In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transiti...

In this paper we investigate Isotropic Multiresolution Analysis(IMRA), isotropic refinable functions, and wavelets. The main results are the characterization of IMRAs in terms of the Lax-Wiener Theorem, and the characterization of isotropic refinable functions in terms of the support of their Fourier transform. As an immediate consequence of these results, there are no compactly supported (in t...

We establish a sharp concentration of mass inequality for isotropic convex bodies: there exists an absolute constant c > 0 such that if K is an isotropic convex body in R, then Prob ({ x ∈ K : ‖x‖2 > c √ nLKt }) 6 exp ( − √ nt ) for every t > 1, where LK denotes the isotropic constant.

Reverberant sound fields are often modeled as isotropic. However, it has been observed that spatial properties change during the decay of the sound field energy, due to non-isotropic attenuation in non-ideal rooms. In this letter, a model for the spatial coherence between two sensors in a decaying reverberant sound field is developed for rectangular rooms. The modeled coherence function depends...

The anisotropic sparse grid is a natural extension of the isotropic sparse grid, adapted for situations in which the behavior of the data varies with respect to particular spatial dimensions. An appropriately configured anisotropic sparse grid can achieve accuracy comparable to that of an isotropic sparse grid, while further compounding the reduction in the number of function evaluations that a...

Phase separation in salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the mixtures are carried out and demonstrate that electrostatic interactions favor nematic ordering. Coexistence curves for the symmetric mixtures are also con...

Meshes with planar quadrilateral faces are desirable discrete surface representations for architecture. The present paper introduces new classes of planar quad meshes, which discretize principal curvature lines of surfaces in so-called isotropic 3-space. Like their Euclidean counterparts, these isotropic principal meshes meshes are visually expressing fundamental shape characteristics and they ...

Clarke’s classical model of mobile radio reception assumes isotropic rich scattering around the mobile receiver antenna. The assumption of isotropic scattering is valid only in limited circumstances. In this contribution we develop a generalized Clarke model, which is applicable to mobile radio reception in general scattering environments. We give expressions for the autocorrelation and power s...

The most sophisticated existing methods to generate 3D isotropic super-resolution (SR) from non-isotropic electron microscopy (EM) are based on learned dictionaries. Unfortunately, none of the existing methods generate practically satisfying results. For 2D natural images, recently developed super-resolution methods that use deep learning have been shown to significantly outperform the previous...

In this paper, we present a new linear MEM algorithm for 2-D isotropic random fields. Our procedure differs from previous 2-D MEM algorithms by the fact that we take maximal advantage of the symmetries implied by isotropy, which is the natural generalization to several dimensions of the l-D notion of stationarity. Unlike general 2-D covariances, isotropic covariance functions which are positive...