相关论文: Geodesic models generated by Lie symmetries
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
Within the context of a cosmic space whose energy source is modeled with a perfect fluid, a uniform model of Universe based on a standard FRW cosmology containing decoupled mixed matter sources namely stiff matter and cosmic dust together…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
This manuscript aims to establish the gravitational junction conditions(JCs) for the $f(\mathcal{G},~T)$ gravity. In this gravitational theory, $f$ is an arbitrary function of Gauss-Bonnet invariant $\mathcal{G}$ and the trace of the…
The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the…
We study dusty winds driven by radiation pressure in the atmosphere of a rapidly star-forming environment. We apply the variable Eddington tensor algorithm to re-examine the two-dimensional radiation hydrodynamic problem of a column of gas…
We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a…
We simulate numerically the surface flow of a gas-supplying companion star in a semi-detached binary system. Calculations are carried out for a region including only the mass-losing star, thus not the mass accreting star. The equation of…
We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles…
We explore the conditions required for isolated vortices to exist in sheared zonal flows and the stability of the underlying zonal winds. This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming…
Using the relativistic equations of radiation hydrodynamics in the viscous limit, we analyze the boundary layers that develop between radiation-dominated jets and their environments. In this paper we present the solution for the…
We discuss head-on collisions of neutron stars and disks of dust ("galaxies") following the ideas of equilibrium thermodynamics, which compares equilibrium states and avoids the description of the dynamical transition processes between…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…
We present a differential geometric framework for the motion of a non-Brownian particle in the presence of fixed obstacles in a quiescent fluid, in the deterministic Stokesian regime. While the Helmholtz Minimum Dissipation Theorem suggests…
Turbulent flows in the solar wind, large scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains "turbulent reconnection".…
A remarkable phenomenon in turbulent flows is the spontaneous emergence of coherent large spatial scale zonal jets. Geophysical examples of this phenomenon include the Jovian banded winds and the Earth's polar front jet. In this work a…