Dimensions of finite type for representations of partially ordered sets

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms.Comment: 14 page

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems

Combustion noise from gas turbine aircraft engines measurement of far-field levels

Combustion noise can be a significant contributor to total aircraft noise. Measurement of combustion noise is made difficult by the fact that both jet noise and combustion noise exhibit broadband spectra and peak in the same frequency range. Since in-flight reduction of jet noise is greater than that of combustion noise, the latter can be a major contributor to the in-flight noise of an aircraft but will be less evident, and more difficult to measure, under static conditions. Several methods for measuring the far-field combustion noise of aircraft engines are discussed in this paper. These methods make it possible to measure combustion noise levels even in situations where other noise sources, such as jet noise, dominate. Measured far-field combustion noise levels for several turbofan engines are presented. These levels were obtained using a method referred to as three-signal coherence, requiring that fluctuating pressures be measured at two locations within the engine core in addition to the far-field noise measurement. Cross-spectra are used to separate the far-field combustion noise from far-field noise due to other sources. Spectra and directivities are presented. Comparisons with existing combustion noise predictions are made

Prediction of the noise from a propeller at angle of attack

An analysis is presented to predict the noise of a propeller at angle of attack. The analysis is an extension of that reported by Mani which predicted the change in noise due to angle of attack to both unsteady loading and to azimuthal variation of the radiation efficiency of steady noise sources. Mani's analysis, however, was limited to small angles of attack. The analysis reported herein removes this small angle limitation. Results from the analysis are compared with the data of Woodward for a single rotation propeller and a counter rotating propeller. The comparison shows that including the effect of angle of attack on the steady noise sources significantly improves the agreement with data. Including higher order effects of angle of attack, while changing the predicted noise at far forward and aft angles, has little effect near the propeller plane

Simulation of water vapor condensation on LOX droplet surface using liquid nitrogen

The formation of ice or water layers on liquid oxygen (LOX) droplets in the Space Shuttle Main Engine (SSME) environment was investigated. Formulation of such ice/water layers is indicated by phase-equilibrium considerations under conditions of high partial pressure of water vapor (steam) and low LOX droplet temperature prevailing in the SSME preburner or main chamber. An experimental investigation was begun using liquid nitrogen as a LOX simulant. A monodisperse liquid nitrogen droplet generator was developed which uses an acoustic driver to force the stream of liquid emerging from a capillary tube to break up into a stream of regularly space uniformly sized spherical droplets. The atmospheric pressure liquid nitrogen in the droplet generator reservoir was cooled below its boiling point to prevent two phase flow from occurring in the capillary tube. An existing steam chamber was modified for injection of liquid nitrogen droplets into atmospheric pressure superheated steam. The droplets were imaged using a stroboscopic video system and a laser shadowgraphy system. Several tests were conducted in which liquid nitrogen droplets were injected into the steam chamber. Under conditions of periodic droplet formation, images of 600 micron diameter liquid nitrogen droplets were obtained with the stroboscopic video systems