Ernst-Christoph Haß, Sonja Sauerbrei and Peter Jörg Plath

Hindawi Publishing Corporation
Discrete Dynamics in Nature and Society
Volume 2008, Artikle ID 590142, 26 pages
doi: 10.1155 / 2008 / 590142

Based on Rush's concept of diagram lattices formed by Young diagrams we investigated the possibility to transform incomarable diagrams into comparable ones by means of vector catalysis. Ruch's diagram lattices allow a very general description of comparing frequency distributions by their mixing-characters as an order relation which is equivalent to majorisation in the mathematical theory of inequalities. Dealing with Young diagrams or vector containing only integer componets, respectively, vector catalysis is strongly related to entanglement catalysis in quantum informatics. In a very systematic way the diagram lattics of the partititions up to the number n = 20 have been searched for incomparable pairs which can be catalysed. This concept opens the opportunity for regarding vector catalysis as a universal phenomenon which is not restricted to the quantum mechanical idea of entanglement catalysis. Such a general approach offers the possibility to compare vector catalysis with chemical ideas of catalysis and autocatalysis in a very fundamental sense. We emphasize that vector catalysis is a universally valid procedure for classification purposes, where incomparable sequences of symbols are transformed into comparable ones in a much higher dimensional space ignoring any physical interpretation of these symbols.

Copyright © 2008 Ernst-Christoph Hass et al. This is an open access article ditributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In: „Vernetzte Wissenschaften
- Crosslinks in Natural and Social Sciences -“
(P.J. Plath und E.-C. Haß; Hrsg.)
Logos Verlag Berlin (2008) S. 15 - 46

Summary. In our days the catalytic CO-oxidation using Pd supported catalysts belong to the most famous examples of synergetics[8-19] in heterogeneous chemical systems. This reaction obeys periodic behaviour (see Fig. 2) as well as chaos.
For macroscopic structure formation in this system the cooperation of a lot of small catalytic active palladium particles within the catalyst support is essential.
Which of the palladium particles are acting in synchrony depends on their particle sizes. The reason is that the exothermic CO-oxidation will heat up the small nano-metal particles extraordinarily. Although for small amounts of CO in the carrier gas the reaction can be executed isothermally with respect to the whole catalst bulk. However, the catalytic active palladium particles can be heated up to several hundred degrees Celsius for very short times whereas their surrounding remains almost unaffected.
This very high temperature enables the phase transition from active palladium to catalytic inactive palladium oxide in the presence of oxygen. After fast cooling because of the large temperature gradient between the nano-metal particles and their surrounding the palladium oxide can be reduced by its adsorbed CO via solid state reactions.
The time discrete evolution equation (13) for this system is solved numerically assuming that noise is added to the order parameters of the system.

In: „Vernetzte Wissenschaften
- Crosslinks in Natural and Social Sciences –“
(P.J. Plath und E.-C. Haß; Hrsg.)
Logos Verlag Berlin (2008) S. 153 - 179

Fast eine Schlussbemerkung:

Gehen wir nicht mehr - wie im ursprünglichen Modell - davon aus, dass Probleme Probleme erzeugen, sondern nur das Lösen von Problemen uns zu neuen Problemen verhilft, dann können wir den Begriff der wissenschaftlichen Kreativität im Rahmen dieses Modells mathematisch fassen. Dies eröffnet eine Möglichkeit, durch im wissenschaftlichen Prozess wachsende Probleme immer neue Probleme zu generieren.
Im Gleichungssystem (11) wird dies dadurch erreicht, dass in der Problemkurve y (t+1) der Term Cy_i (y_i (t) - y_i (t-1))" hinzugefügt wird, der vorherige Problemlösungen berücksichtigt. Das Anwachsen von Problemen durch Lösen von Problemen ist in Abb.19 dargestellt.
Wissenschaft ist das Schaffen von Wissen, also das Erzeugen von Problemen / Fragestellungen.