Steady internal flow and aerodynamic loads analysis of shuttle thermal protection system

An analytical model for calculation of ascent steady state tile loading was developed and validated with wind tunnel data. The analytical model is described and results are given. Results are given for loading due to shocks and skin friction. The analysis included calculation of internal flow (porous media flow and channel flow) to obtain pressures and integration of the pressures to obtain forces and moments on an insulation tile. A heat transfer program was modified by using analogies between heat transfer and fluid flow so that it could be used for internal flow calculation. The type of insulation tile considered was undensified reusable surface insulation (RSI) without gap fillers, and the location studied was the lower surface of the orbiter. Force and moment results are reported for parameter variations on surface pressure distribution, gap sizes, insulation permeability, and tile thickness

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Simple mixing criteria for the growth of negatively buoyant phytoplankton

Phytoplankton population dynamics are controlled by the relative rather than absolute timescales of mixing, growth, and loss processes such as sedimentation, grazing, and so on. Here, the vertical distribution and biomass of phytoplankton populations are quantified by two timescale ratios: the Peclet number Pe the ratio of mixing and sedimentation timescales-and the growth number G the ratio of sedimentation and net growth timescales. Three mixing regimes are defined for phytoplankton and other particles. For Pe greater than or equal to 100, the population is translated linearly down the water column over time and will leave the surface mixing layer completely after sedimentation time 7, For 0.

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

Tissue inhibitor of metalloproteinase-1 (TIMP-1) regulates mesenchymal stem cells through let-7f microRNA and Wnt/β-catenin signaling

Tissue inhibitor of metalloproteinases 1 (TIMP-1) is a matrix metalloproteinase (MMP)-independent regulator of growth and apoptosis in various cell types. The receptors and signaling pathways that are involved in the growth factor activities of TIMP-1, however, remain controversial. RNA interference of TIMP-1 has revealed that endogenous TIMP-1 suppresses the proliferation, metabolic activity, and osteogenic differentiation capacity of human mesenchymal stem cells (hMSCs). The knockdown of TIMP-1 in hMSCs activated the Wnt/β-catenin signaling pathway as indicated by the increased stability and nuclear localization of β-catenin in TIMP-1–deficient hMSCs. Moreover, TIMP-1 knockdown cells exhibited enhanced β-catenin transcriptional activity, determined by Wnt/β-catenin target gene expression analysis and a luciferase-based β-catenin– activated reporter assay. An analysis of a mutant form of TIMP-1 that cannot inhibit MMP indicated that the effect of TIMP-1 on β-catenin signaling is MMP independent. Furthermore, the binding of CD63 to TIMP-1 on the surface of hMSCs is essential for the TIMP-1–mediated effects on Wnt/β-catenin signaling. An array analysis of microRNAs (miRNAs) and transfection studies with specific miRNA inhibitors and mimics showed that let-7f miRNA is crucial for the regulation of β-catenin activity and osteogenic differentiation by TIMP-1. Let-7f was up-regulated in TIMP-1–depleted hMSCs and demonstrably reduced axin 2, an antagonist of β-catenin stability. Our results demonstrate that TIMP-1 is a direct regulator of hMSC functions and reveal a regulatory network in which let-7f modulates Wnt/β-catenin activity