相关论文: Improving the Lagrangian perturbative solution for…
In the era of precision cosmology, the cosmological constant $\Lambda$ gives quite an accurate description of the evolution of the Universe, but it is still plagued with the fine-tuning problem and the cosmic coincidence problem. In this…
We present a consistent high-order staggered Lagrangian hydrodynamics framework designed to reconcile an underlying disparity in existing curvilinear formulations: the mismatch between quadrature-based "strong" mass conservation and the…
We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the…
We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid…
A higher-order analysis of the evolution of cosmological perturbations in a Friedman universe is given by using the PMF method. The essence of the PMF approach is to choose a gauge where all fluctuations of the density, the pressure, and…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We discuss various analytical approximation methods for the evolution of the density fluctuation in the Universe. From primordial density fluctuation, the large-scale structure is formed via its own self-gravitational instability. For this…
The shrinking core model describes the reaction of a spherical solid particle with a surrounding fluid. In this work, we revisit the SCM by deriving it from the underlying physical processes and performing a careful non-dimensionalisation,…
Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type $p=w_{\rm eff}(\rho)\,\rho$, and has been used in previous…
Our ignorance about the source of cosmic acceleration has stimulated study of a wide range of models and modifications to gravity. Cosmological scaling solutions in any of these theories are privileged because they represent natural…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
We apply the Lagrangian perturbation theory with time-dependent growth functions at second and third order of perturbation with the aim to model the effect of dynamical dark energy on redshift-space distortions. Our fiducial galaxy redshift…
In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
In arXiv:1601.02203 and arXiv:1702.07063, we have proposed a topological model with a simple Lagrangian density and have tried to solve one of the cosmological constant problems. The Lagrangian density is the BRS exact and therefore the…
This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…