Poincar{\'e} series and linking of Legendrian knots

On a negatively curved surface, we show that the Poincar{\'e} series counting geodesic arcs orthogonal to some pair of closed geodesic curves has a meromorphic continuation to the whole complex plane. When both curves are homologically trivial, we prove that the Poincar{\'e} series has an explicit rational value at 0 interpreting it in terms of linking number of Legendrian knots. In particular, for any pair of points on the surface, the lengths of all geodesic arcs connecting the two points determine its genus, and, for any pair of homologically trivial closed geodesics, the lengths of all geodesic arcs orthogonal to both geodesics determine the linking number of the two geodesics.Comment: Minor modifications, 78

Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces

We prove the existence of a discrete correlation spectrum for Morse-Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with anisotropic Sobolev regularity on which the Lie derivative has a discrete spectrum

ASSESSING ONGOING SOURCES AND FATE OF DISSOLVED POLYCHLORINATED BIPHENYLS (PCBs) IN A STREAM

Polychlorinated biphenyls (pcbs) contamination remains a concern due to their persistence and the risk to human health associated with them. Once released into the environment, these substances are mainly associated with sediment particles and sediment organic carbon matter. They bioaccumulate in organisms via contaminated food and only a small faction is desorbed from sediment into the water column. Given the discontinuity of active discharge, pcbs are currently entering the water via groundwater inputs, soil erosion, and/or ongoing leakage from the point source. It is the dissolved form that 1) can be either absorbed by biofilm attached to stream leaves, which is a basal resource of stream food webs, and 2) can cross the air-water interface and sorb to leaves while they are still on the plants. Many studies have investigated the fate and transport of pcbs in fish and consumers at higher trophic levels. However, limited knowledge exists on the source and fate of bioavailable pcbs as a result of the complexity in accurately measuring the dissolved fraction. This research thus aimed to provide insight into the potential of ongoing sources and the entry of dissolved pcbs to a stream food web. Studies were conducted in Town Creek, a recipient of the Twelvemile Creek/Lake Hartwell Superfund site, sc. The system is a second order stream contaminated with pcbs from a former Sangamo Weston capacitor manufacturer (s–w) in Pickens County, sc. Assessing potential ongoing sources of dissolved pcbs were based on total pcb concentrations, congener composition profile, and chiral signatures with collection by polyethylene passive samplers (pes). The concentrations of pcb in the pes at 0 km downstream of the plant were 2-5 fold lower than downstream pe concentrations. The congener profile in the pes 0 km downstream of the s–w site was similar to that of a mixture of Aroclors 1016 and 1254 (4:1 v/v), historically released from the s–w plant. Chiral pcbs 91 and 95 were the only two congeners detected in the passive samplers. While the enantiomeric fraction (ef) values for pcb 91 were non-racemic (\u3e0.5), the efs for pcb 95 were either racemic (=0.5) or nearly racemic. Increasing pcb concentrations downstream and a composition of predominantly low-weight congeners in the pes at 0 km downstream of the plant site suggested ongoing sources of dissolved pcbs from the original s–w facility to the system. Consistent ef values were likely indicative of aerobic biotransformation of dissolved pcbs, but did not provide strong evidence for potential ongoing pcb inputs into the system. Uptake rates of dissolved pcbs by microbial decomposing leaves were monitored by deploying fresh leaves in the streambed. Four individual leaf species including three deciduous species (Acer rubrum, Quercus rubra L., Liriodendron tulipifera) and and one evergreen (Rhododendron maximum) were used due to their different leaf quality. Uptake rates and pcb concentrations were significantly changed with time for the deciduous species, but not for the evergreen rhododendron. The deciduous species was subject to microbial colonization which drives microbial decomposition at a greater extent, and thus faster uptake of pcbs, than the evergreen rhododendron. A positive correlation was observed between pcb concentrations and lipid content in all four species, but the correlations were not strong pcb homologue distribution was time consistent among species and in a good agreement with congener patterns of dissolved pcbs in the passive samplers. The sources and magnitude of pcbs in the evergreen rhododendron next to a contaminated stream were investigated due to its long-lived foliage and an elevated pcb concentration measured in fresh leaves. Leaves were collected from the same shrubs in Town Creek throughout three seasons (fall 2010, winter and spring 2011). Concentrations were similar between fall and winter, and then decreased in spring. High concentrations in fall were likely related to high flow rate and seasonal precipitation, while increased revolatilization of low chlorinated congeners with increasing temperature could result in decreased pcb concentrations in spring. Two other evergreen species (American holly and blue spruce) collected 1 km upstream of the s–w plant site had pcb concentrations below the detection limit. In addition, congener pattern in rhododendron leaves was similar to the pes, while it differed from the congener distribution in surficial soils. These observations suggest that the source of pcbs in the rhododendron is through volatilization of dissolved PCBs in the water rather than uptake from soil or atmospheric long-range transport. Dissolved phase organochlorine compounds are of great concern due to their ability to transport to biological membrane. This dissertation proposed and examined a conceptual model to better understanding the potential for current sources and fate of dissolved pcbs in a small stream. Results from this research demonstrate the knowledge gaps about the entry of contaminants to food webs. The study will also serve as fundamental to assess source control and human health risk