Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

Evaluation of the S(T) assimilation method with the Argo dataset

Recent observations from the Argo dataset of temperature and salinity profiles are used to evaluate a series of 3-year data assimilation experiments in a global ice–ocean general circulation model. The experiments are designed to evaluate a new data assimilation system whereby salinity is assimilated along isotherms, S(T ). In addition, the role of a balancing salinity increment to maintain water mass properties is investigated. This balancing increment is found to effectively prevent spurious mixing in tropical regions induced by univariate temperature assimilation, allowing the correction of isotherm geometries without adversely influencing temperature–salinity relationships. In addition, the balancing increment is able to correct a fresh bias associated with a weak subtropical gyre in the North Atlantic using only temperature observations. The S(T ) assimilation method is found to provide an important improvement over conventional depth level assimilation, with lower root-mean-squared forecast errors over the upper 500 m in the tropical Atlantic and Pacific Oceans. An additional set of experiments is performed whereby Argo data are withheld and used for independent evaluation. The most significant improvements from Argo assimilation are found in less well-observed regions (Indian, South Atlantic and South Pacific Oceans). When Argo salinity data are assimilated in addition to temperature, improvements to modelled temperature fields are obtained due to corrections to model density gradients and the resulting circulation. It is found that observations from the Argo array provide an invaluable tool for both correcting modelled water mass properties through data assimilation and for evaluating the assimilation methods themselves.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

Modified level set method with Canny operator for image noise removal

The level set method is commonly used to address image noise removal. Existing studies concentrate mainly on determining the speed function of the evolution equation. Based on the idea of a Canny operator, this letter introduces a new method of controlling the level set evolution, in which the edge strength is taken into account in choosing curvature flows for the speed function and the normal to edge direction is used to orient the diffusion of the moving interface. The addition of an energy term to penalize the irregularity allows for better preservation of local edge information. In contrast with previous Canny-based level set methods that usually adopt a two-stage framework, the proposed algorithm can execute all the above operations in one process during noise removal.

Interference cancellation in two-path successive relay system with network coding

This paper proposes a novel interference cancellation algorithm for the two-path successive relay system using network coding. The two-path successive relay scheme was proposed recently to achieve full date rate transmission with half-duplex relays. Due to the simultaneous data transmission at the relay and source nodes, the two-path relay suffers from the so-called inter-relay interference (IRI) which may significantly degrade the system performance. In this paper, we propose to use the network coding to remove the IRI such that the interference is first encoded with the network coding at the relay nodes and later removed at the destination. The network coding has low complexity and can well suppress the IRI. Numerical simulations show that the proposed algorithm has better performance than existing approaches.

Taxonomic free sorting: a successful method with older consumers and a novel approach to preference mapping

Taxonomic free sorting (TFS) is a fast, reliable and new technique in sensory science. The method extends the typical free sorting task where stimuli are grouped according to similarities, by asking respondents to combine their groups two at a time to produce a hierarchy. Previously, TFS has been used for the visual assessment of packaging whereas this study extends the range of potential uses of the technique to incorporate full sensory analysis by the target consumer, which, when combined with hedonic liking scores, was used to generate a novel preference map. Furthermore, to fully evaluate the efficacy of using the sorting method, the technique was evaluated with a healthy older adult consumer group. Participants sorted eight products into groups and described their reason at each stage as they combined those groups, producing a consumer-specific vocabulary. This vocabulary was combined with hedonic data from a separate group of older adults, to give the external preference map. Taxonomic sorting is a simple, fast and effective method for use with older adults, and its combination with liking data can yield a preference map constructed entirely from target consumer data.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

GC/multiple collector-ICPMS method for chlorine stable isotope analysis of chlorinated aliphatic hydrocarbons

Stable isotopic characterization of chlorine in chlorinated aliphatic pollution is potentially very valuable for risk assessment and monitoring remediation or natural attenuation. The approach has been underused because of the complexity of analysis and the time it takes. We have developed a new method that eliminates sample preparation. Gas chromatography produces individually eluted sample peaks for analysis. The He carrier gas is mixed with Ar and introduced directly into the torch of a multicollector ICPMS. The MC-ICPMS is run at a high mass resolution of >= 10 000 to eliminate interference of mass 37 ArH with Cl. The standardization approach is similar to that for continuous flow stable isotope analysis in which sample and reference materials are measured successively. We have measured PCE relative to a laboratory TCE standard mixed with the sample. Solvent samples of 200 nmol to 1.3 mu mol ( 24- 165 mu g of Cl) were measured. The PCE gave the same value relative to the TCE as measured by the conventional method with a precision of 0.12% ( 2 x standard error) but poorer precision for the smaller samples.

Interaction of 2-(arylazo)phenols with rhodium. Usual coordination vs. C-H and C-C activation

Reaction of 2-(2'-hydroxyphenylazo)phenol with [Rh(PPh3)(3)Cl] in refluxing benzene in presence of triethylamine afforded a red complex in which the ligand is coordinated to rhodium as a tridentate O,N,O-donor. However, similar reaction of [Rh(PPh3)(3)Cl] with 2-(2'carboxyphenylazo)-4-methylphenol yielded two complexes, viz. a blue one and a green one. In both the complexes the ligand is coordinated as C,N,O-donor. However, in the blue complex orthometallation takes place from the ortho-carbon atom, which bears -COOH group via decarboxylation and in green one orthometallation occurs from the other ortho-carbon. Structures of all the three complexes were determined by X-ray crystallography. In all the three complexes rhodium is sharing the equatorial plane with the tridentate ligand and a chloride, and the two triphenylphosphines are axially disposed. All of the complexes show intense MLCT transitions in the visible region. Cyclic voltammetry on these complexes shows a Rh(III)-Rh(IV) oxidation on the positive side of SCE and a reduction of the coordinated azophenolate ligand on the negative side. (c) 2006 Elsevier B.V. All rights reserved.