Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to get upscaled model equations, but also to prepare a proper framework for getting a convergence rate (corrector estimates) of the averaging procedure. Keywords: Corrector estimates, periodic unfolding, homogenization, sulfate corrosion of concrete, reaction-diffusion systems

From individual-based mechanical models of multicellular systems to free-boundary problems

In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered whereby: (i) every cell is identified by the position of its centre; (ii) mechanical interactions between cells are described via generic nonlinear force laws; and (iii) cell proliferation is contact inhibited. We formally show that the continuum counterpart of this discrete model is given by a free-boundary problem for the cell densities. The results of the derivation demonstrate how the parameters of continuum mechanical models of multicellular systems can be related to biophysical cell properties. We prove an existence result for the free-boundary problem and construct travelling-wave solutions. Numerical simulations are performed in the case where the cellular interaction forces are described by the celebrated Johnson-Kendalli-Roberts model of elastic contact, which has been previously used to model cell-cell interactions. The results obtained indicate excellent agreement between the simulation results for the individual-based model, the numerical solutions of the corresponding free-boundary problem and the travelling-wave analysis

Enhancing phosphorus and zinc acquisition efficiency in rice: a critical review of root traits and their potential utility in rice breeding

Background: Rice is the world's most important cereal crop and phosphorus (P) and zinc (Zn) deficiency are major constraints to its production. Where fertilizer is applied to overcome these nutritional constraints it comes at substantial cost to farmers and the efficiency of fertilizer use is low. Breeding crops that are efficient at acquiring P and Zn from native soil reserves or fertilizer sources has been advocated as a cost-effective solution, but would benefit from knowledge of genes and mechanisms that confer enhanced uptake of these nutrients by roots. Scope: This review discusses root traits that have been linked to P and Zn uptake in rice, including traits that increase mobilization of P/Zn from soils, increase the volume of soil explored by roots or root surface area to recapture solubilized nutrients, enhance the rate of P/Zn uptake across the root membrane, and whole-plant traits that affect root growth and nutrient capture. In particular, this review focuses on the potential for these traits to be exploited through breeding programmes to produce nutrient-efficient crop cultivars. Conclusions: Few root traits have so far been used successfully in plant breeding for enhanced P and Zn uptake in rice or any other crop. Insufficient genotypic variation for traits or the failure to enhance nutrient uptake under realistic field conditions are likely reasons for the limited success. More emphasis is needed on field studies in mapping populations or association panels to identify those traits and underlying genes that are able to enhance nutrient acquisition beyond the level already present in most cultivars.T. J. Rose, S. M. Impa, M. T. Rose, J. Pariasca-Tanaka, A. Mori, S. Heuer, S. E. Johnson-Beebout and M. Wissuw

A dynamic model of nutrient uptake by root hairs

Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.<br/