A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

A variable diffusivity model for the drying of spherical food particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.

The impacts of variable speed limit on speed variation and headway distribution

This thesis investigates the impacts of variable speed limit on motorway speed variation and headway distribution. Initiative techniques of traffic flow categorisation study contribute in analysing the effects of variable speed limit on various traffic states. The project focuses on the speed harmonisation impacts within and across lanes as well as the uniformity of headway spread in the application of variable speed limit.

Imputing a continuous income variable from a bracketed income variable with special attention to missing observations

This paper proposes a method, based on polychotomous discrete choice methods, to impute a continuous measure of income when only a bracketed measure of income is available and for only a subset of the obsevations. The method is shown to perform well with CP5 data. © 1991.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

Evolution of Langmuir waves in a plasma contaminated by variable-charge impurities

The propagation of Langmuir waves in nonisothermal plasmas contaminated by fine dust particles with variable charge is investigated for a self-consistent closed system. Dust charge relaxation, ionization, recombination, and collisional dissipation are taken into account. It is shown that the otherwise unstable coupling of the Langmuir and dust-charge relaxation modes becomes stable and the Langmuir waves are frequency down-shifted.

Low-frequency dispersion properties of plasmas with variable-charge impurities

A theory of low-frequency dust-acoustic waves in low-temperature collisional plasmas containing variable-charge impurities is presented. Physical processes such as dust-charge relaxation, ionization-recombination of the electrons and ions, electron and ion elastic collisions with neutrals and dusts, as well as charging collisions with the dusts, are taken into account. Inclusion of these processes allows a balance of the plasma particles and thus a self-consistent determination of the stationary state of the unperturbed plasma. The generalized dispersion relation describing the propagation and damping of the dust acoustic waves is derived and analyzed. © 2000 American Institute of Physics.

Rectifier systems for variable speed wind generation : a review

The drive towards high efficiency wind energy conversion systems has resulted in almost all the modern wind turbines to operate in the variable speed mode which inevitably requires back-to-back power electronic converters to decouple generator dynamics from the grid. The aim of this paper is to present an analysis on suitable topologies for the generator-side converter (rectifier) of the back-to-back converter arrangement. Performance of the two most popular rectifier systems, namely, the passive diode bridge rectifier and the active six-switch two-level rectifier are taken as two extremes to evaluate other topologies presented in this paper. The other rectifier systems considered in this study include combinations of a diode bridge rectifier and electronic reactance(s), a combination of a rectifier and a dc-dc converter and a half controlled rectifier. Diode-clamped and capacitor-clamped three-level active rectifier topologies and their possible switch reductions are also discussed in relation to the requirements of modern high power wind energy conversion systems (WECSs). Simulation results are presented to support conclusion derived from this analysis.

Controller design for variable-speed permanent magnet wind turbine generators interfaced with Z-source inverter

Increased awareness of environmental concerns has caused greater interest in developing power sources based on renewable technologies, such as wind. Due to the intermittent nature of the wind speed, output voltage and frequency of the direct driven permanent magnet synchronous generators (PMSG) are normally unsteady. Recently proposed Z-source inverter has been considered as a potential solution for grid interfacing wind power generators, thanks to buck-boost function that the single stage Z-source inverter can offer. Two control methodologies, namely unified controller for isolated operation and a multi-loop controller for grid interfaced operation are investigated in this paper. Theoretical analysis of these two control schemes is presented and experimental results to verify the effectiveness of the control method are also included.

Z-source converter based grid-interface for variable-speed permanent magnet wind turbine generators

A Z-source inverter based grid-interface for a variable-speed wind turbine connected to a permanent magnet synchronous generator is proposed. A control system is designed to harvest maximum wind energy under varied wind conditions with the use of the permanent magnet synchronous generator, diode-rectifier and Z-source inverter. Control systems for speed regulation of the generator and for DC- and AC- sides of the Z-source inverter are investigated using computer simulations and laboratory experiments. Simulation and experimental results verify the efficacy of the proposed approach.

Die Auswirkungen von Neid auf individuelle Leistungen: Ergebnisse einer Panelanalyse

Relative Einkommensunterschiede lösen innerhalb einer Referenzgruppe oftmals Neid aus und beeinflussen damit die individuelle Leistungsbereitschaft. In der ökonomischen Forschung ist bislang dieser Zusammenhang wenig untersucht worden. Unser Beitrag analysiert den Einfluss von relativen Einkommensunterschieden auf die Leistung von Fußballprofis der deutschen Bundesliga. Insgesamt werden 1040 Spieler über einen Zeitraum von 8 Spielzeiten zwischen 1995 und 2004 untersucht. Relative Einkommensunterschiede zwischen Mannschaftskollegen erweisen sich als entscheidender Einfluss auf die individuelle Leistung der Spieler. Eine Verschlechterung in der relativen Einkommensposition vermindert ceteris paribus die individuelle Leistungsbereitschaft. Eine höhere Einkommensungleichheit verstärkt solche positionsbedingten Externalitäten. Relative income differences are likely to lead to envy within a reference group. Envy in turn influences social behavior and individual performance. While positional concerns are apparent in daily life, empirical evidence is rare in the economic literature. This paper investigates the impact of the relative income position on individuals’ performance or productivity. As „performance“ is difficult to measure we turn to soccer players whose performance has been well documented. The broad sample covers eight seasons of the German premier soccer league (Bundesliga) between 1995 and 2004, and includes 1040 players, a salary proxy and several performance variables. The results show that player performance is strongly affected by relative income position. A disadvantage in the relative income position reduces productivity. The larger the income differences within a team, the stronger are the effects of positional concern. Team composition also significantly affects behaviour.