Incompressible Limit of a Compressible Liquid Crystals System

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space $\mathbb{R}^{\mathbb{N}}$ and a bounded domain of $\mathbb{R}^{\mathbb{N}}$ with Dirichlet boundary conditions. Here the number of dimension $\mathbb{N}=2$ or 3

Global Weak Solutions to a General Liquid Crystals System

We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$

Bifurcation analysis on a delayed SIS epidemic model with stage structure

In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given

Development and Validation of Machine-Learning Clear-Sky Detection Method Using 1-Min Irradiance Data and Sky Imagers at a Polluted Suburban Site, Xianghe

Clear-sky detection (CSD) is of critical importance in solar energy applications and surface radiative budget studies. Existing CSD methods are not sufficiently validated due to the lack of high-temporal resolution and long-term CSD ground observations, especially at polluted sites. Using five-year high resolution ground-based solar radiation data and visual inspected Total Sky Imager (TSI) measurements at polluted Xianghe, a suburban site, this study validated 17 existing CSD methods and developed a new CSD model based on a machine-learning algorithm (Random Forest: RF). The propagation of systematic errors from input data to the calculated global horizontal irradiance (GHI) is confirmed with Mean Absolute Error (MAE) increased by 99.7% (from 20.00 to 39.93 W·m−2). Through qualitative evaluation, the novel Bright-Sun method outperforms the other traditional CSD methods at Xianghe site, with high accuracy score 0.73 and 0.92 under clear and cloudy conditions, respectively. The RF CSD model developed by one-year irradiance and TSI data shows more robust performance, with clear/cloudy-sky accuracy score of 0.78/0.88. Overall, the Bright-Sun and RF CSD models perform satisfactorily at heavy polluted sites. Further analysis shows the RF CSD model built with only GHI-related parameters can still achieve a mean accuracy score of 0.81, which indicates RF CSD models have the potential in dealing with sites only providing GHI observations