Effect of acetate on ferrihydrite crystallization

Mössbauer spectroscopy was used to follow the aging of ferrihydrite with different amounts of acetate, to achieve more crystalline products. Mössbauer spectra of fresh samples did not show any magnetic components. After two years aging, the solids presented crystalline fractions. Hematite formation was inhibited as acetate content increased in solids. For an acetate/iron molar ratio equal to 0.63 goethite was formed instead of hematite. X-ray diffraction confirmed these results. This work shows that synthetic samples can be used for elucidating the anti-hematitic effect of organic matter already detected in soils.     

Combining search directions using gradient flows

 The efficient combination of directions is a significant problem in line search methods that either use negative curvature, or wish to include additional information such as the gradient or different approximations to the Newton direction. In this paper we describe a new procedure to combine several of these directions within an interior-point primal-dual algorithm. Basically, we combine in an efficient manner a modified Newton direction with the gradient of a merit function and a direction of negative curvature, if it exists. We also show that the procedure is well-defined, and it has reasonable theoretical properties regarding the rate of convergence of the method. We also present numerical results from an implementation of the proposed algorithm on a set of small test problems from the CUTE collection. Received: November 2000 / Accepted: October 2002 Published online: February 14, 2003 Key Words. negative curvature – primal-dual methods – interior-point methods – nonconvex optimization – line searches Mathematics Subject Classification (1991): 49M37, 65K05, 90C30     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.     

Tuning inventory policy parameters in a small chemical company

A project to improve inventory management in a small UK chemical company is described. A research group comprising university academics and company managers for logistics and information technology examined current practices and analysed a database of historical records of business operations of the company. Based on the analysis, a scheme to categorise stock and set ordering policies to optimise inventory costs was developed. Some comments are made on process issues and the learning that took place.     

A supraconvergent scheme for the Korteweg-de Vries equation

Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.     

Phase diagram of the ANNNI model in the Hamiltonian limit

The Hamiltonian limit of the ANNNI model in (1+1) dimensions is studied by using the Quantum Statistical Monte Carlo method. Even if recent results suggest that Monte Carlo calculations may prove unreliable in the study of this system, the phase diagram of the quantum version of the model was successfully obtained. In particular, the clusive transitions between the disordered, the floating incommensurate and the degenerate 2, 2 are determined by analysing the correlation length behaviour in finite lattices.Partially supported by CONICET Argentina