Computational and structural studies on the complexation of cobalt(II) acetate by water and pyridine

Four different complexes of the cobalt(II) acetate–pyridine–water system were obtained as dominant species by crystallization from a series of dichloromethane and toluene solutions. The complexes were characterized by terms of X-ray crystal structure determination. Factors in solution properties leading to crystallization of certain complexes are discussed. Furthermore, trends in terms of structure and binding energies in a systematic series of mononuclear cobalt(II) complexes were studied using density functional calculations.     

A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate.     

Efficient enforcement of far-field boundary conditions in the Transformed Field Expansions method

The Method of Transformed Field Expansions (TFE) has been demonstrated to be a robust and highly accurate numerical scheme for simulating solutions of boundary value and free boundary problems from the sciences and engineering. As a Boundary Perturbation Method it builds highly accurate solutions based upon exact solutions in a simple, canonical, geometry and corrects these via Taylor series to fit the actual geometry at hand. The TFE method has significantly enhanced stability properties when compared with other Boundary Perturbation approaches, however, this comes at the cost of requiring a full volumetric discretization as opposed the surface formulation that other methods can realize. In this paper we outline two techniques for ameliorating this shortcoming, first by employing a Legendre Spectral Element Method to implement efficient, graded meshes, and second by utilizing an Artificial Boundary with a Transparent Boundary Condition placed quite close to the boundary of the domain. In this contribution we focus on the specific problem of simulating the Dirichlet–Neumann operator associated to Laplace’s equation on a periodic cell (which arises in the water wave problem). While the details of our results are specific to this problem, the general conclusions are valid for the wider class of problems to which the TFE method can be applied. For each technique we discuss implementation details and display numerical results which support the conclusion that each of these techniques can greatly reduce the computational cost of using the TFE method.     

Confidence limits,error bars and method comparison in molecular modeling. Part 1: The calculation of confidence intervals

Computational chemistry is a largely empirical field that makes predictions with substantial uncertainty. And yet the use of standard statistical methods to quantify this uncertainty is often absent from published reports. This article covers the basics of confidence interval estimation for molecular modeling using classical statistics. Alternate approaches such as non-parametric statistics and bootstrapping are discussed.     

The Development of an Integrated Mathematical Model of an Aluminium Smelter

This paper outlines the development of an integrated mathematical model of an aluminium smelter incorporating the raw materials feed, carbon bake, rodding, potrooms and ingot mill areas, together with non-linear feedback loops. The model is structured to facilitate its use for planning and managing both technological and economic change.     

The Development of a Mathematical Model of the Operations of a National Glass Manufacturer

In this paper, a mathematical model of the entire operations of a national glass manufacturer is developed. This includes the float glass manufacture, distribution, storage operations and the technical considerations dictated by the plant as well as the operating procedures. The model is initially for a planning year, and is generated from a ‘monthly model’. This monthly model interconnects with other monthly models primarily via stock flows. The mathematical model is formulated in a unique way that allows certain production aspects to be modelled using a ‘pseudo-continuous’ time frame, rather than a discrete one. The generation of the overall model (as a mixed integer linear programming problem) and its solution is also discussed.     

A shock tube determination of the CN ground state dissociation energy and the CN violet electronic transition moment

The CN ground state (X²∑⁺) dissociation energy and the electronic transition moment of the CN violet B²∑⁺ ? X²∑⁺ bands have been simultaneously determined from spectral emission measurements behind incident shock waves. The unshocked test gases were composed of various CO₂-CO-N₂-Ar mixtures, and the temperatures behind the incident shocks ranged from 3500 to 8000°K. The dissociation energy was determined to be 7.89 eV with a statistical precision of ±0.02 eV; a conservative estimate of the absolute error was ±0.13 eV. The value obtained for the Δυ = 0 sequence electronic transition moment was 0.90 ± 0.14, corresponding to an electronic absorption f-number of 0.035 ± 0.005 at a wavelength of 3860 Å. The electronic transition moment variation with internuclear separation was also measured.     

Multiple autoregressive models with random coefficients

This paper derives conditions for the stationarity of a class of multiple autoregressive models with random coefficients. The models considered include as special cases those previously discussed by Andel (Ann. Math. Statist.42 (1971), 755–759; Math. Operationsforsch. Statist.7 (1976), 735–741).