Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called cylindric scatterers) have been removed. We prove that every such system is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for the ergodicity is present.Comment: 24 pages, AMS-TeX fil

A kidney resident macrophage subset is a candidate biomarker for renal cystic disease in preclinical models

Although renal macrophages have been shown to contribute to cyst development in polycystic kidney disease (PKD) animal models, it remains unclear whether there is a specific macrophage subpopulation involved. Here, we analyzed changes in macrophage populations during renal maturation in association with cystogenesis rates in conditional Pkd2 mutant mice. We observed that CD206(+) resident macrophages were minimal in a normal adult kidney but accumulated in cystic areas in adult-induced Pkd2 mutants. Using Cx3cr1 null mice, we reduced macrophage number, including CD206(+) macrophages, and showed that this significantly reduced cyst severity in adult-induced Pkd2 mutant kidneys. We also found that the number of CD206(+) resident macrophage-like cells increased in kidneys and in the urine from autosomal-dominant PKD (ADPKD) patients relative to the rate of renal functional decline. These data indicate a direct correlation between CD206(+) resident macrophages and cyst formation, and reveal that the CD206(+) resident macrophages in urine could serve as a biomarker for renal cystic disease activity in preclinical models and ADPKD patients. This article has an associated First Person interview with the first author of the paper

Ergodicity of a single particle confined in a nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i. e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit