Nondigital Implementation of the Arithmetic of Real Numbers

In the framework of a model for quantum computer media, a nondigital implementation of the arithmetic of the real numbers is described. For this model, an elementary storage cell is an ensemble of qubits (quantum bits). It is found that to store an arbitrary real number it is sufficient to use four of these ensembles and the arithmetical operations can be implemented by fixed quantum circuits.     

A Lattice Gas Automaton Simulation of the Nonlinear Diffusion Equation: A Model for Moisture Flow in Unsaturated Porous Media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local density of fluid particles which statistically determines the collision rate and thus, the mean free path of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moisture flow in unsaturated porous media. The capability of the LGA to account for unsaturated flow is tested through a set of numerical experiments simulating one-dimensional infiltration in a simplified semi-infinite homogenous isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid–solid interfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagation of the infiltration front is visualized at different time steps through concentration profiles parallel to the applied concentration gradient and the infiltration rate is measured continuously until steady-state flow is reached. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t ^1/2 dependence. The evolution of the effective diffusion coefficient with the particle concentration is estimated from the measured density profiles for the various porous materials. Depending on the applied fluid–solid interactions, the macroscopic effective diffusivity may vary by more than two orders of magnitude with density.     

Interaction of evaporation fronts with a formation interface in a porous medium

The evolutionarity and structure of water-vapor phase discontinuities formed in a geothermal reservoir on the interface between permeable formations with different properties are considered. In the short-wave approximation a graphic method is proposed for solving the problem of breakdown of an arbitrary discontinuity in a geothermal reservoir consisting of two formations with different properties.     

Viscous Fingering Instability in Porous Media: Effect of Anisotropic Velocity-Dependent Dispersion Tensor

The viscous fingering of miscible flow displacements in a homogeneous porous media is examined to determine the effects of an anisotropic dispersion tensor on the development of the instability. In particular, the role of velocity-dependent transverse and longitudinal dispersions is investigated through linear stability analysis and nonlinear simulations. It is found that an isotropic velocity-dependent dispersion tensor does not affect substantially the development of the instability and effectively has the same effect as molecular diffusion. On the other hand, an anisotropic velocity-dependent dispersion tensor results in different instability characteristics and more intricate finger structures. It is shown that anisotropic dispersion has profound effects on the development of the fingers and on the mechanisms of interactions between neighboring fingers. The development of the new finger structures is explained by examining the velocity field and characterized qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the sweep efficiency and relative contact area.     

Effect of Reactive Surface Areas Associated with Different Particle Shapes on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Rocks

In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.     

A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).     

Determination of Permeability Distributions Using NMR Velocity Imaging

This study develops a methodology for determining the absolute permeability distribution in a porous media sample using velocity data obtained from NMR imaging experiments. An objective function describing the discrepancy between observed and simulated data is reduced by iteratively updating the permeability. This parameter estimation scheme is based on an iterative method which uses optimal control theory to refine the estimates. Although this theory is developed for both isotropic and anisotropic porous media, the permeability reconstructions examined in this paper are restricted to the isotropic case. Synthetic data are used to investigate the impact of varying the noise in the experimental data, the degree of parameterization, the relative weighting of the regularization term in the objective function, and the amount and type of data required to obtain a satisfactory permeability reconstruction. These synthetic data are extracted from the solution of numerical experiments that have utilized an assumed permeability distribution. The methodology is also applied to data gathered in laboratory experiments for water flow in a sandstone sample.     

Density-driven compactional flow in porous media

In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic. However, at depths deeper than 1 km where the pressure is high, compaction becomes more akin to a viscous one. Two mathematical models of compaction in porous media are formulated and the nonlinear equations are then solved numerically. The essential features of numerical profiles of poroelastic and viscous compaction are thus compared with asymptotic solutions. Two distinguished styles of density-driven compaction in fast and slow compacting sediments are analysed and shown in this paper.     

An investigation into melt flow dynamics during repetitive pulsed laser drilling of transparent media

This paper presents an investigation into the dynamics of repetitive pulsed laser drilling of a visually transparent media using a CO₂ laser source. This enabled the use of a high-speed imaging system for observing, in real time, the behaviour of the drilling process in the laser drilled cavity of 1.5 mm diameter holes of up to 18.5 mm in depth. The work revealed that the instantaneous drilling velocity within each laser pulse can vary considerably from the average drilling velocity as a result of the non-uniform temporal pulse shape and the oscillation of the melt ejection rate. During beam breakthrough, both upward and downward melt ejections were observed to occur inside the drilled hole for a short period of time, after which the material was ejected through the exit end of the holes. It has been shown in this work that the downward melt flow velocity increases with hole depth for a positively tapered hole (from 0.09 to 1.43 m/s) and decreases with hole depth for a negatively tapered hole geometry (from 0.4 to 0.1 m/s), as a result of the change in the assist gas velocity inside the drilled hole with respect to the hole taper geometry. The mechanisms of forming the positively and negatively tapered holes in the transparent media have been correlated with the hole geometry and melt flow velocity. The work has demonstrated a new method of studying the melt dynamics in laser drilling.     

手性介质中椭圆偏振光诱导非线性旋光的表征

给出了方便实用的计算非线性旋光角Δθ的公式 ,在理论上分析了非线性旋光角随椭圆特征参量改变的变化规律 ,给出了数值模拟的结果 ,并针对具体手性材料与入射光强估算了非线性旋光角的量级