Linear and nonlinear thermal instability of Newtonian and non-Newtonian fluid saturated porous media

The present work aims to investigate the influence of different aspects, such as non-standard steady solutions, complex fluid rheologies and non-standard porous-channel geometries, on the stability of a Darcy-Bénard system. In order to do so, both linear and nonlinear stability theories are considered. A linear analysis focuses on studying the dynamics of the single disturbance wave present in the system, while its nonlinear counterpart takes into consideration the interactions among the single modes. The scope of the stability analysis is to obtain information regarding the transition from an equilibrium solution to another one, and also information regarding the transition nature and the emergent solution after the transition. The disturbance governing equations are solved analytically, whenever possible, and numerical by considering different approaches. Among other important results, it is found that a cylinder cross-section does not affect the thermal instability threshold, but just the linear pattern selection for dilatant and pseudoplastic fluid saturated porous media. A new rheological model is proposed as a solution for singular issues involving the power-law model. Also, a generalised class of one parameter basic solutions is proposed as an alternative description of the isoflux Darcy--Bénard problem. Its stability is investigated.

Harnessing the power of Drosophila model to obtain new insights on MYC and ABCC1 cellular functions: from neuroblastoma to autism spectrum disorder

MYCN amplification is a genetic hallmark of the childhood tumour neuroblastoma. MYCN-MAX dimers activate the expression of genes promoting cell proliferation. Moreover, MYCN seems to transcriptionally repress cell differentiation even in absence of MAX. We adopted the Drosophila eye as model to investigate the effect of high MYC to MAX expression ratio on cells. We found that dMyc overexpression in eye cell precursors inhibits cell differentiation and induces the ectopic expression of Antennapedia (the wing Hox gene). The further increase of MYC/MAX ratio results in an eye-to-wing homeotic transformation. Notably, dMyc overexpression phenotype is suppressed by low levels of transcriptional co-repressors and MYCN associates to the promoter of Deformed (the eye Hox gene) in proximity to repressive sites. Hence, we envisage that, in presence of high MYC/MAX ratio, the “free MYC” might inhibit Deformed expression, leading in turn to the ectopic expression of Antennapedia. This suggests that MYCN might reinforce its oncogenic role by affecting the physiological homeotic program. Furthermore, poor neuroblastoma outcome associates with a high level of the MRP1 protein, encoded by the ABCC1 gene and known to promote drug efflux in cancer cells. Intriguingly, this correlation persists regardless of chemotherapy and ABCC1 overexpression enhances neuroblastoma cell motility. We found that Drosophila dMRP contributes to the adhesion between the dorsal and ventral epithelia of the wing by inhibiting the function of integrin receptors, well known regulators of cell adhesion and migration. Besides, integrins play a crucial role during synaptogenesis and ABCC1 locus is included in a copy number variable region of the human genome (16p13.11) involved in neuropsychiatric diseases. Interestingly, we found that the altered dMRP/MRP1 level affects nervous system development in Drosophila embryos. These preliminary findings point out novel ABCC1 functions possibly defining ABCC1 contribution to neuroblastoma and to the pathogenicity of 16p13.11 deletion/duplication