Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Improving stability of a DFIG-based wind power system with tuned damping controller

This paper focuses on the implementation of a damping controller for the doubly fed induction generator (DFIG) system. Coordinated tuning of the damping controller to enhance the damping of the oscillatory modes is presented using bacterial foraging technique. The effect of the tuned damping controller on converter ratings of the DFIG system is also investigated. The results of both eigenvalue analysis and the time-domain simulation studies are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The improvement of the fault ride-through capability of the system is also demonstrated.

Rough fuzzy control of SVC for power system stability enhancement

This paper presents a new approach to the design of a rough fuzzy controller for the control loop of the SVC (static VAR system) in a two area power system for stability enhancement with particular emphasis on providing effective damping for oscillatory instabilities. The performances of the rough fuzzy and the conventional fuzzy controller are compared with that of the conventional PI controller for a variety of transient disturbances, highlighting the effectiveness of the rough fuzzy controller in damping the inter-area oscillations. The effect of the rough fuzzy controller in improving the CCT (critical clearing time) of the two area system is elaborated in this paper as well.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Probability analysis of machine angle stability with non-gaussian wind power input

The security of power transfer across a given transmission link is typically a steady state assessment. This paper develops tools to assess machine angle stability as affected by a combination of faults and uncertainty of wind power using probability analysis. The paper elaborates on the development of the theoretical assessment tool and demonstrates its efficacy using single machine infinite bus system.

Performance evaluation of onsite sewage treatment : results of soil investigations

Background The onsite treatment of sewage and effluent disposal is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. It is important therefore that careful consideration is given to the design and location of onsite sewage treatment systems. This requires an understanding of the factors that influence treatment performance. The use of subsurface absorption systems is the most common form of effluent disposal for onsite sewage treatment, particularly for septic tanks. Also, in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Site specific factors play a key role in the onsite treatment of sewage. The project The primary aims of the research project were: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to evaluate current research relating to onsite sewage treatment; and, • to identify key issues where currently there is a lack of relevant research. These tasks were undertaken with the objective of facilitating the development of performance based planning and management strategies for onsite sewage treatment. The primary focus of this research project has been on septic tanks. By implication, the investigation has been confined to subsurface soil absorption systems. The design and treatment processes taking place within the septic tank chamber itself did not form a part of the investigation. Five broad categories of soil types prevalent in the Brisbane region have been considered in this project. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each of the different soil types. In the initial phase of the investigation, the majority of the systems evaluated were septic tanks. However, a small number of aerobic wastewater treatment systems (AWTS) were also included. The primary aim was to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of each different type of system investigated was relatively small. Consequently, this does not permit a statistical analysis to be undertaken of the results obtained for comparing different systems. This is an important issue considering the large number of soil physico-chemical parameters and landscape factors that can influence treatment performance and their wide variability. The report This report is the last in a series of three reports focussing on the performance evaluation of onsite treatment of sewage. The research project was initiated at the request of the Brisbane City Council. The project component discussed in the current report outlines the detailed soil investigations undertaken at a selected number of sites. In the initial field sampling, a number of soil chemical properties were assessed as indicators to investigate the extent of effluent flow and to help understand what soil factors renovate the applied effluent. The soil profile attributes, especially texture, structure and moisture regime were examined more in an engineering sense to determine the effect of movement of water into and through the soil. It is important to note that it is not only the physical characteristics, but also the chemical characteristics of the soil as well as landscape factors play a key role in the effluent renovation process. In order to understand the complex processes taking place in a subsurface effluent disposal area, influential parameters were identified using soil chemical concepts. Accordingly, the primary focus of this final phase of the research project was to identify linkages between various soil chemical parameters and landscape patterns and their contribution to the effluent renovation process. The research outcomes will contribute to the development of robust criteria for evaluating the performance of subsurface effluent disposal systems. The outcomes The key findings from the soil investigations undertaken are: • Effluent renovation is primarily undertaken by a combination of various soil physico-chemical parameters and landscape factors, thereby making the effluent renovation processes strongly site dependent. • Decisions regarding site suitability for effluent disposal should not be based purely in terms of the soil type. A number of other factors such as the site location in the catena, the drainage characteristics and other physical and chemical characteristics, also exert a strong influence on site suitability. • Sites, which are difficult to characterise in terms of suitability for effluent disposal, will require a detailed soil physical and chemical analysis to be undertaken to a minimum depth of at least 1.2 m. • The Ca:Mg ratio and Exchangeable Sodium Percentage are important parameters in soil suitability assessment. A Ca:Mg ratio of less than 0.5 would generally indicate a high ESP. This in turn would mean that Na and possibly Mg are the dominant exchangeable cations, leading to probable clay dispersion. • A Ca:Mg ratio greater than 0.5 would generally indicate a low ESP in the profile, which in turn indicates increased soil stability. • In higher clay percentage soils, low ESP can have a significant effect. • The presence of high exchangeable Na can be counteracted by the presence of swelling clays, and an exchange complex co-dominated by exchangeable Ca and exchangeable Mg. This aids absorption of cations at depth, thereby reducing the likelihood of dispersion. • Salt is continually added to the soil by the effluent and problems may arise if the added salts accumulate to a concentration that is harmful to the soil structure. Under such conditions, good drainage is essential in order to allow continuous movement of water and salt through the profile. Therefore, for a site to be sustainable, it would have a maximum application rate of effluent. This would be dependent on subsurface characteristics and the surface area available for effluent disposal. • The dosing regime for effluent disposal can play a significant role in the prevention of salt accumulation in the case of poorly draining sites. Though intermittent dosing was not considered satisfactory for the removal of the clogging mat layer, it has positive attributes in the context of removal of accumulated salts in the soil.

Stability studies of HIV-1 Pr55gag virus-like particles made in insect cells after storage in various formulation media

Background: HIV-1 Pr55gag virus-like particles (VLPs) expressed by baculovirus in insect cells are considered to be a very promising HIV-1 vaccine candidate, as they have been shown to elicit broad cellular immune responses when tested in animals, particularly when used as a boost to DNA or BCG vaccines. However, it is important for the VLPs to retain their structure for them to be fully functional and effective. The medium in which the VLPs are formulated and the temperature at which they are stored are two important factors affecting their stability. FINDINGS We describe the screening of 3 different readily available formulation media (sorbitol, sucrose and trehalose) for their ability to stabilise HIV-1 Pr55gag VLPs during prolonged storage. Transmission electron microscopy (TEM) was done on VLPs stored at two different concentrations of the media at three different temperatures (4[degree sign]C, --20[degree sign]C and -70[degree sign]C) over different time periods, and the appearance of the VLPs was compared. VLPs stored in 15% trehalose at -70[degree sign]C retained their original appearance the most effectively over a period of 12 months. VLPs stored in 5% trehalose, sorbitol or sucrose were not all intact even after 1 month storage at the temperatures tested. In addition, we showed that VLPs stored under these conditions were able to be frozen and re-thawed twice before showing changes in their appearance. Conclusions Although the inclusion of other analytical tools are essential to validate these preliminary findings, storage in 15% trehalose at -70[degree sign]C for 12 months is most effective in retaining VLP stability.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Delineating the practice profile of advanced practice nursing : a cross-sectional survey using the modified strong model of advanced practice

AIMS: To test a model that delineates advanced practice nursing from the practice profile of other nursing roles and titles. BACKGROUND: There is extensive literature on advanced practice reporting the importance of this level of nursing to contemporary health service and patient outcomes. Literature also reports confusion and ambiguity associated with advanced practice nursing. Several countries have regulation and delineation for the nurse practitioner, but there is less clarity in definition and service focus of other advanced practice nursing roles. DESIGN: A statewide survey. METHODS: Using the modified Strong Model of Advanced Practice Role Delineation tool, a survey was conducted in 2009 with a random sample of registered nurses/midwives from government facilities in Queensland, Australia. Analysis of variance compared total and subscale scores across groups according to grade. Linear, stepwise multiple regression analysis examined factors influencing advanced practice nursing activities across all domains. RESULTS: There were important differences according to grade in mean scores for total activities in all domains of advanced practice nursing. Nurses working in advanced practice roles (excluding nurse practitioners) performed more activities across most advanced practice domains. Regression analysis indicated that working in clinical advanced practice nursing roles with higher levels of education were strong predictors of advanced practice activities overall. CONCLUSION: Essential and appropriate use of advanced practice nurses requires clarity in defining roles and practice levels. This research delineated nursing work according to grade and level of practice, further validating the tool for the Queensland context and providing operational information for assigning innovative nursing service.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Natural convection flow in a strong cross magnetic field with radiation

The problem of MHD natural convection boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed in the presence of strong cross magnetic field with radiative heat transfer. In the analysis radiative heat flux is considered by adopting optically thick radiation limit. Attempt is made to obtain the solutions valid for liquid metals by taking Pr≪1. Boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation (SFF) and primitive variable formulation (PVF). Non-similar equations obtained from SFF are then simulated by implicit finite difference (Keller-box) method whereas parabolic partial differential equations obtained from PVF are integrated numerically by hiring direct finite difference method over the entire range of local Hartmann parameter, $xi$ . Further, asymptotic solutions are also obtained for large and small values of local Hartmann parameter $xi$ . A favorable agreement is found between the results for small, large and all values of $xi$ . Numerical results are also demonstrated graphically by showing the effect of various physical parameters on shear stress, rate of heat transfer, velocity and temperature.

Small signal stability analysis of a DFIG based wind power system with tuned damping controller under super/sub-synchronous mode of operation

This paper focuses on the super/sub-synchronous operation of the doubly fed induction generator (DFIG) system. The impact of a damping controller on the different modes of operation for the DFIG based wind generation system is investigated. The co-ordinated tuning of the damping controller to enhance the damping of the oscillatory modes using bacteria foraging (BF) technique is presented. The results from eigenvalue analysis are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The robustness issue of the damping controller is also investigated