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Modeling Performance Assessment
Published in Wolff-Michael Roth, Cognition, Assessment and Debriefing in Aviation, 2017
Classification, which is based on a true decision between qualitatively different options, may also be modeled using catastrophe theory. The mathematician who created this theory describes it as a method and language, which, as any language, serves to describe reality without being capable of asserting itself as truth or the appropriateness the descriptions it generates (Thom 1981). Catastrophe theory is a mathematical approach that may be used to describe the existence and emergence of any empirical morphology (qualities, types) from quantitative changes. In the natural sciences, a typical case that has been modeled using this approach is the transition from liquid water to vapor (gas), two qualitatively different states of water. Transitions between binomial situations, such as changes in attitudes, conceptual changes of scientists, war and peace, stepwise changes in the development of human beings, and category formation among scientists all have been described mathematically drawing on this theory.
Numerical simulation and analysis of five-stage lifting pump by improved turbulence model and catastrophe theory
Published in Engineering Applications of Computational Fluid Mechanics, 2020
Zhuo Zhou, Lin Zhang, Jiu Hui Wu, Xiao Liang, Hailiang Xu, Mei Lin, XiaoYang Yuan
Figure 12 shows the variation in the turbulent kinetic energy spectrum with time in the process of turbulence formation. The abscissa is time factor (ts). The turbulent kinetic energy spectrum Ek under different flow conditions is shown in Figure 9. We can see that the Ek varies with time. The highest point of the turbulent kinetic energy spectrum is ts= 2. With ts from 0 to 1, the region is called the large eddy range; with ts from 1 to 5.6, the region is the energy-containing range; with ts from 5.6 to 8.8, the region is the inertial subrange; with ts from 4 to 8.8, the region is called the dissipation range; and after 8.8, the system reaches fully developed turbulence. These values are in accordance with the changing trends derived from Equation (9). One of the important characteristics of catastrophe theory is that it can quantitatively predict the phase transition of a system even without knowing the differential equation of the system. The numerical results of turbulence transformation obtained by catastrophe theory are in agreement with the numerical simulation of the differential equations.