A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Focus on opportunities as a boundary condition of the relationship between job control and work engagement: A multi-sample, multi-method study

The concept of focus on opportunities describes how many new goals, options, and possibilities employees believe to have in their personal future at work. In this multi-sample, multi-method study, the authors investigated relationships between focus on opportunities and general and daily work engagement and the moderating role of focus on opportunities on between- and within-person relationships between job control and work engagement. Based on a social cognitive theory framework on the motivating potential of a future temporal focus, it was hypothesized that focus on opportunities is positively related to work engagement. Further, consistent with the notion of compensatory resources, it was expected that job control is not related to work engagement among employees with a high focus on opportunities, whereas job control, as an external resource of the work environment, is positively related to work engagement among employees with a low focus on opportunities. Both a cross-sectional survey study (N=174) and a daily diary study (N=64) supported the hypotheses. The study contributes to research on the job demands-resources model as it emphasizes the role of focus on opportunities as a motivational factor in the relationship between job control and work engagement.

How do consumers react to physically larger models? Effects of model body size, weight control beliefs and product type on evaluations and body perceptions

The purpose of this article is to examine how a consumer’s weight control beliefs (WCB), a female advertising model’s body size (slim or large) and product type influence consumer evaluations and consumer body perceptions. The study uses an experiment of 371 consumers. The design of the experiment was a 2 (weight control belief: internal, external) X 2 (model size: larger sized, slim) X 2 (product type: weight controlling, non-weight controlling) between-participants factorial design. Results reveal two key contributions. First, larger sized models result in consumers feeling less pressure from society to be thin, viewing their actual shape as slimmer relative to viewing a slim model and wanting a thinner ideal body shape. Slim models result in the opposite effects. Second this research reveals a boundary condition for the extent to which endorser–product congruency theory can be generalized to endorsers of a larger body size. Results indicate that consumer WCB may be a useful variable to consider when marketers consider the use of larger models in advertising.

Shock control bump design optimization on Natural Laminar Aerofoil

The chapter investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic flow on the suction/pressure sides of transonic aerofoil that leads delaying shock occurrence or weakening of shock strength. Such an AFC technique reduces significantly the total drag at transonic speeds. This chapter considers the SCB shape design optimisation at two boundary layer transition positions (0 and 45%) using an Euler software coupled with viscous boundary layer effects and robust Evolutionary Algorithms (EAs). The optimisation method is based on a canonical Evolution Strategy (ES) algorithm and incorporates the concepts of hierarchical topology and parallel asynchronous evaluation of candidate solution. Two test cases are considered with numerical experiments; the first test deals with a transition point occurring at the leading edge and the transition point is fixed at 45% of wing chord in the second test. Numerical results are presented and it is demonstrated that an optimal SCB design can be found to significantly reduce transonic wave drag and improves lift on drag (L/D) value when compared to the baseline aerofoil design.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

Hierarchical robust design optimisation of shock control bump devices for airfoil drag reduction

The paper investigates a detailed Active Shock Control Bump Design Optimisation on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 to reduce cruise drag at transonic flow conditions using Evolutionary Algorithms (EAs) coupled to a robust design approach. For the uncertainty design parameters, the positions of boundary layer transition (xtr) and the coefficient of lift (Cl) are considered (250 stochastic samples in total). In this paper, two robust design methods are considered; the first approach uses a standard robust design method, which evaluates one design model at 250 stochastic conditions for uncertainty. The second approach is the combination of a standard robust design method and the concept of hierarchical (multi-population) sampling (250, 50, 15) for uncertainty. Numerical results show that the evolutionary optimization method coupled to uncertainty design techniques produces useful and reliable Pareto optimal SCB shapes which have low sensitivity and high aerodynamic performance while having significant total drag reduction. In addition,it also shows the benefit of using hierarchical robust method for detailed uncertainty design optimization.

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Maintaining a cognitive map in darkness : the need to fuse boundary knowledge with path integration

Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's "cognitive map", or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and - we conjecture - necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on their implications and significance for the design, analysis and interpretation of experiments.

Compaction control of topography and fault network structure along strike-slip faults in sedimentary basins

Strike-slip faults commonly display structurally complex areas of positive or negative topography. Understanding the development of such areas has important implications for earthquake studies and hydrocarbon exploration. Previous workers identified the key factors controlling the occurrence of both topographic modes and the related structural styles. Kinematic and stress boundary conditions are of first-order relevance. Surface mass transport and material properties affect fault network structure. Experiments demonstrate that dilatancy can generate positive topography even under simple-shear boundary conditions. Here, we use physical models with sand to show that the degree of compaction of the deformed rocks alone can determine the type of topography and related surface fault network structure in simple-shear settings. In our experiments, volume changes of ∼5% are sufficient to generate localized uplift or subsidence. We discuss scalability of model volume changes and fault network structure and show that our model fault zones satisfy geometrical similarity with natural flower structures. Our results imply that compaction may be an important factor in the development of topography and fault network structure along strike-slip faults in sedimentary basins.

Targeted control of feral pigs in far north Queensland : defining management units using molecular techniques

The feral pig, Sus scrofa, is a widespread and abundant invasive species in Australia. Feral pigs pose a significant threat to the environment, agricultural industry, and human health, and in far north Queensland they endanger World Heritage values of the Wet Tropics. Historical records document the first introduction of domestic pigs into Australia via European settlers in 1788 and subsequent introductions from Asia from 1827 onwards. Since this time, domestic pigs have been accidentally and deliberately released into the wild and significant feral pig populations have become established, resulting in the declaration of this species as a class 2 pest in Queensland. The overall objective of this study was to assess the population genetic structure of feral pigs in far north Queensland, in particular to enable delineation of demographically independent management units. The identification of ecologically meaningful management units using molecular techniques can assist in targeting feral pig control to bring about effective long-term management. Molecular genetic analysis was undertaken on 434 feral pigs from 35 localities between Tully and Innisfail. Seven polymorphic and unlinked microsatellite loci were screened and fixation indices (FST and analogues) and Bayesian clustering methods were used to identify population structure and management units in the study area. Sequencing of the hyper-variable mitochondrial control region (D-loop) of 35 feral pigs was also examined to identify pig ancestry. Three management units were identified in the study at a scale of 25 to 35 km. Even with the strong pattern of genetic structure identified in the study area, some evidence of long distance dispersal and/or translocation was found as a small number of individuals exhibited ancestry from a management unit outside of which they were sampled. Overall, gene flow in the study area was found to be influenced by environmental features such as topography and land use, but no distinct or obvious natural or anthropogenic geographic barriers were identified. Furthermore, strong evidence was found for non-random mating between pigs of European and Asian breeds indicating that feral pig ancestry influences their population genetic structure. Phylogenetic analysis revealed two distinct mitochondrial DNA clades, representing Asian domestic pig breeds and European breeds. A significant finding was that pigs of Asian origin living in Innisfail and south Tully were not mating randomly with European breed pigs populating the nearby Mission Beach area. Feral pig control should be implemented in each of the management units identified in this study. The control should be coordinated across properties within each management unit to prevent re-colonisation from adjacent localities. The adjacent rainforest and National Park Estates, as well as the rainforest-crop boundary should be included in a simultaneous control operation for greater success.

Unsteady buoyancy driven flows and heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.