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Melamine formaldehyde (MF) foam is a kind of fire-retardant material, which has many excellent properties. In this paper, the effect of foaming agent on foam-cell structure of MF foam was discussed, along with the compressive property, the water absorption and its thermo gravimetric behavior as well as its fire-retardant property behaved by limited oxygen index (LOI). Through the analysis of different factors affected on MF foam and its properties we hope to get practical products with good properties. Keywords: melamine foam; foaming agent; foam-structure; thermal property; fire-retardancy

The gas diffusion layers (GDLs) are key components in proton exchange membrane fuel cells and understanding fluid flow through them plays a significant role in improving fuel cell performance. In this paper we used a combination of multiple-relaxation time lattice Boltzmann method and imaging technology to simulate fluid flow through the void space in a carbon paper GDL. The micro-structures of the GDL were obtained by digitizing 3D images acquired by Xray computed micro-tomography at a resolution of 1.76 lm, and fluid flow through the structures was simulated by applying pressure gradient in both through-plane and inplane directions, respectively. The simulated velocity field at micron scale was then used to estimate the anisotropic permeability of the GDL. To test the method, we simulated fluid flow in a column packed with glass beads and the estimated permeability was found to be in good agreement with The gas diffusion layers (GDLs) are key components in proton exchange membrane fuel cells and understanding fluid flow through them plays a significant role in improving fuel cell performance. In this paper we used a combination of multiple-relaxation time lattice Boltzmann method and imaging technology to simulate fluid flow through the void space in a carbon paper GDL. The micro-structures of the GDL were obtained by digitizing 3D images acquired by Xray computed micro-tomography at a resolution of 1.76 lm, and fluid flow through the structures was simulated by applying pressure gradient in both through-plane and inplane directions, respectively. The simulated velocity field at micron scale was then used to estimate the anisotropic permeability of the GDL. To test the method, we simulated fluid flow in a column packed with glass beads and the estimated permeability was found to be in good agreement with The gas diffusion layers (GDLs) are key components in proton exchange membrane fuel cells and understanding fluid flow through them plays a significant role in improving fuel cell performance. In this paper we used a combination of multiple-relaxation time lattice Boltzmann method and imaging technology to simulate fluid flow through the void space in a carbon paper GDL. The micro-structures of the GDL were obtained by digitizing 3D images acquired by Xray computed micro-tomography at a resolution of 1.76 lm, and fluid flow through the structures was simulated by applying pressure gradient in both through-plane and inplane directions, respectively. The simulated velocity field at micron scale was then used to estimate the anisotropic permeability of the GDL. To test the method, we simulated fluid flow in a column packed with glass beads and the estimated permeability was found to be in good agreement with experimental measurements. The simulated results for the GDL revealed that the increase of permeability with porosity was well fitted by the model of Tomadakis–Sotirchos [48] without fitting parameters. The permeability calculated using fluids with different viscosities indicated that the multiple- relaxation time lattice Boltzmann method provides robust solutions, giving a viscosity-independent permeability. This is a significant improvement over the commonly used single-time relaxation lattice Boltzmann model which was found to give rise to a unrealistic viscosity-dependent permeability because of its inaccuracy in solving the fluid– solid boundaries.

Field effect transistors (FET) based on Single-Walled Carbon Nanotubes (SWNTs) become the hot topic in fields of nano-electronic, clinical diagnostics, environmental testing etc. in recent years. In this paper, we reported a simple, scalable way to enrich semiconducting SWNTs by using HNO3/H2SO4. Then carbon nanotube field-effect transistors (CNTFET) biosensor was fabricated with the enrichment SWNTs for Escherichia coli O157︰H7 detection. The response of each CNTFET was monitored in real time before and after introduction of the Escherichia coli O157︰H7 at various concentrations. The results show that CNT-FET biosensors we fabricated are sensitive to change of concentration of solution and response time is really short.

Melamine formaldehyde (MF) foam is kind of fire-retardant material and has great potential in acoustic and thermal insulation area. In this article, MF resin foam was prepared by microwave radiation. We discussed the thermal stability of MF foam and the effect of different emulsifiers on its morphology, apparent density, fire-retardancy and mechanical property. The decomposition temperature of MF foam we prepared is nearly 400℃ and the constitution of residue after combustion is made up of carbon and graphite. Emulsifier influenced the apparent density of MF foam and using coemulsifiers can get flexible foam with uniform cell size, good morphology and low apparent density. When the fire-retardant MF foam’s apparent density is low of 5.53 kg/cm-3, its value of LOI can reach 32.4. The mechanical property of foam is consistent with apparent density.

Depositing single-walled carbon nanotubes (SWNTs) with controllable density, pattern and orientation on electrodes presents a challenge in today’s research. Here, we report a novel solvent evaporation method to align SWNTs in patterns havingnanoscale width and micronscale length. SWNTs suspension has been introduced dropwise onto photoresist resin microchannels; and the capillary force can stretch and align SWNTs into strands with nanoscale width in the microchannels. Then these narrow and long aligned SWNTs patterns were successfully transferred to a pair of gold electrodes with different gaps to fabricate carbon nanotube field-effect transistor (CNTFET). Moreover, the electrical performance of the CNTFET show that the SWNTs strands can bridge different gaps and fabricate good electrical performance CNTFET with ON/OFF ratio around 106. This result suggests a promising and simple strategy for assembling well-aligned SWNTs into CNTFET device with good electrical performance.

By activating protective pathways, tumour cells are not only capable of survival in stress, but often associated with increased aggressiveness and metastasis. Activating transcription factor 4 (ATF4) is a major coordinator of tumour cell survival in stress and is commonly overexpressed in tumours. Numerous studies suggested that the ATF4 is a potential therapeutic target for cancer. In this report, we describe that a small ribosomal peptide, RPL41, induced rapid ATF4 degradation. By immunofluorescence staining, RPL41 induced ATF4 relocation from nuclei to cytoplasm, where ATF4 co-stained with a proteasome marker; the RPL41-induced ATF4 relocation and degradation were blocked by the proteasome inhibitor MG132. An in vivo phosphorylation study showed that RPL41 induced ATF4 phosphorylation and serine 219 of ATF4 was essential for RPL41-induced ATF4 degradation. Cells with RPL41 knockdown had significantly increased ATF4, suggesting that RPL41 could play a physiological role in regulating the cellular ATF4 level. RPL41 was capable of inducing tumour cell death and cell cycle arrest; at low dose, RPL41 sensitized tumour cells A549 to the DNA damage agent cisplatin. These studies suggest that RPL41, a small peptide that is chemically synthesizable and capable of self-cell penetration, may have potential as an anti-ATF4 agent for cancer therapy.

This study reports the feasibility of newly simulating liquid water intrusion into the porous gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) using X-ray nano-tomography and two-phase lattice Boltzmann (LB) simulation. A digital 3D model of the GDL is reconstructed using X-ray nanotomography while two-phase porous flow is simulated at two different levels of surface wettability by applying a newly-developed numerical LB model. The results show liquid infiltration in a hydrophobic GDL is comparatively lower (pore saturation of 0.11 to 0.90) than that for a hydrophilic GDL (pore saturation of 0.36 to 0.96) over the liquid intrusion range of 1 kPa . 100 kPa. Visualisation of simulated results in three dimensions reveal dissimilar liquid infiltration characteristics for the two levels of wettability considered, yet also reveal a general breakthrough of liquid water at a pressure of 10 kPa due to specific structural features of the GDL.

The effect of compression on the actual structure and transport properties of the carbon cloth gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) are studied here. Structural features of GDL samples compressed in the 0.0 – 100.0 MPa range are encapsulated using polydimethylsiloxane (PDMS) and by employing X-ray micro-tomography to reconstruct direct digital 3D models. Pore size distribution (PSD) and porosity data are acquired directly from these models while permeability, degree of anisotropy and tortuosity are determined through lattice Boltzmann (LB) numerical modelling. The structural models reveal that structural change proceeds through a three-step process, while PSD data suggests a characteristic peak in the pore diameter of 10-14 microns and a decrease in the mean pore diameter from 33 to 12 microns over the range of tested pressures. A mathematical relationship between compression pressure and permeability is determined based on the Kozeny-Carman equation, revealing a one order of magnitude reduction in through-plane permeability for a two order of magnitude increase in pressure. The results also reveal that the degree of anisotropy peaks in the 0.3 – 10.0 MPa range, suggesting that in-plane permeability can be maximised relative to through-plane permeability within a material-specific range of compression pressures.

Single ZnO nanorods were studied with cathodoluminescence at high spatial and angular resolution. A newly developed luminescence detector consisting a fiber probe controlled by a nano-manipulator is attached to a scanning electron microscope to carry out the cathodoluminescence measurements. Excitonic emission from the sidewalls and redshifted near band edge emission guided along the nanorod axis are observed as the fiber probe axis is aligned to be perpendicular and parallel to the nanorod axis, respectively, demonstrating the angular resolving power of the experimental setup and waveguiding behavior of the nanorods. High spatial resolution cathodoluminescence measurement shows that the near band edge emission can propagate parallel and perpendicular to the nanorod axis and an increased propagation distance results in more redshift of the guided luminescence. In addition, the high spatial resolution and temperature dependent cathodoluminescence measurements demonstrate the important role of free exciton-longitudinal optical phonon interaction in the waveguiding behavior and the propagation of the near band edge emission in ZnO nanorods.

A feasibility study into the development and application of a single-phase multi-component (SPMC) lattice Boltzmann (LB) model to simulate the movement of a three-species gas through the cathode gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC) has been reported in this paper. The porous geometry of the GDL is captured and digitally reconstructed for the numerical model using X-ray computed micro-tomography. The boundary conditions at the channel and catalyst layer interfaces for the SPMC-LB simulations including species partial pressures and through-plane flow rates are obtained using a previously-developed and validated electrochemical model of the complete multi-layer PEFC, which is based on the general transport equation (GTE). The results reveal that the SPMC-LB model has the capability to precisely detail the distribution of multi-species gas components through the heterogeneous porous structure of the GDL.

One-dimensional (1-D) semiconductor nanostructures can effectively transport electrons and photons, and are considered to be promising building blocks for future optoelectronic nanodevices. In this review, we present our recent efforts to integrate optical techniques and in situ electron microscopy for comprehensively characterizing individual 1-D optoelectronic nanostructures and nanodevices. The technical strategies and their applications in “green” emission and optical confinement in 1-D ZnO nanostructures will be introduced. We also show in situ assembly and characterization of nanostructures for optoelectronic device purposes. Using these examples, we demonstrate that the combination of optical techniques and in situ electron microscopy can be powerful for the studies of optoelectronic nanomaterials and nanodevices.

An investigation of the anisotropic permeability of a carbon cloth gas diffusion layer (GDL) based on the integration of X-ray micro-tomography and lattice Boltzmann (LB) simulation is presented. The method involves the generation of a 3D digital model of a carbon cloth GDL as manufactured using X-ray shadow images acquired through X-ray micro-tomography at a resolution of 1.74 µm. The resulting 3D model is then split into 21 volumes and integrated with a LB single-phase numerical solver in order to predict three orthogonal permeability tensors when a pressure difference is prescribed in the through-plane direction. The 21 regions exhibit porosity values in the range of 0.910–0.955, while the average fibre diameter is 4 µm. The results demonstrate that the simulated through-plane permeability is about four times higher than the in-plane permeability for the sample imaged and that the corresponding degrees of anisotropy for the two orthogonal off-principal directions are 0.22 and 0.27. The results reveal that flow channelling can play an important role in gas transport through the GDL structure due to the non-homogeneous porosity distribution through the material. The simulated results are also applied to generate a parametric coefficient for the Kozeny–Carman (KC) method of determining permeability. The current research reveals that by applying the X-ray tomography and LB techniques in a complementary manner, there is a strong potential to gain a deeper understanding of the microscopic fluidic phenomenon in representative models of porous fuel cell structures and how this can influence macroscopic transport characteristics which govern fuel cell performance.

Field-emitted, low-energy electrons from the conducting tip of an atomic force microscope were adopted for nanolithography on calixarene ultrathin films coated on silicon wafers. A structural evolution from protrusion to depression down to a 30 nm spatial resolution was reproducibly obtained by tuning the sample voltage and exposure current in the lithography process. Close analyses of the profiles showed that the nanostructures formed by a single exposure with a high current are almost identical to those created by cumulative exposure with a lower current but an equal number of injected electrons. Surface potential imaging by Kelvin probe force microscopy found a negatively charged region surrounding the groove structures once the structures were formed. We conclude that the mechanism related to the formation of a temporary negative state and molecule decomposition, rather than thermal ablation, is responsible for the low-energy field-emission electron lithography on a calixarene molecular resist. We hope that our elucidation of the underlying mechanism is helpful for molecular resist design and further improving the reproducibility and throughput of nanolithography.

We report on the anisotropic optical emission of individual ZnO nanorods directly measured by angular-resolved photoluminescence imaging and spectroscopy with independent excitation and detection optics. A reduced diameter at the subwavelength scale results in degraded waveguiding efficiency and more divergent emission at the top ends of individual ZnO nanorods grown by chemical vapor deposition. The near-band-edge (NBE) emission from the nanorod ends exhibits strong angular dependence in both emission intensity and spectral line shape. A continuous intensity increase and spectral red shift of the NBE emission have been observed as the detection direction varies from the radial direction to the axial direction. The pronounced red shift (>60 meV) is primarily attributed to the transition from free exciton (FX) emission to its 2LO phonon replica (FX-2LO) emission. Our results support an exciton−polariton model for the waveguiding behavior of ZnO nanorods and demonstrate the dominant role of the FX-2LO excit...

This research reports a feasibility study into multiscale polymer electrolyte fuel cell (PEFC) modeling through the simulation of macroscopic flow in the multilayered cell via one-dimensional (1D) electrochemical modeling, and the simulation of microscopic flow in the cathode gas diffusion layer (GDL) via three-dimensional (3D) single-phase multicomponent lattice Boltzmann (SPMC-LB) modeling. The heterogeneous porous geometry of the carbon-paper GDL is digitally reconstructed for the SPMC-LB model using X-ray computer microtomography. Boundary conditions at the channel and catalyst layer interfaces for the SPMC-LB simulations such as specie partial pressures and through-plane flowrates are determined using the validated 1D electrochemical model, which is based on the general transport equation (GTE) and volume-averaged structural properties of the GDL. The calculated pressure profiles from the two models are cross-validated to verify the SPMC-LB technique. The simulations reveal a maximum difference of 2.4% between the thickness-averaged pressures calculated by the two techniques, which is attributable to the actual heterogeneity of the porous GDL structure.

A common challenge in the X-ray nanotomography of porous media, such as fuel cell gas diffusion layers (GDLs), is to binarize nanotomography greyscale images in order to differentiate between solids and voids for structural characterisation and numerical flow analysis. In the process threshold determination is critical. This paper presents a study on determination of and fine-tuning threshold value based on comparison of material porosity and average fibre diameter obtained from nanotomography images with porosity data from density experiments and average fibre diameter achieved from scanning electron microscopy images respectively. The more accurate 3D reconstructed model is then used to calculate pore size distribution and average pore size, while the gas permeability of the representative 3D binary images are calculated using a single phase Lattice Boltzmann (LB) model in the D3Q19 regime.

The focus of the current study is on a state-of-the-art twin-layer gas diffusion layer (GDL) which consists of carbon tissues with a fibre diameter of 5–20 μm, and contains a microporous layer (MPL) coating which has sub-micron porous features. In the current study, real-world digital three-dimensional images of the GDL-MPL assembly are created through X-ray nano-tomography with a 680 nm pixel resolution for the GDL and focused ion beam/scanning electron microscopy (FIB/SEM) nano-tomography with a 14 nm pixel resolution for the MPL. The critical nano-structural features including porosity, characteristic lengths and 3D pore size distribution are determined directly from the 3D digital representation. In addition to morphological parameters, the FIB/SEM nano-tomography technique has been combined with lattice Boltzmann (LB) numerical modelling in order to calculate the tortuosity and permeability of the MPL.

Morphological parameters of a 3D binary image of a porous carbon gas diffusion layer (GDL) for polymer electrolyte fuel cells (PEFC) reconstructed using X-ray nano-tomography scanning have been obtained, and influence of small alterations in the threshold value on the simulated flow properties of the reconstructed GDL has been determined. A range of threshold values with 0.4% increments on the greyscale map have been applied and the gas permeability of the binary images have been calculated using a single-phase lattice Botlzmann model (LBM), which is based on the treatment of nineteen velocities in the three dimensional domain (D3Q19). The porosity, degrees of anisotropy and the mean pore radius have been calculated directly from segmented voxel representation. A strong relationship between these parameters and threshold variation has been established. These findings suggest that threshold selection can significantly affect some of the flow properties and may strongly influence the computational simulation of micro and nano-scale flows in a porous structure.

Soil-dwelling insect herbivores are significant pests in many managed ecosystems. Because eggs and larvae are difficult to observe, mathematical models have been developed to predict life-cycle events occurring in the soil. To date, these models have incorporated very little empirical information about how soil and drought conditions interact to shape these processes. This study investigated how soil temperature (10, 15, 20 and 25 °C), water content (0.02 (air dried), 0.10 and 0.25 g g−1) and pH (5, 7 and 9) interactively affected egg hatching and early larval lifespan of the clover root weevil (Sitona lepidus Gyllenhal, Coleoptera: Curculionidae). Eggs developed over 3.5 times faster at 25 °C compared with 10 °C (hatching after 40.1 and 11.5 days, respectively). The effect of drought on S. lepidus eggs was investigated by exposing eggs to drought conditions before wetting the soil (2–12 days later) at four temperatures. No eggs hatched in dry soil, suggesting that S. lepidus eggs require water to remain viable. Eggs hatched significantly sooner in slightly acidic soil (pH 5) compared with soils with higher pH values. There was also a significant interaction between soil temperature, pH and soil water content. Egg viability was significantly reduced by exposure to drought. When exposed to 2–6 days of drought, egg viability was 80–100% at all temperatures but fell to 50% after 12 days exposure at 10 °C and did not hatch at all at 20 °C and above. Drought exposure also increased hatching time of viable eggs. The effects of soil conditions on unfed larvae were less influential, except for soil temperature which significantly reduced larval longevity by 57% when reared at 25 °C compared with 10 °C (4.1 and 9.7 days, respectively). The effects of soil conditions on S. lepidus eggs and larvae are discussed in the context of global climate change and how such empirically based information could be useful for refining existing mathematical models of these processes.

Summary The adsorptive kinetics of reactive solutes in soils is usually measured in batch experiments by keeping the water stagnant. One concern over such measured parameters is their representative of describing the adsorption in field where the water is not stagnant but moves in a spatially variable velocity. Answer to this question appears to be conflict in the literature with some finding a dependence of the adsorptive kinetics on water flow rate and others showing contradiction. Since the adsorption occurring at water–solid interface is inaccessible, affected by various physical and biochemical processes, the existing explanations about an dependence, or independence, of the adsorptive kinetics on water flow rate are not consensus. In this paper a pore-scale model was developed to investigate the adsorptive kinetics of solute in soil. It was assumed that each water–solid interface has a limited number of adsorptive sites to adsorb solute, and that the rate at which the interface adsorbs solute is proportional to the number of the adsorptive sites that still remain unoccupied by solute particles. In the meantime, each adsorbed solute particle can come off the interface at a given probability to become desorbed. Water flow and solute transport through the void space was simulated using a lattice Boltzmann method, and the simulated solute distribution at pore scale was then spatially averaged to yield two profiles: one for solute in fluid and one for solute adsorbed on the fluid–solid interface, in an attempt to test if the spatial average leads to a macroscopic adsorptive kinetics that changes with water flow rate. The results indicated that when the microscopic adsorptive kinetics is homogeneous in that the adsorption and desorption rates operating on the fluid–solid interface are both constants, the associated macroscopic adsorptive rates do not change with water flow rate and their values measured in batch experiments can accurately predict solute displacement under different pore-water velocities. When the microscopic adsorptive kinetics becomes spatially heterogeneous, however, the macroscopic adsorption rates measured in the batch experiments are no longer able to describe solute displacement. The results presented in this paper provide some insight into the adsorptive kinetics of solute in soils, suggesting that the reported dependence of adsorptive rates on water flow rate could be due to an inappropriate use of adsorptive models in describing the heterogeneous adsorption in soil, rather than truly that a change in pore-water velocity indeed results in a change in adsorption rates.

We demonstrate a promising route to fabricate large scale hexagonally patterned, vertically aligned ZnO nanorod arrays with small diameter. By adding 3-mercaptopropyltriethoxysilane (MPTES) molecules as a connection between catalyst and substrate the large size dispersion resulting from the removal of catalyst pattern is avoided, thus the catalyst particle pattern with tiny size dispersion and regular shape is obtained; the size can be tuned in a large range from 50 nm to 300 nm. Using this technique, ZnO nanorod arrays with tunable spacings and diameters are achieved, which also have uniform shape and length, good crystal quality, and vertical alignment on the substrate. Moreover, a pronounced blue-shift of ultraviolet (UV) luminescence spectra of ZnO nanorods with their diameters decreasing is observed. Combining the temperature-dependent photoluminescence (PL), we suggest that a materially decreased exciton-phonon interaction with the reduced diameter of ZnO nanorods is the main reason for the blue-shift of UV luminescence.

Exact integration of discontinuous quartic boundary element for evaluation of potential, its first-order and second-order derivative is presented. A patch test problem with three kinds of boundary conditions is implemented to show that the discontinuous boundary element with exact integration can evaluate the potential, its first-order and second-order derivative on boundary with high accuracy. Copyright © 2008 John Wiley & Sons, Ltd.

Some researchers suggest that the changes of cell cycle under the effect of microgravity may be associated with many serious adverse physiological changes. In the search for underlying mechanisms and possible new countermeasures, we used the slime mold Physarum polycephalum in which all the nuclei traverse the cell cycle in natural synchrony to study the effects of altered gravity on the cell cycle, actin cytoskeleton and proteome. In parallel, the cell cycle was analyzed in Physarum incubated (1) in altered gravity for 20 h, (2) in altered gravity for 40 h, (3) in altered gravity for 80 h, and (4) in ground controls. The cell cycle, the actin cytoskeleton, and proteome in the altered gravity and ground controls were examined. The results indicated that the duration of the G2 phase was lengthened 20 min in high aspect ratio vessel (HARV) for 20 h, and prolonged 2 h in altered gravity either for 40 h or for 80 h, whereas the duration of other phases in the cell cycle was unchanged with respect to the control. The microfilaments in G2 phase had a reduced number of fibers and a unique abnormal morphology in altered gravity for 40 h, whereas the microfilaments in other phases of cell cycle were unchanged when compared to controls. Employing classical two-dimensional electrophoresis (2-DE), we examined the effect of the altered gravity on P. polycephalum proteins. The increase in the duration of G2 phase in altered gravity for 40 h was accompanied by changes in the 2-DE protein profiles, over controls. Out of a total of 200 protein spots investigated in G2 phase, which were reproducible in repeated experiments, 72 protein spots were visually identified as specially expressed, and 11 proteins were up-regulated by 2-fold and 28 proteins were down-regulated by 2-fold over controls. Out of a total of three low-expressed proteins in G2 phase in altered gravity for 40 h, two proteins were unknown proteins, and one protein was spherulin 3b by MALDI-TOF mass spectrometry (MS). Our results suggest that a low level of spherulin 3b in G2 phase, which may lead to a reduction of Poly(b-L-malate) (PMLA), may contribute to the lengthened duration of G2 phase in altered gravity for 40 h. Present results indicate that altered gravity results in the prolongation of G2 phase with significantly altered actin cytoskeleton and proteome in P. polycephalum.

PurposeThe cell‐based method of domain decomposition was first introduced for complex 3D geometries. To further assess the method, the aim is to carry out flow simulation in rectangular ducts to compare the known analytical solutions.Design/methodology/approachThe method is not based on equal subvolumes but on equal numbers of active cells. The variables of the simulation are stored in ordered 1D arrays to replace the conventional 3D arrays, and the domain decomposition of the complex 3D problems therefore becomes 1D. Finally, the 3D results can be recovered using a coordinate matrix. Through the flow simulation in the rectangular ducts how the algorithm of the domain decompositions works was illustrated clearly, and the numerical solution was compared with the exact solutions.FindingsThe cell‐based method can find the subdomain interfaces successfully. The parallelization based on the algorithm does not cause additional errors. The numerical results agree well with the exact solutions. Furthermore, the results of the parallelization show again that domains of 3D geometries can be decomposed automatically without inducing load imbalances.Practical implicationsAlthough, the approach is illustrated with lattice Boltzmann method, it is also applicable to other numerical methods in fluid dynamics and molecular dynamics.Originality/valueUnlike the existing methods, the cell‐based method performs the load balance first based on the total number of fluid cells and then decomposes the domain into a number of groups (or subdomains). Thus, the task of the cell‐based method is to recover the interface rather than to balance the load as in the traditional methods. This work has examined the celled‐based method for the flow in rectangular ducts. The benchmark test confirms that the cell‐based domain decomposition is reliable and convenient in comparison with the well‐known exact solutions.

Modelling adsorptive solute transport in soils needs a number of parameters to describe its reaction kinetics and the values of these parameters are usually determined from batch and displacement experiments. Some experimental results reveal that when describing the adsorption as first-order kinetics, its associated reaction rates are not constants but vary with pore water velocity. Explanation of this varies but an independent verification of each explanation is difficult because simultaneously measuring the spatiotemporal distributions of dissolved and adsorbed solutes in soils is formidable. Pore-scale modelling could play an important role to address this gap and has received increased attention over the past few years. This paper investigated the transport of adsorptive solute in a simple porous medium using pore-scale modelling. Fluid flow through the void space of the medium was assumed to be laminar and in saturated condition, and solute transport consisted of advection and molecular diffusion; the sorption and desorption occurring at the fluid–solid interface were modelled as linear first-order kinetics. Based on the simulated spatiotemporal distribution of dissolved and adsorbed solutes at pore scale, volumetric-average reaction kinetics at macroscopic scale and its associated reactive parameters were measured. Both homogeneous adsorption where the reaction rates at microscopic scale are constant, and heterogeneous adsorption where the reaction rates vary from site to site, were investigated. The results indicate that, in contrast to previously thought, the macroscopic reaction rates directly measured from the pore-scale simulations do not change with pore velocity under both homogeneous and heterogeneous adsorptions. In particular, we found that for the homogeneous adsorption, the macroscopic adsorption remains first-order kinetic and can be described by constant reaction rates, regardless of flow rate; whilst for the heterogeneous adsorption, the macroscopic adsorption kinetics continues not to be affected by flow rate but is no longer first-order kinetics that can be described by constant reaction rates. We discuss how these findings could help explain some contrary literature reports over the dependence of reaction rates on pore water velocity.

Summary The nature of flow paths, determined by soil structural features, may greatly influence solute breakthrough in a soil profile. We compared two contrasting methods of characterising flow within an upland soil with distinct organic and mineral horizons: saturated conductivity measured on cores sampled destructively; and breakthrough measurements for chloride in 2.4 × 3.4 × 1 m in situ lysimeter. Chloride tracer was applied to the soil surface, and soil solution samples collected at 20 known locations using suction cup samplers. Breakthrough curves were classified into statistically distinct pathway types using Principal Coordinate Analysis, according to peak concentration and the time to peak concentration. Of the 20 locations, two exhibited rapid macropore flow, two intermediate mesopore flow, and seven slower micropore flow. The remaining nine samplers did not register breakthrough within the 16-day duration of the experiment. Destructive core (6 cm diameter by 6 cm deep) sampling was used to characterise saturated hydraulic conductivity at 116 locations within the soil block. Solute breakthrough speed was linearly related to kriged values of saturated conductivity for the meso and micropore flow paths (r = 0.88 for initial breakthrough; r = 0.85 for peak concentration breakthrough), but not for macropore flow. This indicates that kriged saturated conductivities provided good prediction of the speed of the meso and micro flow paths. Frequency distributions of saturated hydraulic conductivities and breakthrough speeds did not differ significantly, although the breakthrough speed distribution was truncated by the limited duration of the lysimeter experiment. Lysimeter breakthrough for macropore pathways was faster than predicted from the core conductivities, indicating that the locations of these fast flow paths were not predicted accurately by the kriged saturated conductivities. Longer duration lysimeter experiments would be required to characterise breakthrough through the slowest pathways, and so these pathways were better characterised using the destructive saturated conductivity technique.

Today's standardized computer models for simulating flow through in-ground sustainable urban drainage systems (SUDS) require substantial monitoring data in order to allow for a realistic representation of system behaviour, as they are based on predefined or user-specific head-discharge relationships. Darcy's law in combination with the finite volume method was applied to compute the flow through filter material and validated against monitored data. The finite volume Darcy's flow (FVD) model is based on physical characteristics, which represents flow through gravel material. Flow characteristics are dependent on the dimensions and materials used and an excellent model fit was achieved when compared with monitoring data.

The inherent heterogeneity of geological media often results in anomalous dispersion for solute transport through them, and how to model it has been an interest over the past few decades. One promising approach that has been increasingly used to simulate the anomalous transport in surface and subsurface water is the fractional advection–dispersion equation (FADE), derived as a special case of the more general continuous time random walk or the stochastic continuum model. In FADE, the dispersion is not local and the solutes have appreciable probability to move long distances, and thus reach the boundary faster than predicted by the classical advection–dispersion equation (ADE). How to deal with different boundaries associated with FADE and their consequent impact is an issue that has not been thoroughly explored. In this paper we address this by taking one-dimensional solute movement in soil columns as an example. We show that the commonly used FADE with its fractional derivatives defined by the Riemann–Liouville definition is problematic and could result in unphysical results for solute transport in bounded domains; a modified method with the fractional dispersive flux defined by the Caputo derivatives is presented to overcome this problem. A finite volume approach is given to numerically solve the modified FADE and its associated boundaries. With the numerical model, we analyse the inlet-boundary treatment in displacement experiments in soil columns, and find that, as in ADE, treating the inlet as a prescribed concentration boundary gives rise to mass-balance errors and such errors could be more significant in FADE because of its non-local dispersion. We also discuss a less-documented but important issue in hydrology: how to treat the upstream boundary in analysing the lateral movement of tracer in an aquifer when the tracer is injected as a pulse. It is shown that the use of an infinite domain, as commonly assumed in literature, leads to unphysical backward dispersion, which has a significant impact on data interpretation. To avoid this, the upstream boundary should be flux-prescribed and located at the upstream edge of the injecting point. We apply the model to simulate the movement of Cl− in a tracer experiment conducted in a saturated hillslope, and analyse in details the significance of upstream-boundary treatments in parameter estimation.

Insect herbivores that have soil-dwelling larval stages usually lay eggs directly or indirectly into the soil. Following egg hatch, emergent larvae must locate host plant roots to avoid starvation and this represents the most vulnerable part of the life cycle. We present a model for this aspect of the life cycle, specifically modelling the egg development rate and survival time of the clover root weevil, Sitona lepidus. The model is based on a partial differential equation, developed from age-structure models that are widely used in ecology. The model incorporates stochastic random variation caused by environmental fluctuation and genetic variation in a population, and treats chronological time and biological age as two independent variables. The average developmental rate and the impact of randomness are described by a first-order and a second-order derivative term, respectively. The significance of this model is that it can combine two biological events (egg development and larval survival time) into a single functional event, a potentially important feature for soil-dwelling insects because their concealed habitat does not permit all biological events to be observed. The model was tested against experimental observations of egg development and larval survival time under different soil conditions, firstly by considering egg development and larval survival time as independent biological events and secondly by combining both into a single functional event. Model simulations and experimental observations were in close agreement in all cases. To further test whether the model could be applied to other insect taxa and incorporate more than two biological events, we compared model simulations with published experimental results for the cereal leaf beetle (Oulema duftschmidi). Simulations of egg hatching and the larval development through several instars compared favourably with all experimental observations, demonstrating that the model has multiple applications.

Root-feeding insects are now considered to play a greater role in ecosystem proc- esses than previously thought, yet little is known about their specific interactions with host plants compared with above-ground insect herbivores. Methodological difficulties associated with studying these insects in the soil, together with the lack of empirical and theoretical frameworks, have conventionally hindered progress in this area. 2 This paper reviews recent empirical and theoretical developments that have been adopted for studying root-feeding insects, focusing on the non-invasive tech- niques of X-ray tomography and acoustic field detection and how these can be integrated with new mathematical modelling approaches. 3 X-ray tomography has been used for studying the movements of several insects within the soil and has helped to characterize the host plant location behaviour of the clover root weevil, Sitona lepidus . Acoustic detection of soil insects has been used in various managed systems, ranging from nursery containers to citrus groves. 4 Mathematical modelling plays a complementary role for investigating root-feed- ing insects, illustrated by a number of published models. A model is presented for the movement of S. lepidus in the soil, which suggests that these insects un- dergo Levy movements, similar to those recently demonstrated for above-ground organisms. 5 The future directions and challenges for investigating root-feeding insects are discussed in the context of the wider ecosystem, incorporating both above and below-ground organisms.

The movement of organisms is usually leptokurtic in which some individuals move long distances while the majority remains at or near the area they are released. There has been extensive research into the origin of such leptokurtic movement, but one important aspect that has been overlooked is that the foraging behaviour of most organisms is not Brownian as assumed in most existing models. In this paper we show that such non-Brownian foraging indeed gives rise to leptokurtic distribution. We first present a general random walk model to describe the organism movement by breaking the foraging of each individual into events of active movement and inactive stationary period; its foraging behaviour is therefore fully characterized by a joint probability of how far the individual can move in each active movement and the duration it remains stationary between two consecutive movements. The spatio-temporal distribution of the organism can be described by a generalized partial differential equation, and the leptokurtic distribution is a special case when the stationary period is not exponentially distributed. Empirical observations of some organisms living in different habitats indicated that their rest time shows a power-law distribution, and we speculate that this is general for other organisms. This leads to a fractional diffusion equation with three parameters to characterize the distributions of stationary period and movement distance. A method to estimate the parameters from empirical data is given, and we apply the model to simulate the movement of two organisms living in different habitats: a stream fish (Cyprinidae: Nocomis leptocephalus) in water, and a root-feeding weevil, Sitona lepidus in the soil. Comparison of the simulations with the measured data shows close agreement. This has an important implication in ecology that the leptokurtic distribution observed at population level does not necessarily mean population heterogeneity as most existing models suggested, in which the population consists of different phenotypes; instead, a homogeneous population moving in homogeneous habitat can also lead to leptokurtic distribution.

The activities of hormones in the Arabidopsis root depend on cellular context and exhibit either synergistic or antagonistic interactions. Patterning in Arabidopsis root development is coordinated via a localized auxin concentration maximum in the root tip, mediating transcription of key regulatory genes. Auxin concentration and response are each regulated by diverse interacting hormones and gene expression and therefore cannot change independently of those hormones and genes. For example, experimental data accumulated over many years have shown that both ethylene and cytokinin regulate auxin concentration and response. Using the crosstalk of auxin-ethylene-cytokinin as a paradigm, we discuss the links between experimental data, reaction kinetics and spatiotemporal modelling to dissect hormonal crosstalk. In particular, we discuss how kinetic equations for modelling auxin concentration are formulated based on experimental data and also the underlying assumptions for deriving those kinetic equations. Furthermore, we show that, by integrating kinetic equations with spatial root structure, modelling of spatiotemporal hormonal crosstalk is a powerful tool for analysing and predicting the roles of multiple hormone interactions in auxin patterning. Finally, we summarise important considerations in developing a spatiotemporal hormonal crosstalk model for plant root development.

Fully understanding the effect and the molecular mechanisms of plasma damage and silylation repair on low dielectric constant (low-k) materials is essential to the design of low-k dielectrics with defined properties and the integration of low-k dielectrics into advanced interconnects of modern electronics. Here, analytical techniques including sum frequency generation vibrational spectroscopy (SFG), Fourier transform infrared spectroscopy (FTIR), contact angle goniometry (CA) and X-ray photoelectron spectroscopy (XPS) have been employed to provide a comprehensive characterization of the surface and bulk structure changes of poly(methyl)silsesquioxane (PMSQ) low-k thin films before and after O2 plasma treatment and silylation repair. O2 plasma treatment altered drastically both the molecular structures and water structures at the surfaces of the PMSQ film while no bulk structural change was detected. For example, ∼34% Si-CH3 groups were removed from the PMSQ surface, and the Si-CH3 groups at the film surface tilted toward the surface after the O2 plasma treatment. The oxidation by the O2 plasma made the PMSQ film surface more hydrophilic and thus enhanced the water adsorption at the film surface. Both strongly and weakly hydrogen bonded water were detected at the plasma-damaged film surface during exposure to water with the former being the dominate component. It is postulated that this enhancement of both chemisorbed and physisorbed water after the O2 plasma treatment leads to the degradation of low-k properties and reliability. The degradation of the PMSQ low-k film can be recovered by repairing the plasma-damaged surface using a silylation reaction. The silylation method, however, cannot fully recover the plasma induced damage at the PMSQ film surface as evidenced by the existence of hydrophilic groups, including C-O/C[double bond, length as m-dash]O and residual Si-OH groups. This work provides a molecular level picture on the surface structural changes of low-k materials after plasma treatment and the subsequent silylation repair.

Sugar coatings can stabilize the “native” structure and control the orientation of surface-immobilized peptides in air, providing a potential approach to retain biological functions of surface-immobilized biomolecules in air. This method is general and applicable to complex enzymes.

• Patterning in Arabidopsis root development is coordinated via a localized auxin concentration maximum in the root tip, requiring the regulated expression of specific genes. However, little is known about how hormone and gene expression patterning is generated. • Using a variety of experimental data, we develop a spatiotemporal hormonal crosstalk model that describes the integrated action of auxin, ethylene and cytokinin signalling, the POLARIS protein, and the functions of PIN and AUX1 auxin transporters. We also conduct novel experiments to confirm our modelling predictions. • The model reproduces auxin patterning and trends in wild-type and mutants; reveals that coordinated PIN and AUX1 activities are required to generate correct auxin patterning; correctly predicts shoot to root auxin flux, auxin patterning in the aux1 mutant, the amounts of cytokinin, ethylene and PIN protein, and PIN protein patterning in wild-type and mutant roots. Modelling analysis further reveals how PIN protein patterning is related to the POLARIS protein through ethylene signalling. Modelling prediction of the patterning of POLARIS expression is confirmed experimentally. • Our combined modelling and experimental analysis reveals that a hormonal crosstalk network regulates the emergence of patterns and levels of hormones and gene expression in wild-type and mutants.

The creation of a 3D pore-scale model of a porous medium is often an essential step in quantitatively characterising the medium and predicting its transport properties. Here we describe a new stochastic pore space reconstruction approach that uses thin section images as its main input. The approach involves using a third-order Markov mesh where we introduce a new algorithm that creates the reconstruction in a single scan, thus overcoming the computational issues normally associated with Markov chain methods. The technique is capable of generating realistic pore architecture models (PAMs), and examples are presented for a range of fairly homogenous rock samples as well as for one heterogeneous soil sample. We then apply a Lattice–Boltzmann (LB) scheme to calculate the permeabilities of the PAMs, which in all cases closely match the measured values of the original samples. We also develop a set of software methods – referred to as pore analysis tools (PATs) – to quantitatively analyse the reconstructed pore systems. These tools reveal the pore connectivity and pore size distribution, from which we can simulate the mercury injection process, which in turn reproduces the measured curves very closely. Analysis of the topological descriptors reveals that a connectivity function based on the specific Euler number may serve as a simple predictor of the threshold pressure for geo-materials.

Summary The knowledge of hydraulic conductivity and solute transport parameters of top-soil is important in a variety of fields and their measurement has been an interest in both theory and practice. In this paper we present an in situ method to measure the longitudinal and transverse dispersion coefficients of solute movement by modifying the double-ring infiltrometer into a triple-ring infiltrometer. Water flow in the apparatus is controlled in one dimension and solute movement in three dimensions. The solute transport parameters can be measured simultaneously with the hydraulic conductivity. Analytical solutions are derived to describe the solute movement, and field experiment was carried out to calculate the solute parameters in homogeneous soil using a simple method developed based on the analytical solutions. Simulating results using these estimated parameters predict the observed breakthrough curves reasonably well.

White clover ( Trifolium repens ) is an important pasture legume but is often difficult to sustain in a mixed sward because, among other things, of the damage to roots caused by the soil-dwelling larval stages of S. lepidus . Locating the root nodules on the white clover roots is crucial for the survival of the newly hatched larvae. This paper presents a numerical model to simulate the movement of newly hatched S. lepidus larvae towards the root nodules, guided by a chemical signal released by the nodules. The model is based on the diffusion–chemotaxis equation. Experimental observations showed that the average speed of the larvae remained approximately constant, so the diffusion–chemotaxis model was modified so that the larvae respond only to the gradient direction of the chemical signal but not its magnitude. An individual-based lattice Boltzmann method was used to simulate the movement of individual larvae, and the parameters required for the model were estimated from the measurement of larval movement towards nodules in soil scanned using X-ray microtomography. The model was used to investigate the effects of nodule density, the rate of release of chemical signal, the sensitivity of the larvae to the signal, and the random foraging of the larvae on the movement and subsequent survival of the larvae. The simulations showed that the most significant factors for larval survival were nodule density and the sensitivity of the larvae to the signal. The dependence of larval survival rate on nodule density was well fitted by the Michealis–Menten kinetics.

The clover root weevil, Sitona lepidus, frequently feeds on N2 fixing rhizobial root nodules of white clover (Trifolium repens), which may contain isoflavonoids with defensive and plant regulatory properties. This study investigated the isoflavonoids present in N2 fixing (active) root nodules, root nodules that were not fixing N2 (inactive), and roots without nodules, and tested the behavioral responses of neonatal S. lepidus larvae to aglycones of the identified compounds. Formononetin concentrations were higher in the active nodules compared with inactive nodules and roots alone. Moreover, there was a statistically significant attraction to formononetin by S. lepidus in arena experiments, whereas the other isoflavonoids were unattractive. It is suggested that S. lepidus may have become tolerant to the toxic effects of formononetin with repeated exposure, and that it may play a role in root nodule location. Such coevolutionary relationships are widely reported for aboveground insects and plants, but the present study suggests they may also occur belowground.

A pore-scale modelling of soil hydraulic conductivity using the lattice Boltzmann equation method and thin-section technique is presented in this paper. Two-dimensional thin sections taken from soil samples were used to measure soil pore geometry, and three-dimensional soil structures were then reconstructed based on the thin-section measurements and an assumption that the soil structure can be fully characterised by its porosity and variogram. The hydraulic conductivity of the reconstructed three-dimensional soil structures was calculated from a lattice Boltzmann simulation of water flow in the structures, in which the water-solid interface was treated as a non-slip boundary (zero-velocity boundary) and solved by the bounce-back method. To improve the accuracy of the bounce-back method, the particle distribution functions were located at the centre of the cube that was fully occupied either by water or by solid. The simulated hydraulic conductivity was compared with measured hydraulic conductivity and the results showed good agreement. We also analysed the probability distribution of the simulated water velocity and the results indicated that the transverse velocity components had a non-Gaussian symmetric distribution, while the longitudinal velocity component had a skewed-forward distribution. Both distributions had a marked peak for velocity close to zero, indicating a significant portion of stagnant water.

This study investigated the ability of neonatal larvae of the root-feeding weevil, Sitona lepidus Gyllenhal, to locate white clover Trifolium repens L. (Fabaceae) roots growing in soil and to distinguish them from the roots of other species of clover and a co-occurring grass species. Choice experiments used a combination of invasive techniques and the novel technique of high resolution X-ray microtomography to non-invasively track larval movement in the soil towards plant roots. Burrowing distances towards roots of different plant species were also examined. Newly hatched S. lepidus recognized T. repens roots and moved preferentially towards them when given a choice of roots of subterranean clover, Trifolium subterraneum L. (Fabaceae), strawberry clover Trifolium fragiferum L. (Fabaceae), or perennial ryegrass Lolium perenneL. (Poaceae). Larvae recognized T. repens roots, whether released in groups of five or singly, when released 25 mm (meso-scale recognition) or 60 mm (macro-scale recognition) away from plant roots. There was no statistically significant difference in movement rates of larvae.

This paper presents an exact integration to evaluate the stress in the boundary element analysis of two-dimensional elastostatics. The boundary is discretized by straight segment and the exact integration is derived for those that the physical variables on the boundary are approximated by constant, discontinuous linear and discontinuous quadratic elements, respectively. The accuracy of the exact integration is verified against two examples and the results show that the exact integration can accurately calculate the stress on the boundary by simply treating boundary points as special interior points.

High-order boundary elements are efficient for solving problems with high stress gradient and are necessary for adaptive boundary element analysis. This paper derives the exact integrations of the integrals of the discontinuous cubic and quartic boundary element analysis of two-dimensional elstostatics problems. The derived exact integrations enable the non-singular and singular integrals to be evaluated in the same way, making special treatment of the singular integrals unnecessary. This greatly simplifies the computer code and improves solution efficiency as a result. The advantages of the exact integrations are verified against two examples.

Agrochemical transport in soils is complicated and involves physical, chemical and biochemical reactions; its mathematical modelling remains a challenging task. This paper presents a lattice Boltzmann model to simulate the agrochemical movement. The lattice Boltzmann model is a microscopic and process-based model, simulating the transport process by tracking chemical particles. The model presented in this paper is for one-dimensional vertical leaching and assumes that the chemical particles at the microscopic level move in five directions: one stagnant, two in vertical direction and two in an internal horizontal direction bounded by two reactive walls. Reactions at the walls are assumed to take place at two different rates, one in fast rate where the chemicals in the solution and on the wall are in an instant equilibrium, and the other in slow rate where the mass exchange rate between the chemicals in the solution and on the wall is a first-order kinetic. The reactions on both walls are assumed to occur instantly when the chemical particles moving in the internal direction hit the walls. To test the model, we measured the leaching of atrazine through soil columns in the laboratory. The results simulated with the lattice Boltzmann model are compared with the measured breakthrough curves and the non-equilibrium two-site convection-dispersion model; they all show close agreement. The transport parameters needed in the models are obtained from the measurement of adsorption isotherm of atrazine, bromide leaching in the same soil columns and calibration.

This paper derives the exact integrations for the integrals in the boundary element analysis of two-dimensional elastostatics. For facilitation, the derivation is based on the simple forms of the fundamental functions by taking constant, discontinuous linear and discontinuous quadratic elements as examples. The efficiency and accuracy of the derived exact integrations are verified against five benchmark problems; the results indicate that the derived exact integrations significantly reduces the CPU time for forming the matrices of the boundary element analysis and solving the internal displacements.

Let F be a general dynamical system defined on a complete locally compact metric space X . We give a slightly improved version of the Lyapunov characterization of asymptotic stability in one of our previous works and provide a short self-contained proof for the existence of arbitrarily small positively invariant neighborhoods of compact asymptotically stable sets in the present context. Based on these results, we prove that the uniform attractors of F are connected and are stable with respect to perturbations under appropriate conditions. We are also interested in the dynamical properties of differential inclusion: x′(t)∈f(x(t)) on R m . First, we show that if no solutions of the system blow up in finite future time, then its reachable mapping F is a general dynamical system. Then we discuss some asymptotic stability properties of the system. In particular, we prove that if there exists a nonempty compact connected subset M of R m such that M attracts a neighborhood of itself, then the system has a connected uniform attractor A . We also prove that A is stable with respect to both internal and external perturbations. More precisely, we prove that when λ>0 is sufficiently small, the perturbed system: x′(t)∈ con f(x(t)+λ B 1 )+λ B 1 has a connected uniform attractor A λ ; moreover, δ H ( A λ , A )→0 as λ→0 , where δ H (· ,·) is the Hausdorff distance in R m .

This paper presents a new method to couple the finite element method (FEM) and the discontinuous boundary element method (BEM) for fluid–structure interaction and 2D elastostatics. The converting matrix for coupling the FEM and the discontinuous BEM is obtained in an explicit form; and the relationship between the physical variables at the FEM nodes and those at the BEM collocation points is established. The proposed method overcomes the numerical difficulties caused by the discontinuous traction and corner nodes, and was applied to a fluid–structure interaction problem in time domain, a 2D elastostatics problem and the patch test given in Lu et al. [Comput. Meth. Appl. Mech. 85 (1991) 21]. The results indicate that the proposed method is accurate and efficient.

A mirror-image method is proposed in this paper to solve the boundary conditions in the lattice Boltzmann model proposed by Zhang et al. [Adv. Water Resour. 25 (2002) 1] for the advection and anisotropic dispersion of solute transport in porous media. Three types of boundary are considered: prescribed concentration boundary, prescribed flux boundary and prescribed concentration-gradient boundary. The accuracy of the proposed method is verified against benchmark problems and finite difference method.

The non-linear solvers in numerical solutions of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties and in this paper we address the gravity term and the prescribed-flux boundary in the Picard iteration. The problem of the gravity term in the Picard iteration is iteration-to-iteration oscillation as the gravity term is treated, by analogy with the time-step advance technique, ‘explicitly’ in the iteration. The proposed method for the gravity term is an improvement of the ‘implicit’ approach of Zhang and Ewen [Water Resour. Res. 36 (2000) 2777] by extending it to heterogeneous soil and approximating the inter-nodal hydraulic conductivity in the diffusive term and the gravity term with the same scheme. The prescribed-flux boundary in traditional methods also gives rise to iteration-to-iteration oscillation because there is no feedback to the flux in the solution at the new iteration. To reduce such oscillation, a new method is proposed to provide such a feedback to the flux. Comparison with traditional Picard and Newton iteration methods for a wide range of problems show that a combination of these two proposed methods greatly improves the stability and consequently the computational efficiency, making the use of small time step and/or under-relaxation solely for convergence unnecessary.