In this paper, we propose a method for solving some classes of the singular fractional nonlinear Lane-Emden type equations. The is proposed by utilizing second-kind Chebyshev wavelets in conjunction with quasilinearization technique. operational matrices are used. tested on standard equation, isothermal gas spheres and other examples. We compare results produced present well-known to show accur...

X-ray emitting clusters of galaxies are considered in the context of modified Newtonian dynamics (MOND). I show that self-gravitating isothermal gas spheres are not good representations of rich clusters with respect to the radial gas density distribution as indicated by the X-ray surface brightness. Pure gas spheres with a density distribution described by a β model, as observed, also fail beca...

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application branches physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising astrophysics: the positive negative indices polytropic gas spheres, isothermal sphere, white dwarf equation. calcula...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...

The isothermal gas sphere is a particular type of Lane-Emden equation and used widely to model many problems in astrophysics, like the formation stars, star clusters galaxies. In this paper, we present computational scheme simulate conformable fractional using an artificial neural network (ANN) technique, compare obtained results with analytical solution deduced Taylor series. We performed our ...

The gravitational lensing properties of cosmological halos depend upon the mass distribution within each halo. The description of halos as nonsingular, truncated isothermal spheres, a particular solution of the isothermal Lane-Emden equation (suitably modified for Λ 6= 0), has proved to be a useful approximation for the halos which form from realistic initial conditions in a CDM universe. We de...

Bird flocks, mammal herds, cellular tissue, and artificial self-propelled colloids are all examples of “active” matter—an assembly of self-driven units that take energy from the environment to produce motion [1]. Active matter is, in many ways, analogous to a gas of atoms or molecules, except that the particles are far from equilibrium, and therefore cannot be described with standard statistica...

effect of water gas shift reaction (co+h2o=co2+h2) on wustite reduction has been investigated by a transient, non-isothermal mathematical model based on grain model. in this model, wustite porous pellet is reduced using syngas, namely a mixture of hydrogen, carbon monoxide, carbon dioxide and water vapor. for this purpose, governing equations containing continuity equation of species and energy...