The magnetorotational instability (MRI) is a shear instability and thus its sensitivity to the shear parameter q = −d ln Ω/d ln r is of interest to investigate. Motivated by astrophysical disks, most (but not all) previous MRI studies have focused on the Keplerian value of q = 1.5. Using simulation with 8 vertical density scale heights, we contribute to the subset of studies addressing the the effect of varying q in stratified numerical simulations. We discuss why shearing boxes cannot easily be used to study q > 2 and thus focus on q < 2. As per previous simulations, which were either unstratified or stratified with a smaller vertical domain, we find that the q dependence of stress for the stratified case is not linear, contrary to the Shakura-Sunyaev model. We find that the scaling agrees with Abramowicz et al. (1996) who found it to be proportional to the shear to vorticity ratio q/(2 − q). We also find however, that the shape of the magnetic and kinetic energy spectra are relatively insensitive to q and that the ratio of Maxwell stress to magnetic energy ratio also remains nearly independent of q. This is consistent with a theoretical argument in which the rate of amplification of the azimuthal field depends linearly on q and the turbulent correlation time τ depends inversely on q. As such, we measure the correlation time of the turbulence and find that indeed it is inversely proportional to q.

The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different quantities, including magnetic energy and Maxwell stresses and find that they are dominated by contributions from the lowest wave numbers. This is even more dramatic for the corona than the disc, suggesting that transport in the corona region is dominated by larger structures than the disc. By calculating averaged power spectra in one direction of k space at a time, we also show that the MRI turbulence is strongly anisotropic on large scales when analyzed by this method, but isotropic on small scales. Although the shearing box itself is meant to represent a local section of an accretion disc, the fact that the stress and energy are dominated by the largest scales highlights that the locality is not captured within the box. This helps to quantify the intuitive importance of global simulations for addressing the question of locality of transport, for which similar analyses can be performed.

We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337-355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

The basis of many systems that integrate data from multiple sources is a set of correspondences between source schemata and a target schema. Correspondences express a relationship between sets of source attributes, possibly from multiple sources, and a set of target attributes. Clio is an integration tool that assists users in dening value correspondences between attributes [1].In real life scenarios there may be many sources and the source relations may have many attributes. Users can get lost and might miss or be unable to nd some correspondences. Also, in many real life schemata the attribute names reveal little or nothing about the semantics of the data values. Only the data values in the attribute columns can convey the semantic meaning of the attribute. Our work relieves users of the problems of too many attributes and meaningless attribute names, by automatically suggesting correspondences between source and target attributes. For each attribute, we analyze the data values and derive a set of features. The overall feature set forms the characteristic signature of an attribute. There are more likely to be correspondences between attributes with similar signatures than between others. Our results show that a properly chosen small set of domain-independent features can mostly capture structural information of attributes. We describe the problem of nding corresponding attributes as a classication problem, and use the Naïve Bayes classier to decide upon most likely matches. Several dierent domains served to test the features and Naïve Bayes classier: a set of three bibliography databases, data from three real estate Web sites, a commercial semiconductor manufacturers database collecting, and an insurance database. The experiments showed an expected strong dependency between column size and accuracy. For all domains we observed satisfying misclassication rates below 5% for > 250 training data and > 16 test data values. Numerical attributes. For numerical attributes we use a non-Boolean feature set: To best model the range and distribution of the values of an attribute, we choose 18 quantile features for our implementationthe 10%, 20%, to 90% quantiles of each data column, and the 10%, 20%, to 90% quantiles of each data column after removing all data of value zero.To decide upon most likely correspondences, we introduce a new quantile-based classication method. As before, we generate one signature for each numerical attribute from the training column. We then generate the signature for the numerical test attribute to be classied. We evaluate the quantile-based classication methods by applying them to two real world databases and a synthetic data set. The rst database is a collection of numerical attributes taken from a large biochemical database; the second is an insurance database. Finally, we generated several data columns with synthetic data and only slightly diering distributions. We achieved on average misclassication rates below 5% for > 64 training and test data values. Summary. The techniques described a...