Related papers: Excision and avoiding the use of boundary conditio…
We present a realistic scenario of tracking of scalar fields with varying equation of state. The astrophysical constraints on the evolution of scalar fields in the physical universe are discussed. The nucleosynthesis and the galaxy…
In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution…
We study Hamilton-Jacobi equations in [0, +$\infty$) of evolution type with nonlinear boundary conditions of Neumann type in the case where the Hamiltonian is non necessarily convex with respect to the gradient variable. In this paper, we…
A new set of nonlocal boundary conditions are proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear…
We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…
We present an approach for computing extensions of velocities or other fields in level set methods by solving a biharmonic equation. The approach differs from other commonly used approaches to velocity extension because it deals with the…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion,…
Emulation has been successfully applied across a wide variety of scientific disciplines for efficiently analysing computationally intensive models. We develop known boundary emulation strategies which utilise the fact that, for many…
Motivated by modelling rotating turbulence in planetary fluid layers, we investigate precession-driven flows in ellipsoids subject to stress-free boundary conditions (SF-BC). The SF-BC could indeed unlock numerical constraints associated…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
We show that a single constrained scalar field with non-minimal coupling to gravity can give rise to an accelerating Universe. First, we consider this model in the absence of external matter. In the original Jordan frame, we show that the…
I review a class of nonlocally modified gravity models which were proposed to explain the current phase of cosmic acceleration without dark energy. Among the topics considered are deriving causal and conserved field equations, adjusting the…
We describe an implicit general relativistic hydrodynamics code. The evolution equations are formulated in comoving coordinates. A conservative finite differencing of the Einstein equations is outlined, and artificial viscosity and…
The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…