Meissner States of Type II Superconductors

This paper concerns mathematical theory of Meissner states of a bulk superconductor of type $I\!I$, which occupies a bounded domain $\Omega$ in $\Bbb R^3$ and is subjected to an applied magnetic field below the critical field $H_{S}$. A Meissner state is described by a solution $(f,\mathbf A)$ of a nonlinear partial differential system called Meissner system, where $f$ is a positive function on $\Omega$ which is equal to the modulus of the order parameter, and $\mathbf A$ is the magnetic potential defined on the entire space such that the inner trace of the normal component on the domain boundary $\partial\Omega$ vanishes. Such a solution is called a Meissner solution. Various properties of the Meissner solutions are examined, including regularity, classification and asymptotic behavior for large value of the Ginzburg-Landau parameter $\kappa$. It is shown that the Meissner solution is smooth in $\Omega$, however the regularity of the magnetic potential outside $\Omega$ can be rather poor. This observation leads to the ides of decomposition of the Meissner system into two problems, a boundary value problem in $\Omega$ and an exterior problem outside of $\Omega$. We show that the solutions of the boundary value problem with fixed boundary data converges uniformly on $\Omega$ as $\kappa$ tends to $\infty$, where the limit field of the magnetic potential is a solution of a nonlinear curl system. This indicates that, the magnetic potential part $\mathbf A$ of the solution $(f,\mathbf A)$ of the Meissner system, which has same tangential component of $curl \mathbf A$ on $\partial\Omega$, converges to a solution of the curl system as $\kappa$ increases to infinity, which verifies that the curl system is indeed the correct limit of the Meissner system in the case of three dimensions.Comment: Published in: J. Elliptic and Parabolic Equations, {\bf 4} (2) (2018), 441-523. https://link.springer.com/article/10.1007/s41808-018-0027-0 Springer Nature Sharedit initiative link https://rdcu.be/bbM8

The order analysis for the two loop corrections to lepton MDM

The experimental data of the magnetic dipole moment(MDM) of lepton($e$, $\mu$) is very exact. The deviation between the experimental data and the standard model prediction maybe come from new physics contribution. In the supersymmetric models, there are very many two loop diagrams contributing to the lepton MDM. In supersymmetric models, we suppose two mass scales $M_{SH}$ and $M$ with $M_{SH}\gg M$ for supersymmetric particles. Squarks belong to $M_{SH}$ and the other supersymmetric particles belong to $M$. We analyze the order of the contributions from the two loop diagrams. The two loop triangle diagrams corresponding to the two loop self-energy diagram satisfy Ward-identity, and their contributions possess particular factors. This work can help to distinguish the important two loop diagrams giving corrections to lepton MDM.Comment: 12 pages, 3 figure

The naturalness in the BLMSSM and B-LSSM

In order to interpret the Higgs mass and its decays more naturally, we hope to intrude the BLMSSM and B-LSSM. In the both models, the right-handed neutrino superfields are introduced to better explain the neutrino mass problems. In addition, there are other superfields considered to make these models more natural than MSSM. In this paper, the method of $\chi^2$ analyses will be adopted in the BLMSSM and B-LSSM to calculate the Higgs mass, Higgs decays and muon $g-2$. With the fine-tuning in the region $0.67\%-2.5\%$ and $0.67\%-5\%$, we can obtain the reasonable theoretical values that are in accordance with the experimental results respectively in the BLMSSM and B-LSSM. Meanwhile, the best-fitted benchmark points in the BLMSSM and B-LSSM will be acquired at minimal $(\chi^{BL}_{min})^2 = 2.34736$ and $(\chi^{B-L}_{min})^2 = 2.47754$, respectively

Transient dynamics of molecular devices under step-like pulse bias

We report first principles investigation of time-dependent current of molecular devices under a step-like pulse.Our results show that although the switch-on time of the molecular device is comparable to the transit time, much longer time is needed to reach the steady state. In reaching the steady state the current is dominated by resonant states below Fermi level. The contribution of each resonant state to the current shows the damped oscillatory behavior with frequency equal to the bias of the step-like pulse and decay rate determined by the life time of the corresponding resonant state. We found that all the resonant states below Fermi level have to be included for accurate results. This indicates that going beyond wideband limit is essential for a quantitative analysis of transient dynamics of molecular devices

26Al/10Be Age of Peking Man

The chronological position of Peking Man, or Homo erectus pekinensis, has long been pursued, but has remained problematic due to lack of a suitable dating method^1-7^. Here we report cosmogenic ^26^Al/ ^10^Be burial dating of quartz sediments and artifacts from the lower strata of Zhoukoudian Locality 1 where the remains of early members of the Peking Man family were discovered. This study marks the first radioisotopic dating of any early hominin site in China beyond the range of mass spectrometric U-series dating. The weighted mean of six meaningful measurements, 0.75 +/-; 0.09 (0.11) Ma (million years), provides the best age estimate for lower cultural Layers ^7-10^. Together with previously reported U-series^3^ and paleomagnetic^4^ data, as well as sedimentological considerations^8, 9^ these layers may be further correlated to S6-S7 in Chinese loess stratigraphy or marine isotope stages 17-18, in the range of ~0.68-0.75 Ma. These ages are substantially older than previously supposed and may imply hominin presence in northern China throughout early Middle Pleistocene climate cycles

Covariance, correlation matrix and the multi-scale community structure of networks

Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this article, we consider detecting the multi-scale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multi-scale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multi-scale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix, we further conclude that the rescaling transformation is crucial to identify the multi-scale community structure of network, as well as the translation and rotation transformations.Comment: 10 pages, 7 figure