1,721,059 research outputs found
Growth model for arbuscular mycorrhizal fungi
No full textIn order to quantify the contribution of arbuscular mycorrhizal (AM) fungi to plant phosphorus nutrition, the development and extent of the external fungal mycelium and its nutrient uptake capacity are of particular importance. We develop and analyse a model of the growth of AM fungi associated with plant roots, suitable for describing mechanistically the effects of the fungi on solute uptake by plants. The model describes the development and distribution of the fungal mycelium in soil in terms of the creation and death of hyphae, tip–tip and tip–hypha anastomosis, and the nature of the root–fungus interface. It is calibrated and corroborated using published experimental data for hyphal length densities at different distances away from root surfaces. A good agreement between measured and simulated values was found for three fungal species with different morphologies: Scutellospora calospora (Nicol. & Gerd.) Walker & Sanders; Glomus sp.; and Acaulospora laevis Gerdemann & Trappe associated with Trifolium subterraneum L. The model and findings are expected to contribute to the quantification of the role of AM fungi in plant mineral nutrition and the interpretation of different foraging strategies among fungal specie
The solution of convection–diffusion equations for solute transport to plant roots
No full textTo help develop models of solute uptake that are computationally efficient and suitable for up-scaling to whole root systems, we provide three alternative analytical solutions of equations for transport to absorbing roots by convection and diffusion, and we compare their performance with a numerical solution over the range of plant and soil conditions found in practice. We point out an important pitfall in commonly used methods to solve convection–diffusion equations numerically and show how it can be avoided. We identify a simple analytical solution that is valid for all realistic combinations of parameter values, and show that for most purposes it performs as well as a complete, but more complex, analytical solution allowing fully for both convection and diffusion. We conclude that this solution is suitable for use in general solute uptake models
Homogenization of two fluid flow in porous media
No full textThe macroscopic behavior of air and water in porous media is often approximated using Richards’ equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e., constant gas pressure, this model is shown to reduce to the simpler form of Richards’ equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media to the underlying geometrical and material properties
A dynamic model of annual foliage growth and carbon uptake in trees
No full textThe growth of trees and other plants occurs through the interactive combination of photosynthesis and carbon (and other nutrient) assimilation. Photosynthesis enables the production of carbohydrate that can then be used in growing foliage, whereby photosynthesis is enabled. We construct a mathematical model of carbon uptake and storage, which allows the prediction of the growth dynamics of trees. We find that the simplest model allows uncontrolled foliage production through the positive feedback outlined above, but that leaf shading provides an automatic saturation to carbon assimilation, and hence to foliage production. The model explains the necessity for finite leaf area production at outbreak, and it explains why foliage density reaches a constant value during a growing season, while also non-leaf tissue also continues to grow. It also explains why trees will die when their carbon stores are depleted below a certain threshold, because the cost of foliage growth and maintenance exceeds the dynamic supply of carbon by photosynthesis
A mathematical model for simultaneous spatio-temporal dynamics of calcium and inositol 1,4,5-trisphosphate in Madin–Darby canine kidney epithelial cells
Get PDFThe landmark paper by Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527–1530, 1999) presented experimental investigations to show that not only can calcium upregulate IP3, but that it can also have an inhibitory effect on IP3. In this paper, we present a preliminary model, which is consistent with these experiments. This model includes positive and negative feedback between calcium and IP3 and is able to reproduce more precisely the data presented in Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527–1530, 1999). In the second part of the paper, the intracellular and intercellular calcium movement in Madin–Darby canine kidney epithelial cells is investigated. With the aid of the model we are able to identify the aspects of IP3 and calcium signalling, which should be studied further experimentally before refining the mode
Mathematical modelling of water and solute movement in ridge plant systems with dynamic ponding
No full textWe present a mathematical model that describes the movement of water and solutes in a ridge and furrow geometry. We focus on the effects of two physical processes: root water uptake and pond formation in the furrows. Special attention is paid to the physical description of ponding as an effect of transient rain events. We focus on phenomena taking place in the furrow cross section, not on the drainage along the furrow. The resulting model comprises of a coupled system of partial and ordinary differential equations that describe the mathematical interplay between solute transport, water movement and furrow pond depth. The system of equations is solved numerically using finite element techniques. We conducted numerical simulations to determine how mobile solutes with low buffer powers penetrate into the soil. We considered two cases; low rainfall, in which pond formation does not occur, and high rainfall, in which significant ponding is observed in the furrows. We found, in the presence of roots, that mobile solutes collected into a concentrated spot adjacent to the root system independent of rainfall intensity. In the absence of roots, however, we observed that water infiltration from ponding acted as the dominant transport mechanism for mobile solutes. This resulted in deep solute penetration into the soil when compared to non-ponded furrows
Image based modeling of nutrient movement in and around the rhizosphere
No full textIn this study, we developed a spatially explicit model for nutrient uptake by root hairs based on X-ray computed tomography images of the rhizosphere soil structure. This work extends our previous work to larger domains and hence is valid for longer times. Unlike the model used previously, which considered only a small region of soil about the root, we considered an effectively infinite volume of bulk soil about the rhizosphere. We asked the question: At what distance away from root surfaces do the specific structural features of root-hair and soil aggregate morphology not matter because average properties start dominating the nutrient transport? The resulting model was used to capture bulk and rhizosphere soil properties by considering representative volumes of soil far from the root and adjacent to the root, respectively. By increasing the size of the volumes that we considered, the diffusive impedance of the bulk soil and root uptake were seen to converge. We did this for two different values of water content. We found that the size of region for which the nutrient uptake properties converged to a fixed value was dependent on the water saturation. In the fully saturated case, the region of soil we needed to consider was only of radius 1.1mm for poorly soil-mobile species such as phosphate. However, in the case of a partially saturated medium (relative saturation 0.3), we found that a radius of 1.4mm was necessary. This suggests that, in addition to the geometrical properties of the rhizosphere, there is an additional effect of soil moisture properties, which extends further from the root and may relate to other chemical changes in the rhizosphere. The latter were not explicitly included in our model
Analytical equation for rapid estimation of pesticide leaching risk accounting for nonlinear sorption with bulk soil biodegradation
No full textMathematical models are used extensively to estimate soil pesticide leaching in regulatory risk assessments and are often solved numerically, which can obscure simple insights. We developed an analytical solution that highlights the role of the ratio of sorption to degradation in compound leaching, denoted as the sorption-extinction (Se) coefficient. We extend the classic analytical work of Jury to derive a steady-state solution for pesticide concentrations as a function of soil depth considering nonlinear sorption. We consider degradation in the soil water and solid phases and transport driven by advection, diffusion, and dispersion. Nonlinear sorption was handled using the mathematical technique of asymptotic expansions. We compared the steady-state analytic solution with extended duration simulations of the European regulatory numerical model PEARL for all FOCUS scenarios (i.e., nine European regions). The analytic solution was consistent with the long-term PEARL results across most FOCUS scenarios, and the results show that for a fixed Se coefficient, similar mean pesticide concentrations at the regulatory leaching depth (1 m) are obtained despite varying the sorption and degradation by an order of magnitude. This indicates that the Se coefficient is a dominant component of mean leaching behavior rather than degradation or sorption alone. However, as the absolute value of degradation and sorption decreases, variability of the pesticide concentration increases. While we demonstrate the approach using the FOCUS scenarios weather and soil data, this method can be applied as a rapid and time-efficient predictive tool for any region with either highly or more scarcely parameterized soil/weather data
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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