New non-equilibrium matrix imbibition equation for Kondaurov's double porosity model

The paper deals with the global Kondaurov double porosity model describing a non-equilibrium two-phase immiscible flow in fractured-porous reservoirs when non-equilibrium phenomena occur in the matrix blocks, only. It is shown that the homogenized model can be represented as usual equations of two-phase incompressible immiscible flow, except for the addition of two source terms calculated by a solution to a local problem which is a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter.Comment: 11 pages, 1 figur

Fine tuning of phase qubit parameters for optimization of fast single-pulse readout

We analyze a two-level quantum system, describing the phase qubit, during a single-pulse readout process by a numerical solution of the time-dependent Schroedinger equation. It has been demonstrated that the readout error has a minimum for certain values of the system`s basic parameters. In particular, the optimization of the qubit capacitance and the readout pulse shape leads to significant reduction of the readout error. It is shown that in an ideal case the fidelity can be increased to almost 97% for 2 ns pulse duration and to 96% for 1 ns pulse duration.Comment: 4 pages, 5 figure

Nonlinear double porosity models with non-standard growth

Abstract We study the solutions to quasilinear elliptic equations with high contrast coefficients. The energy formulation leads to work with variable exponent Lebesgue spaces L p ε (·) in domains with a complex microstructure scaled by a small parameter ε. We derive rigorously the corresponding homogenized problem. It is completely described in terms of local energy characteristics of the original domain. Version française abrégée Nous considérons le problème variationnel (2), où K ε est une fonction qui dégénère sur une partie asymptotiquement dense du domaine (voir (K.1)-(K.2)). Le domaine est un milieu dispersé vérifiant (C.1)-(C.2). En contrôlant les caractéristiques locales (7)-(8) du domaine, nous obtenons rigoureusement le problème homogénéisé correspondant à (2). Il est décrit dans le théorème 2.1 : la solution u ε de (2) converge dans [m3SC+; v 1.113; Prn:18/09/2009; 9:34] plus, dans la partie matricielle du domaine, ( (Ω)) ; 3. on prouve le résultat de convergence dans la partie matricielle. Finalement, nous illustrons notre résultat dans le cadre d'un exemple périodique, retrouvant ainsi une formulation plus usuelle du problème homogénéisé

Approaching microwave photon sensitivity with Al Josephson junctions

Here, we experimentally test the applicability of an aluminium Josephson junction of a few micrometers size as a single photon counter in the microwave frequency range. We have measured the switching from the superconducting to the resistive state through the absorption of 10 GHz photons. The dependence of the switching probability on the signal power suggests that the switching is initiated by the simultaneous absorption of three and more photons, with a dark count time above 0.01 s