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Socio-technical scenarios for energy-intensive industries: the future of steel production in Germany
(2019)
Soft Materials in Technology and Biology – Characteristics, Properties, and Parameter Identification
(2008)
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
Recently, the SHARP Corporation, Japan, has developed the world’s first "Plasma Cluster Ions (PCI)" air purification technology using plasma discharge to generate cluster ions. The new plasma cluster device releases positive and negative ions into the air, which are able to decompose and deactivate harmful airborne substances by chemical reactions. Because cluster ions consist of positive and negative ions that normally exist in the natural world, they are completely harmless and safe to humans. The amount of ozone generated by cluster ions is less than 0.01 ppm, which is significantly less than the 0.05-ppm standard for industrial operations and consumer electronics. This amount, thus, has no harming effects whatsoever on the human body. But particular properties and chemical processes in PCI treatment are still under study. It has been shown that PCI in most cases show strongly pronounced irreversible killing effects in respect of airborne microflora due to free-radical induced reactions and can be considered as a potent technology to disinfect both home, medical and industrial appliances.