Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Operational performance of low-cost carriers and international airlines : New evidence using a bootstrap truncated regression

Between 2001 and 2005, the US airline industry faced financial turmoil. At the same time, the European airline industry entered a period of substantive deregulation. This period witnessed opportunities for low-cost carriers to become more competitive in the market as a result of these combined events. To help assess airline performance in the aftermath of these events, this paper provides new evidence of technical efficiency for 42 national and international airlines in 2006 using the data envelopment analysis (DEA) bootstrap approach first proposed by Simar and Wilson (J Econ, 136:31-64, 2007). In the first stage, technical efficiency scores are estimated using a bootstrap DEA model. In the second stage, a truncated regression is employed to quantify the economic drivers underlying measured technical efficiency. The results highlight the key role played by non-discretionary inputs in measures of airline technical efficiency.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Learning multidimensional joint control of a robot using receding horizon locally weighted regression

In this paper we explore the ability of a recent model-based learning technique Receding Horizon Locally Weighted Regression (RH-LWR) useful for learning temporally dependent systems. In particular this paper investigates the application of RH-LWR to learn control of Multiple-input Multiple-output robot systems. RH-LWR is demonstrated through learning joint velocity and position control of a three Degree of Freedom (DoF) rigid body robot.

Efficiency of research performance of Australian universities : a reappraisal using a bootstrap truncated regression approach

The motivation of the study stems from the results reported in the Excellence in Research for Australia (ERA) 2010 report. The report showed that only 12 universities performed research at or above international standards, of which, the Group of Eight (G8) universities filled the top eight spots. While performance of universities was based on number of research outputs, total amount of research income and other quantitative indicators, the measure of efficiency or productivity was not considered. The objectives of this paper are twofold. First, to provide a review of the research performance of 37 Australian universities using the data envelopment analysis (DEA) bootstrap approach of Simar and Wilson (2007). Second, to determine sources of productivity drivers by regressing the efficiency scores against a set of environmental variables.

A nonlinear PI and backstepping based controller for tractor-steerable trailer influenced by slip

Autonomous guidance of agricultural vehiclesis vital as mechanized farming production becomes more prevalent. It is crucial that tractor-trailers are guided with accuracy in both lateral and longitudinal directions, whilst being affected by large disturbance forces, or slips, owing to uncertain and undulating terrain. Successful research has been concentrated on trajectory control which can provide longitudinal and lateral accuracy if the vehicle moves without sliding, and the trailer is passive. In this paper, the problem of robust trajectory tracking along straight and circular paths of a tractor-steerable trailer is addressed. By utilizing a robust combination of backstepping and nonlinear PI control, a robust, nonlinear controller is proposed. For vehicles subjected to sliding, the proposed controller makes the lateral deviations and the orientation errors of the tractor and trailer converge to a neighborhood near the origin. Simulation results are presented to illustrate that the suggested controller ensures precise trajectory tracking in the presence of slip.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.