相关论文: Non--Linear Dynamics of Irrotational Dust: Euleria…

A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…

The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…

This paper develops a geometric mechanics framework for the reduction of general relativistic hydrodynamic variational principles, from the variation of worldlines approach in 4D spacetime to 3-dimensional Eulerian descriptions. We consider…

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…

In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent…

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of…

We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion…

Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual…

The standard nonlinear perturbation theory of the gravitational instability is extended to incorporate the nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. We show that local Eulerian bias is not generally…

In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron…

We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, ${\rm St} < 1$, using both Lagrangian and Eulerian…

We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination…

In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous…

Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to…

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations…

In this paper we present a new local Lagrangian approximation to the gravitational dynamics of cold matter. We describe the dynamics of a Lagrangian fluid element through only one quantity, the deformation tensor. We show that this tensor…

We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein…

An exact expression for the gravitational field strength in a self-gravitating dust continuum is derived within the Lagrangian picture of continuum mechanics. From the Euler-Newton system a transport equation for the gravitational field…

The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are…