Different choices of scaling in homogenization of diffusion and interfacial exchange in a porous medium

Several choices of scaling are investigated for a coupled system of parabolic partial differential equations in a two‐phase medium at the microscopic scale. This system may be regarded as modelling a reaction–diffusion problem, the Stokes problem of single‐phase flow of a slightly compressible fluid or as a heat conduction problem (with or without interfacial resistance), for example. It is shown that, starting with the same problem on the microscopic scale, different choices of scaling of the diffusion coefficients (resp. permeability or conductivity) and the interfacial‐exchange coefficient lead to different types of macroscopic systems of equations. The characterization of the limit problems in terms of the scaling parameters constitutes a modelling tool because it allows to determine the right type of limit problem. New macroscopic models, not previously dealt with, arise and, for some scalings, classical macroscopic models are recovered. Using the method of two‐scale convergence, a unified approach yielding rigorous proofs is given covering a very broad class of different scalings. Copyright © 2008 John Wiley & Sons, Ltd.     

A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O(h⁴+τ⁵). It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.     

Detection of deletion mutations in DNA using water-soluble cationic fluorescent thiophene copolymer

In this contribution, we designed a fluorescent thiophene copolymer to detect insertion/deletion mutation in DNA by doping aldehyde group in the main chain. The fluorescence of the copolymer could be dramatically quenched on the addition of single-stranded DNA (ssDNA) via strong electrostatic interactions and electronic/energy transfer. Although the complementary ssDNA made the fluorescence recover, the hydrogen bonds and chemical coupling also played a significant role between the unpaired bases and aldehyde group, which could differentiate the subtle differences in such mutant DNA. The influence of buffer pH, concentration of NaCl, heating time and the temperature was systemically investigated and the proposed method was then successfully applied to detect real sample. With the respect to the linearity, limit of detection precision, specificity, this procedure could provide sensitive methodologies for the rapid detection and identification of nucleic acids.     

Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

ENERGY ESTIMATES FOR DELAY DIFFUSION-REACTION EQUATIONS

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems （IBVPs） are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.     

GLOBAL EXISTENCE AND EXTINCTION FOR A DEGENERATE NONLINEAR DIFFUSION PROBLEM WITH NONLINEAR GRADIENT TERM AND ABSORPTION

Existence and extinction in finite time of global weak solutions for the problem （P） are proved.     

Isomerization kinetics of small hydrocarbons in confinement

Chemical reactions are often carried out in nano-structured materials, which can enhance reactions due to their large specific surface area, their interactions with the reacting mixture and confinement effects. In this work, we present a systematic study of the effect that the geometrical restrictions imposed by the pore walls can have on reactions that involve a three dimensional rearrangement of the atoms in a molecule. In particular, we consider the isomerization of three 4-membered hydrocarbons—n-butane, 1-butene and 1,3-butadiene confined in carbon nanopores of slit geometry. Our results illustrate the fact that, in the molecular sieving limit, the reaction rates change as the double exponential of the pore size (Santiso et al., in J. Chem. Phys., 2007a, submitted), and therefore the transition rates in nanopores can be many orders of magnitude different from the corresponding bulk values. These results can be used as a guideline for the molecular-level design of improved catalytic materials.     

A REACTION–DIFFUSION EQUATION MODELING THE INVASION OF THE ARGENTINE ANT POPULATION,LINEPITHEMA HUMILE,AT JASPER RIDGE BIOLOGICAL PRESERVE

Abstract A continuous reaction–diffusion model is developed for the invasive Argentine ant population within a preserve in northern California. The model is a second‐order partial differential equation incorporating a logistic growth term. The dispersal distance traveled during the reproductive process of budding is used to estimate the diffusion coefficient. The model has two homogeneous steady states, one occurring at the propagation front where the Argentine ant population does not yet exist and one occurring where the population has reached carrying capacity. The traveling wave solutions of the model depict the population density for a given time and location. Using current research, parameter values for the model are estimated and a traveling wave solution for the average parameter values is numerically demonstrated.     

The Cardbox/Cardview Database for residues in live animals and their products

The growing interest of the public opinion in environmental problems has resulted in the establishment of national and international norms and regulations. Among others, the protection of human health requires the constant monitoring of several groups of potentially toxic substances as well as of their residues in live animals and their products. For this reason in recent years the European Commission decided to establish four Community Reference Laboratories (CRLs) for the analysis of residues in products of animal origin. The current mandate and operative conditions of the CRLs are described in the Council Directive 96/23/EC of 29 April 1996, which has the goal of promoting and supporting the harmonization of approaches among National Reference Laboratories (NRLs). In this context the CRL at the Istituto Superiore di Sanità of Rome is responsible for chemical elements, organochlorine compounds (including PCBs), carbamates, pyrethroids and organophosphorus compounds. The supply of updated information on the literature of relevance to the tasks of the NRLs is one of the duties of the Rome CRL. To this end, the so-called Cardbox Database has been set up, which for the time being is fully operative for chemical elements and organochlorine compounds.