Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.     

Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy.The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.     

Wave breaking in Boussinesq models for undular bores

A nonlinear dispersive model equation is used to study the onset of breaking in long waves behind the front of an undular bore. According to experiments conducted by Favre (1935) [1], weak bores have a smooth, but oscillatory structure, with undulations appearing behind the bore front. With increasing bore strength, the amplitude of these oscillations grows until one or several of them start breaking. The change in type from the purely undular bore occurs at a sharply defined depth ratio which is under review in this article. A convective breaking criterion is put forward, and numerical computations are used to compare the predictions of this model to Favre?s wavetank experiments. It appears that the numerical results underpredict the appearance of breaking waves, but are in good qualitative agreement with the experiments. The results are interpreted with the aid of exact solitary-wave solutions, and it is found that the transition from purely undular to breaking bore may be recast with the help of a breaking criterion for solitary waves.     

Exponential convergence of a spectral projection of the KdV equation

It is shown that a spectral approximation of the Korteweg–de Vries equation converges exponentially fast to the true solution if the Fourier basis is used and if the solution is analytic in a fixed strip about the real axis. Computations are carried out which show that the exponential convergence rate can be achieved in practice.     

A Markov Chain Model for Effective Relative Permeabilities and Capillary Pressure

We present a new method for calculating the effective two-phase parameters of one-dimensional randomly heterogeneous porous media, which avoids the timeconsuming use of simulations on explicit realizations. The procedure is based on the steady state saturation distribution. The idea is to model the local variation of saturation and saturation dependent parameters as Markov chains, in such a way that the effective parameters are given by the asymptotic expectations of the chains. We derive the exact asymptotic moment equations and solve them numerically, based on their second order approximation. The method determines the effective parameters to a high degree of accuracy, even with large variations in rock properties. In particular, the capillary limit and viscous limit effective parameters are recovered exactly. The applicability of the effective parameters in the unsteady state case is studied by comparing the displacement production profiles in heterogeneous media and their homogenized counterpart.     

Expression patterns of Neil3 during embryonic brain development and neoplasia

Background  

The base excision repair pathway is responsible for repairing small DNA base lesions caused by endogenous and exogenous damaging agents. Repair is initiated by DNA glycosylases that recognize and remove the lesions. NEIL3 is one of 11 mammalian DNA glycosylases identified to date and it was discovered on the basis of sequence homology to the E. coli Fpg and Nei glycosylases. Difficulties in purifying the protein have limited its biochemical characterization and in contrast to the other glycosylases, its function remains unclear.