Related papers: The post--quasi-static approximation: An analytica…
Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion…
We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical…
Theories of modified gravity, in both the linear and fully non-linear regime, are often studied under the assumption that the evolution of the new (often scalar) degree of freedom present in the theory is quasi-static. This approximation…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of $\Gamma\to 1$. We calculate the limiting continuously self similar (CSS) solution and the…
We quantify if the chemical abundance gradients given by a dynamical model of core collapse including time-dependent changes in density and temperature differ greatly from abundances derived from static models, where the density and…
The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wave function of the system and the semiclassical limit is considered for the gravitational part. The method of…
We carry out numerical simulations of the gravitational collapse of a rotating perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in axisymmetry in $2+1$ spacetime dimensions with $\Lambda<0$. We show that for…
We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…
We propose two methods that enable us to obtain approximate solutions of the lens equation near a fold caustic with an arbitrary degree of accuracy. We obtain "post-linear" corrections to the well-known formula in the linear caustic…
This paper reviews the essential physics of gravitational instability in a Robertson-Walker background spacetime. Three approaches are presented in a pedagogical manner, based on (1) the Eulerian fluid equations, (2) the Lagrangian…
In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dimensional one. In this paper, we formulate a generic scheme…
We investigate the dynamics of triaxial collapse in terms of eigenvalues of the deformation tensor, the velocity derivative tensor and the gravity Hessian. Using the Bond-Myers model of ellipsoidal collapse, we derive a new set of equations…
A quasi-static approximation (QSA) for modified gravity can be applied in a number of ways. We consider three different analytical formulations based on applying this approximation to: (1) the field equations; (2) the equations for the two…
We study the development of gravitational instability in the strongly non-linear regime. For this purpose we use a number of statistical indicators such as filamentary statistics, spectrum of overdense/underdense regions and the void…
A new class of self-gravitating collapsing star models with perfect fluid distributions is discussed in this work. The paper has a comprehensive analysis of a homogeneous gravitational collapsing system wherein using a parametrization…
In this paper, we obtain analytical approximate black hole solutions in the framework of $f(R)$ gravity and the absence of a cosmological constant. In this area, we apply the equations of motion of the theory to a spherically symmetric…
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…
We study the equation of one-dimensional quasistatic nonlinear viscoelasticity with Dirichlet boundary conditions, in the particular case that the underlying dissipation geometry (provided by the viscosity) is comparable to the Bhattacharya…