Adaptive Finite Element Approximations for Kohn-Sham Models

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.Comment: 38pages, 7figure

Convergence of the Planewave Approximations for Quantum Incommensurate Systems

Incommensurate structures come from stacking the single layers of low-dimensional materials on top of one another with misalignment such as a twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. This paper studies the spectrum distribution of incommensurate Schr\"{o}dinger operators. We characterize the density of states for the incommensurate system and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; and (ii) propose efficient numerical schemes to evaluate the density of states based on planewave approximations and reciprocal space sampling. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms.Comment: 29 page

Molecular characterization of vernalization and response genes in bread wheat from the Yellow and Huai Valley of China

BACKGROUND: Flowering time greatly influences the adaptation of wheat cultivars to diverse environmental conditions and is mainly controlled by vernalization and photoperiod genes. In wheat cultivars from the Yellow and Huai Valleys, which represent 60%-70% of the total wheat production in China, the large-scale genotyping of wheat germplasms has not yet been performed in terms of vernalization and photoperiod response alleles, limiting the use of Chinese wheat germplasms to a certain extent. RESULTS: In this study, 173 winter wheat cultivars and 51 spring wheat cultivars from China were used to identify allelic variations of vernalization and photoperiod genes as well as copy number variations of Ppd-B1 and Vrn-A1. Two new co-dominant markers were developed in order to more precisely examine Vrn-A1b, Vrn-B1a, and Vrn-B1b. Two novel alleles at the Vrn-B3 locus were discovered and were designated Vrn-B3b and Vrn-B3c. Vrn-B3b had an 890-bp insertion in the promoter region of the recessive vrn-B3 allele, and Vrn-B3c allele had 2 deletions (a 20-bp deletion and a 4-bp deletion) in the promoter region of the dominant Vrn-B3a allele. Cultivar Hemai 26 lacked the Vrn-A1 gene. RT-PCR indicated that the 890-bp insertion in the Vrn-B3b allele significantly reduced the transcription of the Vrn-B3 gene. Cultivars Chadianhong with the Vrn-B3b allele and Hemai 26 with a Vrn-A1-null allele possessed relatively later heading and flowering times compared to those of Yanzhan 4110, which harbored recessive vrn-B3 and vrn-A1 alleles. Through identification of photoperiod genes, 2 new polymorphism combinations were found in 6 winter wheat cultivars and were designated Hapl-VII and Hapl-VIII, respectively. Distribution of the vernalization and photoperiod genes indicated that all recessive alleles at the 4 vernalization response loci, truncated “Chinese Spring” Ppd-B1 allele at Ppd-B1 locus and Hapl-I at the Ppd-D1 locus were predominant in Chinese winter wheat cultivars. CONCLUSION: This study illustrated the distribution of vernalization and photoperiod genes and identified 2 new Vrn-B3 alleles, 1 Vrn-A1-null allele, and two new Ppd-D1 polymorphism combinations, using developed functional markers. Results of this study have the potential to provide useful information for screening relatively superior wheat cultivars for better adaptability and maturity

Electroacupuncture activates corticotrophin-releasing hormone-containing neurons in the paraventricular nucleus of the hypothalammus to alleviate edema in a rat model of inflammation

<p>Abstract</p> <p>Background</p> <p>Studies show that electroacupuncture (EA) has beneficial effects in patients with inflammatory diseases. This study investigated the mechanisms of EA anti-inflammation, using a rat model of complete Freund's adjuvant (CFA)-induced hind paw inflammation and hyperalgesia.</p> <p>Design</p> <p>Four experiments were conducted on male Sprague-Dawley rats (n = 6–7/per group). Inflammation was induced by injecting CFA into the plantar surface of one hind paw. Experiment 1 examined whether EA increases plasma adrenocorticotropic hormone (ACTH) levels. Experiments 2 and 3 studied the effects of the ACTH and corticotropin-releasing hormone (CRH) receptor antagonists, ACTH_(11–24)and astressin, on the EA anti-edema. Experiment 4 determined whether EA activates CRH neurons in the paraventricular nucleus of the hypothalammus. EA treatment, 10 Hz at 3 mA and 0.1 ms pulse width, was given twice for 20 min each, once immediately post and again 2 hr post-CFA. Plasma ACTH levels, paw thickness, and paw withdrawal latency to a noxious thermal stimulus were measured 2 h and 5 h after the CFA.</p> <p>Results</p> <p>EA significantly increased ACTH levels 5 h (2 folds) after CFA compared to sham EA control, but EA alone in naive rats and CFA alone did not induce significant increases in ACTH. ACTH_(11–24)and astressin blocked EA anti-edema but not EA anti-hyperalgesia. EA induced phosphorylation of NR1, an essential subunit of the N-methyl-D-aspartic acid (NMDA) receptor, in CRH-containing neurons of the paraventricular nucleus.</p> <p>Conclusion</p> <p>The data demonstrate that EA activates CRH neurons to significantly increase plasma ACTH levels and suppress edema through CRH and ACTH receptors in a rat model of inflammation.</p