Related papers: Numerical approximation of systems modeling large …
We consider the gravitational clustering of a multicomponent fluid in an expanding Newtonian universe, taking into account the mutual gravitational interactions of the medium. We obtain a set of exact and approximate solutions for two fluid…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism 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…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
Dipole cosmology is the maximally Copernican generalization of the FLRW paradigm that can incorporate bulk flows in the cosmic fluid. In this paper, we first discuss how multiple fluid components with independent flows can be realized in…
We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements' form. We apply it to…
We present a set of cosmological variables, called "supercomoving variables," which are particularly useful for describing the gas dynamics of cosmic structure formation. For ideal gas with gamma=5/3, the supercomoving position, velocity,…
This work devises a formalism to obtain the equations of motion for a black hole-fluid configuration. Our approach is based on a Post-Newtonian expansion and adapted to scenarios where obtaining the relevant dynamics requires long…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly…
A new truncation scheme based on the cumulant expansion of the one-particle phase-space distribution function for dark matter particles is developed. Extending the method of moments in relativistic kinetic theory, we derive evolution…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality. A brief literature review of AdS/CFT and gauge/gravity duality is presented first. This is followed by a pedagogical introduction to the use of…
I give a geometric construction of certain first order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such…
This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading…
The understanding of the large-scale structure formation requires the resolution of coupled nonlinear equations describing the cosmic density and velocity fields. This is a complicated problem that, for the last decade, has been essentially…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…
We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an astronomical N-body system. To do this, we generalize…