We present a model for studying communities of epistemically interacting agents who update their belief states by averaging (in a specified way) the belief states of other agents in the community. The agents in our model have a rich belief state, inv
olving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating (in the given way). To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study.
We discuss two research projects in material science in which the results cannot be stated with an estimation of the error: a spectro- scopic ellipsometry study aimed at determining the orientation of DNA molecules on diamond and a scanning tunneling
microscopy study of platinum-induced nanowires on germanium. To investigate the reliability of the results, we apply ideas from the philosophy of models in science. Even if the studies had reported an error value, the trustworthiness of the result would not depend on that value alone.
The modification of the properties of CeO$_2$ through aliovalent doping are investigated within the emph{ab-initio} density functional theory framework. Lattice parameters, dopant atomic radii, bulk moduli and thermal expansion coefficients of fluori
te type Ce$_{1-x}$M$_{x}$O$_{2-y}$ (with M$ = $ Mg, V, Co, Cu, Zn, Nb, Ba, La, Sm, Gd, Yb, and Bi)are presented for dopant concentrations in the range $0.00 leq x leq 0.25$. The stability of the dopants is compared and discussed, and the influence of oxygen vacancies is investigated. It is shown that oxygen vacancies tend to increase the lattice parameter, and strongly decrease the bulk modulus. Defect formation energies are correlated with calculated crystal radii and covalent radii of the dopants, but are shown to present no simple trend. The previously observed inverse relation between the thermal expansion coefficient and the bulk modulus is shown to persist independent of the inclusion of charge compensating vacancies.
The appearance of microcracks in CeO$_2$ buffer layers, as used in buffer layer architectures for coated superconductors, indicates the presence of stress between this buffer layer and the substrate. This stress can originate from the differences in
thermal expansion or differences in lattice parameters between the CeO$_2$ buffer layer and the substrate. In this article, we study, by means of textit{ab initio} density functional theory calculations, the influence of group IV doping elements on the lattice parameter and bulk modulus of CeO$_2$. Vegards law behavior is found for the lattice parameter in systems without oxygen vacancies, and the Shannon crystal radii for the doping elements are retrieved from the lattice expansions. We show that the lattice parameter of the doped CeO$_2$ can be matched to that of the La$_2$Zr$_2$O$_7$ coated NiW substrate substrate for dopant concentrations of about $5%$, and that bulk modulus matching is either not possible or would require extreme doping concentrations.
