Effective conductivity of 2D isotropic two-phase systems in magnetic field

Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They allow to describe sigma_{e} of various inhomogeneous media at arbitrary phase concentrations x and magnetic fields. the x-dependence plots of sigma_e at some values of inhomogeneity and magnetic field are constructed. Their behaviour is qualitatively compatible with the existing experimental data. The obtained results are applicable for different two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and admit a direct experimental checking.Comment: 9 pages, 2 figures, Latex2e, small corrections and new figure

Planar isotropic two-phase systemsin perpendicular magnetic field: effective conductivity

Three explicit approximate expressions for the effective conductivity sigma_e of various planar isotropic two-phase systems in a magnetic field are obtained using the dual linear fractional transformation, connecting sigma_e of these systems with and without magnetic field. The obtained results are applicable for two-phase systems (regular and nonregular as well as random), satisfying the symmetry and self-duality conditions, and allow to describe sigma_e of various two-dimensional and layered inhomogeneous media at arbitrary phase concentrations and magnetic fields. All these results admit a direct experimental checking.Comment: 10 pages, Latex2e, 3 figure

Clocking Schemes for High Speed Digital Systems

A key element (one is tempted to say the heart) of most digital systems is the clock. Its period determines the rate at which data are processed, and so should be made as small as possible, consistent with reliable operation. Based on a worst case analysis, clocking schemes for high-performance systems are analyzed. These are 1- and 2-phase systems using simple clocked latches, and 1-phase systems using edge-triggered D-flip-flops. Within these categories (any of which may be preferable in a given situation), it is shown how optimal tradeoffs can be made by appropriately choosing the parameters of the clocking system as a function of the technology parameters. The tradeoffs involve the clock period (which of course determines the data rate) and the tolerances that must be enforced on the propagation delays through the logic. Clock-pulse edge tolerances are shown to be an important factor. It is shown that, for systems using latches, their detrimental effects on the clock period can be converted to tighter bounds on the short-path delays by allowing D changes to lag behind the leading edges of the clock pulses and by using wider clock pulses or, in the case of 2-phase systems, by overlapping the clock pulses

Effect of solid thermal conductivity and particle-particle contact on effective thermodiffusion coefficient in porous media

Transient mass transfer associated to a thermal gradient through a saturated porous medium is studied experimentally and theoretically to determine the effect of solid thermal conductivity and particle-particle contact on thermodiffusion processes. In this study, the theoretical volume averaging model developed in a previous study has been adopted to determine the effective transport coefficients in the case of particle-particle contact configurations. The theoretical results revealed that the effective thermodiffusion coefficient is independent of the thermal conductivity ratio for pure diffusive cases. In all cases, even if the effective thermal conductivity depends on the particle-particle contact, the effective thermodiffusion coefficient remains independent of the solid phase connectivity. We also found that the porosity can change the impact of dispersion effects on the thermodiffusion coefficients. For large values of the thermal conductivity contrast, dispersion effects are negligible and the effective thermal conductivity coefficients are the same as the ones for the pure diffusion case. Experimental results obtained for the purely diffusive case, using a special two-bulb apparatus, confirm the theoretical results. These results also show that, for non-consolidated porous media made of spheres, the thermal conductivity ratio has no significant influence on the thermodiffusion process for pure diffusion. Finally, the particle-particle contact also does not show a considerable influence on the thermodiffusion process

Fine Scale Simulation of Fractured Reservoirs: Applications and Comparison

Imperial Users onl

Forward-Invariance and Wong-Zakai Approximation for Stochastic Moving Boundary Problems

We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution remains negative on one side and positive on the other side of the moving interface, when started with the appropriate initial conditions. To extend results from deterministic settings to the stochastic case, we establish a Wong-Zakai type approximation. After a coordinate transformation the problems are reformulated and analysed in terms of stochastic evolution equations on domains of fractional powers of linear operators.Comment: 46 page