Thin films flowing down inverted substrates: Three dimensional flow

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three dimensional setting. In the previous work (Phys. Fluids, {\bf 22}, 052105 (2010)), we considered two dimensional flow, finding formation of surface waves whose properties within the implemented long wave model depend on a single parameter, $D=(3Ca)^{1/3}\cot\alpha$, where $Ca$ is the capillary number and $\alpha$ is the inclination angle. In the present work we consider fully 3D setting and discuss the influence of the additional dimension on stability properties of the flow. In particular, we concentrate on the coupling between the surface instability and the transverse (fingering) instabilities of the film front. We furthermore consider these instabilities in the setting where fluid viscosity varies in the transverse direction. It is found that the flow pattern strongly depends on the inclination angle and the viscosity gradient

Arithmetic Properties of Overpartition Pairs

Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of $\bar{pp}(n)$, the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number $\bar{pp}(n)$. In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for $\bar{pp}(n)$. Moreover, we find three ranks as combinatorial interpretations of the fact that $\bar{pp}(n)$ is divisible by three for any n. We also construct infinite families of congruences for $\bar{pp}(n)$ modulo 3, 5, and 9.Comment: 19 page

Adhesive and mechanical regulation of mesenchymal stem cell differentiation in human bone marrow and periosteum-derived progenitor cells

It has previously been demonstrated that cell shape can influence commitment of human bone marrow-derived mesenchymal stem cells (hBMCs) to adipogenic, osteogenic, chondrogenic, and other lineages. Human periosteum-derived cells (hPDCs) exhibit multipotency similar to hBMCs, but hPDCs may offer enhanced potential for osteogenesis and chondrogenesis given their apparent endogenous role in bone and cartilage repair in vivo. Here, we examined whether hPDC differentiation is regulated by adhesive and mechanical cues comparable to that reported for hBMC differentiation. When cultured in the appropriate induction media, hPDCs at high cell seeding density demonstrated enhanced levels of adipogenic or chondrogenic markers as compared with hPDCs at low cell seeding density. Cell seeding density correlated inversely with projected area of cell spreading, and directly limiting cell spreading with micropatterned substrates promoted adipogenesis or chondrogenesis while substrates promoting cell spreading supported osteogenesis. Interestingly, cell seeding density influenced differentiation through both changes in cell shape and non-shape-mediated effects: density-dependent adipogenesis and chondrogenesis were regulated primarily by cell shape whereas non-shape effects strongly influenced osteogenic potential. Inhibition of cytoskeletal contractility by adding the Rho kinase inhibitor Y27632 further enhanced adipogenic differentiation and discouraged osteogenic differentiation of hPDCs. Together, our results suggest that multipotent lineage decisions of hPDCs are impacted by cell adhesive and mechanical cues, though to different extents than hBMCs. Thus, future studies of hPDCs and other primary stem cell populations with clinical potential should consider varying biophysical metrics for more thorough optimization of stem cell differentiation.R01 EB000262 - NIBIB NIH HHS; R01 GM060692 - NIGMS NIH HHSPublished versio