On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data

Electromagnetic energy storage and power dissipation in nanostructures

The processes of storage and dissipation of electromagnetic energy in nanostructures depend on both the material properties and the geometry. In this paper, the distributions of local energy density and power dissipation in nanogratings are investigated using the rigorous coupled-wave analysis. It is demonstrated that the enhancement of absorption is accompanied by the enhancement of energy storage both for material at the resonance of its dielectric function described by the classical Lorentz oscillator and for nanostructures at the resonance induced by its geometric arrangement. The appearance of strong local electric field in nanogratings at the geometry-induced resonance is directly related to the maximum electric energy storage. Analysis of the local energy storage and dissipation can also help gain a better understanding of the global energy storage and dissipation in nanostructures for photovoltaic and heat transfer applications

Resonant Tunneling through S- and U-shaped Graphene Nanoribbons

We theoretically investigate resonant tunneling through S- and U-shaped nanostructured graphene nanoribbons. A rich structure of resonant tunneling peaks are found eminating from different quasi-bound states in the middle region. The tunneling current can be turned on and off by varying the Fermi energy. Tunability of resonant tunneling is realized by changing the width of the left and/or right leads and without the use of any external gates.Comment: 6 pages, 7 figure

Unitarity and Complete Reducibility of Certain Modules over Quantized Affine Lie Algebras

Let $U_q(\hat{\cal G})$ denote the quantized affine Lie algebra and $U_q({\cal G}^{(1)})$ the quantized {\em nontwisted} affine Lie algebra. Let ${\cal O}_{\rm fin}$ be the category defined in section 3. We show that when the deformation parameter $q$ is not a root of unit all integrable representations of $U_q(\hat{\cal G})$ in the category ${\cal O}_{\rm fin}$ are completely reducible and that every integrable irreducible highest weight module over $U_q({\cal G}^{(1)})$ corresponding to $q>0$ is equivalent to a unitary module.Comment: 17 pages (minor errors corrected

Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole

In this paper, we extend Parikh' work to the non-stationary black hole. As an example of the non-stationary black hole, we study the tunnelling effect and Hawking radiation from a Vaidya black hole whose Bondi mass is identical to its mass parameter. We view Hawking radiation as a tunnelling process across the event horizon and calculate the tunnelling probability. We find that the result is different from Parikh's work because $\frac{dr_{H}}{dv}$ is the function of Bondi mass m(v)

Updated Estimate of the Muon Magnetic Moment Using Revised Results from e+e- Annihilation

A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e+e- annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e+e- and tau spectral functions in the pi pi channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and 1.0 GeV, so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are a_mu[had,LO] = (696.3 +- 6.2[exp] +- 3.6[rad])e-10 (e+e- -based) and a_mu[had,LO] = (711.0 +- 5.0[exp] +- 0.8[rad] +- 2.8[SU2])e-10 (tau-based), where the errors have been separated according to their sources: experimental, missing radiative corrections in e+e- data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read a_mu = (11,659,180.9 +- 7.2[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (e+e- -based) and a_mu = (11,659,195.6 +- 5.8[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (tau-based), where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be (22.1 +- 7.2 +- 3.5 +- 8.0)e-10 (1.9 sigma) and (7.4 +- 5.8 +- 3.5 +- 8.0)e-10 (0.7 sigma) for the e+e- and tau-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Comment: 14 pages, 7 figures (to be submitted to Phys Lett B

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.Comment: 11 pages, 4 figure

Dimerization in a half-filled one-dimensional extended Hubbard model

We use a density matrix renormalization group method to study quantitatively the phase diagram of a one-dimensional extended Hubbard model at half-filling by investigating the correlation functions and structure factors. We confirm the existence of a novel narrow region with long-rang bond-order-wave order which is highly controversial recently between the charge-density-wave phase and Mott insulator phase. We determined accurately the position of the tricritical point $U_t\simeq 7.2t$, $V_t\simeq 3.746t$ which is quite different from previous studies