Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

An improved digital deconvolution equation

This paper first points out the important fact that the rectangle formulas of continuous convolution discretization, which was widely used in conventional digital deconvolution algorithms, can result in zero-time error. Then, an improved digital deconvolution equation is suggested which is equivalent to the trapezoid formulas of continuous convolution discretization and can overcome the disadvantage of conventional equation satisfactorily. Finally, a simulation in computer is given, thus confirming the theoretical result.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

The influence of carbon surface oxygen groups on Dubinin–Astakhov equation parameters calculated from CO2 adsorption isotherm

We present the results of a systematic study of the influence of carbon surface oxidation on Dubinin–Astakhov isotherm parameters obtained from the fitting of CO2 adsorption data. Using GCMC simulations of adsorption on realistic VPC models differing in porosity and containing the most frequently occurring carbon surface functionalities (carboxyls, hydroxyls and carbonyls) and their mixtures, it is concluded that the maximum adsorption calculated from the DA model is not strongly affected by the presence of oxygen groups. Unfortunately, the same cannot be said of the remaining two parameters of this model i.e. the heterogeneity parameter (n) and the characteristic energy of adsorption (E0). Since from the latter the pore diameters of carbons are usually calculated, by inverse-type relationships, it is concluded that they are questionable for carbons containing surface oxides, especially carboxyls.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Application of logistic regression for fault analysis in an industrial printing process

A statistical technique for fault analysis in industrial printing is reported. The method specifically deals with binary data, for which the results of the production process fall into two categories, rejected or accepted. The method is referred to as logistic regression, and is capable of predicting future fault occurrences by the analysis of current measurements from machine parts sensors. Individual analysis of each type of fault can determine which parts of the plant have a significant influence on the occurrence of such faults; it is also possible to infer which measurable process parameters have no significant influence on the generation of these faults. Information derived from the analysis can be helpful in the operator's interpretation of the current state of the plant. Appropriate actions may then be taken to prevent potential faults from occurring. The algorithm is being implemented as part of an applied self-learning expert system.