Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

Evaluating Flexible Transport Solutions

Flexible transport services (FTS) have been of increasing interest in developed countries as a bridge between the use of personal car travel and fixed route transit services. This paper reports on findings from a recent study in Queensland Australia, which identified lessons from an international review and implications for Australia. Potential strategic directions, including a vision, mission, key result areas, strategies, and identified means of measuring performance are described. Evaluation criteria for assessing flexible transport proposals were developed, and approaches to identifying and assessing needs and demands outlined. The use of emerging technologies is also a key element of successful flexible transport services.

Capillary network models for transport in packed beds: Considerations of pore aspect ratio

The conventional analysis for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed for unconsolidated and grainy media.

hnRNP A2 selectively binds the cytoplasmic transport sequence of myelin basic protein mRNA

Segregation of mRNAs in the cytoplasm of polar cells has been demonstrated for proteins involved in Xenopus and Drosophila oogenesis, and for some proteins in somatic cells. It is assumed that vectorial transport of the messages is generally responsible for this localization. The mRNA encoding the basic protein of central nervous system myelin is selectively transported to the distal ends of the processes of oligodendrocytes, where it is anchored to the myelin membrane and translated. This transport is dependent on a 21-nucleotide cis-acting segment of the 3'-untranslated region (RTS). Proteins that bind to this cis-acting segment have now been isolated from extracts of rat brain. A group of six 35-42-kDa proteins bind to a 35-base oligoribonucleotide incorporating the RTS, but not to several oligoribonucleotides with the same composition but randomized sequences, thus establishing specificity for the base sequence in the RTS. The most abundant of these proteins has been identified, by Edman sequencing of tryptic peptides and mass spectroscopy, as heterogeneous nuclear ribonucleoprotein (hnRNP) A2, a 36-kDa member of a family of proteins that are primarily, but not solely, intranuclear. This protein was most abundant in samples from rat brain and testis, with lower amounts in other tissues. It was separated from the other polypeptides by using reverse-phase HPLC and shown to retain preferential association with the RTS. In cultured oligodendrocytes, hnRNP A2 was demonstrated by confocal microscopy to be distributed throughout the nucleus, cell soma, and processes.

Transport, storage and mobilization of nitrogen by trees and shrubs in the wet/dry tropics of northern Australia

Xylem sap from woody species in the wet/dry tropics of northern Australia was analyzed for N compounds. At the peak of the dry season, arginine was the main N compound in sap of most species of woodlands and deciduous monsoon forest. In the wet season, a marked change occurred with amides becoming the main sap N constituents of most species. Species from an evergreen monsoon forest, with a permanent water source, transported amides in the dry season. In the dry season, nitrate accounted for 7 and 12% of total xylem sap N in species of deciduous and evergreen monsoon forests, respectively In the wet season, the proportion of N present as nitrate increased to 22% in deciduous monsoon forest species. These results suggest that N is taken up and assimilated mainly in the wet season and that this newly assimilated N is mostly transported as amide-N (woodland species, monsoon forest species) and nitrate (monsoon forest species). Arginine is the form in which stored N is remobilized and transported by woodland and deciduous monsoon forest species in the dry season. Several proteins, which may represent bark storage proteins, were detected in inner bark tissue from a range of trees in the dry season, indicating that, although N uptake appears to be limited in the dry season, the many tree and shrub species that produce flowers, fruit or leaves in the dry season use stored N to support growth. Nitrogen characteristics of the studied species are discussed in relation to the tropical environment.

Epidermal iontophoresis: II. Application of the ionic mobility-pore model to the transport of local anesthetics

Purpose, An in vitro study was carried out to determine the iontophoretic permeability of local anesthetics through human epidermis. The relationship between physicochemical structure and the permeability of these solutes was then examined using an ionic mobility-pore model developed to define quantitative relationships. Methods. The iontophoretic permeability of both ester-type anesthetics (procaine, butacaine, tetracaine) and amide-type anesthetics (prilocaine, mepivacaine, lidocaine, bupivacaine, etidocaine, cinchocaine) were determined through excised human epidermis over 2 hrs using a constant d.c. current and Ag/AgCl electrodes. Individual ion mobilities were determined from conductivity measurements in aqueous solutions. Multiple stepwise regression was applied to interrelate the iontophoretic permeability of the solutes with their physical properties to examine the appropriateness of the ionic mobility-pore model and to determine the best predictor of iontophoretic permeability of the local anesthetics. Results. The logarithm of the iontophoretic permeability coefficient (log PCj,iont) for local anesthetics was directly related to the log ionic mobility and MW for the free volume form of the model when other conditions are held constant. Multiple linear regressions confirmed that log PCj,iont was best defined by ionic mobility (and its determinants: conductivity, pK(a) and MW) and MW. Conclusions. Our results suggest that of the properties studied, the best predictors of iontophoretic transport of local anesthetics are ionic mobility (or pK(a)) and molecular size. These predictions are consistent with the ionic mobility pore model determined by the mobility of ions in the aqueous solution, the total current, epidermal permselectivity and other factors as defined by the model.

Incoherent interlayer transport and angular-dependent magnetoresistance oscillations in layered metals

The effect of incoherent interlayer transport on the interlayer resistance of a layered metal is considered. We find that for both quasi-one-dimensional and quasi-two-dimensional Fermi liquids the angular dependence of the magnetoresistance is essentially the same for coherent and incoherent transport. Consequently, the existence of a three-dimensional Fermi surface is not necessary to explain the oscillations in the magnetoresistance that are seen in many organic conductors as the field direction is varied. [S0031-9007(98)07660-1].

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

An investigation of localised soil heterogeneities on solute transport using a multisegment percolation system

A multisegment percolation system (MSPS) consisting of 25 individual collection wells was constructed to study the effects of localised soil heterogeneities on the transport of solutes in the vadose zone. In particular, this paper discusses the transport of water and nutrients (NO3-, Cl-, PO43-) through structurally stable, free-draining agricultural soil from Victoria, Australia. A solution of nutrients was irrigated onto the surface of a large undisturbed soil core over a 12-h period. This was followed by a continuous irrigation of distilled water at a fate which did not cause pending for a further 18 days. During this time, the volume of leachate and the concentration of nutrients in the leachate of each well were measured. Very significant variation in drainage patterns across a small spatial scale was observed. Leaching of nitrate-nitrogen and chloride from the core occurred two days after initial application. However, less than 1% of the total applied phosphate-phosphorus leached from the soil during the 18-day experiment, indicating strong adsorption. Our experiments indicate considerable heterogeneity in water flow patterns and solute leaching on a small spatial scale. These results have significant ramifications for modelling solute transport and predicting nutrient loadings on a larger scale.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

Quantifying the influence of intra-aggregate concentration gradients on solute transport

The physical nonequilibrium of solute concentration resulting from preferential now of soil water has often led to models where the soil is partitioned into two regions: preferential flow paths, where solute transport occurs mainly by advection, and the remaining region, where significant solute transport occurs through diffusive exchange with the flow paths. These two-region models commonly ignore concentration gradients within the regions. Our objective was to develop a simple model to assess the influence of concentration gradients on solute transport and to compare model results with experiments conducted on structured materials. The model calculates the distribution of solutes in a single spherical aggregate surrounded by preferential now paths and subjected to alternating boundary conditions representing either an exchange of solutes between the two regions (a wet period) or no exchange but redistribution of solutes within the aggregate (a dry period). The key parameter in the model is the aggregate radius, which defines the diffusive time scales. We conducted intermittent leaching experiments on a column of packed porous spheres and on a large (300 mm long by 216 mm diameter) undisturbed field soil core to test the validity of the model and its application to field soils. Alternating wet and dry periods enhanced leaching by up to 20% for this soil, which was consistent with the model's prediction, given a fitted equivalent aggregate radius of 1.8 cm, If similar results are obtained for other soils, use of alternating wet and dry periods could improve management of solutes, for example in salinity control and in soil remediation.

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport, and makes use of results of semiclassical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional organic metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals. [S0163-1829(99)02236-5].