Generic Transport Aft-body Drag Reduction using Active Flow Control

Active flow-separation control is an effective and efficient mean for drag reduction and unsteady load alleviation resulting from locally or massively separated flow. Such a situation occurs in configurations where the aerodynamic performance is of secondary importance to functionality. The performance of heavy transport helicopters and aeroplanes, having a large, and almost flat, aft loading ramp suffer from the poor aerodynamics of the aft body. Hence, a combined experimental and numerical investigation was undertaken on a generic transport aeroplane/helicopter configuration. The experimental study provided surface pressures, direct drag measurements, surface and smoke flow visualization. The baseline flow was numerically analyzed, using finite volume solutions of the RANS equations. The baseline flow around the model was insensitive to the Reynolds number in the range it was tested. The flow separating from the aft body was characterized by two main sources of drag and unsteadiness. The first is a separation bubble residing at the lower ramp corner and the second is a pair of vortex systems developing and separating from the sides of the ramp. As the model incidence is decreased, the pair of vortex systems also penetrates deeper towards the centerline of the ramp, decreasing the pressure and increasing the drag. As expected, the ramp lower corner bubble was highly receptive to periodic excitation introduced from four addressable piezo-fluidic actuators situated at the ramp lower corner. Total drag was reduced by 3–11%, depending on the model incidence. There are indications that the flow in the wake of the model is also significantly steadier when the bubble at the lower ramp corner is eliminated. The vortex system is tighter and steadier when the ramp-corner bubble is eliminated.     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

On centroid branches of trees from certain families

We obtain various results involving the centroid branches of randomly chosen trees from simply generated families.     

Thermal characterization of social vespid silk

In this paper we try to establish a link between the microclimate in the wasp nest and the structure and thermal stability of vespid silk. We suggest that there are at least two types of water that is absorbed by the silk of Oriental hornets, namely, surface water and intrinsic structural water. The release of both types of water was found to be reversible. The enthalpy values of the endothermic peaks associated with the release of water from different silk samples do not differ substantially and are in the range of 106 to 130 J g^-1 for the Vespa orientalis male larvae silk (sample #1), Paravespula germanica (yellowjacket) worker larvae silk (#3) and Vespa orientalis nest envelope(#4). For the Vespa orientalis worker larvae silk (sample #2), however, it is twice as large (228 J g^-1). This is in agreement with the increased total amount of absorbed water. The silk studied has a fibrilar structure with interconnecting surfaces overlying entire regions. It is assumed that the initial water loss stems from water evaporation from the coat of the fibers - a daily occurrence in the hornets' nest. Heating to above 70°C may result in structural changes in the silk core. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some asymptotic results useful in enumeration problems

Suppose one is given two related generating functionsa(x) = a _n x ⁿ andb(x) = b _n x ⁿ , often it is of interest to determine the limiting behaviour of the quantitiesa _n /b _n We survey some earlier results of this nature and give some new ones     

Antiparallel triple helices. Structural characteristics and stabilization by 8-amino derivatives

The structural, dynamical, and recognition properties of antiparallel DNA triplexes formed by the antiparallel d(G#G.C), d(A#A.T), and d(T#A.T) motifs (the pound sign and dot mean reverse-Hoogsteen and Watson-Crick hydrogen bonds, respectively) are studied by means of "state of the art" molecular dynamics simulations. Once the characteristics of the helix are defined, molecular dynamics and thermodynamic integration calculations are used to determine the expected stabilization of the antiparallel triplex caused by the introduction of 8-aminopurines. Finally, oligonucleotides containing 8-aminopurine derivatives are synthesized and tested experimentally using several approaches in a variety of systems. A very large stabilization of the triplex is found experimentally, as predicted by simulations. These results open the possibility for the use of oligonucleotides carrying 8-aminopurines to bind single-stranded nucleic acids by formation of antiparallel triplexes.