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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 The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid.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.

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.

In dem Buch über „Wissenschaft und Menschenbild“ werden verschiedene Wege zu einem Verständnis unserer Spezies „Mensch“ begangen: Zum einen zeigt uns die Geschichte und die geistige Struktur der modernen Naturwissenschaft sowohl die umfassende Reichweite als auch die prinzipiellen Grenzen menschlicher Erkenntnis auf, und zwar wohl besser und genauer als jede andere Kulturleistung. Zum anderen ergibt die Evolutions- und die Gehirnbiologie Einsichten in menschliche Grundfähigkeiten wie Sprache, Selbstrepräsentation und strategisches Denken. Sie sind Ergebnisse genetischer Evolution, bildeten aber dann die Voraussetzung dynamischer kultureller Entwicklung, die nicht mehr auf genetischen Änderungen beruht. Die moderne Wissenschaft ist, indem sie ihre eigenen Grenzen begründet, offen für verschiedene, natürlich nicht für alle kulturellen und philosophischen Interpretationen des Menschen und der Welt. Menschliches Bewusstsein ist ein Ergebnis der Evolution des Gehirns, und doch ist die Gehirn-Geist-Beziehung aus entscheidungstheoretischen Gründen vermutlich nicht vollständig dekodierbar. Eine wesentliche Fähigkeit unserer Spezies Mensch ist kognitionsgestützte Empathie. Sie entstand vielleicht im Kontext der Evolution strategischen Denkens, indem sie es erleichtert, das Verhalten anderer vorherzusehen, ist aber auch Motivation für altruistisches Verhalten. Stereotype Kontroversen zwischen Sozialwissenschaftlern und Soziobiologen erscheinen heute eher überflüssig; es gibt eine, wenn auch begrenzte, biologische Basis auch für freundliche menschliche Eigenschaften wie Kooperativität und Vertrauen und nicht nur für Egoismus. Moralische Vorstellungen sollten die biologischen Grundlagen menschlichen Verhaltens respektieren: Gemeinwohl ist eine durchaus reale, aber doch begrenzte Ressource unserer Spezies „Mensch“. Sie ist eher behutsam zu aktivieren, und moralische Überforderungen sind kontraproduktiv.

Understanding cooperative human behaviour depends on insights into the biological basis of human altruism, as well as into socio-cultural development. In terms of evolutionary theory, kinship and reciprocity are well established as underlying cooperativeness. Reasons will be given suggesting an additional source, the capability of a cognition-based empathy that may have evolved as a by-product of strategic thought. An assessment of the range, the intrinsic limitations, and the conditions for activation of human cooperativeness would profit from a systems approach combining biological and socio-cultural aspects. However, this is not yet the prevailing attitude among contemporary social and biological scientists who often hold prejudiced views of each other's notions. It is therefore worth noticing that the desirable integration of aspects has already been attempted, in remarkable and encouraging ways, in the history of thought on human nature. I will exemplify this with the ideas of the fourteenth century Arab-Muslim historian Ibn Khaldun. He set out to explicate human cooperativeness - "asabiyah" - as having a biological basis in common descent, but being extendable far beyond within social systems, though in a relatively unstable and attenuated fashion. He combined psychological and material factors in a dynamical theory of the rise and decline of political rulership, and related general social phenomena to basic features of human behaviour influenced by kinship, expectation of reciprocity, and empathic emotions.

Full applicability of physics to human biology does not necessarily imply that one can uncover a comprehensive, algorithmic correlation between physical brain states and corresponding mental states. The argument takes into account that information processing is finite in principle in a finite world. Presumbly the brain-mind-relation cannot be resolved in all essential aspects, particularly when high degrees of abstraction or self-analytical processes are involved. Our conjecture plausibly unifies the universal validity of physics and a logical limitation of human thought, and it does not regard consciousness -the most basic human experience - as a marginal phenomenon. ++++ RATIO appeared up to 1987 in both a German and an English version. The German title of this article: Alfred Gierer, Der physikalische Grundlegungsversuch in der Biologie und das psychophysische Problem. RATIO XII, Heft 1, 1970, S. 40-54.