A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Factors influencing biodiversity and distributional gradients in mangroves

Numerous factors affect the distribution of mangrove plants. Most mangrove species are typically dispersed by water-buoyant propagules, allowing them to lake advantage of estuarine, coastal and ocean currents both to replenish existing stands and to establish new ones. The direction they travel depends on sea currents and land barriers, but the dispersal distance depends on the time that propagules remain buoyant and viable. This is expected to differ for each species. Similarly, each species will also differ in establishment success and growth development rate, and each has tolerance limits and growth responses which are apparently unique. Such attributes are presumably responsible for the characteristic distributional ranges of each species, as each responds to the environmental, physical and biotic settings they might occupy. In practice, species are often ordered by the interplay of different factors along environmental gradients, and these may conveniently be considered at four geographic scales-global, regional, estuarine and intertidal. We believe these influencing factors act similarly around the world, and to demonstrate this point, we present examples of distributional gradients from the two global biogeographic regions, the Atlantic East Pacific and the Indo-West Pacific.

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.

Moisture is required for the termination of egg diapause in the chrysomelid beetle, Homichloda barkeri

Four factors (moisture, light regime, temperature, food type) were examined for their effects on the embryonic diapause of Homichloda (Weiseana) barkeri (Jacoby) (Coleoptera: Chrysomelidae), a biocontrol agent for prickly acacia, Acacia nilotica (L.) Willdenew ex Delile (Mimosaceae). Moisture is critical for termination of diapause. A single wetting of eggs resulted in a low hatch rate while a sequence of wetting events followed by periods of dryness produced a high hatch rate. A relatively constant proportion of embryos within each batch initiated development at each wetting event, with hatching complete after the eighth wetting event in these trials. An extended interval between wetting events, tested at up to 23 days, did not result in a decreased overall hatch rate. A threshold time of exposure to moisture of between 3 to 6 h is required before development proceeds. The response of eggs to the moisture regime is seen as a strategy for taking advantage of available food after rainfall by terminating diapause, rather than merely a quiescent response to the absence of moisture. Temperature affected development time and the proportion of eggs that developed. Experimental manipulations of photoperiod and host-plant availability showed no effect on embryonic development.

Closely related Symbiodinium spp. differ in relative dominance in coral reef host communities across environmental, latitudinal and biogeographic gradients

The diversity and community structures of symbiotic dinoflagellates are described from reef invertebrates in southern and central provinces of the Great Barrier Reef (GBR), Australia, and Zamami Island, Okinawa, Japan. The symbiont assemblages from region to region were dominated by Clade C Symbiodinium spp. and consisted of numerous host-specific and/or rare types (specialists), and several types common to many hosts (generalists). Prevalence in the host community among certain host-generalist symbionts differed between inshore and offshore environments, across latitudinal (central versus southern GBR) gradients, and over wide geographic ranges (GBR versus Okinawa). One particular symbiont (C3h) from the GBR had a dramatic shift in dominance. Its prevalence ranged from being extremely rare, or absent on high-latitude reefs to dominating the scleractinian diversity on a mid-latitude inshore reef. These changes occurred among coral fauna whose larvae must acquire symbionts from environmental sources (horizontal symbiont acquisition). Such differences did not occur among 'vertical transmitters' such as Porites spp., Montipora spp. and pocilloporids (corals that directly transmit symbionts to their offspring) or among those hosts displaying 'horizontal acquisition', but that associate with specific symbionts. Most host-specialized types were found to be characteristic of a particular geographic region (i.e. Okinawa versus Central GBR versus Southern GBR). The mode of symbiont acquisition may play an important role in how symbiont composition may shift in west Pacific host communities in response to climate change. There is no indication that recent episodes of mass bleaching have provoked changes in host-symbiont combinations from the central GBR.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Body size and latitudinal gradients in regional diversity of New World birds

Axe latitudinal gradients in regional diversity random or biased with respect to body size? Using data for the New World avifauna, I show that the slope of the increase in regional species richness from the Arctic to the equator is not independent of body size. The increase is steepest among small and medium-sized species, and shallowest among the largest species. This is reflected in latitudinal variation in the shape of frequency distributions of body sizes in regional subsets of the New World avifauna. Because species are added disproportionately in small and medium size classes towards low latitudes, distributions become less widely spread along the body size axis than expected from the number of species. These patterns suggest an interaction between the effects of latitude and body size on species richness, implying that mechanisms which vary with both latitude and body size may be important determinants of high tropical diversity in New World birds.

The life-history basis of latitudinal diversity gradients: how do species traits vary from the poles to the equator.

1. Latitudinal variation among species in life-history traits is often suggested to contribute to high tropical species richness. However, traditional methods of analysing such variation rarely control for phylogeny and latitudinal range overlap between species, potentially giving misleading results. 2. Using a method of pairwise independent contrasts which overcomes these problems, I tested for latitudinal variation among bird species in a number of traits which have been linked, theoretically or empirically, with both latitude and species richness. 3. This method indicates strong support for Rapoport's Rule and decreasing clutch size towards the equator in both hemispheres, but only partial support for decreasing body size and ecological generalism towards the equator. 4. Indirect measures of sexual selection (sexual dichromatism and size dimorphism) show no variation with latitude; an apparent increase in dichromatism towards the equator is shown to be an artefact of phylogeny. 5. Many of the associations between life history and latitude were not detected by traditional cross-species analyses, highlighting the importance of incorporating phylogeny and overlap in studies of geographical life-history variation. Establishing associations between life-history traits and latitude does not prove, but is a necessary prerequisite for., a link between these traits and latitudinal diversity gradients.

Application of a simplified method based on regular regime approach to determine the effective moisture diffusivity of mixture of low molecular weight sugars and maltodextrin during desorption

The binary diffusivities of water in low molecular weight sugars; fructose, sucrose and a high molecular weight carbohydrate; maltodextrin (DE 11) and the effective diffusivities of water in mixtures of these sugars (sucrose, glucose, fructose) and maltodextrin (DE 11) were determined using a simplified procedure based on the Regular Regime Approach. The effective diffusivity of these mixtures exhibited both the concentration and molecular weight dependence. Surface stickiness was observed in all samples during desorption, with fructose exhibiting the highest and maltodextrin the lowest. (C) 2002 Elsevier Science Ltd. All rights reserved.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may he one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time.-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.