal stars structure within the generalized polytropic model

Possibility of stable thin-shell around wormholes within string cloud and quintessential field via the van der Waals and polytropic EOS

In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwarzschild BH surrounded by cloud and quintessence-type fluid distribution by using a well-known cut and paste approach. We have also performed stability analysis using the linearized radial perturbation method for the van der Waals EOS and polytropic EOS. Several interesting points have evolved from the entire investigation along with the features of the thin shell around the wormhole. It is interesting to mention that the van der Walls equation of state plays a remarkable role to maintain the stability of the thin-shell around the wormhole structure as compared to polytropic model for both choices of shape functions.

The impact of halo concentration on the Sunyaev Zel’dovich effect signal from massive galaxy clusters

ABSTRACT The Sunyaev Zel’dovich (SZ) effect is sensitive to the pressure of ionized gas inside galaxy clusters, which is in turn controlled largely by the gravitational potential of the cluster. Changing the concentration parameter describing the cluster mass distribution impacts the gravitational potential and thus the cluster SZ signal, with implications for cosmological and other analyses of SZ-selected clusters. We investigate the concentration–SZ relation in theory and simulations. We find that the impact of concentration on the inner SZ profile (R ≲ 0.75R200c) can be captured with standard polytropic gas models. However, we find that such models do a poor job of reproducing the outer SZ profiles (R ≳ 0.75R200c) and the relation between the integrated SZ signal, Y, and concentration. This disagreement results from a sharp truncation of the gas pressure profile near the splashback radius, likely caused by virial shocks. We develop a simple description of the truncation that leads to a good match with the simulated SZ profiles out to several R200c for clusters of varying mass and concentration, and that also accurately predicts the concentration–Y relationship. Finally, we determine how inference of the linear bias parameter and splashback radius for SZ-selected clusters can be biased by ignoring the concentration dependence of the SZ signal, finding that bias to the former is essentially negligible, while bias to the latter can be as much as 2 per cent.

Order-preserving fuzzy transform for singular boundary value problems of polytropic gas flow and sewage diffusion

We describe a fuzzy transform method to analyze two-point singular and non-singular boundary value problems with high-order solution accuracies. This framework implements a fuzzy transform that approximates solutions with fourth-order accuracy at the interior mesh points. The fuzzy components and the triangular base function are locally arranged with a three-point linear combination of solution values. This yields a tri-diagonal Jacobian matrix that can be easily computed in a space-time efficient manner. Since a linear system relates solution values and fuzzy components, it is easy to obtain solution approximations via fuzzy components by a tri-diagonal matrix inversion. In addition to the numerical solution, it is easy to determine an approximate analytic solution using a cubic spline interpolating polynomial from the data available with fuzzy components. The error estimates for approximate analytical solutions and numerical solutions are obtained by integrated absolute error and maximum absolute errors. The new mechanism is analyzed for convergence using matrix theory. Several linear and nonlinear equations of practical importance related to sewage diffusion and polytropic gas flow models are simulated to corroborate the new scheme's utility and fourth-order convergence. Mathematics subject classification03B80, 65L10, 65L12

Study of Neutron Star in [formula omitted] and [formula omitted] gravity framework with Polytropic Gas Background

This study reformulates f(T) and f(G) gravity for neutron stars using a modified Tolman–Oppenheimer–Volkoff equation. Reconstruction approaches have been developed in the polytropic gas model context assuming that the star’s density is a quadratic, linear, or exponential function of the radius r. Studies have been carried out on the behaviour of modified gravity theories reconstructed through analytical solutions and the assumption of some already valid forms. The evolution of the radial density of the neutron star has been studied in every instance. For f(T) gravity, it is determined that the density of the neutron star increases with radius, which is explainable as a result of accretion surrounding the neutron star. Additionally, as r→∞, the reconstructed models show asymptotic flatness. As a result, it has been hypothesised that the interior mass of the neutron star resembles an ideal fluid, which results in decreased viscosity and lessened internal resistance. This lowers the possibility of collapse for the neutron star.

RUBIS: A simple tool for calculating the centrifugal deformation of stars and planets

Aims. We present the Rotation code Using Barotropy conservation over Isopotential Surfaces (RUBIS), a fully Python-based centrifugal deformation program that is available publicly. The code has been designed to calculate the centrifugal deformation of stars and planets resulting from a given cylindrical rotation profile, starting from a spherically symmetric non-rotating model. Methods. The underlying assumption in RUBIS is that the relation between density and pressure is preserved during the deformation process. This leads to many procedural simplifications. For instance, RUBIS only needs to solve Poisson’s equation in either spheroidal or spherical coordinates, depending on whether the 1D model has discontinuities. Results. We present the benefits of using RUBIS to deform polytropic models and more complex barotropic structures, thus providing insights into baroclinic models to a certain extent. The resulting structures can be used for a wide range of applications, including the seismic study of models. Finally, we illustrate how RUBIS is beneficial specifically in the analysis of Jupiter’s gravitational moments through its ability to handle discontinuous models while retaining a high accuracy compared to current methods.

Reconstruction of f(R) Gravity from a Polytropic Gas Scalar Field Dark Energy Model

Reconstruction of f(R) Gravity from a Polytropic Gas Scalar Field Dark Energy Model

The Polytropic Behavior of Solar Wind Protons as Observed by the Ulysses Spacecraft during Solar Minimum

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.

Analysis of class I complexity induced spherical polytropic models for compact objects

In this research, we present a comprehensive framework that uses a complexity factor to analyze class I generalized relativistic polytropes. We establish class I generalized Lane–Emden equations using the Karmarkar condition under both isothermal and non-isothermal regimes. Our approach considers a spherically symmetric fluid distribution for two cases of the generalized polytropic equation of state: 1) the mass density case μo and 2) the energy density case μ. To obtain numerical solutions for both cases, we solve two sets of differential equations that incorporate the complexity factor. Finally, we conduct a graphical analysis of these solutions.

NIRwave: A wave-turbulence-driven solar wind model constrained by PSP observations

Aims. We generate a model description of the solar wind based on an explicit wave-turbulence-driven heating mechanism, and constrain our model with observational data. Methods. We included an explicit coronal heating source term in the general 3D magnetohydrodynamic code NIRVANA to simulate the properties of the solar wind. The adapted heating mechanism is based on the interaction and subsequent dissipation of counter-propagating Alfvén waves in the solar corona, accounting for a turbulent heating rate Qp. The solar magnetic field is assumed to be an axisymmetric dipole with a field strength of 1 G. Our model results are validated against observational data taken by the Parker Solar Probe (PSP). Results. Our NIRwave solar wind model reconstructs the bimodal structure of the solar wind with slow and fast wind speeds of 410 km s−1 and 650 km s−1 respectively. The global mass-loss rate of our solar wind model is 2.6 × 10−14 M⊙ yr−1. Despite implementing simplified conditions to represent the solar magnetic field, the solar wind parameters characterising our steady-state solution are in reasonable agreement with previously established results and empirical constraints. The number density from our wind solution is in good agreement with the derived empirical constraints, with larger deviations for the radial velocity and temperature. In a comparison to a polytropic wind model generated with NIRVANA, we find that our NIRwave model is in better agreement with the observational constraints that we derive.