TY - JOUR A1 - Bärenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - constraints JF - Journal of geophysical research : Solid earth N2 - Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001–2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012464 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 1343 EP - 1364 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Cattiaux, Patrick A1 - Fradon, Myriam A1 - Kulik, Alexei M. A1 - Roelly, Sylvie T1 - Long time behavior of stochastic hard ball systems JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - We study the long time behavior of a system of n = 2, 3 Brownian hard balls, living in R-d for d >= 2, submitted to a mutual attraction and to elastic collisions. KW - hard core interaction KW - local time KW - Lyapunov function KW - normal reflection KW - Poincare inequality KW - reversible measure KW - stochastic differential equations Y1 - 2016 U6 - https://doi.org/10.3150/14-BEJ672 SN - 1350-7265 SN - 1573-9759 VL - 22 SP - 681 EP - 710 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Benini, Marco T1 - Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies JF - Journal of mathematical physics N2 - Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing. Y1 - 2016 U6 - https://doi.org/10.1063/1.4947563 SN - 0022-2488 SN - 1089-7658 VL - 57 SP - 1249 EP - 1279 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Holschneider, Matthias A1 - Lesur, Vincent A1 - Mauerberger, Stefan A1 - Baerenzung, Julien T1 - Correlation-based modeling and separation of geomagnetic field components JF - Journal of geophysical research : Solid earth N2 - We introduce a technique for the modeling and separation of geomagnetic field components that is based on an analysis of their correlation structures alone. The inversion is based on a Bayesian formulation, which allows the computation of uncertainties. The technique allows the incorporation of complex measurement geometries like observatory data in a simple way. We show how our technique is linked to other well-known inversion techniques. A case study based on observational data is given. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012629 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 3142 EP - 3160 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Hermann, Andreas A1 - Humbert, Emmanuel T1 - About the mass of certain second order elliptic operators JF - Advances in mathematics N2 - Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved. KW - Yamabe operator KW - Surgery KW - Positive mass theorem Y1 - 2016 U6 - https://doi.org/10.1016/j.aim.2016.03.008 SN - 0001-8708 SN - 1090-2082 VL - 294 SP - 596 EP - 633 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kistner, Saskia A1 - Vollmeyer, Regina A1 - Burns, Bruce D. A1 - Kortenkamp, Ulrich T1 - Model development in scientific discovery learning with a computer-based physics task JF - Computers in human behavior N2 - Based on theories of scientific discovery learning (SDL) and conceptual change, this study explores students' preconceptions in the domain of torques in physics and the development of these conceptions while learning with a computer-based SDL task. As a framework we used a three-space theory of SDL and focused on model space, which is supposed to contain the current conceptualization/model of the learning domain, and on its change through hypothesis testing and experimenting. Three questions were addressed: (1) What are students' preconceptions of torques before learning about this domain? To do this a multiple-choice test for assessing students' models of torques was developed and given to secondary school students (N = 47) who learned about torques using computer simulations. (2) How do students' models of torques develop during SDL? Working with simulations led to replacement of some misconceptions with physically correct conceptions. (3) Are there differential patterns of model development and if so, how do they relate to students’ use of the simulations? By analyzing individual differences in model development, we found that an intensive use of the simulations was associated with the acquisition of correct conceptions. Thus, the three-space theory provided a useful framework for understanding conceptual change in SDL. KW - Scientific discovery learning KW - Multiple problem spaces KW - Computer simulations KW - Physics concepts KW - Misconceptions KW - Conceptual change Y1 - 2016 U6 - https://doi.org/10.1016/j.chb.2016.02.041 SN - 0747-5632 SN - 1873-7692 VL - 59 SP - 446 EP - 455 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Kretschmer, Marlene A1 - Coumou, Dim A1 - Donges, Jonathan A1 - Runge, Jakob T1 - Using Causal Effect Networks to Analyze Different Arctic Drivers of Midlatitude Winter Circulation JF - Journal of climate N2 - In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes. Y1 - 2016 U6 - https://doi.org/10.1175/JCLI-D-15-0654.1 SN - 0894-8755 SN - 1520-0442 VL - 29 SP - 4069 EP - 4081 PB - American Meteorological Soc. CY - Boston ER - TY - JOUR A1 - Becker, Christian T1 - Cheeger-Chern-Simons Theory and Differential String Classes JF - Annales de l'Institut Henri Poincaré N2 - We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory. Y1 - 2016 U6 - https://doi.org/10.1007/s00023-016-0485-6 SN - 1424-0637 SN - 1424-0661 VL - 17 SP - 1529 EP - 1594 PB - Springer CY - Basel ER - TY - JOUR A1 - Lyu, Xiaojing A1 - Schulze, Bert-Wolfgang T1 - Mellin Operators in the Edge Calculus JF - Complex analysis and operator theory N2 - A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities. KW - Edge degenerate operators KW - Mellin and Green operators edge symbols Y1 - 2016 U6 - https://doi.org/10.1007/s11785-015-0511-6 SN - 1661-8254 SN - 1661-8262 VL - 10 SP - 965 EP - 1000 PB - Springer CY - Basel ER - TY - JOUR A1 - Kistner, Saskia A1 - Burns, Bruce D. A1 - Vollmeyer, Regina A1 - Kortenkamp, Ulrich T1 - The importance of understanding: Model space moderates goal specificity effects JF - The quarterly journal of experimental psychology N2 - The three-space theory of problem solving predicts that the quality of a learner's model and the goal specificity of a task interact on knowledge acquisition. In Experiment 1 participants used a computer simulation of a lever system to learn about torques. They either had to test hypotheses (nonspecific goal), or to produce given values for variables (specific goal). In the good- but not in the poor-model condition they saw torque depicted as an area. Results revealed the predicted interaction. A nonspecific goal only resulted in better learning when a good model of torques was provided. In Experiment 2 participants learned to manipulate the inputs of a system to control its outputs. A nonspecific goal to explore the system helped performance when compared to a specific goal to reach certain values when participants were given a good model, but not when given a poor model that suggested the wrong hypothesis space. Our findings support the three-space theory. They emphasize the importance of understanding for problem solving and stress the need to study underlying processes. KW - Goal specificity KW - Problem solving KW - Three-space theory KW - Scientific discovery learning Y1 - 2016 U6 - https://doi.org/10.1080/17470218.2015.1076865 SN - 1747-0218 SN - 1747-0226 VL - 69 SP - 1179 EP - 1196 PB - Optical Society of America CY - Abingdon ER -