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
Kallima butterflies are famous for their leaf-mimicking wing patterns.Yet the characterization of Kallima species is still under debate owing to their high phenotypic similarity.With the release of the K.inachus refer...Kallima butterflies are famous for their leaf-mimicking wing patterns.Yet the characterization of Kallima species is still under debate owing to their high phenotypic similarity.With the release of the K.inachus reference genome,phylogenetic studies based on genome-wide data have been carried out,thus improving the understanding of the evolutionary relationships of the genus Kallima.However,we noticed that there is some conflict between genome-based phylogenies and morphological classifications in butterflies.We further examined the cause of this conflict by conducting an in-depth study of the relationships among Kallima butterflies to test possible reticulate phylogenetic topologies.We constructed phylogenies based on various datasets(including SNPs in single-copy genes,coding sequences,neutral regions and all remaining sites across the genome)to compare the topologies,revealing the complex evolutionary history of Kallima butterflies.Our results suggest that the reticulate species topology may constitute a pervasive pattern present not only in species with adaptive radiations but also in gradually evolving species,with Kallima butterflies as an example.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.
基金supported by grants from the National Natural Science Foundation of China(32325009,32170420)the Peking-Tsinghua Center for Life Sciences,and the State Key Laboratory of Protein and Plant Gene Research to WZ and grants from the China Postdoctoral Science Foundation(2023M730082,BX20230026)to SW.
文摘Kallima butterflies are famous for their leaf-mimicking wing patterns.Yet the characterization of Kallima species is still under debate owing to their high phenotypic similarity.With the release of the K.inachus reference genome,phylogenetic studies based on genome-wide data have been carried out,thus improving the understanding of the evolutionary relationships of the genus Kallima.However,we noticed that there is some conflict between genome-based phylogenies and morphological classifications in butterflies.We further examined the cause of this conflict by conducting an in-depth study of the relationships among Kallima butterflies to test possible reticulate phylogenetic topologies.We constructed phylogenies based on various datasets(including SNPs in single-copy genes,coding sequences,neutral regions and all remaining sites across the genome)to compare the topologies,revealing the complex evolutionary history of Kallima butterflies.Our results suggest that the reticulate species topology may constitute a pervasive pattern present not only in species with adaptive radiations but also in gradually evolving species,with Kallima butterflies as an example.
