Sap transport in trees has long fascinated scientists, and a vast literature exists on experimental and modelling studies of trees during the growing season when large negative stem pressures are generated by transpiration from leaves. Much less attention has been paid to winter months when trees are largely dormant but nonetheless continue to exhibit interesting flow behaviour. A prime example is sap exudation, which refers to the peculiar ability of sugar maple (Acer saccharum) and related species to generate positive stem pressure while in a leafless state. Experiments demonstrate that ambient temperatures must oscillate about the freezing point before significantly heightened stem pressures are observed, but the precise causes of exudation remain unresolved. The prevailing hypothesis attributes exudation to a physical process combining freeze-thaw and osmosis, which has some support from experimental studies but remains a subject of active debate. We address this knowledge gap by developing the first mathematical model for exudation, while also introducing several essential modifications to this hypothesis. We derive a multiscale model consisting of a nonlinear system of differential equations governing phase change and transport within wood cells, coupled to a suitably homogenized equation for temperature on the macroscale. Numerical simulations yield stem pressures that are consistent with experiments and provide convincing evidence that a purely physical mechanism is capable of capturing exudation.

Calcium is one of the most important intracellular messengers, which occurs in the cytosol and the endoplasmic reticulum of animal cells. While most calcium dynamics models either do not account properly for the fact that the endoplasmic reticulum constitutes a microstructure of the cell or are infeasible by resolving the fine structure very explicitly, Goel et al. [1] derived an effective macroscopic model by formal homogenization. In this paper, this approach is made rigorous using periodic homogenization techniques to upscale the nonlinear coupled system of reaction-diffusion equations and, moreover, the appropriate scaling of the interfacial exchange term is taken into consideration.

In the context of periodic homogenization based on the periodic unfolding method, we extend the existing convergence results for the boundary periodic unfolding operator to gradients defined on manifolds. These general results are then used to homogenize a system of five coupled reaction-diffusion equations, three of which are defined on a manifold. The system describes the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. The binding process to the surface of the endoplasmic reticulum is modeled in a nonlinear way taking into account the number of free receptors.

Based on the periodic unfolding method in periodic homogenization, we deduce a convergence result for gradients of functions defined on connected, smooth and periodic manifolds. Under the assumption of certain a-priori estimates of the gradient, which are typical for fast diffusion, the sum of a term involving a gradient with respect to the slow variable and one with respect to the fast variable is obtained in the homogenization limit. In addition, we show in a brief example how to apply this result and find for a reaction-diffusion equation defined on a periodic manifold that the homogenized equation contains a term describing macroscopic diffusion. RésuméA l'aide de la méthode d'éclatement périodique, nous démontrons un résultat de convergence des gradients de fonctions définies sur des variétés connexes, différentiables et périodiques. Sous certaines conditions d'estimation du gradient, typiques de la diffusion rapide, nous obtenonsà la limite d'homogénéisation la somme d'un gradient de la variable globale et d'un gradient de la variable locale. Un exemple illustre l'utilisation de ce résultat: pour uné equation de réaction et diffusion définie sur une variété périodique, nous démontrons que l'équation homogénéisée contient un terme décrivant une diffusion globale.

BackgroundAnnually, 10 million adults transition through prisons or jails in the United States (US) and the prevalence of HIV among entrants is three times higher than that for the country as a whole. We assessed the potential impact of increasing HIV Testing/Treatment/Retention (HIV-TTR) in the community and within the criminal justice system (CJS) facilities, coupled with sexual risk behavior change, focusing on black men-who-have-sex-with-men, 15–54 years, in Atlanta, USA.MethodsWe modeled the effect of a HIV-TTR strategy on the estimated cumulative number of new (acquired) infections and mortality, and on the HIV prevalence at the end of ten years. We additionally assessed the effect of increasing condom use in all settings.ResultsIn the Status Quo scenario, at the end of 10 years, the cumulative number of new infections in the community, jail and prison was, respectively, 9246, 77 and 154 cases; HIV prevalence was 10815, 69 and 152 cases, respectively; and the cumulative number of deaths was 2585, 18 and 34 cases, respectively. By increasing HIV-TTR coverage, the cumulative number of new infections could decrease by 15% in the community, 19% in jail, and 8% in prison; HIV prevalence could decrease by 8%, 9% and 7%, respectively; mortality could decrease by 20%, 39% and 18%, respectively. Based on the model results, we have shown that limited use and access to condoms have contributed to the HIV incidence and prevalence in all settings.ConclusionsAggressive implementation of a CJS-focused HIV-TTR strategy has the potential to interrupt HIV transmission and reduce mortality, with benefit to the community at large. To maximize the impact of these interventions, retention in treatment, including during the period after jail and prison release, and increased condom use was vital for decreasing the burden of the HIV epidemic in all settings.