Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page

Solving the Dirac equation with nonlocal potential by Imaginary Time Step method

The Imaginary Time Step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schr\"odinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schr\"odinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus $^{16}$O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained

A key management architecture and protocols for secure smart grid communications

Providing encrypted communications among power grid components is expected to be a basic requirement of smart grid systems in the future. Here, we propose a key management architecture and associated protocols tailored to support encrypted smart grid communications. The architecture consists of two levels structured around the grid control system hierarchy. At the top level, which consist of control centers and regional coordinators, a bottom-up key structure is adopted using hash chaining and a logical key hierarchy. The lower level of the architecture consists of the regional coordinators (i.e., substations and distribution systems) and remote ends (e.g., meters and pole-top sensors) and utilizes a top-down key management approach built on an inverse element method. The proposed key management schema supports the hierarchical structure of the smart grid control mechanisms, and it takes the resource and electronic/physical security differences of the control levels into account. We define a set of protocols utilizing the architecture to provide secure unicast, multicast, and broadcast communications. Furthermore, we illustrate how the architecture is flexible enough to easily handle power grid nodes joining and leaving the system at the different levels. Lastly, we compare the proposed schema with existing ones and show that our architecture can achieve efficient key management to provide secure communications. Copyright © 2016 John Wiley & Sons, Ltd

Edge Shear Flows and Particle Transport near the Density Limit in the HL-2A Tokamak

Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit $n_G$. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as $n_G$ is approached in ohmic L-mode discharges. As the normalized line-averaged density $\bar{n}_e/n_G$ is raised, the shearing rate of the mean poloidal flow $\omega_{\rm sh}$ drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power $\mathcal{P}_{Re}$) collapses. Correspondingly, the turbulent particle transport increases drastically with increasing collision rates. The geodesic acoustic modes (GAMs) gain more energy from the ambient turbulence at higher densities, but have smaller shearing rate than low-frequency zonal flows. The increased density also introduces decreased adiabaticity which not only enhances the particle transport but is also related to a reduction in the eddy-tilting and the Reynolds power. Both effects may lead to the cooling of edge plasmas and therefore the onset of MHD instabilities that limit the plasma density

Role of electromagnetic dipole operator in the electroweak penguin dominated vector meson decays of BB meson

The pure annihilation type decays $B^0_d\to\phi\gamma$ and $B_s\to\rho\gamma$ receive only color suppressed penguin contributions with a very small branching ratio in the standard model. When we include the previously neglected electromagnetic dipole operator, the branching ratios can be enhanced one order magnitude larger than previous study using QCD factorization approach. That is ${\cal BR}(\bar B^0_d\to\phi\gamma)\simeq 1 \times 10^{-11}$ and ${\cal BR}(B_s\to\rho\gamma) \sim (6-16)\times 10^{-10}$. The new effect can also give a large contribution, of order $10^{-9}$, to transverse polarization of $B\to\phi\rho$ and $B\to \omega\phi$ which is comparable to the longitudinal part. These effects can be detected in the LHCb experiment and the Super-B factories.Comment: Revised extensively. 8 pages, 4 figure

The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

Reconstruction of 2D Al Ti on TiB in an aluminium melt

It has been widely considered that Al Ti is involved in the aluminium nucleation on TiB , although the mechanism has not been fully understood. In this paper molecular dynamics has been conducted to investigate this phenomenon at an atomistic scale. It was found that a two-dimensional Al Ti layer may remain on TiB above the aluminium liquidus. In addition, the results showed that this 2D Al Ti undergoes interface reconstruction by forming a triangular pattern. This triangular pattern consists of different alternative stacking sequences. The transition region between the triangles forms an area of strain concentration. By means of this mechanism, this interfacial Al Ti layer stabilizes itself by localizing the large misfit strain between TiB and Al Ti This reconstruction is similar to the hdp-fcc interface reconstruction in other systems which has been observed experimentally.EPSR