arXiv subjects

Puja Bharti

Publications and source records attributed to Puja Bharti.

4 recordsLinked to original sources

arXiv2024

(w, c)-periodic functions on time scales and application for families of delayed dynamic equations representing population models

This paper delves into a novel class of functions defined on an invariant under translation time scale T, known as (w, c)-periodic functions. This class encompasses various types of functions, such as periodic, anti-periodic, Bloch, and unbounded functions. To equip this set of functions with a comprehensive mathematical framework, we introduce a suitable norm on T, transforming the space consisting of (ω, c)-periodic functions into a Banach space. Several fundamental properties of this newly established class are examined. Furthermore, we present a significant application of our theoretical findings. We investigate the unique existence of asymptotically exponentially stable (w, c)-periodic solutions for some families of generalized dynamic equations on time scales. These dynamic equations represent population models incorporating feedback and time-varying delays. Our study outlines sufficient conditions for the emergence of such solutions, highlighting their importance in understanding the dynamics of complex systems over time scales. In particular, we explore (w, c)-periodic solutions for prominent models, such as the Nicholsan model, Lasota- Wazewska model, and their mixed versions on time scales. Our investigations are groundbreaking, as they encompass both discrete and continuous cases, presenting a unified perspective on periodic behavior across various systems.

math.DS↗

arXiv2022

The classification of interior solutions of anisotropic fluid configurations

The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the solutions of field equations have a long and rich history. It took a year for Karl Schwarzschild to obtain the first exact solution of Einstein's field equations since general theory of relativity was published. The number of viable solutions has been growing since then. Many authors have adopted several methods to obtain the solution. Different models have been constructed for a variety of applications. To produce feasible models of compact stars, a considerable amount of effort has been applied in gaining an understanding of the properties of anisotropic matter. Theoretical study indicates that pressure within compact stars with extreme internal density and strong gravity is mostly anisotropic. Anisotropy was found sufficient for the study of compact stars with the dense nuclear matter. It is claimed that it is important to consider the pressure experienced to be anisotropic whenever relativistic fluids are involved. In this review article, we have discussed different ways of generating a static spherically symmetric anisotropic fluid model. The purpose of the article is to present a simple classification scheme for static and spherically symmetric anisotropic fluid solutions. The known solutions are reviewed and compartmentalized as per the proposed scheme so that we can illustrate general ideas about these solutions without being exhaustive.

gr-qc↗

arXiv2021

An isotropic compact stellar model in curvature coordinate system consistent with observational data

This paper investigates a spherically symmetric compact relativistic body with isotropic pressure profiles within the framework of general relativity. In order to solve the Einstein's field equations, we have considered the Vaidya-Tikekar type metric potential, which depends upon parameter K. We have presented a perfect fluid model, considering K<0 or K>1, which represent compact stars like SMC X-1, Her X-1, 4U 1538-52, SAX J1808.4-3658, LMC X-4, EXO 1785-248 and 4U1820-30, to an excellent degree of accuracy. We have investigated the physical features such as the energy conditions, velocity of sound, surface redshift, adiabatic index of the model in detail and shown that our model obeys all the physical requirements for a realistic stellar model. Using the Tolman-Oppenheimer-Volkoff equations, we have explored the hydrostatic equilibrium and the stability of the compact objects. This model also fulfils the Harrison-Zeldovich-Novikov stability criterion. The results obtained in this paper can be used in analyzing other isotropic compact objects.

astro-ph.GA↗

arXiv2021

Pulsar PSR B0943+10 as an isotropic Vaidya-Tikekar type compact star : A comprehensive study

In this paper, we have constructed a model for well behaved isotropic compact star in the presence of charged perfect fluid, by considering a static and spherically symmetric metric in Schwarzschild's canonical coordinate system. To put the resulting differential equations into a closed system, we have employed the Vaidya & Tikekar (J. Astrophys. Astron. 3:325, 1982) form of the metric potential grr. The resulting energy-momentum components, i.e., energy density and pressure contain six constants; two of these are determined through the junction condition (matching the interior with the exterior Schwarzschild solution) and by the property of vanishing pressure on the boundary. The remaining constants are constrained by requirements of a real compact star. The physical acceptability of our model is tested using the data of the pulsar PSR B0943+10. Using graphical analysis and tabular information we have shown that our model obeys all the physical requirements. The stability of this model is evaluated using the Tolman-Oppenheimer-Volkoff equation, the adiabatic index and the Harrison-Zeldovich-Novikov Criterion and it has passed the evaluation.

gr-qc↗