Holographic entanglement entropy in two-order insulator/superconductor transitions

We study holographic superconductor model with two scalar fields coupled to one single Maxwell field in the AdS soliton background away from the probe limit. We disclose properties of phase transitions mostly from the holographic topological entanglement entropy approach. With different sets of parameters, we observe various types of transitions, especially a new first order phase transition between the condensation of different order parameters in the insulator/superconductor system. Our results show that the entanglement entropy is a good probe to critical phase transition points and the order of phase transitions in the two-order model. We also conclude that the entanglement entropy is useful to some extent in determining the physically supported phases. In addition, we investigate properties of the condensation through the scalar operator and the charge density in the dual theory. As a summary, we draw the complete phase diagram of the effects of the scalar charge on phase transitions. At last, we give some qualitative understanding and obtain the analytical condition for the first order phase transition to occur.Comment: 12 pages, 7 figures. arXiv admin note: text overlap with arXiv:1512.0895

Relating Weight Constraint and Aggregate Programs: Semantics and Representation

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint programs and the answer set semantics based on conditional satisfaction for aggregate programs. Both classes of programs are instances of logic programs with constraints, and in particular, the answer set semantics for aggregate programs can be applied to weight constraint programs. We show that the two semantics are closely related. First, we show that for a broad class of weight constraint programs, called strongly satisfiable programs, the two semantics coincide. When they disagree, a stable model admitted by the stable model semantics may be circularly justified. We show that the gap between the two semantics can be closed by transforming a weight constraint program to a strongly satisfiable one, so that no circular models may be generated under the current implementation of the stable model semantics. We further demonstrate the close relationship between the two semantics by formulating a transformation from weight constraint programs to logic programs with nested expressions which preserves the answer set semantics. Our study on the semantics leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by weight constraint programs. We show that almost all standard aggregates can be encoded by weight constraints compactly. This makes it possible to compute the answer sets of aggregate programs using the ASP solvers for weight constraint programs. This approach is compared experimentally with the ones where aggregates are handled more explicitly, which show that the weight constraint encoding of aggregates enables a competitive approach to answer set computation for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011. 30 page

The microchannel flow of a micropolar fluid

Micro-channel flows have been computed to investigate the influence of Navier-Stokes formulation for the slip-flow boundary condition, and a micro-polar fluid model, respectively. The results of the slip boundary condition show that the current methodology is valid for slip-flow regime (i.e., for values of Knudsen number less than approximately 0.1). Drag reduction phenomena apparent in some micro-channels can be explained by slip-flow theory. These results are in agreement with some computations and experiments. An ad hoc micro-polar fluid model is developed to investigate the influence of micro effects, such as micro-gyration, in micro-scale flows. The foundation of the ad hoc micro-polar fluid is based on Eringen\u27s micro simple fluid, and is simplified for incompressible, two-dimensional, iso-thermal, and micro-isotropic case. Our model contains two material constants, μ and κ, one scale parameter, m × Kn, and one boundary condition parameter n. The number of parameters is significantly reduced from general micro-polar fluid model and makes the theory practical. The scale parameter m × Kn introduces the Knudsen number into the micro-polar fluid dynamics by statistical explanation. Therefore, the effect of rarefaction can be accounted into the model by modeling this parameter. The parameter μ is classical bulk viscosity. The vortex Viscosity κ is related to micro-gyration, and needs modeling at current time. It affects the flow field in two aspects, by modifying the apparent viscosity and by introducing the effect of microgyration. In the simplest case of fully-developed channel flow, the overall effect is equivalent to lessen the Reynolds number by (I + k/ 2). The current micro-polar fluid model explains the drag increase phenomenon in some micro-channel flows from both experimental and computational data. This result is exactly opposite to that predicted by slip-flow theory. The existence of micro-effect needs to be taken into account for the micro-scale flow. A projection method is used as a numerical technique for both models to solve the difficulty of implicit pressure equation, with the help of staggered grids. An explicit Euler scheme is used for solving the steady flow

No long hair behaviors of ultra-compact objects

We investigate distributions of matter fields outside spherically symmetric ultra-compact objects in the asymptotically flat background. Based on the dominant energy condition and the non-negative trace condition, we analytically find a no long hair behavior, which states that the effective radius of matter field hairs cannot extend beyond the outermost null circular orbit.Comment: 7 page

A no-go theorem for scalar fields with couplings from Ginzburg-Landau models

Recently Hod proved a no-go theorem that static scalar fields cannot form spherically symmetric boson stars in the asymptotically flat background. On the other side, scalar fields can be coupled to the gradient according to next-to-leading order Ginzburg-Landau models. In the present work, we extend Hod's discussions by considering couplings between static scalar fields and the field gradient. For a non-negative coupling parameter, we show that there is no asymptotically flat spherically symmetric boson stars made of coupled static scalar fields.Comment: 6 page

Yetter–Drinfel’d Hopf algebras on basic cycle

A class of Yetter–Drinfel’d Hopf algebras on basic cycle is constructed.Побудовано клас хопфових алгебр Єттера-Дрінфельда на базовому циклі

A pathway analysis of genome-wide association study highlights novel type 2 diabetes risk pathways.

Genome-wide association studies (GWAS) have been widely used to identify common type 2 diabetes (T2D) variants. However, the known variants just explain less than 20% of the overall estimated genetic contribution to T2D. Pathway-based methods have been applied into T2D GWAS datasets to investigate the biological mechanisms and reported some novel T2D risk pathways. However, few pathways were shared in these studies. Here, we performed a pathway analysis using the summary results from a large-scale meta-analysis of T2D GWAS to investigate more genetic signals in T2D. Here, we selected PLNK and VEGAS to perform the gene-based test and WebGestalt to perform the pathway-based test. We identified 8 shared KEGG pathways after correction for multiple tests in both methods. We confirm previous findings, and highlight some new T2D risk pathways. We believe that our results may be helpful to study the genetic mechanisms of T2D