An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Moduli of flat conformal structures of hyperbolic type

"Vegeu el resum a l'inici del document del fitxer adjunt."

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

Integrin-Specific Mechanoresponses to Compression and Extension Probed by Cylindrical Flat-Ended AFM Tips in Lung Cells

Cells from lung and other tissues are subjected to forces of opposing directions that are largely transmitted through integrin-mediated adhesions. How cells respond to force bidirectionality remains ill defined. To address this question, we nanofabricated flat-ended cylindrical Atomic Force Microscopy (AFM) tips with ~1 µm2 cross-section area. Tips were uncoated or coated with either integrin-specific (RGD) or non-specific (RGE/BSA) molecules, brought into contact with lung epithelial cells or fibroblasts for 30 s to form focal adhesion precursors, and used to probe cell resistance to deformation in compression and extension. We found that cell resistance to compression was globally higher than to extension regardless of the tip coating. In contrast, both tip-cell adhesion strength and resistance to compression and extension were the highest when probed at integrin-specific adhesions. These integrin-specific mechanoresponses required an intact actin cytoskeleton, and were dependent on tyrosine phosphatases and Ca2+ signaling. Cell asymmetric mechanoresponse to compression and extension remained after 5 minutes of tip-cell adhesion, revealing that asymmetric resistance to force directionality is an intrinsic property of lung cells, as in most soft tissues. Our findings provide new insights on how lung cells probe the mechanochemical properties of the microenvironment, an important process for migration, repair and tissue homeostasis.