On nonlinear conservation laws with a nonlocal diffusion term

Scalar one-dimensional conservation laws with a nonlocal diffusion term corresponding to a Riesz-Feller differential operator are considered. Solvability results for the Cauchy problem in L^∞ are adapted from the case of a fractional derivative with homogeneous symbol. The main interest of this work is the investigation of smooth shock profiles. In the case of a genuinely nonlinear smooth flux function we prove the existence of such travelling waves, which are monotone and satisfy the standard entropy condition. Moreover, the dynamic nonlinear stability of the travelling waves under small perturbations is proven, similarly to the case of the standard diffusive regularisation, by constructing a Lyapunov functional.     

Convergence to Global Equilibrium for Spatially Inhomogeneous Kinetic Models of Non-Micro-Reversible Processes

We study the long-time asymptotics of linear kinetic models with periodic boundary conditions or in a rectangular box with specular reflection boundary conditions. An entropy dissipation approach is used to prove decay to the global equilibrium under some additional assumptions on the equilibrium distribution of the mass preserving scattering operator. We prove convergence at an algebraic rate depending on the smoothness of the solution. This result is compared to the optimal result derived by spectral methods in a simple one dimensional example.     

Aggregation Behavior of Nonionic Clycolipid Vesicles in Acidic Region

Large unilamellar vesicles composed of a nonionic synthetic glycotipid, 1,3 - di- 0 - phylanyl -2-0-(β- maltotriosyl ) glycerol show pH-dependent aggregation - dissocialion process, that is, vesicle aggregation occurs in the lower pH region and vesicle dissociation occurs in the higher pH region. This process is almost reversible and the aggregation threshold pH is dependent on NaCl concentration. Fluorescence technique has been applied to study whether the vesicle fusion occurs or not during the aggregation-dissociation process. It is concluded pH can only induce the aggregation of this nonionic glycoltpid vesicle.     

Existence and Convergence to Equilibrium of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on moments of the distribution function. An earlier existence result is extended to bounded domains with reflecting boundaries and to initial conditions permitting vacuum regions. The long time behaviour is investigated. Convergence on compact time intervals (shifted to infinity) to the set of equilibrium solutions is proven. The set of smooth equilibrium solutions is computed.     

Long-time behaviour of a one-dimensional BGK model: convergence to macroscopic rarefaction waves

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, we prove that the macroscopic density converges to the rarefaction wave solution of the corresponding scalar conservation law in the long time limit, and that the phase space density approaches an equilibrium distribution with the rarefaction wave as macroscopic density. The proof requires a smallness assumption on the amplitude of the rarefaction waves and uses a micro-macro decomposition of the perturbation equation.     

Diffusive Limit of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved.     

Determination of genomic N3‐methylthymidine in human cancer cells treated with nitrosamines using capillary electrophoresis with laser‐induced fluorescence

Methylating substances alter DNA by forming N3‐methylthymidine (N3mT), a mutagenic base modification. To develop a sensitive analytical method for the detection of N3mT in DNA based on capillary electrophoresis with laser‐induced fluorescence detection (CE‐LIF), we synthesized the N3mT‐3’‐phosphate as a chemical standard. The limit of detection was 1.9 amol of N3mT, which corresponds to one molecule of N3mT per 1000 normal nucleotides or 0.1%. With this method, we demonstrated that the carcinogenic nitrosamine N’‐nitrosonornicotine (NNN) induced N3mT in the human lung cancer cell line A549. Treatment with NNN also caused an elevated degree of 5‐hydroxymethylcytidine (5hmdC) in DNA, while the methylation degree (i.e. 5‐methylcytidine; 5mdC) stayed constant. According to our data, NNN could, via yet unknown mechanisms, play a role in the formation of N3mT as well as 5hmdC. In this study we have developed a new sensitive analytical method using CE‐LIF for the simultaneous detection of the three DNA modifications, 5mdC, 5hmdC and N3mT.     

Interglycolipid Membrane Interactions: pH-Dependent Aggregation of Nonionic Synthetic Glycolipid Vesicles

Large unilamellar vesicles composed of a nonionic synthetic glycolipid, 1,3-di-O-phytanyl-2-O-(beta-D-maltotriosyl)glycerol exhibited a pH-dependent aggregation-disaggregation process; vesicle aggregation occurred in a lower pH region and vesicle disaggregation occurred in a higher pH region. This process was almost reversible and the aggregation threshold pH increased as NaCl concentration increased. Electrophoretic mobility measurements revealed that the glycolipid vesicles are negatively charged in the range pH 1.6-13. The change in zeta-potentials as functions of pH and NaCl concentration could be well described by the Gouy-Chapman expression of the surface charges with an assumption that the interfacial charges arise from the "adsorption" of OH(-) at the vesicle-water interface and the dissociation of hydroxyl groups of the sugar headgroup in a higher pH regime (>pH 10). The pH-dependent aggregation process was reasonably well described by the classical DLVO theory. Thus, the double-layer repulsive forces appear to be a major factor in stabilizing the glycolipid vesicle suspension. Copyright 2000 Academic Press.     

Detection and separation of nucleoside-5'-monophosphates of DNA by conjugation with the fluorescent dye BODIPY and capillary electrophoresis with laser-induced fluorescence detection

We investigated the separation and detection of the 5'-monophosphates of 2'-deoxynucleosides selectively conjugated with 4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-propionyl ethylene diamine hydrochloride (BODIPY FL EDA) at the 5'-phosphate group using capillary electrophoresis with laser-induced fluorescence detection (CE-LIF). BODIPY conjugates of the four common deoxynucleoside-5'-monophosphates (2'-deoxyguanosine-5'-monophosphate, 2'-deoxyadenosine-5'-monophosphate, 2'-deoxycytidine-5'-monophosphate, and thymidine-5'-monophosphate) were prepared and subjected to CE-LIF to serve as standard compounds for peak assignment and to develop separation conditions for the analysis of DNA. BODIPY conjugates were detected and resolved by CE-LIF after digestion of DNA or an oligonucleotide to 5'-monophosphates by nuclease P1 (NP 1) and fluorescence labeling without further purification step. Comparative analyses of calf-thymus DNA digested either with micrococcal nuclease/spleen phosphodiesterase to 3'-monophosphates or with NP 1 to 5'-monophosphates showed that both versions of the fluorescence postlabeling assay were equally efficient and sensitive. Moreover, using the same assay, 2'-deoxyuridine and 2'-deoxy-5methylcytidine were identified in bisulfite treated DNA after NP 1 digestion indicating that fluorescence postlabeling of 2'-deoxyribonucleoside-5'-monophosphates with BODIPY FL EDA and detection by CE-LIF has the potential to determine DNA damage and genomic DNA methylation.