Independence, Relative Randomness, and PA Degrees

We study pairs of reals that are mutually Martin-L\"{o}f random with respect to a common, not necessarily computable probability measure. We show that a generalized version of van Lambalgen's Theorem holds for non-computable probability measures, too. We study, for a given real $A$, the \emph{independence spectrum} of $A$, the set of all $B$ so that there exists a probability measure $\mu$ so that $\mu\{A,B\} = 0$ and $(A,B)$ is $\mu\times\mu$-random. We prove that if $A$ is r.e., then no $\Delta^0_2$ set is in the independence spectrum of $A$. We obtain applications of this fact to PA degrees. In particular, we show that if $A$ is r.e.\ and $P$ is of PA degree so that $P \not\geq_{T} A$, then $A \oplus P \geq_{T} 0'$

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchet-like transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained resorting to a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus and identifying (within this scheme) a mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000

ICT as learning media and research instrument: What eResearch can offer for those who research eLearning?

Students‘ interactions in digital learning environments are distributed over time and space, and many aspects of eLearning phenomenon cannot be investigated using traditional research approaches. At the same time, the possibility to collect digital data about students‘ online interactions and learning opens a range of new opportunities to use ICT as research tool and apply new research approaches. This symposium brings together some of the recent advancements in the area of ICT-enhanced research and aims to discuss future directions for methodological innovation in this area. The session will include four presentations that will explore different directions of ICT use for eLearning research

Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schr\"odinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments suggested by the refere

Provenance of Ordovician and Devonian sandstones from southern Peru and northern Bolivia - U-Pb and Lu-Hf isotope evidence of detrital zircons and its implications for the geodynamic evolution of the Western Gondwana margin (14° - 17° S)

In an attempt to trace the provenance of sedimentary detritus and to gain information on the crustal evolution of the Early Paleozoic western Gondwana margin (14°-17°S) we applied a combined in situ U-Pb and Lu-Hf LA-ICP-MS isotope analysis on detrital zircon from 12 Ordovician and Devonian sandstones in southern Peru and northern Bolivia. The sandstones are exposed in the Eastern Cordillera, the Altiplano and the Coastal Cordillera. The sedimentary basins are part of the Peru-Bolivia trough. Few intrusive and extrusive Early Paleozoic rocks indicate that the Ordovician basins developed in a back-arc position, with the arc on the Arequipa Massif in the west and the Amazonian craton in the east. This plate-tectonic setting appears to have changed into a passive margin in the Early Devonian. The U-Pb zircon age distribution of the Ordovician sandstones from the Eastern Cordillera has the most distinctive peak between 0.7 and 0.5 Ga (Brazilian interval). Contrastingly, the most prominent U-Pb zircon age peak of the Ordovician sandstones from the Altiplano is at 1.2-0.9 Ga (Grenvillian interval) with a smaller peak at 1.85-1.7 Ga. The Devonian sandstones from the same locality on the Altiplano contain zircons with a major age peak at 0.5-0.4 Ga (Famatinian interval). Smaller U-Pb age peaks can be connected to the Brazilian, Grenvillian and Transamazonian (2.2-1.8 Ga) intervals. Zircons of the Devonian sandstones from the Coastal Cordillera have a similar age distribution but the Grenvillian ages, in one case also the Transamazonian ages are significantly more pronounced than the Brazilian ages. Zircons formed during the Brazilian interval could have been derived from various eastern sources on the Amazonian craton, those with Grenvillian ages were derived either from the Sunsas belt to the east or from the Arequipa Massif to the west of the sedimentary basin. Zircons related to the Famatinan event most probably originated in the Arequipa Massif, the closest place where respective magmatic arc rocks were available. Thus, the Ordovician sandstones of the Eastern Cordillera and the Altiplano had an eastern source, while the Altiplano locality was fed from a very limited source area, probably the Sunsas belt. The Devonian siliciclastic strata instead were mainly influenced by the Arequipa Massif. Minor influences of eastern sources are documented by the presence of Brazilian zircon ages. The in situ Lu-Hf isotope signature provides information about crustal recycling. Together with the U-Pb zircon ages, crustal evolution paths can be reconstructed. εHf(t) values of the analysed zircons spread between –20 and +12. Zircons with a very juvenile signatures (less than 5 εHf-units below the respective depleted mantle composition) we detected only in the interval between 1.5 and 0.9 Ga. Hence, of the Brazilian and Famatinian events we only find zircons derived from an evolved crust. A striking feature is the common Hf model ages (c.1.5-1.2 Ga) of zircons formed during the Grenvillian, Brazilian and Famatinian orogenies. This indicates that Famatinian-aged crystalline rocks of the Arequipa Massif and the Brazilianaged crystalline rocks of the Amazonian craton have a similar crustal origin

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio

Resonant Activation Phenomenon for Non-Markovian Potential-Fluctuation Processes

We consider a generalization of the model by Doering and Gadoua to non-Markovian potential-switching generated by arbitrary renewal processes. For the Markovian switching process, we extend the original results by Doering and Gadoua by giving a complete description of the absorption process. For all non-Markovian processes having the first moment of the waiting time distributions, we get qualitatively the same results as in the Markovian case. However, for distributions without the first moment, the mean first passage time curves do not exhibit the resonant activation minimum. We thus come to the conjecture that the generic mechanism of the resonant activation fails for fluctuating processes widely deviating from Markovian.Comment: RevTeX 4, 5 pages, 4 figures; considerably shortened version accepted as a brief report to Phys. Rev.