On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials

The works of V. A. Vinokurov have shown that eigenvalues and normalized eigenfunctions of Sturm-Liouville problems are analytic in potentials, considered as mappings from the Lebesgue space to the space of real numbers and the Banach space of continuous functions respectively. Moreover, the first-order Frechet derivatives are known and paly an important role in many problems. In this paper, we will find the second-order Frechet derivatives of eigenvalues in potentials, which are also proved to be negative definite quadratic forms for some cases.Comment: 10 page

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents $b_{1}=\nu/(1+\nu z)$ and $b_{2}=1/(1+\nu z)$, which give the static correlation-length critical exponent $\nu$ and the dynamic critical exponent $z$. Our approach provides an efficient way to simultaneous determination of the critical exponents $\nu$ and $z$ for a continuous phase transition.Comment: 6 pages, 4 figures, accepted for publication in EPL (Europhysics Letters

Nitrogen deprivation-induced de novo transcriptomic profiling of the oleaginous green alga Botryococcus braunii 779

AbstractTo assess the effect of nitrogen deprivation (ND), a moderately growing A-race Botryococcus braunii subisolate 779 was subjected to nitrogen deprivation for 3days. De novo transcriptome was assembled and annotated by using Trinity software and Basic Local Alignment Search Tools (BLAST), respectively. Comparative analysis indicates that transcriptomes of A-races differ from those of B-races. Furthermore, majority of the homologous ESTs in A-race but not B-race transcriptomes were unknown sequences. Upon ND, level of photosynthetic transcripts, but not photosynthetic efficiency was downregulated. Unlike hydrocarbon contents, ESTs involved in hydrocarbon biosynthesis were not upregulated. Taken together, our results imply that A- and B-races belong to different B. braunii subspecies. Upon ND, excess photosynthetic transcripts are recycled for nitrogen; and hydrocarbon accumulation is not via de novo biosynthesis. Here we describe in details the data contents and analytic methodologies associated with the data uploaded to Gene Expression Omnibus (accession number GSE71296)