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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 The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid.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.
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.
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.
Die moderne Naturwissenschaft zeigt eindrucksvoll die große Reichweite des menschlichen Denkens - sie wirft aber auch die Frage nach ihrer menschengerechten Anwendung auf und führt an unüberwindliche Grenzen jeder Erkenntnis. Tragweite und Grenzen der Wissenschaft verweisen uns zurück auf uralte Fragen der Philosophie, zum Beispiel auf die Suche altgriechischer Denker nach den Urprinzipien der Natur oder auf das „Wissen vom Nichtwissen“ des Nikolaus von Kues. Der Blick auf 2500 Jahre Geschichte des Denkens über die Natur soll dabei helfen, die moderne Naturwissenschaft wieder in die großen Sinn- und Wertzusammenhänge menschlichen Lebens zu stellen.
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.
Die volle Anwendbarkeit der Physik auf die Biologie des menschlichen Gehirns bedeutet nicht notwendig, dass es ein finitistisches und zugleich vollständiges, algorithmisches Verfahren der Korrelation mentaler mit physikalischen Zuständen geben kann. Vielmehr gibt es Gründe für die Hypothese, dass eine umfassende Theorie der psychophysischen Beziehung prinzipiell unmöglich sein könnte. Diese Auffassung verbindet die Universalität der Physik mit der logischen Begrenztheit des menschlichen Denkens (z. B. in Bezug auf sich selbst) und betrachtet Bewusstsein - die ursprünglichste menschliche Erfahrung - nicht als Randphänomen. ++++ Die Zeitschrift RATIO erschien bis 1987 in einer deutschen und in einer englischen Ausgabe. Die englische Version des Artikels lautet: A. Gierer, The physical foundations of biology and the problems of psychophysics. RATIO XII, No. 1, 1970. S. 47-64.
Die Anwendung der Naturgesetze auf das verhaltenslenkende Gehirn widerspricht auf den ersten Blick der Freiheit des menschlichen Willens. Entsprechendes gilt für die Anwendung der Allmacht Gottes auf alle Vorgänge einschliesslich des menschlichen Verhaltens. Bei einem zweiten Blick auf diese scheinbar so konsequenten Gedankengänge erkennt man aber Verstrickungen in Selbstbezüglichkeiten, die jeweils Mehrdeutigkeiten und Grenzen unseres möglichen Wissens implizieren. Diese zeigten sich schon in Gödels Grenzen mathematisch-logischer Entscheidbarkeit ebenso wie in Heisenbergs Unbestimmtheitsgesetzen der Quantenphysik. Entsprechende Grenzen könnte es für eine vollständige physikalisch begründete Theorie unseres Bewußtseins und damit auch des menschlichen Willens geben - schliesslich würde sie Bewußtsein von Bewußtsein implizieren. In der theologischen Gedankenlinie wiederum kann sich die Allmacht Gottes auch auf die Allmacht selbst richten, indem sie eine weise naturgesetzliche Ordnung ohne ständige göttliche Eingriffe begr ündet und darin den Menschen als Freien will - so etwa sahen es freiheitsfreundliche unter den Theologen wie Eriugena und Cusanus. Mein Essay weist darauf hin, dass selbst bei so verschiedenen Denkweisen wie den naturwissenschaftlichen und theologischen jeweils analoge Selbstbezüglichkeiten auftreten, die unsere Erkenntnis begrenzen.
The topic of this article is the relation between bottom-up and top-down, reductionist and “holistic” approaches to the solution of basic biological problems. While there is no doubt that the laws of physics apply to all events in space and time, including the domains of life, understanding biology depends not only on elucidating the role of the molecules involved, but, to an increasing extent, on systems theoretical approaches in diverse fields of the life sciences. Examples discussed in this article are the generation of spatial patterns in development by the interplay of autocatalysis and lateral inhibition; the evolution of integrating capabilities of the human brain, such as cognition-based empathy; and both neurobiological and epistemological aspects of scientific theories of consciousness and the mind.
Biological evolution and technological innovation, while differing in many respects, also share common features. In particular, the implementation of a new technology in the market is analogous to the spreading of a new genetic trait in a population. Technological innovation may occur either through the accumulation of quantitative changes, as in the development of the ocean clipper, or it may be initiated by a new combination of features or subsystems, as in the case of steamships. Other examples of the latter type are electric networks that combine the generation, distribution, and use of electricity, and containerized transportation that combines standardized containers, logistics, and ships. Biological evolution proceeds, phenotypically, in many small steps, but at the genetic level novel features may arise not only through the accumulation of many small, common mutational changes, but also when distinct, relatively rare genetic changes are followed by many further mutations. New evolutionary directions may be initiated by, in particular, some rare combinations of regulatory sections within the genome. The combinatorial type of mechanism may not be a logical prerequisite for biological innovation, but it can be efficient, especially when novel features arise out of already highly developed systems. Such is the case with the evolution of general, widely applicable capabilities of the human brain. Hypothetical examples include the evolution of strategic thought, which encompasses multiple self-representations, cognition-based empathy, meta-levels of abstraction, and symbolic language. These capabilities of biologically modern man may have been initiated, perhaps some 150 000 years ago, by one or few accidental but distinct combinations of modules and subroutines of gene regulation which are involved in the generation of the neural network in the cerebral cortex. This hypothesis concurs with current insights into the molecular biology of the combinatorial and hierarchical facets of gene regulation that underlie brain development. A theory of innovation encompassing technological as well as biological development cannot per se dictate alternative explanations of biological evolution, but it may help in adding weight and directing attention to notions outside the mainstream, such as the hypothesis that few distinct genetic changes were crucial for the evolution of modern man.
