Using Lin's method to solve Bykov's problems

We consider nonwandering dynamics near heteroclinic cycles between two hyperbolic equilibria. The constituting heteroclinic connections are assumed to be such that one of them is transverse and isolated. Such heteroclinic cycles are associated with the termination of a branch of homoclinic solutions, and called T-points   in this context. We study codimension-two T-points and their unfoldings in Rⁿ${\mathbb{R}}^n$. In our consideration we distinguish between cases with real and complex leading eigenvalues of the equilibria. In doing so we establish Lin's method as a unified approach to (re)gain and extend results of Bykov's seminal studies and related works. To a large extent our approach reduces the study to the discussion of intersections of lines and spirals in the plane.     

Environmental Fate of 1,2,3,4,7-Pentachlorodibenzo-p-Dioxin in a Canadian Prairie Soil

Abstract

The fate of 1,2,3,4,7-pentachlorodibenzo-p-dioxin (P₅CDD) was studied in a Canadian prairie soil under field conditions by applying ¹⁴C-labelled P₅CDD to a series of soil microplots and sampling the 0–2 and 2–5 cm depths over a period of 2 years. Analysis by HPLC-LSC revealed that, although P₅CDD dissipated from the plots with a half-life of approximately 1.1 y, leaching and biodegradation were unable to account for the observed losses. Only 1.3% of the applied ¹⁴C-P₅CDD appeared in the 2–5 cm depth at 639 days indicating minimal leaching during the course of the experiment. Furthermore, since only 0.9% of the applied radiolabel appeared as extractable degradation products at day 639, biodegradation was not an important loss pathway for P₅CDD in soil. Nonextractable ¹⁴C, representing an irreversibly bound fraction of P₅CDD, stabilized at approximately 10% leaving roughly 70% of the radiolabel unaccounted for at day 639. The observed losses are attributed to volatilization of parent P₅CDD from the soil plots.     

A neutron reflectivity study of surfactant self-assembly in weak polyelectrolyte brushes at the sapphire-water interface

Poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes grown by surface-initiated polymerization from a polyanionic macroinitiator adsorbed at the sapphire-water interface have been used as a substrate to study the interaction between the weak polyelectrolyte PDMAEMA and the oppositely charged surfactant sodium dodecyl sulfate (SDS) with neutron reflectivity. At pH 3, multilayered structures are formed in which the interlayer separation (～40 ?) is comparable to the dimensions of a SDS bilayer or micelle. The number of repeating layers that form depends on brush thickness, ranging from three layers in a relatively thin brush (5 nm dry thickness) to 15 layers in a relatively thick brush (17 nm dry thickness). In the 5 nm brush, addition of 0.01 mM SDS leads to brush deswelling, and the distinct layered structure only forms when the SDS concentration reaches 1 mM, with the brush reswelling slightly at 5 mM SDS. In the thicker (11 and 17 nm) brushes, distinct layered structures form at 0.1 mM SDS, in which the molar SDS/DMAEMA ratio is greater than unity. Exposing the 17 nm brush/SDS complex to 1 M NaNO(3) results in the complete removal of the surfactant and recovery of the bare brush structure. At pH 9, there is significant surfactant uptake by the brush, but no multilayer structures are formed. The brush presents a high concentration of DMAEMA segments that are localized to within 500-1000 ? of the sapphire interface. At pH 9 the high local concentration of hydrocarbon segments in the brush screens the hydrophobic tails of the surfactants from the unfavorable interaction with water, leading to significant surfactant uptake by the brush. At pH 3 the high local concentration of charges inside the brush additionally screens the repulsive interactions between the surfactant headgroups, making surfactant uptake even more favorable, leading to the formation of multilayered surfactant aggregates confined within the brush.     

Width of the hexadecane-water interface: a discrepancy resolved

An existing discrepancy in the determined values of the width of the hexadecane-water interface as determined from X-ray reflection (XR) and recent neutron reflection (NR) measurements has been resolved. The NR-determined width reported here is 6.0 +/- 1.0 Angstroms, which compares extremely well with the XR-determined value of 6.0 +/- 0.2 Angstroms. The origin of the discrepancy has been attributed to the thermal history of the interface rather than sample purity or other technique-dependent reasons.     

PHOTOTOXICITY FROM BENOXAPROFEN: IN VIVO AND IN VITRO STUDIES

Abstract Benoxaprofen (2-[4-chlorophenyl]-α-methyl-5-benzoxazole acetic acid), a non-steroidal antiinflammatory drug, was found to provoke phototoxicity reactions in humans. Exposure of the skin of benoxaprofen-treated subjects to either solar simulating radiation or a broad UV-A wavelength band produced intense itching and burning sensations, followed by the development of a classical wheal and flare response within 2-4 min. Phototoxicity was related to both the UV radiation fluence and the dose of orally administered benoxaprofen. Wavelengths between 320 and 340nm were active in provoking urticaria. In vitro studies demonstrated that benoxaprofen and UV irradiation produced a dose-dependent lysis of sheep erythrocytes which did not appear to be dependent on the presence of oxygen. Red cells were not lysed by pre-irradiated benoxaprofen arguing against the production of stable lytic photoproducts. Human neutrophils were lysed by benoxaprofen and UV light which resulted in the liberation of both cytoplasmic and lysosomal enzymes. Benoxaprofen failed to induce photolysis of human platelets and photoactivation of complement in human serum. It is suggested that phototoxic urticaria provoked by benoxaprofen may be due to a direct photolytic effect on human dermal mast cells.     

Time-resolved vibrational spectroscopy of [FeFe]-hydrogenase model compounds

Model compounds have been found to structurally mimic the catalytic hydrogen-producing active site of Fe-Fe hydrogenases and are being explored as functional models. The time-dependent behavior of Fe(2)(μ-S(2)C(3)H(6))(CO)(6) and Fe(2)(μ-S(2)C(2)H(4))(CO)(6) is reviewed and new ultrafast UV- and visible-excitation/IR-probe measurements of the carbonyl stretching region are presented. Ground-state and excited-state electronic and vibrational properties of Fe(2)(μ-S(2)C(3)H(6))(CO)(6) were studied with density functional theory (DFT) calculations. For Fe(2)(μ-S(2)C(3)H(6))(CO)(6) excited with 266 nm, long-lived signals (τ = 3.7 ± 0.26 μs) are assigned to loss of a CO ligand. For 355 and 532 nm excitation, short-lived (τ = 150 ± 17 ps) bands are observed in addition to CO-loss product. Short-lived transient absorption intensities are smaller for 355 nm and much larger for 532 nm excitation and are assigned to a short-lived photoproduct resulting from excited electronic state structural reorganization of the Fe-Fe bond. Because these molecules are tethered by bridging disulfur ligands, this extended di-iron bond relaxes during the excited state decay. Interestingly, and perhaps fortuitously, the time-dependent DFT-optimized exited-state geometry of Fe(2)(μ-S(2)C(3)H(6))(CO)(6) with a semibridging CO is reminiscent of the geometry of the Fe(2)S(2) subcluster of the active site observed in Fe-Fe hydrogenase X-ray crystal structures. We suggest these wavelength-dependent excitation dynamics could significantly alter potential mechanisms for light-driven catalysis.     

水生生物中化学踪迹的水动力学问题

化学踪迹调控着水生生物的许多关键生命过程,如摄食、繁殖和海底沉淀等.随着流体流速和流态的不同,水生生物所释放的化学物质在被生物体接收之前会经历扩散、层流或湍流对流等输运过程.综述了各种流态中的输运机制及生态效应.从浓度梯度、浓度涨落和空间分布模式的角度讨论了化学踪迹的结构,从中总结出水生动物获取信息的策略.在一些情况下,化学物质的输运是通过多种机制联合作用而实现的,需要引入多尺度分析,而流态和尺度问题则是最近研究中显现出的主要议题.尤其是,组合了生物变量和物理变量的无量纲参数揭示了生物体对化学踪迹反应的一般原则,也促进了对水生生物行为模态的区分和定义.     

Extracting extensional properties through excess pressure drop estimation in axisymmetric contraction and expansion flows for constant shear viscosity,extension strain-hardening fluids

In this study, hyperbolic contraction–expansion flow (HCF) devices have been investigated with the specific aim of devising new experimental measuring systems for extensional rheological properties. To this end, a hyperbolic contraction–expansion configuration has been designed to minimize the influence of shear in the flow. Experiments have been conducted using well-characterized model fluids, alongside simulations using a viscoelastic White–Metzner/FENE-CR model and finite element/finite volume analysis. Here, the application of appropriate rheological models to reproduce quantitative pressure drop predictions for constant shear viscosity fluids has been investigated, in order to extract the relevant extensional properties for the various test fluids in question. Accordingly, experimental evaluation of the hyperbolic contraction–expansion configuration has shown rising corrected pressure drops with increasing elastic behaviour (De=0～16), evidence which has been corroborated through numerical prediction. Moreover, theoretical to predicted solution correspondence has been established between extensional viscosity and first normal stress difference. This leads to a practical means to measure extensional viscosity for elastic fluids, obtained through the derived pressure drop data in these HCF devices.     

Efficient algebraic multigrid solvers with elementary restriction and prolongation

An algebraic multigrid (AMG) scheme is presented for the efficient solution of large systems of coupled algebraic equations involving second-order discrete differentials. It is based on elementary (zero-order) intergrid transfer operators but exhibits convergence rates that are independent of the system bandwidth. Inconsistencies in the coarse-grid approximation are minimised using a global scaling approximation which requires no explicit geometrical information. Residual components of the error spectrum that remain poorly represented in the coarse-grid approximations are reduced by exploiting Krylof subspace methods. The scheme represents a robust, simple and cost-effective approach to the problem of slowly converging eigenmodes when low-order prolongation and restriction operators are used in multigrid algorithms. The algorithm investigated here uses a generalised conjugate residual (GCR) accelerator; it might also be described as an AMG preconditioned GCR method. It is applied to two test problems, one based on a solution of a discrete Poisson-type equation for nodal pressures in a pipe network, the other based on coupled solutions to the discrete Navier–Stokes equations for flows and pressures in a driven cavity. © 1998 John Wiley & Sons, Ltd.