Relativistic polytropic models of charged anisotropic compact objects

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(GR).To obtain these solutions,we employed the Finch-Skea spacetime,along with a generalized polytropic equation of state( EoS).We constructed various models of generalized polytropes by assuming different values of the polytropic index,i.e.,η=1/2,2/3,1,and 2.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 EoS.

Stiffness Characteristics of a Basic Nonlinear Air Spring Model

This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.

Stability Analysis of the Viscous Polytropic Dark Energy Model in Einstein Cosmology

The viscous polytropic gas model as one model of dark energy is hot-spot and keystone to the modern cosmology. We study the evolution of the viscous polytropic dark energy model interacting with the dark matter in the Einstein cosmology. Setting the autonomous dynamical system for the interacting viscous polytropic dark energy with dark matter and using the phase space analysis method to investigate the dynamical evolution and its critical stability, we find that the viscosity property of the dark energy creates a benefit for the stable critical dynamical evolution of the interaction model between dark matter and dark energy in the flat Friedmann-Robertson-Walker universe and the viscosity of dark energy will soften the coincidence problem just like the interacting dark energy model.