Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Territorial strategies and regions

The notion of territorial strategy emerged in the 1990s and has become more and more popular since. It refers to that combination of factors purposely assembled by governments, private and public companies, universities, and industrial associations to exploit a specific geographic competitive advantage in order to boost economic growth through the development of entrepreneurial activity and innovation. Three factors are generally considered to be the building blocks of a territorial strategy: natural resources, human capital, and industrial capabilities. Natural resources derive from environ­ mental conditions and represent raw materials or land available in a region. The presence of natural resources characterizes the typology of an industry (related to tourism, oil, wood, fish, and so forth) that exists or could exist in a certain area. Human capital refers to the stock of competences available in a certain region resulting from education and work experience. Industrial capabilities relate to complex constructs of specialized expertise, the confidence to apply knowledge and skills in various contexts and under changing conditions, and an ability repeatedly to improve methods and processes in a specific industry.

From slum to suburbia : examining a spectrum of planned and unplanned urban morphology in humid sub-tropical regions of the world

The current rapid urban growth throughout the world manifests in various ways and historically cities have grown, similarly, alternately or simultaneously between planned extensions and organic informal settlements (Mumford, 1989). Within cities different urban morphological regions can reveal different contexts of economic growth and/or periods of dramatic social/technological change (Whitehand, 2001, 105). Morpho-typological study of alternate contexts can present alternative models and contribute to the present discourse which questions traditional paradigms of urban planning and design (Todes et al, 2010). In this study a series of cities are examined as a preliminary exploration into the urban morphology of cities in ‘humid subtropical’ climates. From an initial set of twenty, six cities were selected: Sao Paulo, Brazil; Jacksonville, USA; Maputo, Mozambique; Kanpur, India; Hong Kong, China; and Brisbane, Australia. The urban form was analysed from satellite imagery at a constant scale. Urban morphological regions (types) were identified as those demonstrating particular consistant characteristics of form (density, typology and pattern) different to their surroundings when examined at a constant scale. This analysis was correlated against existing data and literature discussing the proliferation of two types of urban development, ‘informal settlement’ (defined here as self-organised communities identifiable but not always synonymous with ‘slums’) and ‘suburbia’ (defined here as master planned communities of generally detached houses prevalent in western society) - the extreme ends of a hypothetical spectrum from ‘planned’ to ‘spontaneous’ urban development. Preliminary results show some cities contain a wide variety of urban form ranging from the highly organic ‘self-organised’ type to the highly planned ‘master planned community’ (in the case of Sao Paulo) while others tend to fall at one end of the planning spectrum or the other (more planned in the cases of Brisbane and Jacksonville; and both highly planned and highly organic in the case of Maputo). Further research will examine the social, economical and political drivers and controls which lead to this diversity or homogeneity of urban form and speculates on the role of self-organisation as a process for the adaptation of urban form.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

An assessment tool for selection of appropriate daylighting solutions for buildings in tropical and subtropical regions : Validation using radiance simulation

A new decision-making tool that will assist designers in the selection of appropriate daylighting solutions for buildings in tropical locations has been previously proposed by the authors. Through an evaluation matrix that prioritizes the parameters that best respond to the needs of tropical climates (e.g. reducing solar gain and protection from glare) the tool determines the most appropriate devices for specific climate and building inputs. The tool is effective in demonstrating the broad benefits and limitations of the different daylight strategies for buildings in the tropics. However for thorough analysis and calibration of the tool, validation is necessary. This paper presents a first step in the validation process. RADIANCE simulations were conducted to compare simulation performance with the performance predicted by the tool. To this end, an office building case study in subtropical Brisbane, Australia, and five different daylighting devices including openings, light guiding systems and light transport systems were simulated. Illuminance, light uniformity, daylight penetration and glare analysis were assessed for each device. The results indicate the tool can appropriately rank and recommend daylighting strategies based on specific building inputs for tropical and subtropical regions, making it a useful resource for designers.

Effects of speeding and headway related variable message signs on driver behaviour and attitudes

This research project examined objective measures of driver behaviour and road users' perceptions on the usefulness and effectiveness of three specific VMS (Variable Message Signs) interventions to improve speeding and headway behaviours. The interventions addressed speeding behaviour alone (intervention 1), headway behaviour alone (intervention 2) and a combination of speeding and headway behaviour (intervention 3). Six VMS were installed along a segment of the Bruce Highway, with a series of three signs for each of the northbound and southbound traffic. Speeds and headway distances were measured with loop detectors installed before and after each VMS. Messages addressing speeding and headway were devised for display on the VMS. A driver could receive a message if they were detected as exceeding the posted speed limit (of 90km/hr) or if the distance to the vehicle in front was less than 2.0s. In addition to the on-road objective measurement of speeding and headway behaviours, the research project elicited self-reported responses to the speeding and headway messages from a sample of drivers via a community-based survey. The survey sought to examine the drivers' beliefs about the effectiveness of the signs and messages, and their views about the role, use, and effectiveness of VMS more generally.

Mineralogy of chondritic interplanetary dust particles

From a mineralogical survey of approximately 30 chondritic micrometeorites collected from the lower stratosphere and studied in detail using current electron microscopy techniques, it is concluded that these particles represent a unique group of extraterrestrial materials. These micrometeorites differ significantly in form and texture from components of carbonaceous chondrites and contain some mineral assemblages which do not occur in any meteorite class. Electron microscope investigations of chondritic micrometeorites have established that these materials (1) are extraterrestrial in origin, (2) existed in space as small objects, (3) endured minimal alteration by planetary processes since formation, and (4) can suffer minimal pulse heating (<600°C) on entering earth's atmosphere. The probable sources for chondritic interplanetary dust particles (IDPs) are cometary and asteroidal debris and, perhaps to a lesser extent, interstellar regions. These sources have not been conclusively linked to any specific mineralogical subset of IDP, although the chondritic porous (CP) aggregate is considered of likely cometary origin. Chondritic IDPs occur in two predominant mineral assemblages: (1) carbonaceous phases and phyllosilicates and (2) carbonaceous phases and nesosilicates or inosilicates, although particles with both types of silicate assemblages are observed. Olivines, pyroxenes, layer silicates, and carbon-rich phases are the most commonly occurring minerals in many chondritic IDPs. Other phases often observed in variable proportions include sulphides, spinels, metals, metal carbides, carbonates, and minor amounts of sulphates and phosphates. Individual mineral grain sizes range from micrometers (primarily pyroxenes and olivines) to nanometers, with the predominant size for all phases less than 100 nm. Specific mineral characteristics for particular chondritic IDPs provide an indication of processes which may have occurred prior to collection in the earth's stratosphere. For example, pyroxene mineralogy in some chondritic aggregates is consistent with condensation from a vapor phase and, we consider, with condensation in a turbulent solar nebula at relatively low temperatures (<1000°C). Carbonaceous phases present in other CP aggregates have been used to imply low-temperature formation processes such as Fischer-Tropsch synthesis (∼530°C) or carbonization and graphitization (∼315°C). Alteration processes have been implicated in the formation of some layer silicates in CP aggregates and may have involved hydrocryogenic alteration at <0°C. In general, interpretations of transformation processes on submicrometer-size minerals in chondritic IDPs are consistent with formation at a radius equivalent to the asteroid belt or greater during the later stages of solar nebula evolution using currently available models.

High resolution imaging of boron carbide microstructures

Two samples of boron carbide have been examined using high resolution transmission electron microscopy (HRTEM). A hot pressed B13C2 sample shows a high density of variable width twins normal to (10-11). Subtle shifts or offsets of lattice fringes along the twin plane and normal to (10 5) were also observed. A B4C powder showed little evidence of stacking disorder in crystalline regions.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Consequences of extensional tectonics on volcanic eruption style, compositions and source regions : new insights from the southern Sierra Madre Occidental and Gulf of California regions, western Mexico

Understanding the link between tectonic-driven extensional faulting and volcanism is crucial from a hazard perspective in active volcanic environments, while ancient volcanic successions provide records on how volcanic eruption styles, compositions, magnitudes and frequencies can change in response to extension timing, distribution and intensity. This study draws on intimate relationships of volcanism and extension preserved in the Sierra Madre Occidental (SMO) and Gulf of California (GoC) regions of western Mexico. Here, a major Oligocene rhyolitic ignimbrite “flare-up” (>300,000 km3) switched to a dominantly bimodal and mixed effusive-explosive volcanic phase in the Early Miocene (~100,000 km3), associated with distributed extension and opening of numerous grabens. Rhyolitic dome fields were emplaced along graben edges and at intersections of cross-graben and graben-parallel structures during early stages of graben development. Concomitant with this change in rhyolite eruption style was a change in crustal source as revealed by zircon chronochemistry with rapid rates of rhyolite magma generation due to remelting of mid- to upper crustal, highly differentiated igneous rocks emplaced during earlier SMO magmatism. Extension became more focused ~18 Ma resulting in volcanic activity being localised along the site of GoC opening. This localised volcanism (known as the Comondú “arc”) was dominantly effusive and andesite-dacite in composition. This compositional change resulted from increased mixing of basaltic and rhyolitic magmas rather than fluid flux melting of the mantle wedge above the subducting Guadalupe Plate. A poor understanding of space-time relationships of volcanism and extension has thus led to incorrect past tectonic interpretations of Comondú-age volcanism.

Using variable speed limits for motorway off-ramp queue protection

Motorway off-ramps are a significant source of traffic congestion and collisions. Heavy diverging traffic to off-ramps slows down the mainline traffic speed. When the off-ramp queue spillbacks onto the mainline, it leads to a major breakdown of the motorway capacity and a significant threat to the traffic safety. This paper proposes using Variable Speed Limits (VSL) for protection of the motorway off-ramp queue and thus to promote safety in congested diverging areas. To support timely activation of VSL in advance of queue spillover, a proactive control strategy is proposed based on a real-time off-ramp queue estimation and prediction. This process determines the estimated queue size in the near-term future, on which the decision to change speed limits is made. VSL can effectively slow down traffic as it is mandatory that drivers follow the changed speed limits. A collateral benefit of VSL is its potential effect on drivers making them more attentive to the surrounding traffic conditions, and prepared for a sudden braking of the leading car. This paper analyses and quantifies these impacts and potential benefits of VSL on traffic safety and efficiency using the microsimulation approach.