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Mind, Matter and Mathematics
(2008)
We expose analogies between turbulence in a fluid heated from below (Rayleigh-Bénard (RB) flow) and shear flows: The unifying theory for RB flow (S.Grossmann and D.Lohse, J.Fluid Mech. 407, 27-56 (2000) and subsequent refinements) can be extended to the flow between rotating cylinders (Taylor-Couette flow) and pipe flow. We identify wind dissipation rates and momentum fluxes that are analogous to the dissipation rate and heat flux in RB flow. The proposed unifying description for the three cases is consistent with the experimental data.
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 The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid.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 future of biological diversity in a crowded world (Ernst Mayr Lecture on 29th October 2002)
(2006)
Introduction : The Grants, Dreaming Darwin's Dream ; (Ernst Mayr Lecture am 4. November 2004)
(2006)
The author’s recently published monograph on Alexander von Humboldt' describes the multiple images of this great cultural icon. The book is a metabiographical study that shows how from the middle of the nineteenth century to the present day Humboldt has served as a nucleus of crystallisation for a variety of successive socio-political ideologies, each producing its own distinctive representation of him. The historiographical implications of this biographical diversity are profound and support current attempts to understand historical scholarship in terms of memory cultures.
The article provides historical background for Alexander von Humboldt’s expedition into Russia in 1829. It includes information on Humboldt’s works and publications in Russia over the course of his lifetime, as well as an explanation of the Russian scientific community’s response to those works. Humboldt’s ideas on the existence of an active volcano in Central Asia attracted the attention of two prominent Russian geographers, P.Semenov and P.Kropotkin, whose views on the nature of volcanism were quite different. P.Semenov personally met Humboldt in Berlin. P. Kropotkin made one of the most important geological discoveries of the 19th Century: he found the fresh volcanic cones near Lake Baikal. Soon after Humboldt’s Russian expedition, and partly as a result of it, an important mineral was found in the Ilmen mountains - samarskite, which later gave its name to the chemical element Samarium, developed in 1879. At the beginning of the 20th Century, the Russian scientist V.Vernadskiy pointed out that samarskite was the first uranium-rich mineral found in Russia.
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.