Stochastic analysis of two-phase flow in porous media: II. Comparison between perturbation and Monte-Carlo results

The first paper (Changet al., 1995) described stochastic analysis of two-phase flow in a fully liquid-saturated system. In this paper, the results of Monte-Carlo simulations are compared with the closed-form expressions obtained using the perturbation approach. We present analytical solutions to the one-dimensional, steady-state oil-and-water flow equations. These solutions are subsequently used in the Monte-Carlo analysis to estimate the statistical properties of the key output processes. The comparison between the results of perturbation and Monte-Carlo approaches shows a good agreement between the two methods over a wide range lnk (k is the intrinsic permeability) variability with three different combinations of input stochastic processes of lnk and soil parameter . In particular, a good agreement was obtained for capillary and individual pressure variances and effective phase conductivities. The results showed that as the mean capillary pressure in the profile increased, the variance of capillary pressure increased while the variances of individual pressures decreased. Overall comparison between the two methods showed that the first-order perturbation theory can be successfully used to describe the effective behavior of large-scale, two-phase systems.     

Magnetic Trajectories in an Almost Contact Metric Manifold $${\mathbb{R}^{2N+1}}$$

In this paper we classify magnetic trajectories γ in \({{\mathbb{R}}^{2N+1}}\) endowed with a canonical quasi-Sasakian structure, corresponding to a magnetic field proportional to the fundamental 2-form. We prove that they are helices of order 5 and we show that there exists a totally geodesic \({{\mathbb{R}}^5}\) in \({\mathbb{R}^{2N+1}}\) such that γ lies in \({{\mathbb{R}}^5}\). Moreover, the quasi-Sasakian structure of \({{\mathbb{R}}^5}\) is that induced from the ambient manifold.     

Anodic alumina membranes with defined pore diameters and thicknesses obtained by adjusting the anodizing duration and pore opening/widening time

The through-hole porous anodic aluminum oxide (AAO) membranes were fabricated by a simple two-step anodization of aluminum in 0.3 M oxalic acid, 0.3 M sulfuric acid, and 2 wt.% phosphoric acid solutions under different operating conditions followed by the removal of the remaining Al substrate and the pore opening/widening process. The effect of duration of the second anodizing step on the thickness of the porous oxide layer and the influence of other anodizing conditions such as applied voltage, type of electrolyte, and purity of the substrate on the rate of porous oxide growth were discussed in detail. The pore opening procedure for all synthesized membranes was optimized, and the influence of the duration of chemical etching on structural features of AAO membranes, especially pore diameter, was studied. The rate of pore widening was established for AAO membranes formed in various anodizing electrolytes and for different temperatures of 5 wt.% H₃PO₄ used for alumina dissolution.

     

Morin hydrate as pro-ecological antioxidant and pigment for polyolefin polymers

In our studies, we propose the use of natural, pro-ecological substances, such as flavonoids to protect elastomers against ageing. One of these substances, namely morin hydrate, was incorporated into ethylene–octene rubbers (Engage); then the vulcanisates of Engage containing the antioxidant under investigation were subjected to ageing processes. The changes in deformation energy, colour and cross-linking density and OIT index of the vulcanisates of Engage were measured before and after each ageing process. The test results obtained show that morin hydrate has a very positive influence on the stability of the vulcanisates of Engage, protecting them against the negative effects of ageing. In addition to its anti-oxidative function, morin hydrate changes the colour of the final polymeric product, fulfilling the role of a natural pigment. Thus, morin hydrate is not only a natural antioxidant but also a pigment in the polymers, imparting to them the features of pro-ecological materials.     

PREPARATION OF LARGE-PARTICLE-SIZE MONODISPERSE LATEXES IN SPACE: POLYMERIZATION KINETICS AND PROCESS DEVELOPMENT

Monodisperse polystyrene latexes are prepared by seeded emulsion polymerization; however, sizes larger than 2μm are difficult to prepare because of the creaming and settling of the particles, and their sensitivity to mechanical shear. Preparation in space would obviate the creaming and settling, and allow agitation just sufficient for good heat transfer and mixing. Three polymerizations yielding 3-5μm size particles were carried out successfully on the third flight of the “Columbia” launched March 22, 1982; however, four polymerizations yielding sizes up to 10μm on the fourth flight launched June 27, 1982, were incomplete owing to apparatus malfunction. The results of these polymerizations and the prospects of developing a preparative space process are reviewed     

Enzymatic Apporoach to the Synthesis of Non-Racemic,P-Chiral Hydroxymethylphosphonates and Phosphinates

Abstract

α-Hydroxyalkanephosphonates and phosphinates exhibit interesting biologd achvlty whch IS highly dependent on theu absolute configumon Therefore, a search for efficient and general methods of the synthesis of enantlopure htle compounds continues As part of our studies on the use of enzymes in preparahon of non-racemic heteroorganic compounds,2 we have developed a hpasemediated lunebc resoluhon of racemic hydroxy- methylphosphonates and phosphinates, which is based on ather acetylatlon of the substrates 1, or hydrolysis of thar O-acetyl denvatlves 2 The absolute configurahon of the products has been determined by means of CD and chemical conelatlon     

Billion-atom synchronous parallel kinetic Monte Carlo simulations of critical 3D Ising systems

An extension of the synchronous parallel kinetic Monte Carlo (spkMC) algorithm developed by Martinez et al. [J. Comp. Phys. 227 (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors’ time clocks current in a global sense. Boundary conflicts are resolved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of serial calculations, which confirms the statistical validity of our algorithm. We have analyzed the parallel efficiency of spkMC and find that it scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations.