Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

Crude oil and agricultural futures: An analysis of correlation dynamics

Correlations between oil and agricultural commodities have varied over previous decades, impacted by renewable fuels policy and turbulent economic conditions. We estimate smooth transition conditional correlation models for 12 agricultural commodities and WTI crude oil. While a structural change in correlations occurred concurrently with the introduction of biofuel policy, oil and food price levels are also key influences. High correlation between biofuel feedstocks and oil is more likely to occur when food and oil price levels are high. Correlation with oil returns is strong for biofuel feedstocks, unlike with other agricultural futures, suggesting limited contagion from energy to food markets.

Testing against changing correlation

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.