Related papers: On Local Approximations to the Nonlinear Evolution…
In recent years considerable advances have been made in quantitative homogenization of partial differential equations in the periodic and non-periodic settings. This monograph surveys the theory of quantitative homogenization for…
The computation of Lagrangian coherent structures (LCS) has established itself as a prominent means to reveal significant geometric structures in time-dependent vector fields. Their characterization, however, requires the selection of a…
We evaluate the effect of structure formation on the average expansion rate with a statistical treatment where density peaks and troughs are modelled as homogeneous ellipsoids. This extends earlier work that used spherical regions. We find…
We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then…
The cosmological mass function problem is analyzed in full detail in the case of 1D gravity, with analytical, semi-analytical and numerical techniques. The extended Press & Schechter theory is improved by detailing the relation between…
Aims:In this study we investigate the evolution of shape and kinematics of elliptical galaxies in a cosmological framework. Methods: We use a set of hydrodynamic, self-consistent simulations operating in the context of a concordance…
A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
The linear algorithm of the the full non-linear large scale structure of Gaussian random fields is extended here to to perform non-linear CRs. The procedure consists of: (1) Using linear CR of low resolution data to construct a high…
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to…
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,…
The formalism that describes the non-linear growth of the angular momentum L of protostructures from tidal torques in a Friedmann Universe, as developed in a previous paper, is extended to include non-Gaussian initial conditions. We…
We present a fully probabilistic, physical model of the non-linearly evolved density field, as probed by realistic galaxy surveys. Our model is valid in the linear and mildly non-linear regimes and uses second order Lagrangian perturbation…
A fundamental relation in Lagrangian Kolmogorov theory is concerned with inertial range scaling of the second-order velocity structure function over intermediate time lags at sufficiently high Reynolds numbers. Significant theoretical…
In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation…
We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
We propose a new velocity reconstruction method based on the displacement estimation by recently developed methods. The velocity is first reconstructed by transfer functions in Lagrangian space and then mapped into Eulerian space. High…
The classical problem of spherical homologous gravitational collapse with a polytropic equation of state for pressure is examined in Lagrangian fluid coordinate, where the position of each initial fluid element {\eta} = r(0) is followed in…
We propose two new conformity scores for conformal prediction, in a general multivariate regression framework. The underlying score functions are based on a covariance analysis of the residuals and the input points. We give theoretical…