Large-scale effects on meso-scale modeling for scalar transport

The transport of scalar quantities passively advected by velocity fields with a component at small scale ℓ can be modeled at scales larger than ℓ by means of an effective drift and an effective diffusivity, which can be determined by means of multiple-scale techniques. We show that the presence of a weak flow at large scales Lℓ induces interesting effects on the scalar transport at the meso-scales (i.e. at scales intermediate between ℓ and L). In particular, it gives rise to non-isotropic and non-homogeneous corrections to the meso-scale drift and diffusivity. We discuss an approximation that allows us to retain the second-order effects caused by the large-scale flow. This provides a rather accurate meso-scale modeling for both asymptotic and pre-asymptotic scalar transport properties. Numerical simulations in model flows are used to illustrate the importance of such large-scale effects.     

Particle systems on flows

We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process.     

Pseudo cyclic ionophores: ‘Binary-effect’ of quinolinyloxy groups at both ends of oligoethylene glycols on the conformational stabilization of their complexes with alkali metal salts

A series of noncyclic neutral ionophores has been synthesized by the reaction of oligoethylene glycol dihalides with 8-quinolinol. Complexation properties for alkali metal picrates were evaluated from solvent extraction and bulk liquid membrane transport experiments. Complexation profiles of the newly synthesized ionophores with a hexyl chain were similar to those of their homologues without the hexyl chain in the extraction experiments. Among them, the pentaethylene glycol derivatives showed the highest extraction efficiency and selectivity towards potassium ion. From the¹H NMR spectra (400 MHz), the change in chemical shifts of the aromatic protons upon the addition of alkali metal thiocyanates suggested the existence of a stabilization effect which is caused by intramolecular stacking conformations between the quinoline rings during complexation. Aryl stacking interactions depend on the size of the cations and on the chain length of the oligoethylene glycol. The relationship between transport ability towards alkali metal cations and lipophilicity of these ionophores is also discussed.     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W^{?1, p} spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain L^p estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.     

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L ₁-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C ₀-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

正负系数中立型差分方程的正解的存在性

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature     

Analysis of saltation characteristics of bed-load transport in flowing water

The study of bed-load transport is of great significance both in theory and in practice. This paper discusses the saltation of bed-load solid grains in flowing water. Experiments and theoretic analysis have been made by means of high-speed photographing and advanced data processing technique with a combined method based on mechanical and statistical theories. It indicates that the saltation is the main form of the bed-load transport under ordinary flowing conditions. In the meantime, taking successive saltation as the model of bed-load transport, systematic analysis has been made with regard to the kinematic properties and mechanism of saltation. The statistical analysis shows that the probability density functions of the relative height and length of saltation are in conformity with Γ-type distribution, while the probability density functions of the relative velocities of saltation are in conformity with the Gaussian distribution. The project supported by National Natural Science Foundation of China     

Determination of colloidally-associated polycyclic aromatic hydrocarbons (PAHs) in fresh water using C18 solid phase extraction disks

A new application of reversed-phase octadecyl (C₁₈) solid phase extraction disks has been developed to separate the colloidally-associated polycyclic aromatic hydrocarbons (PAHs) from those that were truly dissolved in the samples of fresh water. A correction for the retention of small amounts of colloidal material on the C₁₈ disks was required, which would have otherwise lead to minor underestimates in the degree of partitioning between the two phases. Using the humic substance Aldrich Humic Acid (AHA) as a model colloid and the 16 PAHs on the US Enrivonmental Protection Agency priority pollutant list, the partitioning coefficients of the PAHs between the colloidal and truly dissolved phases were shown to be proportional to the hydrophobicity of the PAHs, as measured by their octanol water partition coefficients (K_ow). The values for the partition coefficients obtained (cK_doc′) were similar to those previously reported in the literature using alternative methods, confirming that the technique was producing acceptable results. The technique allows the in situ partitioning of PAHs between the truly dissolved and colloidal phases in fresh water bodies to be determined. It will provide an invaluable cross-check of the laboratory-based methods which often require substantial manipulation of the sample and potentially alter the partitioning between the phases.