On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Identification of sources of elevated concentrations of polycyclic aromatic hydrocarbons in an industrial area in Tianjin, China

The concentrations of 16 polycyclic aromatic hydrocarbons (PAHs) were determined by gas chromatography equipped with a mass spectrometry detector in 105 topsoil samples from an industrial area around Bohai Bay, Tianjin in the North of China. Results demonstrated that concentrations of PAHs in 104 soil samples from this area ranged from 68.7 to 5,590 ng g (-aEuro parts per thousand 1) dry weight with a mean of a16PAHs 814 +/- 813 ng g (-aEuro parts per thousand 1), which suggests that there exists mid to high levels of PAH contamination. The concentration of a16PAHs in one soil sample from Tianjin Port was exceptionally high (48,700 ng g (-aEuro parts per thousand 1)). Ninety-three of the 105 soil samples were considered to be contaminated with PAHs (> 200 ng g (-aEuro parts per thousand 1)), and 25 were heavily polluted (> 1,000 ng g (-aEuro parts per thousand 1)). The sites with high PAHs concentration are mainly distributed around chemical industry parks and near highways. Two low molecular weight PAHs, naphthalene and phenanthrene, were the dominant components in the soil samples, which accounted for 22.1% and 10.7% of the a16PAHs concentration, respectively. According to the observed molecular indices, house heating in winter, straw stalk combustion in open areas after harvest, and petroleum input were common sources of PAHs in this area, while factory discharge and vehicle exhaust were the major sources around chemical industrial parks and near highways. Biological processes were probably another main source of low molecular weight PAHs

Regional differences and sources of organochlorine pesticides in soils surrounding chemical industrial parks

Concentrations of organochlorine pesticides (OCPs; dichlorodiphenyltrichloroethanes (DDTs), hexachlorocyclohexanes (HCHs), hexachlorobenzene (HCB)) were investigated in 105 soil samples collected in vicinity of the chemical industrial parks in Tianjin, China. OCP concentrations significantly varied in the study area, high HCH and DDT levels were found close to the chemical industrial parks. The intensity of agricultural activity and distance from the potential OCP emitters have important influences on the OCP residue distributions. Principal component analysis indicates that HCH pollution is a mix of historical technical HCH and current lindane pollution and DDT pollution input is only due to technical DDT sources. The significant correlations of OCP compounds reveal that HCHs, DDTs and HCB could have some similar sources of origin

Critical Engagements with Aging and Care

A predicted and significant increase in the number of elderly has generated a call for increased services and care from many advocates and analysts. In addition to the need for quality care, advocacy groups and researchers have urged attention to issues of equity and services sensitive to the needs of marginalised groups including: low and no income elderly; Indigenous elderly; women; LGBTQI+ elderly; and those with complex health needs (Daly and Armstrong, 2016)