DIFS—a modelling and simulation tool for DGT induced trace metal remobilisation in sediments and soils

The technique of Diffusive Gradients in Thin-films (DGT) can measure in situ fluxes of trace metals in sediments. Interpretation of these measurements requires a numerical model of trace metal reaction and transport in sediments. The DIFS (DGT Induced Fluxes in Sediments) model has permitted quantitative interpretation of DGT measurements in terms of fundamental kinetic and equilibrium resupply parameters. DIFS is here further refined and developed into a software tool which both simulates temporal and spatial changes in concentrations of trace metals in solid and solution phases in sediments during in situ DGT deployments, and estimates resupply parameters from experimental data. The basis of the DIFS model is a pair of linked parabolic PDEs describing dissolved and sorbed trace metal concentrations in the sediment and DGT device. These are solved by the Method of Lines using standard ODE solvers. The solutions are processed to obtain the DGT response. The use of the software, in particular the format of the text file containing input parameters, is described. Illustrative examples of the type of behaviour predicted for DGT by DIFS are provided.     

Computation of Peak Output for Inputs Restricted in L2 and L∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.     

Exact asymptotics of small deviations for a stationary Ornstein-Uhlenbeck process and some Gaussian diffusion processes in the L p -norm, 2 ≤ p ≤ ∞

We prove results on exact asymptotics of the probabilities