Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

New insights on low vitamin D plasma concentration as a potential cardiovascular risk factor

The role of Vitamin D hormone in human health and disease is still debated. Recently, growing attention has been paid to its putative role in cardiovascular system homeostasis with several studies that suggested a correlation between low vitamin D levels and increased cardiovascular risk. Several mechanisms are involved in the development of cardiovascular diseases: systemic inflammation, endothelial dysfunction, arterial hypertension and insulin resistance. In the present paper, we have revised the current literature supporting a role for vitamin D in the development of these pathogenetic processes. Finally, we have evaluated the current evidence linking vitamin D to atherosclerosis and its natural consequence, cardiovascular diseases