Related papers: On the Cylindrical Grad-Shafranov Equation
This paper revises traditional phenomenological approaches to the application of Vlasov equation to describe the dissipative systems. The original equation by A.A. Vlasov obtained differs from the classical Vlasov equation used in the…
Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state,…
Broadband emission from relativistic outflows (jets) of active galactic nuclei (AGN) and gamma-ray bursts (GRBs) contains valuable information about the nature of the jet itself, and about the central engine which launches it. Using special…
In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and…
Existing approaches to solving the Vlasov equation treat the system as a partial differential equation on a phase space grid, and track in either an Eulerian, Lagrangian, or semi-Lagrangian picture. We present an alternative approach, which…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
The Chevalier & Clegg (1985) spherical wind is widely used to model galactic outflows. Efforts are underway to understand the production of multiphase gas in such outflows. Since the important scales for the multiphase gas are very small…
We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities…
The advances in cold atom experiments have allowed construction of confining traps in the form of curved surfaces. This opens up the possibility of studying quantum gases in curved manifolds. On closed surfaces, many fundamental processes…
Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of their collimation angle. Modeling a jet break requires an understanding of the "jet spreading" process, whereby the jet transitions from a collimated outflow into the…
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
We present a new, approximate method for modelling the acceleration and collimation of relativistic jets in the presence of gravity. This method is self-similar throughout the computational domain where gravitational effects are negligible…
We demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may…
We formulate and implement the Euler equations with SGS dynamics and provide numerical tests of an SGS turbulence energy model that predicts the turbulent pressure of unresolved velocity fluctuations and the rate of dissipation for highly…
We present an analytical solution of a highly magnetized jet/wind flow. The left side of the general force-free jet/wind equation (the "pulsar" equation) is separated into a rotating and a nonrotating term. The two equations with either…
A gas-liquid type of phase transition is found based on the particle dynamics on radius-$R$ circle in which the coordinate appears as the angle-variable of 1D XY-model. Due to the specific appearance of compact-space radius (volume) in the…
This note is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of…
The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate…
The observation of the diffuse Galactic gamma ray flux is the most powerful tool to study cosmic rays in different regions of the Galaxy, because the energy and angular distributions of the photons encode information about the density and…
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding…