11 research outputs found

    Hierarchical Stability and Chaotic Motion of Gravitational Few-Body Systems

    Get PDF
    In this thesis the hierarchical stability and chaotic motion of the classical few body system are studied, and then extended into the framework of the relativistic theory of gravitation. Because of the importance of integrability to both hierarchical stability and Hamiltonian chaos, a general discussion is also given on integrals and symmetries using the modern language of differential geometry. The study of this thesis is closely related to the stability problem of our Solar System and the mass transfer process of compact binary star systems. The approach carried out is both computational and theoretical. The computational part is a systematical investigation of the hierarchical stability (no drastic change in orbital elements or of the hierarchy) of the general 3-body problem, in comparison with the Hill-type stability. The importance of eccentricity in relation to stability is manifest, and the complexity of the phase space structure and fractal nature of the boundary between regular and chaotic regions are reflected in this study. The theoretical work is a continuation of the investigations of the effects of integrals on possible motions. Using a canonical transformation method, a stronger inequality is found for the spatial 3-body problem, giving better estimation of the Hill-type stability regions. It is proved that a Hill-type stability guarantees one of the three hierarchical stability conditions. This classical study is then developed into an inequality method establishing restrictions of symmetries (integrals) on possible motions. The method is first applied to gravitational systems in general relativity and their post-Newtonian approximations. The thesis is split into part I, a general introduction and discussion of the relevant methods, and part II, the original research and main body of the thesis. In chapter 1 a general introduction to the problem of the Solar System's stability is given, with an emphasis on Roy's hierarchical stability and the divergence problem of classical perturbation theory due to chaos. Chapter 2 is a review of the theory of Hamiltonian chaos, presented at a level of comprehending chaos mathematically. The importance of number theory, infinite series and integrability to chaos is emphasised. The geometrical method of studying nonlinear dynamical systems is introduced; classical perturbation theory is used to comprehend the KAM theorem. Particular attention is paid to coordinate-free interpretation of the integrability and separability conditions. In this chapter, a collection of integrable and chaotic systems is given because of their conceptual value to later chapters. Based on the Toda and Henon-Heiles Hamiltonian systems, a discussion is given on the general relationship of a system to its truncated system. This suggests a similar situation for the geodesic motion in Kerr geometry. Chapter 3 is the last chapter of part I on chaos. In this chapter we study the history of chaotic dynamics and its impact on science in general. Although it is standard to study quantization of regular and chaotic motions, the present author pays particular attention to a philosophical compatibility between the theory of chaotic attractors and quanium mechanics. Noting that the two revolutionary theories were born at almost the same time, and that Poincare was a contributor to both theories, the present author carries out a historical search for a possible mutual influence in the development of the theories. However, it is found that such a connection is surprisingly tenuous. The original work is included in part II. The classical 3-body problem is studied in chapters 4 and 5; and the relativistic few-body problem is studied in chapters 6 and 7. In chapter 4, we first review the previous approaches on the Hill-type stability of the general 3-body problem. It is found that all results of previous studies are equivalent and do not go beyond a direct use of Sundman's inequality. Zare's (1976) canonical transformation study on the coplanar 3-body problem is modified and applied to the spatial problem, thus obtaining inequalities stronger than Sundman's. These inequalities determine the best possible Hill-type stability regions for the general 3-body problem, although the critical configurations and the value of (C2H)c cannot be improved. In this approach, it is found that the moment of inertia ellipse of the system may be used to simplify the calculation. Because of this, it is hoped that the same stronger inequalities may also apply to systems with more than three bodies. (Abstract shortened by ProQuest.)

    Annals of the History and Philosophy of Biology 24/2019

    Get PDF
    The name DGGTB (Deutsche Gesellschaft für Geschichte und Theorie der Biologie; German Society for the History and Philosophy of Biology) reflects recent history as well as German tradition. The Society is a relatively late addition to a series of German societies of science and medicine that began with the “Deutsche Gesellschaft für Geschichte der Medizin und der Naturwissenschaften”, founded in 1910 by Leipzig University’s Karl Sudhoff (1853-1938), who wrote: “We want to establish a ‘German’ society in order to gather German-speaking historians together in our special disciplines so that they form the core of an international society…”. Yet Sudhoff, at this time of burgeoning academic internationalism, was “quite willing” to accommodate the wishes of a number of founding members and “drop the word German in the title of the Society and have it merge with an international society”. The founding and naming of the Society at that time derived from a specifi c set of historical circumstances, and the same was true some 80 years later when in 1991, in the wake of German reunification, the “Deutsche Gesellschaft für Geschichte und Theorie der Biologie” was founded. From the start, the Society has been committed to bringing studies in the history and philosophy of biology to a wide audience, using for this purpose its Jahrbuch für Geschichte und Theorie der Biologie. Parallel to the Jahrbuch, the Verhandlungen zur Geschichte und Theorie der Biologie has become the by now traditional medium for the publication of papers delivered at the Society’s annual meetings. In 2005 the Jahrbuch was renamed Annals of the History and Philosophy of Biology, reflecting the Society’s internationalist aspirations in addressing comparative biology as a subject of historical and philosophical studies

    Recent Soviet development debates : the 'third world' and the USSR

    No full text
    This thesis investigates three layers of Soviet debate since the mid 1960s about problems of development. A protracted debate about the importance of 'socialist orientation' in the third world is considered principally as a dispute between conservative officials and liberal critics about the significance for Soviet foreign policy of dependent allies in a global struggle with imperialism. A parallel debate about the prospects for a capitalist transformation of the third world is evaluated mainly as the first phase of a substantial discussion amongst leading scholars searching for an adequate theory of the developing world. A subterranean debate about the nature of modem Soviet society is presented as an example of the profound criticism of Brezhnev's regime which some leading scholars were able to make in print during the 'years of stagnation'. These empirical interpretations are based on two theoretical arguments, which establish the main historical contexts of Soviet development debates and the position of an outside reader as someone necessarily concerned with the same questions as the participants in the debates. The thesis demonstrates the intellectual achievements of a group of committed Soviet scholars, whose thought was not constrained by a dogmatic system of censorship. By showing the openness of Soviet discussions to a foreign interpreter, it questions the view that 'Marxism-Leninism' has constituted the language of recent development debates in the USSR

    A Republican Settlement Theory of the Firm: Applied to Retail Banks in England and the Netherlands (1830-2007)

    Get PDF
    The ability to take a leading role in democratic settlements largely shapes a firm’s long term success. A key requirement to occupying such a leading role is the creation of a platform for the execution of democratic principles by customers, shareholders, societal stakeholders, and political actors: the impossibility to dominate others, and the possibility of rivalry and dissent. After careful analysis of the strategies followed by Dutch and English banks, I conclude that building such a platform implies the development of six strategic abilities. Internationally, firms’ ability to take a leading role is enabled and constrained by their affiliation with (a) particular nation-state(s); in particular the geopolitical perception of a nation-state’s capacity to express the ideal of popular sovereignty and the right to self-determination. Drawing on an historical analysis of the strategies followed by the Netherlands and England since early modern times, the US and the EU (including the West-German Republic) since WWII, I clarify how nation-state leaders should go about in securing an advantageous geopolitical perception; and in maximising the possibilities of self-determination and success for affiliated firms

    ECOS 2012

    Get PDF
    The 8-volume set contains the Proceedings of the 25th ECOS 2012 International Conference, Perugia, Italy, June 26th to June 29th, 2012. ECOS is an acronym for Efficiency, Cost, Optimization and Simulation (of energy conversion systems and processes), summarizing the topics covered in ECOS: Thermodynamics, Heat and Mass Transfer, Exergy and Second Law Analysis, Process Integration and Heat Exchanger Networks, Fluid Dynamics and Power Plant Components, Fuel Cells, Simulation of Energy Conversion Systems, Renewable Energies, Thermo-Economic Analysis and Optimisation, Combustion, Chemical Reactors, Carbon Capture and Sequestration, Building/Urban/Complex Energy Systems, Water Desalination and Use of Water Resources, Energy Systems- Environmental and Sustainability Issues, System Operation/ Control/Diagnosis and Prognosis, Industrial Ecology

    Electronic Journal of Qualitative Theory of Differential Equations 2022

    Get PDF

    Being Modern: The Cultural Impact of Science in the Early Twentieth Century

    Get PDF
    In the early decades of the twentieth century, engagement with science was commonly used as an emblem of modernity. This phenomenon is now attracting increasing attention in different historical specialties. Being Modern builds on this recent scholarly interest to explore engagement with science across culture from the end of the nineteenth century to approximately 1940. Addressing the breadth of cultural forms in Britain and the western world from the architecture of Le Corbusier to working class British science fiction, Being Modern paints a rich picture. Seventeen distinguished contributors from a range of fields including the cultural study of science and technology, art and architecture, English culture and literature examine the issues involved. The book will be a valuable resource for students, and a spur to scholars to further examination of culture as an interconnected web of which science is a critical part, and to supersede such tired formulations as 'Science and culture'
    corecore