Euler solutions for self-generated rotor blade-vortex interactions

A finite-difference procedure has been developed for the prediction of three-dimensional rotor blade-vortex interactions. The interaction velocity field was obtained through a non-linear superposition of the rotor flow field, computed using the unsteady three-dimensional Euler equations, and the embedded vortex wake flow field, computed using the law of Biot-Savart. In the Euler model, near wake rotational effects were simulated using the surface velocity ‘transpiration’ approach. As a result, a modified surface boundary condition was prescribed and enforced at each time step of the computations to satisfy the tangency boundary condition. For supercritical interactions using an upstream-generated vortex, accuracy of the numerical results were found to rely on the user-specified vortex core radius and vortex strength. For the more general self-generated subcritical interactions, vortex wake trajectories were computed using the lifting-line helicopter/rotor trim code CAMRAD. For these interactions, accuracy of the results were found to rely heavily on the CAMRAD-predicted vortex strength, vortex orientation with respect to the blade, and to a large extent on the user-specified vortex core radius. Results for the one-seventh scale model OLS rotor and for a non-lifting rectangular blade having a NACA0012 section are presented. Comparisons with the experimental windtunnel data are also made.     

Symmetric marching technique for the Poisson equation. II. mixed boundary conditions

In paper I a symmetric marching technique for the discretized Poisson equation with Dirichlet boundary conditions was developed. In this paper, the symmetric marching technique is extended to cover mixed boundary value problems for Poisson equation. The results of some numerical experiments are also presented.     

Convergence problems in SCF calculations: Further applications of a new technique based on the use of inverse Fock operator

A recently proposed orbital optimization technique based on the use of the inverse of the level-shifted Fock operator is successfully applied to a large number of pathologically divergent cases. The possibility of eliminating convergence problems by adopting a similar modification in the operation of the orthogonal gradient method is also successfully tested.     

Single unit impact damper in free and forced vibration

The single unit impact damper under free and forced vibrations is studied. The effects of mass ratio, coefficient of restitution, and gap size on the free vibrations are determined by simulating motion on the digital computer. Agreement of theoretical results with the present and previous experimental results in the free vibration state is good. In the study of forced motion, charts are developed, by using the closed form solution, showing optimum gaps and corresponding displacement amplitude reduction within the resonant frequency range. The optimum gap at resonance is not necessarily optimal at other frequencies.     

Search for an immobile entity on a network

We consider the problem of searching for a single, uniformly distributed immobile entity on an undirected network. This problem differs from edge-covering problems, e.g., the Chinese Postman Problem (CPP), since the objective here is not to find the minimum length tour that covers all the edges at least once, but instead to minimize the expected time to find the entity. We introduce a heuristic algorithm to deal with the search process given that the entity is equally likely to be at any point on the network. Computational results are presented.     

Structural and stability studies of CdS and SnS nanostructures synthesized by various routes

CdS nanorods and SnS nano-flakes have been synthesized by solvothermal process and CdS nanoparticles have been synthesized by aqueous media process. Structural properties of these nanocomposites are performed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). Chemical purity of these nanocomposites has been confirmed by energy dispersive analysis of X-ray (EDAX). Thermal stability of these nanocomposites is investigated by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Different parameters such as activation energy (E) for the degradation, Arrhenius parameter (A) and the entropy change (ΔS) have been calculated by Coats-Redfern and Satava model. It is observed that the activation energy of the CdS nanorods is much higher compared to that of CdS nanoparticles and SnS nano-flakes.     

Wheel-shaped polyoxotungstate [Cu20Cl(OH)24(H2O)12(P8W48O184)]25- macroanions form supramolecular "blackberry" structure in aqueous solution

The hydrophilic polyoxotungstate [Cu20Cl(OH)24(H2O)12(P8W48O184)]25- ({Cu20P8W48}) self-assembles into single-layer, hollow, spherical "blackberry"-type structures in aqueous solutions, as studied by dynamic light scattering (DLS), static light scattering (SLS), zeta potential analysis, and scanning electron microscopy (SEM) techniques. This represents the first report of blackberry formation for a non-Mo-containing polyoxometalate. There is no obvious change in the shape and size of the blackberries during the slow blackberry formation process, neither with macroionic concentration nor with temperature. Our results suggest that the blackberry-type structure formation is most likely a general phenomenon for hydrophilic macroions with suitable size and charge in a polar solvent, and not a specific property of polyoxomolybdates and their derivatives. The {Cu20P8W48} macroions are thus far the smallest type of macroions to date (equivalent radius < 2 nm) showing the unique self-assembly behavior, helping us to move one step closer toward identifying the transition point from simple ions (can be described by the Debye-Hückel theory) to macroions in very dilute solutions. Moreover, by using {Cu20P8W48} blackberry-type structures as the model system, the electrophoretic properties of macroionic supramolecular structures are studied for the first time via zeta-potential analysis. The mobility of blackberry-type structures is determined and used for understanding the state of small cations in solution. We notice that the average charge density on each {Cu20P8W48} macroanion in a blackberry is much lower than that of discrete "free" {Cu20P8W48} macroions. This result suggests that some small alkali counterions are closely associated with, or even incorporated into, the blackberry-type structures and thus do not contribute to solution conductivity. This model is fully consistent with our speculation that monovalent counterions play an important role in the self-assembly of macroions, possibly providing an attractive force contributing to blackberry formation.