Related papers: Cored DARKexp systems with finite size: numerical …
We develop structure-preserving finite volume schemes for the barotropic Euler equations in the low Mach number regime. Our primary focus lies in ensuring both the asymptotic-preserving (AP) property and the discrete entropy stability. We…
We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in…
The Effective-One-Body (EOB) formalism contains several flexibility parameters, notably $a_5$, $\vp$ and $\a$. We show here how to jointly constrain the values of these parameters by simultaneously best-fitting the EOB waveform to two,…
In this paper, we study the effective field theory (EFT) of dark energy for the $k$-essence model beyond linear order. Using particle-mesh $N$-body simulations that consistently solve the dark energy evolution on a grid, we find that the…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
The kinematics of stars and planetary nebulae in early type galaxies provide vital clues to the enigmatic physics of their dark matter halos. We fit published data for fourteen such galaxies using a spherical, self-gravitating model with…
A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre $\beta$ ensemble, characterised by the Dyson parameter $\beta$, and the Laguerre…
We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. Our method…
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…
On the cosmological length scale, recent measurements by WMAP have validated $\Lambda$CDM to a precision not see before in cosmology. Such is not the case on galactic length scales, however, where the `cuspy-core' problem has demonstrated…
The rotation velocity profiles of galaxies (rotation curves) remain unexpectedly flat at large distances, where visible matter alone should make the rotation velocity decrease with radius. Conventionally, this requires a large amount of…
The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall-Jackiw-Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite…
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
We study the expansion of an interacting atomic system at zero temperature, following its release from an isotropic three-dimensional harmonic trap and calculate the time dependence of its density and momentum distribution, with special…
A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value…
We study the emergence of non-compact degrees of freedom in the low energy effective theory for a class of $\mathbb{Z}_2$-staggered six-vertex models. In the finite size spectrum of the vertex model this shows up through the appearance of a…
We study the problem of planar central configurations with $N$ heavy bodies and $k$ bodies with arbitrary small masses. We derive the equation which describe the limit of light masses going to zero, which can be seen as the equation for…