Emptiness formation in polytropic quantum liquids

We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

Charged anisotropic compact star core-envelope model with polytropic core and linear envelope

This manuscript is related to the construction of relativistic core-envelope model for spherically symmetric charged anisotropic compact objects. The polytropic equation of state is considered for core, while it is linear in the case of envelope. We present that core, envelope and the Reissner Nordstr$$\ddot{o}$$ o ¨ m exterior regions of stars match smoothly. It has been verified that all physical parameters are well behaved in the core and envelope region for the compact stars SAX J1808.4-3658 and 4U1608-52. Various physical parameters inside star are discussed herein, non-singularity and continuity at the junction has been catered as well. Impact of charged compact object together with core-envelope model on the mass, radius and compactification factor is described by graphical representation in both core and envelop regions. The stability of the model is worked out with the help of Tolman–Oppenheimer–Volkoff equations and radial sound speed.

Modeling of thermodynamic processes using the properties of matter presented in the form of spreadsheets

New thermodynamic cycles are developed in which the working fluid used cannot be considered as an ideal gas. This applies to oxy-fuel combustion cycles. In these cycles, oxygen is separated from the air prior to combustion. The combustion chamber is supplied with fuel and pure oxygen. The required temperature at the outlet of the combustion chamber is achieved by supplying some other substances from which it is easy to separate the CO2 formed during the combustion of the fuel. Commonly, CO2, or H2O, or their mixture is used as such substances. Thus, there are no exotic substances in the composition of the working fluid, but such a range of parameters is chosen for such cycles that the working fluid at certain points of the cycle can be both gaseous and liquid, or in a supercritical state. To model thermodynamic processes in such cycles, it is unacceptable to use the polytropic equation of ideal gases. A technique for integrating differential equations describing the state of the working fluid is proposed. This technique is based on the presentation of the thermodynamic properties of pure substances that make up the working fluid in the form of spreadsheets. The proposed technique is implemented in a software-computing module.

STABILITY ANALYSIS OF RELATIVISTIC POLYTROPES

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.

Study of generalized cylindrical polytropes with complexity factor

In this paper, complexity factor is used with generalized polytropic equation of state to develop two consistent systems of three differential equations and a general frame work is established for modify form of Lane-Emden equations. For this purpose anisotropic fluid distribution is considered in cylindrical static symmetry with two cases of generalized polytropic equation of state (i) mass density $$\mu _{o}$$ μ o and (ii) energy density $$\mu $$ μ . A graphical analysis will be carried out for the numerical solution of these systems of three differential equations.

Estimating the Polytropic Indices of Plasmas with Partial Temperature Tensor Measurements: Application to Solar Wind Protons at ~1 au

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.

Measurement of the effective mean-free-path of the solar wind protons

<p>The solar corona is heated and accelerated sufficiently to escape the gravitational bound of the sun into the interplanetary medium as a super-Alfvénic turbulent plasma called the solar wind. The Spitzer-Härm particle mean-free-path and relaxation time (i.e. to an isotropic Maxwellian distribution function) for typical solar wind proton parameters are large compared to the system size and therefore a non-collisional treatment of the plasma can be argued to be appropriate. Despite the long mean-free-path, large scales of the solar wind are fluid-like: density-pressure polarizations follow a polytropic equation of state. These observations suggest effective collisional processes (e.g. quasi-linear relaxation, plasma wave echo) are active, altering the equation of state from a non-collisional (or kinetic) to a polytropic equation of state (e.g. fluid magnetohydrodynamics [MHD]). We employ 13 years of high cadence onboard 0th-2nd moments of the proton velocity distribution function recorded by the Wind spacecraft to study the equation of state via compressive fluctuations. Upon comparison with a collisional kinetic-MHD dispersion relation solver, our analysis indicates an effective mean-free-path (collision frequency) that is [∼10<sup>2</sup>] smaller (larger) than the typical Spitzer-Härm estimate. This effect is scale dependent justifying a fluid approach to large scales which breaks down at smaller scales where a more complex equation of state is necessary.</p>

Acceptability conditions and relativistic barotropic equations of state

We sketch an algorithm to generate exact anisotropic solutions starting from a barotropic EoS and setting an ansatz on the metric functions. To illustrate the method, we use a generalization of the polytropic equation of state consisting of a combination of a polytrope plus a linear term. Based on this generalization, we develop two models which are not deprived of physical meaning as well as fulfilling the stringent criteria of physical acceptability conditions. We also show that some relativistic anisotropic polytropic models may have singular tangential sound velocity for polytropic indexes greater than one. This happens in anisotropic matter configurations when the polytropic equation of state is implemented together with an ansatz on the metric functions. The generalized polytropic equation of state is free from this pathology in the tangential sound velocity.

Gravitational lensing by multi-polytropic wormholes

We obtain static, asymptotically flat, multi-polytropic wormhole solutions in the framework of general relativity. We examine gravitational lensing in the presence of the wormhole and calculate the deflection angle for both weak and strong fields. We investigate microlensing in the weak field limit and obtain corresponding light curves for both galactic and extragalactic situations. We discuss the astrophysical motivation of considering the multi-polytropic equation of state that supports the wormhole geometry. Finally, we investigate the energy conditions.