Asymptotic theory of two-dimensional trailing-edge flows

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient

Entropy and biological systems: experimentally-investigated entropy-driven stacking of plant photosynthetic membranes

According to the Second Law of thermodynamics, an overall increase of entropy contributes to the driving force for any physicochemical process, but entropy has seldom been investigated in biological systems. Here, for the first time, we apply Isothermal Titration Calorimetry (ITC) to investigate the Mg21-induced spontaneous stacking of photosynthetic membranes isolated from spinach leaves. After subtracting a large endothermic interaction of MgCl2 with membranes, unrelated to stacking, we demonstrate that the enthalpy change (heat change at constant pressure) is zero or marginally positive or negative. This first direct experimental evidence strongly suggests that an entropy increase significantly drives membrane stacking in this ordered biological structure. Possible mechanisms for the entropy increase include: (i) the attraction between discrete oppositely-charged areas, releasing counterions; (ii) the release of loosely-bound water molecules from the inter-membrane gap; (iii) the increased orientational freedom of previously-aligned water dipoles; and (iv) the lateral rearrangement of membrane components.This work was supported consecutively by Australian Research Council grants (DP0664719 and DP 1093927)

Viscid-inviscid interaction associated with incompressible flow past wedges at high Reynolds number

An analytical method is suggested for the study of the viscid inviscid interaction associated with incompressible flow past wedges with arbitrary angles. It is shown that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem, and the pressure can only be established from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as the boundary layer buildup, turbulent jet mixing, and recompression are individually analyzed and attached to the inviscid flow in the sense of the boundary layer concept. The interaction between the viscous and inviscid streams is properly displayed by the fact that the aforementioned discrete parameters needed for the inviscid flow are determined by the viscous flow condition at the point of reattachment. It is found that the reattachment point behaves as a saddle point singularity for the system of equations describing the recompressive viscous flow processes, and this behavior is exploited for the establishment of the overall flow field. Detailed results such as the base pressure, pressure distributions on the wedge, and the geometry of the wake are determined as functions of the wedge angle

Large NcN_c Universality of The Baryon Isgur--Wise Form Factor: The Group Theoretical Approach

In a previous article, it has been proved under the framework of chiral soliton model that the same Isgur--Wise form factor describes the semileptonic $\Lambda_b\to\Lambda_c$ and $\Sigma^{(*)}_b\to\Sigma^{(*)}_c$ decays in the large $N_c$ limit. It is shown here that this result is in fact independent of the chiral soliton model and is solely the consequence of the spin-flavor SU(4) symmetry which arises in the baryon sector in the large $N_c$ limit.Comment: 10 pages in REVTeX, no figure

Viscous wing theory development. Volume 1: Analysis, method and results

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers

New negative differential resistance device based on resonant interband tunneling

We propose and demonstrate a novel negative differential resistance device based on resonant interband tunneling. Electrons in the InAs/AlSb/GaSb/AlSb/InAs structure tunnel from the InAs conduction band into a quantized state in the GaSb valence band, giving rise to a peak in the current-voltage characteristic. This heterostructure design virtually eliminates many of the competing transport mechanisms which limit the performance of conventional double-barrier structures. Peak-to-valley current ratios as high as 20 and 88 are observed at room temperature and liquid-nitrogen temperature, respectively. These are the highest values reported for any tunnel structure

An improved viscid/inviscid interaction procedure for transonic flow over airfoils

A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag

Cooperative hunting in a discrete predator-prey system

We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator's maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation

Observation of large peak-to-valley current ratios and large peak current densities in AlSb/InAs/AlSb double-barrier tunnel structures

We report improved peak-to-valley current ratios and peak current densities in InAs/AlSb double-barrier, negative differential resistance tunnel structures. Our peak-to-valley current ratios are 2.9 at room temperature and 10 at liquid-nitrogen temperatures. Furthermore, we have observed peak current densities of 1.7×10^5 A/cm^2. These figures of merit are substantially better than previously reported values. The improvements are obtained by adding spacer layers near the barriers, thinner well regions, and thinner barriers