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Non-Oberbeck-Boussinesq (NOB) effects on the Nusselt number Nu and Reynolds number Re in strongly turbulent Rayleigh-Benard convection in liquids were investigated both experimentally and theoretically. In the experiment, the heat current, the temperature difference, and the temperature at the horizontal mid-plane were measured. Three cells of different heights L, all filled with water and all with aspect ratio T close to 1 were used. For each L, about 1.5 decades in Ra were covered, together spanning the ränge 108 < Ra < 1011. For the largest temperature difference between the bottom and top plates of ? = 40K the kinematic viscosity and the thermal expansion coefficient, due to their temperature dependence, varied by more than a factor of two. The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid. The ratio Ï? of the temperature drops across the bottom and top thermal boundary layers became as small as Ï? = 0.83, as compared to the ratio Ï? = 1 in the OB case. Nevertheless, the Nusselt number Nu was found to be only slightly smaller (at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height-independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus Nu and Re are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of Nu with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference ?. The net effects on Nu are proportional to ?2 and thus increase only slowly and still remain minor despite drastic material parameter changes. We then extend the Prandtl-Blasius boundary-layer theory to NOB Rayleigh-Benard flow with temperature dependent viscosity and thermal diffusivity. This allows the calculation of the shift of the bulk temperature, the temperature drops across the boundary layers, and the ratio Ï? without introducing any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within experimental resolution, the theory also gives the measured small Nusseltnumber reduction for the NOB case. In addition, it predicts an increase by about 0.5% of the Reynolds number, which is also consistent with the experimental data. By theoretically studying hypothetical liquids with only one of the material parameters being temperature dependent, we shed further light on the origin of NOB corrections in water: While the NOB deviation of x from its OB value Ï? = 1 mainly originates from the temperature dependence of the viscosity, the NOB correction of the Nusselt number primarily originates from the temperature dependence of the thermal diffusivity. Finally, we give the predictions from our theory for the NOB corrections if glycerol is used as operating liquid.
The birth of rules
(2001)
Mind, Matter and Mathematics
(2008)
Psychology's territories - historical and contemporary perspective from different disciplines
(2007)
What determines the territories of psychology? How have the boundaries of psychological research and practice been developed in history, and how might or should they be changed nowadays? This volume presents new approaches to these questions, resulting from a three-year collaboration among internationally known psychologists, neuroscientists, social scientists and historians and philosophers of science from Germany and the United States under the auspices of the Berlin-Brandenburg Academy of Sciences and Humanities. The authors reflect critically on traditional and current views of psychology on the basis of focused historical and contemporary case studies of three broad topic areas: How have psychological concepts been used in disciplines such as psychology, philosophy, or neuroscience, as well as in daily life? Has the use of instruments in psychological research expanded or restricted the discipline’s reach? And how have applications of psychological thinking and research worked in practical contexts? The volume thus presents essays that investigate the separations as well as the interactions between psychology and its neighboring disciplines and, moreover, essays that try to overcome disciplinary distinctions in exemplary ways. The contributions aim to make historical and philosophical studies of psychology relevant to contemporary concerns, and to show how psychology can profit from better interdisciplinary cooperation, thus improving mutual understanding between different scientific cultures.
Untersucht wird die Rolle der Psalmen im christlichen Gottesdienst, wie sie in der spätantiken christlichen Exegese deutlich wird.
For a fistful of blogs: Discovery and comparative benchmarking of republishable German content
(2014)
We introduce two corpora gathered on the web and related to computer-mediated communication: blog posts and blog comments. In order to build such corpora, we addressed following issues: website discovery and crawling, content extraction constraints, and text quality assessment. The blogs were manually classified as to their license and content type. Our results show that it is possible to find blogs in German under Creative Commons license, and that it is possible to perform text extraction and linguistic annotation efficiently enough to allow for a comparison with more traditional text types such as newspaper corpora and subtitles. The comparison gives insights on distributional properties of the processed web texts on token and type level. For example, quantitative analysis reveals that blog posts are close to written language, while comments are slightly closer to spoken language.
Stephen Jay Gould wrote recently that “when Church began to paint his great canvases, Alexander von Humboldt may well have been the world’s most famous and influential intellectual.” Humboldt’s influence in the case of the landscape artist Church is especially interesting. If we examine the precise relationship between the German explorer and his American admirer, we gain an insight into how Humboldt transformed Church’s life and signaled a new phase in the career of the artist. Church retraced Humboldt’s travels in Ecuador and in Mexico. If we compare the texts available to Church and the comparison of Church’s paintings and the texts and images of Humboldt’s works we can arrive at new perspectives on Humboldt’s extraordinary influence on American landscape painting in the nineteenth century.