We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through s...We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through solving these difference equations, we obtain the eigenvalues, linked to the coherence length, as a function of magnetic field. The diagram of eigenvalues shows a fractal structure, being so-called Hofstadter＇s butterfly. We also calculate and discuss the dependence of the transition temperature of the checkerboard superconducting wire network on the applied magnetic field, which is related to up-edge of the Hofstadter＇s butterfly spectrum.展开更多
Kuhn＇s incommensurability-thesis is crucial for consequences for the pursuit of epistemology. A interpreting his views on the development of science and their commemoration of the 50th anniversary of the publication ...Kuhn＇s incommensurability-thesis is crucial for consequences for the pursuit of epistemology. A interpreting his views on the development of science and their commemoration of the 50th anniversary of the publication of the original version of Kuhn＇s epoch-making book The Structure of Scientific Revolutions （henceforth： SSR） should thus provide a thorough reflection on this thesis. However, this thesis is not easy to interpret. It is not only complex in itself but has also undergone a historical development--in Kuhn＇s own hands and in those of his interpreters. In this article, I sort out the different interpretations of it, in particular, in Part A. In Part B, I demonstrate their epistemological consequences. Under closer scrutiny, Kuhn＇s incommensurability-thesis contains several sub-theses Different senses of ＂incommensurability＂ thus need to be distinguished. However, the way in which those distinctions are drawn in Kuhn-scholarship differs. In paragraph I of Part A, I provide an overview of the reception of the incommensurability-thesis in Kuhn-scholarship. In Paragraph II, I trace its development in Kuhn＇s later writings： given its importance and contested nature, Kuhn later clarifies his original thesis. Those later clarifications＇ main function consists in domesticating the most radically relativistic aspects his original incommensurability-thesis had, at least, in the eyes of his interpreters. The upshot of Part A （Paragraphs I and II） is to provide a coherent interpretation of Kuhn＇s incommensurability-thesis. To that end, I distinguish in line with much of Kuhn-scholarship a semantic from a methodological sense of incommensurability. In part B, the question is raised： What sort of epistemological consequences follow from both senses of incommensurability？ In particular, what consequences follow for the issues of reference, subjectivity （objectivity）, pluralism, and realism？ The underlying question is to what extent Kuhnian incommensurability caters to a relativistic understanding of those issues. This question is answered in Paragraph Ill with the help of the analyses of a currently leading Kuhn-scholar, C. H. Sankey. His answers are taken as a vantage point for my concluding evaluation of the consequences of Kuhnian incommensurability in Paragraph IV.展开更多
基金Supported by the Teaching and Research Foundation for the Outstanding Young Faculty of Southeast University
文摘We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through solving these difference equations, we obtain the eigenvalues, linked to the coherence length, as a function of magnetic field. The diagram of eigenvalues shows a fractal structure, being so-called Hofstadter＇s butterfly. We also calculate and discuss the dependence of the transition temperature of the checkerboard superconducting wire network on the applied magnetic field, which is related to up-edge of the Hofstadter＇s butterfly spectrum.
文摘Kuhn＇s incommensurability-thesis is crucial for consequences for the pursuit of epistemology. A interpreting his views on the development of science and their commemoration of the 50th anniversary of the publication of the original version of Kuhn＇s epoch-making book The Structure of Scientific Revolutions （henceforth： SSR） should thus provide a thorough reflection on this thesis. However, this thesis is not easy to interpret. It is not only complex in itself but has also undergone a historical development--in Kuhn＇s own hands and in those of his interpreters. In this article, I sort out the different interpretations of it, in particular, in Part A. In Part B, I demonstrate their epistemological consequences. Under closer scrutiny, Kuhn＇s incommensurability-thesis contains several sub-theses Different senses of ＂incommensurability＂ thus need to be distinguished. However, the way in which those distinctions are drawn in Kuhn-scholarship differs. In paragraph I of Part A, I provide an overview of the reception of the incommensurability-thesis in Kuhn-scholarship. In Paragraph II, I trace its development in Kuhn＇s later writings： given its importance and contested nature, Kuhn later clarifies his original thesis. Those later clarifications＇ main function consists in domesticating the most radically relativistic aspects his original incommensurability-thesis had, at least, in the eyes of his interpreters. The upshot of Part A （Paragraphs I and II） is to provide a coherent interpretation of Kuhn＇s incommensurability-thesis. To that end, I distinguish in line with much of Kuhn-scholarship a semantic from a methodological sense of incommensurability. In part B, the question is raised： What sort of epistemological consequences follow from both senses of incommensurability？ In particular, what consequences follow for the issues of reference, subjectivity （objectivity）, pluralism, and realism？ The underlying question is to what extent Kuhnian incommensurability caters to a relativistic understanding of those issues. This question is answered in Paragraph Ill with the help of the analyses of a currently leading Kuhn-scholar, C. H. Sankey. His answers are taken as a vantage point for my concluding evaluation of the consequences of Kuhnian incommensurability in Paragraph IV.
