Polytropic Fluid Research Articles

Formation of singularities of solutions to the IBVP of the Euler–Boltzmann equations

The initial-boundary value problem for the three-dimensional Euler–Boltzmann equations of a polytropic, ideal and isentropic fluid in radiation hydrodynamics is considered outside a unit ball. It is proved that some $$C^{1}$$ solution will develop singularities in a finite time provided that a weighed functional associated with the initial momentum and the initial intensity of radiation is large.

Testing adiabatic expansion of polytropic universe model with SNe Ia data

In order to obtain a better fit for the observational data, various cosmological models have been developed in the literature. For this purpose, we propose an adiabatic expansion of the Universe with a polytropic fluid matter-radiation content and a varying cosmological constant. Basic motivation of this study basically differs from the previous models because our model does not neglect the pressure of the matter content of the Universe. We present the details of our new derivations by obtaining the polytropic matter density and luminosity distances. After constructing the model, two large collections of observational data of supernovae type Ia (SNe Ia) are conducted to diagnose the model. Examining the fitness of our new models of a polytropic universe with the observational data, we find a significant influence of polytropic matter on the cosmological parameters of the expanding universe. We find that our flat constant Λ model and varying Λ model describes the SNe Ia data significantly better than the other models including the standard model for Gold Data and Union2.1 Data, respectively.

Matter accretion onto Einstein-aether black holes via well-known fluids * * Pakistan for its financial support under the grant No: 9290/Balochistan/NRPU/R&D/HEC/2017

We study matter accretion onto Einstein-aether black holes by adopting the Hamiltonian approach. The general solution of accretion is discussed using the isothermal equation of state. Different types of fluids are considered, including ultra-relativistic, ultra-stiff, sub-relativistic, and radiation fluids, and the accretion process onto Einstein-aether black holes is analyzed. The behavior of the fluid flow and the existence of critical points is investigated for Einstein-aether black holes. We further discuss the general expression and behavior of polytropic fluid onto Einstein-aether black holes. The most important feature of this work is the investigation of the mass accretion rate of the above-mentioned fluids and the comparison of our findings with the Schwarzschild black hole, which generates particular signatures. Moreover, the maximum mass accretion rate occurs near the Killing and universal horizons, and the minimum accretion rate lies between them.

Choked Accretion onto a Schwarzschild Black Hole: A Hydrodynamical Jet-launching Mechanism

Abstract We present a novel, relativistic accretion model for accretion onto a Schwarzschild black hole. This consists of a purely hydrodynamical mechanism in which, by breaking spherical symmetry, a radially accreting flow transitions into an inflow-outflow configuration. The spherical symmetry is broken by considering that the accreted material is more concentrated on an equatorial belt, leaving the polar regions relatively under-dense. What we have found is a flux-limited accretion regime in which, for a sufficiently large accretion rate, the incoming material chokes at a gravitational bottleneck and the excess flux is redirected by the density gradient as a bipolar outflow. The threshold value at which the accreting material chokes is of the order of the mass-accretion rate found in the spherically symmetric case studied by Bondi and Michel. We describe the choked accretion mechanism first in terms of a general relativistic, analytic toy model based on the assumption of an ultrarelativistic stiff fluid. We then relax this approximation and, by means of numerical simulations, show that this mechanism can operate also for general polytropic fluids. Interestingly, the qualitative inflow-outflow morphology obtained appears as a generic result of the proposed symmetry break, across analytic and numeric results covering both the Newtonian and relativistic regimes. The qualitative change in the resulting steady-state flow configuration appears even for a very small equatorial-to-polar-density contrast (∼0.1%) in the accretion profile. Finally, we discuss the applicability of this model as a jet-launching mechanism in different astrophysical settings.

The Gravitational Instability of Adiabatic Filaments

Abstract Filamentary structures, or long and narrow streams of material, arise in many areas of astronomy. Here we investigate the stability of such filaments by performing an eigenmode analysis of adiabatic and polytropic fluid cylinders, which are the cylindrical analog of spherical polytropes. We show that these cylinders are gravitationally unstable to perturbations along the axis of the cylinder below a critical wavenumber k crit ≃ few, where k crit is measured relative to the radius of the cylinder. Below this critical wavenumber, perturbations grow as , where τ is time relative to the sound-crossing time across the diameter of the cylinder, and we derive the growth rate σ u as a function of wavenumber. We find that there is a maximum growth rate σ max ∼ 1 that occurs at a specific wavenumber k max ∼ 1, and we derive the growth rate σ max and the wavenumbers k max and k crit for a range of adiabatic indices. To the extent that filamentary structures can be approximated as adiabatic and fluidlike, our results imply that these filaments are unstable without the need to appeal to magnetic fields or external media. Further, the objects that condense out of the instability of such filaments are separated by a preferred length scale, form over a preferred timescale, and possess a preferred mass scale.

Radial instability of trapping polytropic spheres

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.

Mixed star-plus-wormhole systems with a complex scalar field

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

Blow-up criterion for the 3D viscous polytropic fluids with degenerate viscosities

<p style="text-indent:20px;">In this paper, the Cauchy problem of the <inline-formula><tex-math id="M1">$ 3 $</tex-math></inline-formula>D compressible Navier-Stokes equations with degenerate viscosities and far field vacuum is considered. We prove that the <inline-formula><tex-math id="M2">$ L^\infty $</tex-math></inline-formula> norm of the deformation tensor <inline-formula><tex-math id="M3">$ D(u) $</tex-math></inline-formula> (<inline-formula><tex-math id="M4">$ u $</tex-math></inline-formula>: the velocity of fluids) and the <inline-formula><tex-math id="M5">$ L^6 $</tex-math></inline-formula> norm of <inline-formula><tex-math id="M6">$ \nabla \log \rho $</tex-math></inline-formula> (<inline-formula><tex-math id="M7">$ \rho $</tex-math></inline-formula>: the mass density) control the possible blow-up of regular solutions. This conclusion means that if a solution with far field vacuum to the Cauchy problem of the compressible Navier-Stokes equations with degenerate viscosities is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of <inline-formula><tex-math id="M8">$ D(u) $</tex-math></inline-formula> or <inline-formula><tex-math id="M9">$ \nabla \log \rho $</tex-math></inline-formula> as the critical time approaches; equivalently, if both <inline-formula><tex-math id="M10">$ D(u) $</tex-math></inline-formula> and <inline-formula><tex-math id="M11">$ \nabla \log \rho $</tex-math></inline-formula> remain bounded, a regular solution persists.</p>

Simulation of a Plant for the Production of Polyethylene

The simulation of a 270 KTA capacity polyethylene plant was performed using Aspen Hysys version 8.8. A Hysys model of the polyethylene was developed using the polyethylene plant layout of Indorama Eleme Petrochemical Company. A material and energy balance for the various components of the plant was performed manually and with Hysys for comparison. The design of the various components of the Hysys model was performed. The polyethylene reactor was simulated to study the effect of process functional parameters such as reactor dimensions, temperature and pressure. The effect of reactor size and number on polyethylene output was studied by simulating the plant with five continuous stirred tank reactors (CSTRs) in series and a single reactor. The results of the material and energy balance of the various components of the plant were performed manually and with Hysys which showed a maximum deviation of 0.8%. The design results of the sizing parameters for the Multiple and single CSTRs were compared in terms of Volume, Diameter, Height, Spacetime, Space Velocity, and Volumetric flowrate respectively. At 90% Conversion, the multiple CSTRs gave 600 dm3, 0.7668 m, 1.198 m, 0.052 hr, 195.83 hr-1, and 117.5 m3/h for the above listed parameters, while the single CSTR gave 6000 dm3, 1.721 m, 2.581 m, 0.056 hr, 17.867 hr-1 and 107.2 m3/h for the same conversion. The sizing results for each of the five compressors were also compared in terms of the following parameters: Adiabatic Head, Polytropic Head, Adiabatic fluid Head, polytropic Fluid Head, Adiabatic Efficiency, power consumed, polytropic head factor, polytropic exponent and isentropic exponent. The effect of reactor size and number showed that At 90% conversion the multiple CSTRS in series gave a lower volume than the single CSTR for the same conversion, and more Economical than the single CSTR for the same conversion.

On Classical Solutions for Viscous Polytropic Fluids with Degenerate Viscosities and Vacuum

In this paper, we consider the three-dimensional isentropic Navier–Stokes equations for compressible fluids allowing initial vacuum when viscosities depend on density in a superlinear power law. We introduce the notion of regular solutions and prove the local-in-time well-posedness of solutions with arbitrarily large initial data and a vacuum in this class, which is a long-standing open problem due to the very high degeneracy caused by a vacuum. Moreover, for certain classes of initial data with a local vacuum, we show that the regular solution that we obtained will break down in finite time, no matter how small and smooth the initial data are.

On cosmology of interacting varying polytropic dark fluids

In this paper, a possibility of the accelerated expansion of the large scale universe with interacting varying polytropic fluid of a certain type is presented. About a special role of non-gravitational interactions between dark energy and dark matter, in particular, about a possibility of improvement and solution of problems arising in modern cosmology, has been discussed for a long time. This motivates us to consider new models, where non-gravitational interactions between varying polytropic fluid and cold dark matter are allowed. Mainly nonlinear interactions of a specific type is considered, found in recent literature. The present study extends previously obtained results demonstrating that considered new parameterization of dark side of the universe could be supported by available observational data and will present the role of considered non-gravitational interactions in this case. During the study of suggested cosmological models Om analysis is applied. Moreover, with different datasets, including a strong gravitational lensing dataset, the best fit values of the model parameters are obtained using [Formula: see text] analysis.

Singularities of solutions to compressible Euler equations with damping

In this paper, we study the formation of finite-time singularities of smooth solutions to the compressible Euler equations with damping in arbitrary dimensions for isentropic, polytropic fluid flows. The radial component of initial momentum is assumed to be large enough and the smooth solutions are assumed to be decay at far fields, but it is not required that the initial velocity field has a compact support. It is shown that the smooth solutions to the Cauchy problem will break down in a finite time. Our result partially complements the work for the compactly supported initial velocity field (Sideris et al., 2003).

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

The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.

Nonlinear logarithmic interactions and a varying polytropic gas

In this paper, we constructed and demonstrated possible existence of some exotic forms of non-gravitational interaction. In particular, the construction has been done assuming that dark energy in considered models is a varying polytropic fluid suggested recently by one of us. Ongoing research in both directions, i.e. dark energy and non-gravitational interaction, opens very interesting perspectives for solving the problems which are related to the accelerated expansion of the Universe. The fact that available observational data allows to parametrize the dark side of the Universe in the form of interacting dark fluids is not less surprising than the accelerated expansion itself. Therefore, the consideration of new forms of non-gravitational interactions in modern cosmology is still one of the actual topics and requires deep and systematic research. On the other hand, the BOSS experiment announcement about the Hubble value parameter at z = 2.34 allows some authors to conclude that it is going to be an evidence on the existence of non-gravitational interaction between dark energy and dark matter. Concerning this, in this paper we will demonstrate that a specific form of a varying polytropic fluid can do it without requiring any non-gravitational interaction if the Hubble parameter value will be quite less than its present value reported by other missions. Actually, this fact motivates us also to consider various new forms of non-gravitational logarithmic interactions and study their cosmological and BOSS experiment result consequences. A classification of the models in the light of actively discussed Om analysis is also presented in this work allowing also to obtain some constraints on the model parameters.

Dynamics of gravitational instability excitation in viscoelastic polytropic fluids

The evolutionary excitation dynamics of the gravitational instability in a self-gravitating viscoelastic non-thermal polytropic complex fluid is semi-analytically explored on the astro-scales of space and time. The polytropic equation of state is well validated for the hydrostatic equilibrium established by a perfect heating-cooling balancing in the uni-component complex fluid. We apply a generalized gravitating hydrodynamic model in the concurrent presence of buoyancy, thermal fluctuations, volumetric expansion, and so forth. A normal mode (local) analysis yields a quadratic linear dispersion relation with a unique set of multi-parametric coefficients. The analytical reliability is checked by comparing with the existing reports on purely ideal inviscid nebular fluids and non-ideal viscoelastic fluids in isolation. It is seen that, unlike the normal instability mechanisms, the instability here remains unaffected due to the thermo-mechanical diffusion processes. The stabilizing (destabilizing) and accelerating (decelerating) factors of the instability are illustratively explored. The instability features are judged in the light of both impure non-ideal viscoelastic fluid and pure ideal inviscid nebular fluid scenarios. The relevancy of our exploration in superdense compact viscoelastic astro-objects and their surrounding atmospheres is summarily outlined.

Evolution and characteristics of forced shear flows in polytropic atmospheres: large and small Péclet number regimes

Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a `secular' shear instability in the low P\'eclet number regime with large Richardson numbers.

Compact stars in f(T) extended theory of gravity

We consider static spherically symmetric self-gravitating configurations of the perfect fluid within the framework of the torsion-based extended theory of gravity. In particular, we use the covariant formulation of $f(T)$ gravity with $f(T) = T + \frac{\alpha}{2} T^2$, and for the fluid we assume the polytropic equation of state with the adiabatic exponent $\Gamma = 2$. The constructed solutions have a sharply defined radius [as in General Relativity (GR)] and can be considered as models of nonrotating compact stars. The particle number--to--stellar radius curves reveal that with positive (negative) values of $\alpha$ smaller (greater) number of particles can be supported against gravity then in GR. For the interpretation of the energy density and the pressure within the star we adopt the GR picture where the effects due to nonlinearity of $f(T)$ are seen as a $f(T)$ fluid, which together with the polytropic fluid contributes to the effective energy momentum. We find that sufficiently large positive $\alpha$ gives rise to an abrupt sign change (phase transition) in the energy density and in the principal pressures of the $f(T)$ fluid, taking place within the interior of the star. The corresponding radial profile of the effective energy density is approximately constant over the central region of the star, mimicking an incompressible core. This interesting phenomenon is not found in configurations with negative $\alpha$.

Relativistic polytropic spheres with electric charge: Compact stars, compactness and mass bounds, and quasiblack hole configurations

We study the static stellar equilibrium configurations ofuncharged and charged spheres composed by a relativistic polytropic fluid, and compare with those of spheres composed by a non-relativistic polytropic fluid, the later case already being studied in a previous work [J. D. Arba\~nil, P. S. Lemos, V. T. Zanchin, Phys. Rev. D \textbf{88}, 084023 (2013)]. In the relativistic fluid case, a relativistic polytropic equation of state, $p=\omega\delta^{\gamma}$, is assumedd. Here, $\delta=\rho-p/(\gamma-1)$, with $\delta$ and $\rho$ being the rest mass density and the energy density, respectively, and $\omega$ and $\gamma$ are respectively the polytropic constant and the polytropic exponent. We assume that the charge density $\rho_e$ is proportional to the energy density $\rho$, $\rho_e = \alpha\, \rho$, with $\alpha$ being a constant such that $0\leq |\alpha|\leq 1$. Some properties of the charged spheres such as mass, total electric charge, radius, redshift, and the speed of sound are analyzed. The dependence of such properties with the polytropic exponent is also investigated. In addition, some limits that arise in general relativity, such as the Chandrasekhar limit, the Oppenheimer-Volkoff limit, the Buchdahl bound and the Buchdahl-Andr\'easson bound, i.e., the Buchdahl bound for the electric case, are studied. As in a charged non-relativistic polytropic sphere, the charged relativistic polytropic sphere with $\gamma\to\infty$ and $\alpha \to 1$ saturates the Buchdahl-Andr\'easson bound, thus indicating that it reaches the quasiblack hole configuration. We show by means of numerical analysis that, as expected, the major differences between the two cases appear in the high energy density region.

Accretion onto a charged Kiselev black hole

Accretion of matter onto a compact is one of the interesting astrophysical processes. Here, we study the accretion of matter onto a charged Kiselev black hole. The problem of static and spherically symmetric accretion of a polytropic fluid is explored for the analytic solution of equations of motion. We have investigated the necessary conditions for existence of the critical flow points and the mass accretion rate. Finally, we discuss the polytropic gas accretion in detail. It has been found that in the accretion process the quintessence and charge parameters play a dominant role.

Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations

For the three-dimensional full compressible Navier–Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid, we establish the global existence and uniqueness of classical solutions with smooth initial data which are of small energy but possibly large oscillations where the initial density is allowed to vanish. Moreover, for the initial data, which may be discontinuous and contain vacuum states, we also obtain the global existence of weak solutions. These results generalize previous ones on classical and weak solutions for initial density being strictly away from a vacuum, and are the first for global classical and weak solutions which may have large oscillations and can contain vacuum states.