Provability Logic and the Completeness Principle

In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic

Simulating the Emergence of Task Rotation

In work groups, task rotation may decrease the negative consequences of boredom and lead to a better task performance. In this paper we use multi agent simulation to study several organisation types in which task rotation may or may not emerge. By looking at the development of expertise and motivation of the different agents and their performance as a function of self-organisation, boredom, and task rotation frequency, we describe the dynamics of task rotation. The results show that systems in which task rotation emerges perform better than systems in which the agents merely specialise in one skill. Furthermore, we found that under certain circumstances, a task that leads to a high degree of boredom was performed better than a task causing a low level of boredom.Organisation, Task Rotation, Work Groups, Psychological Theory, Multi Agent Simulation

When Does a Newcomer Contribute to a Better Performance? A Multi-Agent Study on Self-Organising Processes of Task Allocation

This paper describes how a work group and a newcomer mutually adapt. We study two types of simulated groups that need an extra worker, one group because a former employee had left the group and one group because of its workload. For both groups, we test three conditions, newcomers being specialists, newcomers being generalists, and a control condition with no newcomer. We hypothesise that the group that needs an extra worker because of its workload will perform the best with a newcomer being a generalist. The group that needs an extra worker because a former employee had left the group, will perform better with a specialist newcomer. We study the development of task allocation and performance, with expertise and motivation as process variables. We use two performance indicators, the performance time of the slowest agent that indicates the speed of the group and the sum of performance of all agents to indicate labour costs. Both are indicative for the potential benefit of the newcomer. Strictly spoken the results support our hypotheses although the differences between the groups with generalists and specialists are negligible. What really mattered was the possibility for a newcomer to fit in.Task Allocation, Group Processes, Psychological Theory, Small Groups, Self-Organisation

Kinematics of the South Atlantic rift

The South Atlantic rift basin evolved as branch of a large Jurassic-Cretaceous intraplate rift zone between the African and South American plates during the final breakup of western Gondwana. By quantitatively accounting for crustal deformation in the Central and West African rift zone, we indirectly construct the kinematic history of the pre-breakup evolution of the conjugate West African-Brazilian margins. Our model suggests a causal link between changes in extension direction and velocity during continental extension and the generation of marginal structures such as the enigmatic Pre-salt sag basin and the S\~ao Paulo High. We model an initial E-W directed extension between South America and Africa (fixed in present-day position) at very low extensional velocities until Upper Hauterivian times ($\approx$126 Ma) when rift activity along in the equatorial Atlantic domain started to increase significantly. During this initial $\approx$17 Myr-long stretching episode the Pre-salt basin width on the conjugate Brazilian and West African margins is generated. An intermediate stage between 126.57 Ma and Base Aptian is characterised by strain localisation, rapid lithospheric weakening in the equatorial Atlantic domain, resulting in both progressively increasing extensional velocities as well as a significant rotation of the extension direction to NE-SW. Final breakup between South America and Africa occurred in the conjugate Santos--Benguela margin segment at around 113 Ma and in the Equatorial Atlantic domain between the Ghanaian Ridge and the Piau\'i-Cear\'a margin at 103 Ma. We conclude that such a multi-velocity, multi-directional rift history exerts primary control on the evolution of this conjugate passive margins systems and can explain the first order tectonic structures along the South Atlantic and possibly other passive margins.Comment: 46 Pages, 22 figures. Submitted to Solid Earth (http://www.solid-earth.net). Abstract shortened due to arXiv restrictions. New version contains revisions and amendments as per reviewers requests. Supplementary data is available at http://datahub.io/en/dataset/southatlanticrif

Characterization of carbon contamination under ion and hot atom bombardment in a tin-plasma extreme ultraviolet light source

Molecular contamination of a grazing incidence collector for extreme ultraviolet (EUV) lithography was experimentally studied. A carbon film was found to have grown under irradiation from a pulsed tin plasma discharge. Our studies show that the film is chemically inert and has characteristics that are typical for a hydrogenated amorphous carbon film. It was experimentally observed that the film consists of carbon (~70 at. %), oxygen (~20 at. %) and hydrogen (bound to oxygen and carbon), along with a few at. % of tin. Most of the oxygen and hydrogen are most likely present as OH groups, chemically bound to carbon, indicating an important role for adsorbed water during the film formation process. It was observed that the film is predominantly sp3 hybridized carbon, as is typical for diamond-like carbon. The Raman spectra of the film, under 514 and 264 nm excitation, are typical for hydrogenated diamond-like carbon. Additionally, the lower etch rate and higher energy threshold in chemical ion sputtering in H2 plasma, compared to magnetron-sputtered carbon films, suggests that the film exhibits diamond-like carbon properties.Comment: 18 pages, 10 figure

The role of antiphase boundaries during ion sputtering and solid phase epitaxy of Si(001)

The Si(001) surface morphology during ion sputtering at elevated temperatures and solid phase epitaxy following ion sputtering at room temperature has been investigated using scanning tunneling microscopy. Two types of antiphase boundaries form on Si(001) surfaces during ion sputtering and solid phase epitaxy. One type of antiphase boundary, the AP2 antiphase boundary, contributes to the surface roughening. AP2 antiphase boundaries are stable up to 973K, and ion sputtering and solid phase epitaxy performed at 973K result in atomically flat Si(001) surfaces.Comment: 16 pages, 4 figures, to be published in Surface Scienc