Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing

We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $\delta_e$ and the leptonic Wolfenstein parameters $\lambda_e$, $A_e$, $\rho_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the leptonic Wolfenstein parameters. It is found that the phase $\delta_e$ is strongly constrained and only a large or nearly maximal leptonic CP-violating phase $|\delta_e| \simeq 3\pi/4 \sim \pi/2$ is favorable when $\lambda_e > 0.15$. In particular, when taking $\lambda_e$ to be the Cabbibo angle \gl_e\simeq \lambda \simeq 0.225, a sensible result for leptonic Wolfenstein parameters and CP violation is obtained with $A_e=1.40$, $\rho_e=0.20$, \delta_{e}\sim 101.76\;^o, which is compatible with the one in quark sector. An interesting correlation between leptons and quarks is observed, which indicates a possible common origin of masses and mixing for the charged-leptons and quarks.Comment: 18 pages, 5 figures, sources of CP-violating phases are clarified, references adde

E-Courant algebroids

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by $E$-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact $E$-Courant algebroids. In addition, we introduce the concepts of $E$-Lie bialgebroids and Manin triples.Comment: 29 pages, no figur

Dirac structures of omni-Lie algebroids

Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid \dev E\oplus \jet E is necessarily a Lie algebroid together with a representation on $E$. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in \huaT=TM\oplus E; we establish the relation between the normalizer $N_{L}$ of a reducible Dirac structure $L$ and the derivation algebra \Der(\pomnib (L)) of the projective Lie algebroid \pomnib (L); we study the cohomology group $\mathrm{H}^\bullet(L,\rho_{L})$ and the relation between $N_{L}$ and $\mathrm{H}^1(L,\rho_{L})$; we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure $L$, which is related with $\mathrm{H}^2(L,\rho_{L})$.Comment: 23 pages, no figure, to appear in International Journal of Mathematic

Scheme for deterministic Bell-state-measurement-free quantum teleportation

A deterministic teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement is not needed in the teleportation process, and the success probability can reach 1.0. In addition, the current scheme is insensitive to the cavity decay and thermal field.Comment: 3 pages, no figur

Development of Large-Scale Unstructured Grid Storm Surge and Sub-Grid Inundation Models for Coastal Applications

Storm surge and inundation induced by hurricanes and nor\u27easters pose a profound threat to coastal communities and ecosystems. These storm events with powerful winds, heavy precipitation, and strong wind waves can lead to major flooding for cities along U.S. Coasts. Recent examples of Hurricane Irene (2011) in North Carolina and Virginia and Hurricane Sandy (2012) in New York City not only demonstrated the immense destructive power by the storms, but also revealed the obvious, crucial need for improved forecasting of storm tide and inundation. in part I, a large-scale unstructured-grid 3-D barotropic storm tide model SCHISM (Semi-implicit Cross-scale Hydroscience Integrated System Model) is developed with open ocean boundary aligning along the 60-degree West longitude to catch most Atlantic hurricanes that may make landfall along U.S. East and Gulf Coasts. The model, driven by high-resolution NAM (North America Mesoscale) and ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric fields, was coupled with Wind Wave Model (WWMIII) to account for wave effects, and used to simulate storm surge in 3-D barotropic mode rather than the traditional 2-D vertical average mode. For Hurricane Sandy, the fully coupled wave-current interaction 3-D model using ECMWF atmospheric forcing performs the best. The storm tide results match well with observation at all nine NOAA tidal gauges along the East Coast. The maximum total water level in New York City, is accurately simulated with absolute error of amplitude less than 8 cm, and timing difference within 10 minutes. The scenarios of 2-D versus 3-D and with versus without wind wave model were compared and discussed in details. Overall, the wave contribution amounts to 5-10% of surge elevation during the event. Also, the large-scale model with similar setup is applied to hindcasting storm tide during Hurricane Irene and the results are excellent when compared with observed water level along Southeast Coast and inside Chesapeake Bay. in part II, a high-resolution sub-grid inundation model ELCIRC-sub (Eulerian-Lagrangian CIRCulation) was developed from the original finite-volume-based ELCIRC model. It utilized the sub-grid method for imbedding high-resolution topography/bathymetry data into the traditional model grid and delivering the inundation simulation on the street level scale. The ELCIRC-sub contains an efficient non-linear solver to increase the accuracy and was executed in the MPI (Message Passing Interface) parallel computing platform to vastly enlarge the water shed coverage, and to expand the numbers of sub-grids allowed. The ELCIRC-sub is first validated with a wetting/drying analytic solution and then applied in New York City for Hurricane Sandy (2012). Temporal comparisons with NOAA and USGS water level gauges showed excellent performance with an average error on the order of 10 cm. It accurately captured the highest surge (during Hurricane Sandy) at Kings Point on both maximum surge height and the explosive surge profile. Spatial comparisons of the modeled peak water level at 80 locations around New York City showed an average error less than 13 cm. The modeled maximum modeled inundation extent also matched well with 80% of the FEMA flooding map. in terms of robustness and efficiency for practical application, ELCIRC-sub surpasses the prototype model UnTRIM2