Related papers: On the Cylindrical Grad-Shafranov Equation
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
This paper explores the cubic-quintic Schr\"odinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the…
In the spirit of analog models of and for general relativity, we explore the isomorphism between the equations of linearized turbulent fluid flow and those of the linearized form of GR, gravitoelectromagnetism. The correspondence between…
The scattering theory approach makes it possible to carry out exact calculations of Casimir energies in any geometry for which the scattering T-matrix and a partial wave expansion of the free Green's function are available. We implement…
A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These…
We examine a model for the observed temporal variability of powerful blazars in the $\gamma$-ray band in which the dynamics is described in terms of a stochastic differential equation, including the contribution of a deterministic drift and…
For jets, with great power comes great opportunity. The unprecedented center of mass energies available at the LHC open new windows on the QGP: we demonstrate that jet shape and jet cross section measurements become feasible as a new,…
In the above entitled recent publication by Giovanni Lapenta [Phys. Rev. Lett. Vol 90, 135005 (2003) ] it is claimed construction of a new class of solitonlike solutions for the Grad-Shafranov equation in plane geometry. It is proved here…
In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is…
The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action…
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
Gas outflows appear to be a phenomenon shared by the vast majority of quasars. Observations indicate that there is wide range in outflow prominence. In this paper we review how the 4D eigenvector 1 scheme helps to organize observed…
A model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field…
We suggest a mathematical potential well with spherical symmetry and apply to the 1d Schr\"odinger equation. We use some well-known techniques as Stationary Perturbation Theory and WKB to gain insight into the solutions and compare them to…
This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight,…
Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained…
The aim of this paper is to investigate the dynamical aspects of charged viscous cylindrical source by using Misner approach. To this end, we have considered the more general charged dissipative fluid enclosed by the cylindrical symmetric…
The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the…
An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…