Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied Mathematics and Computatio

Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media

Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the spatially-varying fine-scale diffusivity with an effective diffusivity calculated from the solution of an appropriate boundary value problem. In this paper, we present a new semi-analytical method for solving this boundary value problem and computing the effective diffusivity for pixellated, locally-isotropic, heterogeneous media. We compare our new solution method to a standard finite volume method and show that equivalent accuracy can be achieved in less computational time for several standard test cases. We also demonstrate how the new solution method can be applied to complex heterogeneous geometries represented by a grid of blocks. These results indicate that our new semi-analytical method has the potential to significantly speed up simulations of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table

Smarter Programming of the Female Condom: Increasing Its Impact on HIV Prevention in the Developing World

The purpose of this study was to investigate the relative value of the female condom for HIV prevention within heterosexual relationships in the developing world. In the last ten years, the world has witnessed both historic financial commitments to HIV/AIDS and new prevention options, including biomedical prevention research, male circumcision, and a dramatic scale-up of voluntary counseling and testing. At the same time, where HIV remains at epidemic levels in many countries, there has been a growing commitment to treatment access alongside prevention programs. However, portions of populations, particularly youth and women, remain highly vulnerable to HIV infection. Accordingly, the global health community can benefit from a better understanding of how existing prevention options should be effectively and efficiently delivered to reduce HIV in the developing world. This report provides guidance for the global health community for considering how the female condom fits within the set of prevention interventions currently available

The Arabidopsis JAGGED gene encodes a zinc finger protein that promotes leaf tissue development

Important goals in understanding leaf development are to identify genes involved in pattern specification, and also genes that translate this information into cell types and tissue structure. Loss-of-function mutations at the JAGGED (JAG) locus result in Arabidopsis plants with abnormally shaped lateral organs including serrated leaves, narrow floral organs, and petals that contain fewer but more elongate cells. jag mutations also suppress bract formation in leafy, apetala1 and apetala2 mutant backgrounds. The JAG gene was identified by map-based cloning to be a member of the zinc finger family of plant transcription factors and encodes a protein similar in structure to SUPERMAN with a single C2H2-type zinc finger, a proline-rich motif and a short leucine-rich repressor motif. JAG mRNA is localized to lateral organ primordia throughout the plant but is not found in the shoot apical meristem. Misexpression of JAG results in leaf fusion and the development of ectopic leaf-like outgrowth from both vegetative and floral tissues. Thus, JAG is necessary for proper lateral organ shape and is sufficient to induce the proliferation of lateral organ tissue