Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Making an IMPACT: Campus-wide collaboration for course and learning space transformation

At Purdue University, the Libraries participate in a provost-initiated, campus-wide course redesign program called Instruction Matters: Purdue Academic Course Transformation (IMPACT). This initiative aims to bring active-learning to foundational courses traditionally taught through lectures. Purdue librarians recognized the IMPACT initiative as one way to enter the conversations blooming on our campus about the nature of learning, curriculum design, and how space design impacts potential learning. This article presents three perspectives: 1) the information literacy coordinator, 2) a libraries’ administrator with a gift for space planning, and; 3) an in-the-trenches liaison to course redesign projects. Each discusses the IMPACT initiative from his or her unique perspective and view of its impact on librarian roles. Collectively, the article explains why we think it is essential that this kind of campus effort is supported by libraries.

Optimal scheduling of hydro-thermal power systems under shortage

The problem of optimal scheduling of the generation of a hydro-thermal power system that is faced with a shortage of energy is studied. The deterministic version of the problem is first analyzed, and the results are then extended to cases where the loads and the hydro inflows are random variables.

A Combination of Hexagonal and 12-Sided Polygonal Voltage Space Vector PWM Control for IM Drives Using Cascaded Two-Level Inverters

This paper proposes a multilevel inverter configuration which produces a hexagonal voltage space vector structure in the lower modulation region and a 12-sided polygonal space vector structure in the overmodulation region. A conventional multilevel inverter produces 6n plusmn 1 (n = odd) harmonics in the phase voltage during overmodulation and in the extreme square-wave mode of operation. However, this inverter produces a 12-sided polygonal space vector location, leading to the elimination of 6n plusmn 1 (n = odd) harmonics in the overmodulation region extending to a final 12-step mode of operation with a smooth transition. The benefits of this arrangement are lower losses and reduced torque pulsation in an induction motor drive fed from this converter at higher modulation indexes. The inverter is fabricated by using three conventional cascaded two-level inverters with asymmetric dc-bus voltages. A comparative simulation study of the harmonic distortion in the phase voltage and associated losses in conventional multilevel inverters and that of the proposed inverter is presented in this paper. Experimental validation on a prototype shows that the proposed converter is suitable for high-power applications because of low harmonic distortion and low losses.

Exploring profit - Sustainability trade-offs in cropping systems using evolutionary algorithms

Models that implement the bio-physical components of agro-ecosystems are ideally suited for exploring sustainability issues in cropping systems. Sustainability may be represented as a number of objectives to be maximised or minimised. However, the full decision space of these objectives is usually very large and simplifications are necessary to safeguard computational feasibility. Different optimisation approaches have been proposed in the literature, usually based on mathematical programming techniques. Here, we present a search approach based on a multiobjective evaluation technique within an evolutionary algorithm (EA), linked to the APSIM cropping systems model. A simple case study addressing crop choice and sowing rules in North-East Australian cropping systems is used to illustrate the methodology. Sustainability of these systems is evaluated in terms of economic performance and resource use. Due to the limited size of this sample problem, the quality of the EA optimisation can be assessed by comparison to the full problem domain. Results demonstrate that the EA procedure, parameterised with generic parameters from the literature, converges to a useable solution set within a reasonable amount of time. Frontier ‘‘peels’’ or Pareto-optimal solutions as described by the multiobjective evaluation procedure provide useful information for discussion on trade-offs between conflicting objectives.

A Multilevel Inverter with Hexagonal and 12-sided Polygonal Space Vector Structure for Induction Motor Drive

This paper proposes a multilevel inverter which produces hexagonal voltage space vector structure in lower modulation region and a 12-sided polygonal space vector structure in the over-modulation region. Normal conventional multilevel inverter produces 6n +/- 1 (n=odd) harmonics in the phase voltage during over-modulation and in the extreme square wave mode operation. However, this inverter produces a 12-sided polygonal space vector location leading to the elimination of 6n 1 (n=odd) harmonics in over-modulation region extending to a final 12-step mode operation. The inverter consists of three conventional cascaded two level inverters with asymmetric dc bus voltages. The switching frequency of individual inverters is kept low throughout the modulation index. In the low speed region, hexagonal space phasor based PWM scheme and in the higher modulation region, 12-sided polygonal voltage space vector structure is used. Experimental results presented in this paper shows that the proposed converter is suitable for high power applications because of low harmonic distortion and low switching losses.

Space allowances for confined livestock and their determination from allometric principles

The amount of space provided to animals governs important elements of their behaviour and, hence, is critical for their health and welfare. We review the use of allometric principles and equations to estimate the static space requirements of animals when standing and lying, and the space required for animals to feed, drink, stand-up and lie-down. We use the research literature relating to transportation and intensive housing of sheep and cattle to assess the validity of allometric equations for estimating space allowances. We investigated these areas because transportation and intensive housing provide points along a continuum in terms of the duration of confinement, (from hours to months) and spatial requirements are likely to increase with increasing duration of confinement, as animals will need to perform a greater behavioural repertoire for long-term survival, health and welfare. We find that, although there are theoretical reasons why allometric relationships to space allowances may vary slightly for different classes of stock, space allowances that have been demonstrated to have adverse effects on animal welfare during transportation correlated well with an inability to accommodate standing animals, as estimated from allometry. For intensive housing, we were able to detect a space allowance below which there were adverse effects on welfare. For short duration transportation during which animals remain standing, a space allowance per animal described by the allometric equation: area (m^2) = 0.020W^0.66, where W = liveweight (kg), would appear to be appropriate. Where it is desirable for all animals to lie simultaneously, then a minimum space allowance per animal described by the allometric equation: area (m^2) = 0.027W^0.66 appears to permit this, given that animals in a group time-share space. However, there are insufficient data to determine whether this allowance onboard a vehicle/vessel would enable animals to move and access food and water with ease. In intensive housing systems, a minimum space allowance per animal described by the allometric equation: area (m^2) = 0.033W^0.66 appears to be the threshold below which there are adverse effects on welfare. These suggested space allowances require verification with a range of species under different thermal conditions and, for transportation, under different conditions of vehicular/vessel stability. The minimum length of trough per animal (L in m) required for feeding and drinking can be determined from L = 0.064W^0.33, with the number of animals required to feed/drink simultaneously taken into account, together with any requirement to minimise competition. This also requires verification with a range of species. We conclude that allometric relationships are an appropriate basis for the formulation of space allowances for livestock.

Using automated supplementation systems to meet growth targets for grazing sheep

Remote drafting technology now available for sheep allows targeted supplementation of individuals within a grazing flock. This paper reports results of three experiments. Experiment 1 examined the weight change of Merino wethers allowed access to either lupin grain or whole cottonseed 0, 1, 2 or 7 days/week for 6 weeks. Experiment 2 examined the weight change of Merino wethers allowed access to either lupins or a sorghum + cottonseed meal (CSM) supplement 0, 2, 4 or 7 days/week for 8 weeks. Experiment 3 investigated the relationship between five allocations of trough space at the supplement self-feeders (5–50 cm/sheep) and the weight change of Merino wethers allowed access to lupins 1 day/week for 8 weeks. In all experiments, the Merino wethers had free access as a single group to drinking water and low quality hay in a large group pen and were allowed access to supplement once per day on their scheduled days of access. No water was available in the areas containing supplement, but one-way flow gates allowed animals to return to the group pen in their own time. There was a linear response in growth rate to increased frequency of access to lupins in Experiments 1 and 2, with each additional day of access increasing liveweight gain by 26 and 21 g/day, respectively. Similarly, the response to the sorghum + CSM supplement was linear, although significantly lower (P < 0.05), at 12 g/day. Providing access to whole cottonseed resulted in no significant change in growth rate compared with the control animals. In Experiment 3, decreasing trough space from 50 to 5 cm/sheep had no effect on sheep liveweight change. It was concluded that the relationships developed here, for growth response to increased frequency of access to lupins or a sorghum + CSM supplement, could be used to indicate the most appropriate frequency of access to supplement, through a remote drafting unit, to achieve sheep weight change targets. Also, that a trough space of 5 cm/sheep appears adequate in this supplementation system.

Assessing the sustainability of wheat-based cropping systems using APSIM: Model parameterisation and evaluation

Assessing the sustainability of crop and soil management practices in wheat-based rotations requires a well-tested model with the demonstrated ability to sensibly predict crop productivity and changes in the soil resource. The Agricultural Production Systems Simulator (APSIM) suite of models was parameterised and subsequently used to predict biomass production, yield, crop water and nitrogen (N) use, as well as long-term soil water and organic matter dynamics in wheat/chickpea systems at Tel Hadya, north-western Syria. The model satisfactorily simulated the productivity and water and N use of wheat and chickpea crops grown under different N and/or water supply levels in the 1998-99 and 1999-2000 experimental seasons. Analysis of soil-water dynamics showed that the 2-stage soil evaporation model in APSIM's cascading water-balance module did not sufficiently explain the actual soil drying following crop harvest under conditions where unused water remained in the soil profile. This might have been related to evaporation from soil cracks in the montmorillonitic clay soil, a process not explicitly simulated by APSIM. Soil-water dynamics in wheat-fallow and wheat-chickpea rotations (1987-98) were nevertheless well simulated when the soil water content in 0-0.45 m soil depth was set to 'air dry' at the end of the growing season each year. The model satisfactorily simulated the amounts of NO3-N in the soil, whereas it underestimated the amounts of NH 4-N. Ammonium fixation might be part of the soil mineral-N dynamics at the study site because montmorillonite is the major clay mineral. This process is not simulated by APSIM's nitrogen module. APSIM was capable of predicting long-term trends (1985-98) in soil organic matter in wheat-fallow and wheat-chickpea rotations at Tel Hadya as reported in literature. Overall, results showed that the model is generic and mature enough to be extended to this set of environmental conditions and can therefore be applied to assess the sustainability of wheat-chickpea rotations at Tel Hadya.

A Pulsewidth Modulated Control of Induction Motor Drive Using Multilevel 12-Sided Polygonal Voltage Space Vectors

In this paper, a novel 12-sided polygonal space vector structure is proposed for an induction motor drive. The space vector pattern presented in this paper consists of two 12-sided concentric polygons with the outer polygon having a radius double the inner one. As compared to previously reported 12-sided polygonal space vector structures, this paper subdivides the space vector plane into smaller sized triangles. This helps in reducing the switching frequency of the inverters without deteriorating the output voltage quality. It also reduces the device ratings and dv/dt stress on the devices to half. At the same time, other benefits obtained from the existing 12-sided space vector structure, such as increased linear modulation range and complete elimination of 5th and 7th order harmonics in the phase voltage, are also retained in this paper. The space vector structure is realized by feeding an open-end induction motor with two conventional three-level neutral point clamped (NPC) inverters with asymmetric isolated dc link voltage sources. The neutral point voltage fluctuations in the three-level NPC inverters are eliminated by utilizing the switching state multiplicities for a space vector point. The pulsewidth modulation timings are calculated using sampled reference waveform amplitudes and are explained in detail in this paper. Experimental verification on a laboratory prototype shows that this configuration may be considered suitable for high power drives.

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

Multi-time scale analysis applied to long time simulation of power systems

The results are presented of applying multi-time scale analysis using the singular perturbation technique for long time simulation of power system problems. A linear system represented in state-space form can be decoupled into slow and fast subsystems. These subsystems can be simulated with different time steps and then recombined to obtain the system response. Simulation results with a two-time scale analysis of a power system show a large saving in computational costs.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

Social work and complex care systems: The case of people hospitalised with a disability

Health and hospital system reforms prioritise efficiency. However, initiatives can impact on people with new or existing disabilities who require time to maximise functional independence. With greater demands for shorter hospital stays social workers face increasing pressure to facilitate discharge. This paper reports findings from research identifying factors contributing to extended stays for adults with disabilities. We sought to better understand patient characteristics and discharge planning challenges by analysing a clinical data set of 80 patients and qualitative interviews with five experienced hospital social workers. Three key factors are identified: issues around rehabilitation services; assessment and planning for community care; and availability of and access to discharge options. Strategies to reduce length of stay are reported. We argue that building collaborative partnerships and working across multiple, complex systems and disciplines are vital to ensure these patients access appropriate community-based resources within the current health reform environment.