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

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)

Experimental Implications for a Linear Collider of the SUSY Dark Matter Scenario

This paper presents the detection issues for the lightest slepton \tilde{\tau}_1 at a future e^+e^- TeV collider given the dark matter constraints set on the SUSY mass spectrum by the WMAP results. It intends to illustrate the importance of an optimal detection of energetic electrons in the very forward region for an efficient rejection of the \gamma\gamma background. The TESLA parameters have been used in the case of head-on collisions and in the case of a 10, mrad half crossing angle.Comment: 24 pages, 13 figures, Work presented at the International Conference on Linear Colliders (LCWS04), 19-23 April 2004, Le Carre des Sciences, Paris, Franc

Detuning effects in the one-photon mazer

The quantum theory of the mazer in the non-resonant case (a detuning between the cavity mode and the atomic transition frequencies is present) is written. The generalization from the resonant case is far from being direct. Interesting effects of the mazer physics are pointed out. In particular, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. It is also shown that the detuning adds a potential step effect not present at resonance and that the use of positive detunings defines a well-controlled cooling mechanism. In the special case of a mesa cavity mode function, generalized expressions for the reflection and transmission coefficients have been obtained. The general properties of the induced emission probability are finally discussed in the hot, intermediate and cold atom regimes. Comparison with the resonant case is given.Comment: 9 pages, 8 figure