Related papers: Conformable Fractional Polytropic Gas Spheres
We consider the velocity distribution for a granular gas of inelastic hard spheres described by the Boltzmann equation. We investigate both the free of forcing case and a system heated by a stochastic force. We propose a new method to…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
Spherically symmetric relativistic stars with the polytropic equation of state (EoS), which possess the local pressure anisotropy, are considered within the framework of general relativity. The generalized Lane-Emden equations are derived…
We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives…
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
We study the dynamical properties of spherical galaxies with surface luminosity profile described by the R^{1/m}-law, in which a variable degree of orbital anisotropy is allowed. The parameter m for the present models covers the range…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
We consider an anisotropic version of Baxter's model of `sticky hard spheres', where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate `dipolar sticky' correction (positive or negative,…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
We consider the supercritical Lane-Emden problem $$(P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} $$ where $\mathcal A$ is an annulus in $\rr^{2m},$ $m\ge2$ and…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
In this work we will analyse the complexity factor, proposed by L. Herrera, for spherically symmetric static matter distributions satisfying a polytropic equation through the gravitational decoupling method. Specifically, we will use the…
We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local density approximation (LDA) and density matrix renormalization group (DMRG)…
The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a…
This article is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in "M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math.…
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, based on frame properties, for equations involving the…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
In this paper, we have introduced new viable solutions of Einstein-Maxwell field equations by incorporating the features of anisotropic matter distribution in the realm of General theory of Relativity ($GR$). For this procurement, we have…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…