Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid

Differential function and maturation of human stem cell-derived islets after transplantation

Insulin-producing stem cell-derived islets (SC-islets) provide a virtually unlimited cell source for diabetes cell replacement therapy. While SC-islets are less functional when first differentiated in vitro compared to isolated cadaveric islets, transplantation into mice has been shown to increase their maturation. To understand the effects of transplantation on maturation and function of SC-islets, we examined the effects of cell dose, transplantation strategy, and diabetic state in immunocompromised mice. Transplantation of 2 and 5, but not 0.75 million SC-islet cells underneath the kidney capsule successfully reversed diabetes in mice with pre-existing diabetes. SQ and intramuscular injections failed to reverse diabetes at all doses and had undetectable expression of maturation markers, such as MAFA and FAM159B. Furthermore, SC-islets had similar function and maturation marker expression regardless of diabetic state. Our results illustrate that transplantation parameters are linked to SC-islet function and maturation, providing ideal mouse models for preclinical diabetes SC therapy research

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.Comment: 10 pages, 7 figures, submitted to Phy. Rew.

Towards a sensitive search for variation of the fine structure constant using radio-frequency E1 transitions in atomic dysprosium

It has been proposed that the radio-frequency electric-dipole (E1) transition between two nearly degenerate opposite-parity states in atomic dysprosium should be highly sensitive to possible temporal variation of the fine structure constant ($\alpha$) [V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. A {\bf 59}, 230 (1999)]. We analyze here an experimental realization of the proposed search in progress in our laboratory, which involves monitoring the E1 transition frequency over a period of time using direct frequency counting techniques. We estimate that a statistical sensitivity of |\adota| \sim 10^{-18}/yr may be achieved and discuss possible systematic effects that may limit such a measurement.Comment: 8 pages, 7 figure

The compensation of Gaussian curvature in developable cones is local

In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a new way to confirm the curvature cancellation phenomenon.Comment: 12 pages; 5 figure

Dynamics of filaments and membranes in a viscous fluid

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.Comment: 26 pages, 12 figures, to be published in Reviews of Modern Physic

Investigation into the cause of spontaneous emulsification of a free steel droplet : validation of the chemical exchange pathway

Small Fe-based droplets have been heated to a molten phase suspended within a slag medium to replicate a partial environment within the basic oxygen furnace (BOF). The confocal scanning laser microscope (CSLM) has been used as a heating platform to interrogate the effect of impurities and their transfer across the metal/slag interface, on the emulsification of the droplet into the slag medium. The samples were then examined through X-ray computer tomography (XCT) giving the mapping of emulsion dispersion in 3D space, calculating the changing of interfacial area between the two materials, and changes of material volume due to material transfer between metal and slag. Null experiments to rule out thermal gradients being the cause of emulsification have been conducted as well as replication of the previously reported study by Assis et al.[1] which has given insights into the mechanism of emulsification. Finally chemical analysis was conducted to discover the transfer of oxygen to be the cause of emulsification, leading to a new study of a system with undergoing oxygen equilibration