Exact Averaging of Stochastic Equations for Flow in Porous Media

It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem

Orchestrating home

The private space of the home is an important site of health care in most industrialised countries, and rehabilitation following intensive in-hospital treatment largely takes place in domestic settings. Home in this context is implicitly understood by individuals affected by illness (people with illness, family members, friends, carers), health care providers, and policy makers as an a priori entity that naturally provides continuity and stability. This takes for granted that family carers will maintain both therapeutic activities and the sense of ‘being at home’ – and all of the accompanying emotional dimensions – within the home environment. Drawing on ethnographic research with relatively young spousal carers in Victoria, Australia, we explore how the reconstruction of home as a site for post-stroke recovery changed the experiences and meanings given to the idea of home. Home as a therapeutic place depended on constant orchestrating work that reconfigured the physical, symbolic, and practical elements of home. This was not a straightforward or singular process, as tensions arose in trying to integrate the new, post-stroke therapeutic landscape and pre-stroke conceptualisations and lived realities of home life

THE REGULATORY LANDSCAPE OF THE RET GENE IN HIRSCHSPRUNG DISEASE

Hirschsprung disease (HSCR), or congenital aganglionosis, is characterized by a contiguous lack of enteric neurons in variable segments of the gut. Both coding and non-coding mutations in the receptor tyrosine kinase RET are the major genetic drivers of the disease, although all disease causing mutations in RET have not yet been identified. A prior Genome Wide Association Study (GWAS) using 220 HSCR trios identified 38 common single nucleotide polymorphisms (SNPs) that are significantly associated with the disease and are located in non-coding regions at the RET locus. Eight of these SNPs disrupt known RET transcription factor binding sites in the human neuroblastoma cell line, SK-N-SH, and are located within enhancer elements. Three of these eight SNPs show differential enhancer activity between the non-risk and disease associated (risk) alleles, or an allelic difference. I sought to determine how many of the remaining 30 SNPs displayed enhancer activity and allelic differences by using a dual in vitro luciferase reporter assay in SK-N-SH cells. My studies revealed that 28 SNPs had enhancer activity while seven of those displayed allelic differences. The SNPs that showed an allelic difference and affected enhancer activity potentially disrupt binding sites for PAX3, MZF1, ZNF263, and Myb/Mybl1. Therefore, the genetic risk of HSCR susceptibility at RET is conferred by allelic differences at at least 10 enhancer elements, demonstrating the high degree of intra-locus risk heterogeneity