Analytical investigation of nonrecoverable stall

A lumped parameter model of the TF34 engine is formulated to study nonrecoverable stall. Features of the model include forward and reverse flow, radial flow in the fan, and variable corrected speed. The purpose of the study is to point out those parameters to which recoverability is highly sensitive but are not well known. Experimental research may then be directed toward identification of the parameters in that category. Compressor performance in the positive flow region and radial flow in the fan are shown to be important but unknown parameters determining recoverability. Other parameters such as compressor performance during reverse flow and in-stall efficiency have relatively small impact on recoverability

The Immediate Exchange model: an analytical investigation

We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter $2$. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter $2$ are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is {\it{not}} a Gamma distribution

Analytical investigation of solid rocket nozzle failure

On April 5, 1983, an Inertial Upper Stage (IUS) spacecraft experienced loss of control during the burn of the second of two solid rocket motors. The anomaly investigation showed the cause to be a malfunction of the solid rocket motor. This paper presents a description of the IUS system, a failure analysis summary, an account of the thermal testing and computer modeling done at Marshall Space Flight Center, a comparison of analysis results with thermal data obtained from motor static tests, and describes some of the design enhancement incorporated to prevent recurrence of the anomaly

Global Liquidity Trap: A Simple Analytical Investigation

How should monetary policy cooperation be designed when more than one country simultaneously faces zero lower bounds on nominal interest rates? To answer this question, we examine monetary policy cooperation with both optimal discretion and commitment policies in a two- country model. We reach the following conclusions. Under discretion, monetary policy cooperation is characterized by the intertemporal elasticity of substitution (IES), a key parameter measuring international spillovers, and no history dependency. On the other hand, under commitment, monetary policy features history dependence with international spillover effects.Optimal Monetary Policy Cooperation, Zero Lower Bound

An Analytical investigation of a failed 1120 Aluminium wire.

a.n alytical investigation was performed on an - 120 aluminum wire which failed under stress test. ~.canning electron microscopy (SEM) examination ''nd the energy depressive spectrometer (EDS) nalysis were the major analytical methods of 1m.vestigation used. The failure mode of the alloy was found to be that of brittle failure interspersed · with ductile failure. The brittle failure results from he second phase particles contained within the luminium matrix which rendered the structure in . J):l .. -/1' ~ . . hif(region -weak and hence susceptible to failure . ,~:~ ABSTRACT a.n analytical investigation was performed on an - 120 aluminum wire which failed under stress test. ~.canning electron microscopy (SEM) examination ''nd the energy depressive spectrometer (EDS) nalysis were the major analytical methods of 1m.vestigation used. The failure mode of the alloy was found to be that of brittle failure interspersed · ith ductile failure. The brittle failure results from he second phase particles contained within the luminum matrix which rendered the structure in . J):l .. -/1' ~ . . hif(region -weak and hence susceptible to failure . ,~:~ , ... . . nder stress tests., ... . . nder stress tests

Democratization in a passive dendritic tree : an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius

Analytical investigation of rotor wake formation and geometry

A number of refinements in the computer code were worked out and tested. Three codes have been written to date. One program is for an isolated wing and is being used to compare with data for the vortex wake (Weston). The second code is for an isolated wing with a streamwise vortex passing above it. This program is being used to validate the computational procedure for incorporating the vortex into the Euler equation calculations. The third program is the hovering rotor code which is the overall objective of the research. The optimization calculations for a hovering helicopter rotor have been completed

An experimental and analytical investigation of axisymmetric diffusers

A finite difference computer program for turbulent compressible flow was used to establish the performance of several diffuser shapes for experimental testing. The diffusers were designed to have a linear change in Mach number, a linear change in pressure, or a curvature fitted by a quadratic equation. Testing was performed with M = 0.1 to 0.9 with and without boundary layer bleed. Above M = 0.6, data were obtained with a normal shock upstream of the diffuser entrance. Peak static pressure recovery occurred with a diffuser inlet M0.75. The quadratic diffuser yielded the highest total pressure recovery