Examples illustrating the use of renormalization techniques for singularly perturbed differential equations

With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

Evaluation of resonant damping techniques for Z-source current-type inverter

For the renewable energy sources whose outputs vary continuously, a Z-source current-type inverter has been proposed as a possible buck-boost alternative for grid-interfacing. With a unique X-shaped LC network connected between its dc power source and inverter topology, Z-source current-type inverter is however expected to suffer from compounded resonant complications in addition to those associated with its second-order output filter. To improve its damping performance, this paper proposes the careful integration of Posicast or three-step compensators before the inverter pulse-width modulator for damping triggered resonant oscillations. In total, two compensators are needed for wave-shaping the inverter boost factor and modulation ratio, and they can conveniently be implemented using first-in first-out stacks and embedded timers of modern digital signal processors widely used in motion control applications. Both techniques are found to damp resonance of ac filter well, but for cases of transiting from current-buck to boost state, three-step technique is less effective due to the sudden intermediate discharging interval introduced by its non-monotonic stepping (unlike the monotonic stepping of Posicast damping). These findings have been confirmed both in simulations and experiments using an implemented laboratory prototype.

A unique battery/supercapacitor direct integration scheme for hybrid electric vehicles

Battery/supercapacitor hybrid energy storage systems have been gaining popularity in electric vehicles due to their excellent power and energy performances. Conventional designs of such systems require interfacing dc-dc converters. These additional dc-dc converters increase power loss, complexity, weight and cost. Therefore, this paper proposes a new direct integration scheme for battery/supercapacitor hybrid energy storage systems using a double ended inverter system. This unique approach eliminates the need for interfacing converters and thus it is free from aforementioned drawbacks. Furthermore, the proposed system offers seven operating modes to improve the effective use of available energy in a typical drive cycle of a hybrid electric vehicle. Simulation results are presented to verify the efficacy of the proposed system and control techniques.

A direct integration scheme for battery-supercapacitor hybrid energy storage systems with the use of grid side inverter

Battery-supercapacitor hybrid energy storage systems are becoming popular in the renewable energy sector due to their improved power and energy performances. These hybrid systems require separate dc-dc converters, or at least one dc-dc converter for the supercapacitor bank, to connect them to the dc-link of the grid interfacing inverter. These additional dc-dc converters increase power losses, complexity and cost. Therefore, possibility of their direct connection is investigated in this paper. The inverter system used in this study is formed by cascading two 3-level inverters, named as the “main inverter” and the “auxiliary inverter”, through a coupling transformer. In the test system the main inverter is connected with the rectified output of a wind generator while the auxiliary inverter is directly attached to a battery and a supercapacitor bank. The major issues with this approach are the dynamic changes in dc-link voltages and inevitable imbalances in the auxiliary inverter voltages, which results in unevenly distributed space vectors. A modified SVM technique is proposed to solve this issue. A PWM based time sharing method is proposed for power sharing between the battery and the supercapacitor. Simulation results are presented to verify the efficacy of the proposed modulation and control techniques.

A hybrid cascaded multilevel inverter with supercapacitor direct integration for wind power systems

This paper presents a grid-side inverter based supercapacitor direct integration scheme for wind power systems. The inverter used in this study consists of a conventional two-level inverter and three H-bridge modules. Three supercapacitor banks are directly connected to the dc-links of H-bridge modules. This approach eliminates the need for interfacing dc-dc converters and thus considerably improves the overall efficiency. However, for the maximum utilization of super capacitors their voltages should be allowed to vary. As a result of this variable voltage space vectors of the hybrid inverter get distributed unevenly. To handle this issue, a modified PWM method and a space vector modulation method are proposed and they can generate undistorted current even in the presence of unevenly distributed space vectors. A supercapacitor voltage balancing method is also presented in this paper. Simulation results are presented to validate the efficacy of the proposed scheme, modulation methods and control techniques.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

A framework for model integration and holistic modelling of socio-technical systems

This paper presents a layered framework for the purposes of integrating different Socio-Technical Systems (STS) models and perspectives into a whole-of-systems model. Holistic modelling plays a critical role in the engineering of STS due to the interplay between social and technical elements within these systems and resulting emergent behaviour. The framework decomposes STS models into components, where each component is either a static object, dynamic object or behavioural object. Based on existing literature, a classification of the different elements that make up STS, whether it be a social, technical or a natural environment element, is developed; each object can in turn be classified according to the STS elements it represents. Using the proposed framework, it is possible to systematically decompose models to an extent such that points of interface can be identified and the contextual factors required in transforming the component of one model to interface into another is obtained. Using an airport inbound passenger facilitation process as a case study socio-technical system, three different models are analysed: a Business Process Modelling Notation (BPMN) model, Hybrid Queue-based Bayesian Network (HQBN) model and an Agent Based Model (ABM). It is found that the framework enables the modeller to identify non-trivial interface points such as between the spatial interactions of an ABM and the causal reasoning of a HQBN, and between the process activity representation of a BPMN and simulated behavioural performance in a HQBN. Such a framework is a necessary enabler in order to integrate different modelling approaches in understanding and managing STS.

Multi-objective models and techniques for analysing the absolute capacity of railway networks

Railway capacity determination and expansion are very important topics. In prior research, the competition between different entities such as train services and train types, on different network corridors however have been ignored, poorly modelled, or else assumed to be static. In response, a comprehensive set of multi-objective models have been formulated in this article to perform a trade-off analysis. These models determine the total absolute capacity of railway networks as the most equitable solution according to a clearly defined set of competing objectives. The models also perform a sensitivity analysis of capacity with respect to those competing objectives. The models have been extensively tested on a case study and their significant worth is shown. The models were solved using a variety of techniques however an adaptive E constraint method was shown to be most superior. In order to identify only the best solution, a Simulated Annealing meta-heuristic was implemented and tested. However a linearization technique based upon separable programming was also developed and shown to be superior in terms of solution quality but far less in terms of computational time.

Green: Exploring the aestheticized use of chroma-key techniques and technologies in two intermedial productions

Peggy Shaw’s RUFF, (USA 2013) and Queensland Theatre Company’s collaboration with Queensland University of Technology, Total Dik!, (Australia 2013) overtly and evocatively draw on an aestheticized use of the cinematic techniques and technologies of Chroma Key to reveal the tensions in their production and add layers to their performances. In doing so they offer invaluable insight where the filmic and theatrical approaches overlap. This paper draws on Eckersall, Grehan and Scheer’s New Media Dramaturgy (2014) to reposition the frame as a contribution to intermedial theatre and performance practices in light of increasing convergence between seemingly disparate discourses. In RUFF, the scenic environment replicates a chroma-key ‘studio’ which facilitates the reconstruction of memory displaced after a stroke. RUFF uses the screen and projections to recall crooners, lounge singers, movie stars, rock and roll bands, and an eclectic line of eccentric family members living inside Shaw. While the show pays tribute to those who have kept her company across decades of theatrical performance, use of non-composited chroma-key technique as a theatrical device and the work’s taciturn revelation of the production process during performance, play a central role in its exploration of the juxtaposition between its reconstructed form and content. In contrast Total Dik! uses real-time green screen compositing during performance as a scenic device. Actors manipulate scale models, refocus cameras and generate scenes within scenes in the construction of the work’s examination of an isolated Dictator. The ‘studio’ is again replicated as a site for (re)construction, only in this case Total Dik! actively seeks to reveal the process of production as the performance plays out. Building on RUFF, and other works such as By the Way, Meet Vera Stark, (2012) and Hotel Modern’s God’s Beard (2012), this work blends a convergence of mobile technologies, models, and green screen capture to explore aspects of transmedia storytelling in a theatrical environment (Jenkins, 2009, 2013). When a green screen is placed on stage, it reads at once as metaphor and challenge to the language of theatre. It becomes, or rather acts, as a ‘sign’ that alludes to the nature of the reconstructed, recomposited, manipulated and controlled. In RUFF and in Total Dik!, it is also a place where as a mode of production and subsequent reveal, it adds weight to performance. These works are informed by Auslander (1999) and Giesenkam (2007) and speak to and echo Lehmann’s Postdramatic Theatre (2006). This paper’s consideration of the integration of studio technique and live performance as a dynamic approach to multi-layered theatrical production develops our understanding of their combinatory use in a live performance environment.

Techniques to effectively buffer schedules in the face of uncertainties

Resource assignment and scheduling is a difficult task when job processing times are stochastic, and resources are to be used for both known and unknown demand. To operate effectively within such an environment, several novel strategies are investigated. The first focuses upon the creation of a robust schedule, and utilises the concept of strategically placed idle time (i.e. buffering). The second approach introduces the idea of maintaining a number of free resources at each time, and culminates in another form of strategically placed buffering. The attraction of these approaches is that they are easy to grasp conceptually, and mimic what practitioners already do in practice. Our extensive numerical testing has shown that these techniques ensure more prompt job processing, and reduced job cancellations and waiting time. They are effective in the considered setting and could easily be adapted for many real life problems, for instance those in health care. This article has more importantly demonstrated that integrating the two approaches is a better strategy and will provide an effective stochastic scheduling approach.

Hybrid metaheuristic techniques for optimising sugarcane rail operations

Mixed integer programming and parallel-machine job shop scheduling are used to solve the sugarcane rail transport scheduling problem. Constructive heuristics and metaheuristics were developed to produce a more efficient scheduling system and so reduce operating costs. The solutions were tested on small and large size problems. High-quality solutions and improved CPU time are the result of developing new hybrid techniques which consist of different ways of integrating simulated annealing and Tabu search techniques.

Simulated systems optimization through response surface techniques [Optimización de sistemas simulados a través de técnicas de superficie de respuesta]

The purpose of this article is to show the applicability and benefits of the techniques of design of experiments as an optimization tool for discrete simulation models. The simulated systems are computational representations of real-life systems; its characteristics include a constant evolution that follows the occurrence of discrete events along the time. In this study, a production system, designed with the business philosophy JIT (Just in Time) is used, which seeks to achieve excellence in organizations through waste reduction in all the operational aspects. The most typical tool of JIT systems is the KANBAN production control that seeks to synchronize demand with flow of materials, minimize work in process, and define production metrics. Using experimental design techniques for stochastic optimization, the impact of the operational factors on the efficiency of the KANBAN / CONWIP simulation model is analyzed. The results show the effectiveness of the integration of experimental design techniques and discrete simulation models in the calculation of the operational parameters. Furthermore, the reliability of the methodologies found was improved with a new statistical consideration.

A mathematical framework for expanding a railway’s theoretical capacity

Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Special Issue on Spatial Moment Techniques for Modelling Biological Processes

Over the last two decades, there has been an increasing awareness of, and interest in, the use of spatial moment techniques to provide insight into a range of biological and ecological processes. Models that incorporate spatial moments can be viewed as extensions of mean-field models. These mean-field models often consist of systems of classical ordinary differential equations and partial differential equations, whose derivation, at some point, hinges on the simplifying assumption that individuals in the underlying stochastic process encounter each other at a rate that is proportional to the average abundance of individuals. This assumption has several implications, the most striking of which is that mean-field models essentially neglect any impact of the spatial structure of individuals in the system. Moment dynamics models extend traditional mean-field descriptions by accounting for the dynamics of pairs, triples and higher n-tuples of individuals. This means that moment dynamics models can, to some extent, account for how the spatial structure affects the dynamics of the system in question.