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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 The Oberbeck-Boussinesq (OB) approximation of temperature independent material parameters thus was no longer valid.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.
Physical principles underlying biological pattern formation are discussed. In particular, the combination of local self-enhancement and long-range (“lateral”) inhibition (Gierer and Meinhardt, 1972) accounts for de-novo pattern formation, and for striking features of developmental regulation such as induction, spacing and proportion regulation of centers of activation in tissues and cells. Part I explains physical principles of spatial organisation in biological development. Part II demonstrates in mathematical terms that and how short-range activation and long-range inhibition are conditions for the generation of spatial concentration patterns. The conditions can be expressed in terms of ranges, rates and orders of reactions. These conditions, in turn, can also be derived by analysis of dynamic instabilities by means of Fourier waves, showing the neither obvious nor trivial relation between the latter approach and the theory based primarily on autocatalysis and lateral inhibition.
Validity of physical laws for any aspect of brain activity and strict correlation of mental to physical states of the brain do not imply, with logical necessity, that a complete algorithmic theory of the mind-body relation is possible. A limit of decodability may be imposed by the finite number of possible analytical operations which is rooted in the finiteness of the world. It is considered as a fundamental intrinsic limitation of the scientific approach comparable to quantum indeterminacy and the theorems of logical undecidability. An analysis of these limits, applied to dispositions of future behaviour, suggests that limits of decodability of the psycho-physic relation may actually exist with respect to brain states with self-referential aspects, as they are involved in mental processes. Limits for an algorithmic theory of the mind-body problem suggested by this study are formally similar to other intrinsic limits of the scientific method such as quantum indeterminacy and mathematical undecidability which are also related to self-referential operations. At the metatheoretical level, hard sciences, despite their reliability, universality and objectivity, depend on metatheoretical presuppositions which allow for multiple philosophical interpretations.
Aside from the increasing, impressive evidence on chemical identification of graded molecules involved, it is the capability of axons for approaching the target position from different aspects in a two-dimensional field which is per se a strong indication for the involvement of gradients. Targeting requires, in the target field, counter-graded effects, either by antagonistic gradients, or by a single gradient in each dimension exerting attractive effects at low, reverting to inhibitory (repulsive) effects at high concentrations. A further requirement for mapping is the modulation of the counter-graded effects by components of the growth cone itself which depends on the origin of the corresponding axon.Transduction and processing of graded signals in the navigating growth cones are proposed to be strongly enhanced by intra-growth-cone pattern formation. The concept also encompasses regulatory and branching processes including the formation of the terminal arbors.
Modern science, based on the laws of physics, claims validity for all events in space and time. However, it also reveals its own limitations, such as the indeterminacy of quantum physics, the limits of decidability, and, presumably, limits of decodability of the mind-brain relationship. At the philosophical level, these intrinsic limitations allow for different interpretations of the relation between human cognition and the natural order. In particular, modern science may be logically consistent with religious as well as agnostic views of humans and the universe. These points are exemplified through the transcript of a discussion between Kurt Gödel and Rudolf Carnap that took place in 1940. Gödel, discoverer of mathematical undecidability, took a proreligious view; Carnap, one of the founders of analytical philosophy, an antireligious view. By the time of the discussion, Carnap had liberalized his ideas on theoretical concepts of science: he believed that observational terms do not suffice for an exhaustive definition of theoretical concepts. Then, responded Gödel, one should formulate a theory or metatheory that is consistent with scientific rationality, yet also encompasses theology. Carnap considered such theories unproductive. The controversy remained unresolved, but its emphasis shifted from rationality to wisdom, not only in the Gödel-Carnap discussion but also in our time.
The development of modern science has depended strongly on specific features of the cultures involved; however, its results are widely and transculturally accepted and applied. The science and technology of electricity, for example, emerged as a specific product of post-Renaissance Europe, rooted in the Greek philosophical tradition that encourages explanations of nature in theoretical terms. It did not evolve in China presumably because such encouragement was missing. The transcultural acceptance of modern science and technology is postulated to be due, in part, to the common biological dispositions underlying human cognition, with generalizable capabilities of abstract, symbolic and strategic thought. These faculties of the human mind are main prerequisites for dynamic cultural development and differentiation. They appear to have evolved up to a stage of hunters and gatherers perhaps some 100 000 years ago. However, the extent of the correspondence between some constructions of the human mind and the order of nature, as revealed by science, is a late insight of the last two centuries. Unless we subscribe to extreme forms of constructivism or historical relativism, we may take the success and the formal structure of science as indications of a close, intrinsic relation between the physical and the mental, between the order of nature and the structure of human cognition. At the metatheoretical level, however, modern science is consistent with philosophical and cultural diversity.
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.