Related papers: On inhomogeneity parameters for Backus average
We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as…
Backus (1962) developed his technique for homogenization of a layered structure solely within the context of linear elastic theory. In this paper we propose an extended use of Backus average for finitely deformed materials of a layered…
Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional…
In order to quantitatively test the ability of averaged inhomogeneous cosmologies to correctly describe observations of the large scale properties of the Universe, we introduce a smoothed template metric corresponding to a constant spatial…
We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure. This is done using both classical periodic homogenization and a new…
We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Euclidean space and estimate its edge boundary through the…
It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note we extend that…
Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic…
We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave…
Understanding the statistical properties of synchrotron emission from our Galaxy is valuable from the perspective of observations targeting signals of cosmological origin, as well as for understanding physical processes in our Galaxy. In…
In previous work, we introduced a new framework to treat large scale backreaction effects due to small scale inhomogeneities in general relativity. We considered one-parameter families of spacetimes for which such backreaction effects can…
A central assumption in our analysis of cosmic structure is that cosmological perturbations have zero ensemble mean. This property is one of the consequences of statistically homogeneity, the invariance of correlation functions under…
The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric inequality (involving circumradius or inradius) for cyclic…
In this paper we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material…
The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic…
A distribution of points that satisfies the property of local isotropy is not necessarily homogeneous: homogeneity is implied by the condition of local isotropy together with the assumption of analyticity or regularity. Here we show that…
Many geologic materials have a composite structure, in which macroscopic mechanical behavior is determined by the properties, shape, and heterogeneous distribution of individual constituents. In particular, sedimentary rocks commonly…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The scattering parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is the one related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine…
We postulate that validity of the Backus (1962) average, whose weights are layer thicknesses, is limited to waves whose incidence is nearly vertical. The accuracy of this average decreases with the increase of the source-receiver offset.…