Bright-dark mixed NN-soliton solutions of the multi-component Mel'nikov system

By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system comprised of multiple (say $M$) short-wave components and one long-wave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed $N$-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the $M$-component Mel'nikov system to obtain its general mixed $N$-soliton solution. The formula obtained unifies the all-bright, all-dark and bright-dark mixed $N$-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a $M$-component Mel'nikov system with $M \geq 3$, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear at least in two short-wave components. Whereas, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which just accompanied by a position shift.Comment: arXiv admin note: substantial text overlap with arXiv:1706.0549

The B−LB-L Scotogenic Models for Dirac Neutrino Masses

We construct the one-loop and two-loop scotogenic models for Dirac neutrino mass generation in the context of $U(1)_{B-L}$ extensions of standard model. It is indicated that the total number of intermediate fermion singlets is uniquely fixed by anomaly free condition and the new particles may have exotic $B-L$ charges so that the direct SM Yukawa mass term $\bar{\nu}_L\nu_R\overline{\phi^0}$ and the Majorana mass term $(m_N/2)\overline{\nu_R^C}\nu_R$ are naturally forbidden. After the spontaneous breaking of $U(1)_{B-L}$ symmetry, the discrete $Z_{2}$ or $Z_{3}$ symmetry appears as the residual symmetry and give rise to the stability of intermediated fields as DM candidate. Phenomenological aspects of lepton flavor violation, DM, leptogenesis and LHC signatures are discussed.Comment: 18 pages, 16 figure

A New Cokriging Method for Variable-Fidelity Surrogate Modeling of Aerodynamic Data

Cokriging is a statistical interpolation method for the enhanced prediction of a less intensively sampled primary variable of interest with assistance of intensively sampled auxiliary variables. In the geostatistics community it is referred to as two- or multi-variable kriging. In this paper, a new cokriging method is proposed and used for variable-fidelity surrogate modeling of aerodynamic data obtained with an expensive high-fidelity CFD code, assisted by data computed with cheaper lower-fidelity codes or by gradients computed with an adjoint version of the high-fidelity CFD code, or both. A self-contained derivation as well as the numerical implementation of this new cokriging method is presented and the comparison with the autoregressive model of Kennedy and O’Hagan is discussed. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil based on sampled CFD data. The numerical examples show that it is efficient, robust and practical for the surrogate modeling of aerodynamic data based on a set of CFD methods with varying degrees of fidelity and computational expense. It can potentially be applied in the efficient CFD-based aerodynamic analysis and design optimization of aircraft

Superfluid density in the slave-boson theory

Despite of the success of the slave-boson theory in capturing qualitative physics of high-temperature superconductors like cuprates, it fails to reproduce the correct temperature-dependent behavior of superfluid density, let alone the independence of the linear temperature term on doping in the underdoped regimes of hole-doped cuprate, a common experimental observation in different cuprates. It remains puzzling up to now in spite of intensive theoretical efforts. For electron-doped case, even qualitative treatment is not reported at present time. Here we revisit these problems and provide an alternative superfluid density formulation by using the London relation instead of employing the paramagnetic current-current correlation function. The obtained formula, on the one hand, provides the correct temperature-dependent behavior of the superfluid density in the whole temperature regime, on the other hand, makes the doping dependence of the linear temperature term substantially weaken and a possible interpretation for its independence on doping is proposed. As an application, electron-doped cuprate is studied, whose result qualitatively agrees with existing experiments and successfully explains the origin of $d$- to anisotropic $s$-wave transition across the optimal doping. Our result remedies some failures of the slave-boson theory as employed to calculate superfluid density in cuprates and may be useful in the understanding of the related physics in other strongly correlated systems, e.g. Na$_{x}$CoO$_{2}$$\cdot$yH$_{2}$O and certain iron-based superconductors with dominating local magnetic exchange interaction.Comment: 7 pages, 4 figure