An algorithm for isentropic flow

An efficient algorithm is presented for the solution of the equations of isentropic gas dynamics with a general convex gas law. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only two function evaluations in each computational cell are required. The scheme is applied to a standard test problem in gas dynamics for a polytropic gas

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.

An isentropic flow algorithm with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional equations of isentropic flow in a generalised coordinate system, and with a general convex gas law. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm requires only one function evaluation of the gas law in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 3 flow of air past a circular cylinder. Furthermore, the algorithm also applies to shallow water flows by employing the familiar gas dynamics analogy.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

An improved algorithm for generating global window brightness temperatures from multiple satellite infrared imagery

An improved algorithm for the generation of gridded window brightness temperatures is presented. The primary data source is the International Satellite Cloud Climatology Project, level B3 data, covering the period from July 1983 to the present. The algorithm rakes window brightness, temperatures from multiple satellites, both geostationary and polar orbiting, which have already been navigated and normalized radiometrically to the National Oceanic and Atmospheric Administration's Advanced Very High Resolution Radiometer, and generates 3-hourly global images on a 0.5 degrees by 0.5 degrees latitude-longitude grid. The gridding uses a hierarchical scheme based on spherical kernel estimators. As part of the gridding procedure, the geostationary data are corrected for limb effects using a simple empirical correction to the radiances, from which the corrected temperatures are computed. This is in addition to the application of satellite zenith angle weighting to downweight limb pixels in preference to nearer-nadir pixels. The polar orbiter data are windowed on the target time with temporal weighting to account for the noncontemporaneous nature of the data. Large regions of missing data are interpolated from adjacent processed images using a form of motion compensated interpolation based on the estimation of motion vectors using an hierarchical block matching scheme. Examples are shown of the various stages in the process. Also shown are examples of the usefulness of this type of data in GCM validation.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

Memory-based Embodied Cognition: a computational architecture

At its most fundamental, cognition as displayed by biological agents (such as humans) may be said to consist of the manipulation and utilisation of memory. Recent discussions in the field of cognitive robotics have emphasised the role of embodiment and the necessity of a value or motivation for autonomous behaviour. This work proposes a computational architecture – the Memory-Based Cognitive (MBC) architecture – based upon these considerations for the autonomous development of control of a simple mobile robot. This novel architecture will permit the exploration of theoretical issues in cognitive robotics and animal cognition. Furthermore, the biological inspiration of the architecture is anticipated to result in a mobile robot controller which displays adaptive behaviour in unknown environments.

A geometric algorithm for an artificial life form based on anachronistic methods

Modern methods of spawning new technological motifs are not appropriate when it is desired to realize artificial life as an actual real world entity unto itself (Pattee 1995; Brooks 2006; Chalmers 1995). Many fundamental aspects of such a machine are absent in common methods, which generally lack methodologies of construction. In this paper we mix classical and modern studies in order to attempt to realize an artificial life form from first principles. A model of an algorithm is introduced, its methodology of construction is presented, and the fundamental source from which it sprang is discussed.

Algorithm for generating defective graphene sheets

An algorithm is presented for the generation of molecular models of defective graphene fragments, containing a majority of 6-membered rings with a small number of 5- and 7-membered rings as defects. The structures are generated from an initial random array of points in 2D space, which are then subject to Delaunay triangulation. The dual of the triangulation forms a Voronoi tessellation of polygons with a range of ring sizes. An iterative cycle of refinement, involving deletion and addition of points followed by further triangulation, is performed until the user-defined criteria for the number of defects are met. The array of points and connectivities are then converted to a molecular structure and subject to geometry optimization using a standard molecular modeling package to generate final atomic coordinates. On the basis of molecular mechanics with minimization, this automated method can generate structures, which conform to user-supplied criteria and avoid the potential bias associated with the manual building of structures. One application of the algorithm is the generation of structures for the evaluation of the reactivity of different defect sites. Ab initio electronic structure calculations on a representative structure indicate preferential fluorination close to 5-ring defects.