A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Pulsed i-PVD of dielectric nanodot arrays using a nanoporous template

The results of multi-scale numerical simulations of pulsed i-PVD template-assisted nanofabrication of ZnO nanodot arrays on a silicon substrate are presented. The ratios and spatial distributions of the ion fluxes deposited on the lateral and bottom surfaces of the nanopores are computed as a function of the external bias and plasma parameters. The results show that the pulsed bias plays a significant role in the ion current distribution inside the nanopores. The results of numerical experiments of this work suggest that by finely adjusting the pulse voltage, the pulse duration and the duty cycle of the external pulsed bias, the nanopore clogging can be successfully avoided during the deposition and the shapes of the deposited ZnO nanodots can be effectively controlled. A figure is presented.

Nanostructures of various dimensionalities from plasma and neutral fluxes

A complex multi-scale model and numerical simulations are used to demonstrate, by simulating the development of patterns of nanotips, nanowalls, nanoislands and nanovoids of a characteristic size of 5-100 nm, a greater degree of determinism in the formation of various nanostructures by using the low-density, low-temperature plasma-based processes. It is shown that in the plasma, in contrast to the neutral gas-based processes, one can synthesize nanostructures of various dimensionalities and shapes with a larger surface density, desired geometrical parameters and narrower size distribution functions. This effect is mainly attributed to strong ion focusing by irregular electric fields in the nanopatterns, which effectively redistributes the influxes of plasma-generated building units and thus provides a selective control of their delivery to the growing nanostructures.

Multiscale features and information extraction of online strain for long-span bridges

The strain data acquired from structural health monitoring (SHM) systems play an important role in the state monitoring and damage identification of bridges. Due to the environmental complexity of civil structures, a better understanding of the actual strain data will help filling the gap between theoretical/laboratorial results and practical application. In the study, the multi-scale features of strain response are first revealed after abundant investigations on the actual data from two typical long-span bridges. Results show that, strain types at the three typical temporal scales of 10^5, 10^2 and 10^0 sec are caused by temperature change, trains and heavy trucks, and have their respective cut-off frequency in the order of 10^-2, 10^-1 and 10^0 Hz. Multi-resolution analysis and wavelet shrinkage are applied for separating and extracting these strain types. During the above process, two methods for determining thresholds are introduced. The excellent ability of wavelet transform on simultaneously time-frequency analysis leads to an effective information extraction. After extraction, the strain data will be compressed at an attractive ratio. This research may contribute to a further understanding of actual strain data of long-span bridges; also, the proposed extracting methodology is applicable on actual SHM systems.

Towards Vision-Based Pose- and Condition-Invariant Place Recognition along Routes

Vision-based place recognition involves recognising familiar places despite changes in environmental conditions or camera viewpoint (pose). Existing training-free methods exhibit excellent invariance to either of these challenges, but not both simultaneously. In this paper, we present a technique for condition-invariant place recognition across large lateral platform pose variance for vehicles or robots travelling along routes. Our approach combines sideways facing cameras with a new multi-scale image comparison technique that generates synthetic views for input into the condition-invariant Sequence Matching Across Route Traversals (SMART) algorithm. We evaluate the system’s performance on multi-lane roads in two different environments across day-night cycles. In the extreme case of day-night place recognition across the entire width of a four-lane-plus-median-strip highway, we demonstrate performance of up to 44% recall at 100% precision, where current state-of-the-art fails.

Spatial disaggregation of land systems mapping in the Burnett catchment (South-East Queensland)

This project examined the potential for historical mapping of land resources to be upgraded to meet current requirements for natural resource management. The methods of spatial disaggregation used to improve the scale of mapping were novel and provide a method to rapidly improve existing information. The thesis investigated the potential to use digital soil mapping techniques and the multi-scale identification of areas within historical land systems mapping to provide enhanced information to support modern natural resource management needs. This was undertaken in the Burnett Catchment of South-East Queensland.

The navigation and visualisation of environmental audio using zooming spectrograms

Acoustic recordings play an increasingly important role in monitoring terrestrial and aquatic environments. However, rapid advances in technology make it possible to accumulate thousands of hours of recordings, more than ecologists can ever listen to. Our approach to this big-data challenge is to visualize the content of long-duration audio recordings on multiple scales, from minutes, hours, days to years. The visualization should facilitate navigation and yield ecologically meaningful information prior to listening to the audio. To construct images, we calculate acoustic indices, statistics that describe the distribution of acoustic energy and reflect content of ecological interest. We combine various indices to produce false-color spectrogram images that reveal acoustic content and facilitate navigation. The technical challenge we investigate in this work is how to navigate recordings that are days or even months in duration. We introduce a method of zooming through multiple temporal scales, analogous to Google Maps. However, the “landscape” to be navigated is not geographical and not therefore intrinsically visual, but rather a graphical representation of the underlying audio. We describe solutions to navigating spectrograms that range over three orders of magnitude of temporal scale. We make three sets of observations: 1. We determine that at least ten intermediate scale steps are required to zoom over three orders of magnitude of temporal scale; 2. We determine that three different visual representations are required to cover the range of temporal scales; 3. We present a solution to the problem of maintaining visual continuity when stepping between different visual representations. Finally, we demonstrate the utility of the approach with four case studies.

Relocation of Intensive Agriculture to Northern Queensland The Cotton Industry

Development of new agricultural industries in northern Australia is often perceived as a solution to changes in water availability that have occurred within southern Australia as a result of changes to government policy in response to and exacerbated by climate change. This report examines the likely private, social and community costs and benefits associated with the establishment of a cotton industry in the Burdekin. The research undertaken covers three spatial scales by modelling the response of cotton and to climate change at the crop and farm scale and linking this to regional scale modelling of the economy. Modelling crop growth as either a standalone crop or as part of a farm enterprise provides the clearest picture of how yields and water use will be affected under climate change. The alternative to this is to undertake very costly trials in environmental chambers. For this reason it is critical that funding for model development especially for crops being crop in novel environments be seen as a high priority for climate change and adaptation studies. Crop level simulations not only provide information on how the crop responds to climate change, they also illustrate that that these responses are the result of complex interactions and cannot necessarily be derived from the climate information alone. These simulations showed that climate change would lead to decreased cotton yields in 2030 and 2050 without the affect of CO2 fertilisation. Without CO2 fertilisation, yields would be decreased by 3.2% and 17.8%. Including CO2 fertilisation increased yields initially by 5.9%, but these were reduced by 3.6% in 2050. This still represents a major offset and at least ameliorates the impact of climate change on yield. To cope with the decreased in-crop rainfall (4.5% by 2030 and 15.8% in 2050) and an initial increase in evapotranspiration of 2% in 2030 and

VisArchive: a time and relevance based visual interface for searching, browsing, and exploring project archives

Background Project archives are becoming increasingly large and complex. On construction projects in particular, the increasing amount of information and the increasing complexity of its structure make searching and exploring information in the project archive challenging and time-consuming. Methods This research investigates a query-driven approach that represents new forms of contextual information to help users understand the set of documents resulting from queries of construction project archives. Specifically, this research extends query-driven interface research by representing three types of contextual information: (1) the temporal context is represented in the form of a timeline to show when each document was created; (2) the search-relevance context shows exactly which of the entered keywords matched each document; and (3) the usage context shows which project participants have accessed or modified a file. Results We implemented and tested these ideas within a prototype query-driven interface we call VisArchive. VisArchive employs a combination of multi-scale and multi-dimensional timelines, color-coded stacked bar charts, additional supporting visual cues and filters to support searching and exploring historical project archives. The timeline-based interface integrates three interactive timelines as focus + context visualizations. Conclusions The feasibility of using these visual design principles is tested in two types of project archives: searching construction project archives of an educational building project and tracking of software defects in the Mozilla Thunderbird project. These case studies demonstrate the applicability, usefulness and generality of the design principles implemented.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Population dynamics of blue mussels in a variable environment at the edge of their range

Spatial and temporal variation in the abundance of species can often be ascribed to spatial and temporal variation in the surrounding environment. Knowledge of how biotic and abiotic factors operate over different spatial and temporal scales in determining distribution, abundance, and structure of populations lies at the heart of ecology. The major part of the current ecological theory stems from studies carried out in central parts of the distributional range of species, whereas knowledge of how marginal populations function is inadequate. Understanding how marginal populations, living at the edge of their range, function is however in a key position to advance ecology and evolutionary biology as scientific disciplines. My thesis focuses on the factors affecting dynamics of marginal populations of blue mussels (Mytilus edulis) living close to their tolerance limits with regard to salinity. The thesis aims to highlight the dynamics at the edge of the range and contrast these with dynamics in more central parts of the range in order to understand the potential interplay between the central and the marginal part in the focal system. The objectives of the thesis are approached by studies on: (1) factors affecting regional patterns of the species, (2) long-term temporal dynamics of the focal species spaced along a regional salinity gradient, (3) selective predation by increasing populations of roach (Rutilus rutilus) when feeding on their main food item, the blue mussel, (4) the primary and secondary effects of local wave exposure gradients and (5) the role of small-scale habitat heterogeneity as determinants of large-scale pattern. The thesis shows that populations of blue mussels are largely determined by large scale changes in sea water salinity, affecting mainly recruitment success and longevity of local populations. In opposite to the traditional view, the thesis strongly indicate that vertebrate predators strongly affect abundance and size structure of blue mussel populations, and that the role of these predators increases towards the margin where populations are increasingly top-down controlled. The thesis also indicates that the positive role of biogenic habitat modifiers increases towards the marginal areas, where populations of blue mussels are largely recruitment limited. Finally, the thesis shows that local blue mussel populations are strongly dependent on high water turbulence, and therefore, dense populations are constrained to offshore habitats. Finally, the thesis suggests that ongoing sedimentation of rocky shores is detrimental for the species, affecting recruitment success and post-recruit survival, pushing stable mussel beds towards offshore areas. Ongoing large scale changes in the Baltic Sea, especially dilution processes with attendant effects, are predicted to substantially contract the distributional range of the mussel, but also affect more central populations. The thesis shows that in order to understand the functioning of marginal populations, research should (1) strive for multi-scale approaches in order to link ecosystem patterns with ecosystem processes, and (2) challenge the prevailing tenets that origin from research carried out in central areas that may not be valid at the edge.

Architecture designed ZnO hollow microspheres with wide-range visible-light photoresponses

It is a challenge to increase the visible-light photoresponses of wide-gap metal oxides. In this study, we proposed a new strategy to enhance the visible-light photoresponses of wide-gap semiconductors by deliberately designing a multi-scale nanostructure with controlled architecture. Hollow ZnO microspheres with constituent units in the shape of one-dimensional (1D) nanowire networks, 2D nanosheet stacks, and 3D mesoporous nanoball blocks are synthesized via an approach of two-step assembly, where the oligomers or the constituent nanostructures with specially designed structures are first formed, and then further assembled into complex morphologies. Through deliberate designing of constituent architectures allowing multiple visible-light scattering, reflections, and dispersion inside the multiscale nanostructures, enhanced wide range visible-light photoresponses of the ZnO hollow microspheres were successfully achieved. Compared to the one-step synthesized ZnO hollow microspheres, where no nanostructured constituents were produced, the ZnO hollow microspheres with 2D nanosheet stacks presented a 50 times higher photocurrent in the visible-light range (λ > 420 nm). The nanostructure induced visible-light photoresponse enhancement gives a direction to the development of novel photosensitive materials.

Lateral impact derailment mechanisms, simulation and analysis

Lateral collisions between heavy road vehicles and passenger trains at level crossings and the associated derailments are serious safety issues. This paper presents a detailed investigation of the dynamic responses and derailment mechanisms of trains under lateral impact using a multi-body dynamics simulation method. Formulation of a three-dimensional dynamic model of a passenger train running on a ballasted track subject to lateral impact caused by a road truck is presented. This model is shown to predict derailment due to wheel climb and car body overturning mechanisms through numerical examples. Sensitivities of the truck speed and mass, wheel/rail friction and the train suspension to the lateral stability and derailment of the train are reported. It is shown that improvements to the design of train suspensions, including secondary and inter-vehicle lateral dampers have higher potential to mitigate the severity of the collision-induced derailments.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.

A “business researcher” view on opportunities for psychology in entrepreneurship research

In this short essay I offer some “business researcher” advice on how to leverage a strong background in psychology when attempting to contribute to the maturing field of “entrepreneurship research”. Psychologists can benefit from within-discipline research, e.g. on emergence, small groups, fit, and expertise as well as method strengths in, e.g. experimentation, operationalisation of constructs, and multi-level modelling. However, achieving full leverage of these strengths requires a clear conceptualisation of “entrepreneurship” as well as insights into the challenges posed by the nature of this class of phenomena.