Partial planning model

Chapman s work produced the following theorem, which provides the necessary and sufficient conditions for guaranteeing the truth of any given statement in a partial plan, if all operations are modeled by STRIPS-like operators. 

We have to realize that sometimes requirements concerning physical properties of model materials exist that cannot be implemented. In such cases only a partial similarity can be realized. For this, essentially only two procedures are available (for details see Refs. 5 and 10). One consists of a well-planned experimental strategy in which the process is divided into parts, which are then investigated separately under conditions of complete similarity. This approach was first applied by William Froude (1810-1879) in his efforts to scale-up the drag resistance of the ship s hull. 

The section that follows describes basic background concepts and nomenclature. Then a classification of various programming models is outlined. Computational chemistry applications rely on many kinds of linear algebra and on equation-solving techniques that use new computer science algorithms. These implementations are delineated. A partial review of current and planned applications, developed on today s MPP supercomputers for chemistry, is presented. The last section of text gives a summary and our conclusions. Finally, we present a glossary and an appendix that reviews the currently available MPP machines. 

A more mathematical approach would invoke a theorem of differential equations, which says that a second order partial differential equation that is as nice as the one we have here, with two initial conditions of the form we just used, must have a unique solution. The branch of mathematics you would have to study to learn this theorem is called partial differential equations sometimes, or if the professor plans to give you the most general version, the area of study might be called differential operators on manifolds. Mathematically, this type of theorem makes the claim for our model of nature that the physical explanation is attempting to make for nature herself. Then we would again invoke the theory of Fourier series to tell us that the sines and cosines are good enough to do the job. 

The present work involves detailed measurements of flow, pollutant emissions, and acoustics in model multiple-swirl, partially-premixed flames and combustors. Complementary computations are also planned, combining computational aeroacoustics approaches with combustion modeling. The focus is on how pollutant control and flame stabilization strategies, such as partial premixing and swirl, respectively, influence combustor noise sources and potential instabilities. Also of interest are flow and acoustics associated with diffuser-combustor interactions and the utility of the trapped-vortex combustor design. A better understanding of pollutant and acoustic sources and how to modify them will aid in the control of emissions, noise, and instabilities in modern swirl combustors. 

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