Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

Space Station Design Report 2007

Design Proposal for the Blue Lunar Support Hub The conceptual design of a space station is one of the most challenging tasks in aerospace engineering. The history of the space station Mir and the assembly of the International Space Station demonstrate that even within the assembly phase quick solutions have to be found to cope with budget and technical problems or changing objectives. This report is the outcome of the conceptual design of the Space Station Design Workshop (SSDW) 2007, which took place as an international design project from the 16th to the 21st of July 2007 at the Australian Centre for Field Robotics (ACFR), University of Sydney, Australia. The participants were tasked to design a human-tended space station in low lunar orbit (LLO) focusing on supporting future missions to the moon in a programmatic context of space exploration beyond low Earth orbit (LEO). The design included incorporating elements from systems engineering to interior architecture. The customised, intuitive, rapid-turnaround software tools enabled the team to successfully tackle the complex problem of conceptual design of crewed space systems. A strong emphasis was put on improving the integration of the human crew, as it is the major contributor to mission success, while always respecting the boundary conditions imposed by the challenging environment of space. This report documents the methodology, tools and outcomes of the Space Station Design Workshop during the SSDW 2007. The design results produced by Team Blue are presented.

Model updating of real structures with ambient vibration data

It is important to develop reliable finite element models for real structures not only in the design phase but also for the structural health monitoring and structural maintenance purposes. This paper describes the experience of the authors in using ambient vibration model identification techniques together with model updating tools to develop reliable finite element models of real civil engineering structures. Case studies of two real structures are presented in this paper. One is a 10 storey concrete building which is considered as a non-slender structure with complex boundary conditions. The other is a single span concrete foot bridge which is also a relatively inflexible planar structure with complex boundary conditions. Both structures are located at the Queensland University of Technology (QUT) and equipped with continuous structural health monitoring systems.

Real-time traffic state estimation in urban corridors from heterogeneous data

In recent years, rapid advances in information technology have led to various data collection systems which are enriching the sources of empirical data for use in transport systems. Currently, traffic data are collected through various sensors including loop detectors, probe vehicles, cell-phones, Bluetooth, video cameras, remote sensing and public transport smart cards. It has been argued that combining the complementary information from multiple sources will generally result in better accuracy, increased robustness and reduced ambiguity. Despite the fact that there have been substantial advances in data assimilation techniques to reconstruct and predict the traffic state from multiple data sources, such methods are generally data-driven and do not fully utilize the power of traffic models. Furthermore, the existing methods are still limited to freeway networks and are not yet applicable in the urban context due to the enhanced complexity of the flow behavior. The main traffic phenomena on urban links are generally caused by the boundary conditions at intersections, un-signalized or signalized, at which the switching of the traffic lights and the turning maneuvers of the road users lead to shock-wave phenomena that propagate upstream of the intersections. This paper develops a new model-based methodology to build up a real-time traffic prediction model for arterial corridors using data from multiple sources, particularly from loop detectors and partial observations from Bluetooth and GPS devices.

Bending and torsion of hollow flange channel beams

The LiteSteel beam (LSB) is a cold-formed high strength steel channel section made of two torsionally rigid closed flanges and a slender web. Due to its mono-symmetric characteristics, its centroid and shear centre do not coincide. The LSBs can be used in floor systems as joists or bearers and in these applications they are often subjected to transverse loads that are applied away from the shear centre. Hence they are often subjected to combined bending and torsion actions. Previous researches on LSBs have concentrated on their bending or shear behaviour and strengths, and only limited research has been undertaken on their combined bending and torsion behaviour. Therefore in this research a series of nine experiments was first conducted on LSBs subject to combined bending and torsion. Three LSB sections were tested to failure under eccentric loading at mid-span, and appropriate results were obtained from seven tests. A special test rig was used to simulate two different eccentricities and to provide accurate simple boundary conditions at the supports. Finite element models of tested LSBs were developed using ANSYS, and the ultimate strengths, failure modes, and load–displacement curves were obtained and compared with corresponding test results. Finite element analyses agreed well with test results and hence the developed models were used in a parametric study to investigate the effects of load locations, eccentricities, and spans on the combined bending and torsion behaviour of LSBs. The interaction between the ultimate bending and torsional moment capacities was studied and a simple design rule was proposed. This paper presents the details of the tests, finite element analyses, and parametric study of LSBs subject to combined bending and torsion, and the results.

Development of a new design expression for the in-plane shear capacity of the partially grouted concrete masonry walls

Partially grouted masonry walls subjected to in-plane shear exhibit a complex behaviour because of the influence of the aspect ratio, the pre-compression, the grouting pattern, the ratios of the horizontal and the vertical reinforcements, the boundary conditions and the characteristics of the constituent materials. The existing in-plane shear expressions for the partially grouted masonry are formulated as sum of strength of three parameters, namely, the masonry, the reinforcement and the axial force. The parameter ‘masonry’ includes the wall aspect ratio and the masonry compressive strength; the aspect ratio of the unreinforced panel inscribed into the grouted cores and bond beams are not considered, although failure is often dominated by these unreinforced masonry panels. This paper describes the dominance of these panels, particularly those that are squat, to the shear capacity of whole of shear walls. Further, the current design formulae are shown highly un-conservative by many researchers; this paper provides a potential reason for this un-conservativeness. It is shown that by including an additional term of the unreinforced panel aspect ratio a rational design formula could be established. This new expression is validated with independent test results reported in the literature – both Australian and overseas; the predictions are shown to be conservative.

Micro paddy lysimeter for monitoring solute transport in paddy environment

The micro paddy lysimeter (MPL) was developed and evaluated for its performance to simulate solute transport in paddy environment under laboratory conditions. MPLs were constructed using soil collected from Field Museum Honmachi of Tokyo University of Agriculture and Technology, Japan. For the physical characteristics of the hardpan layer, parameters such as thickness, and soil aggregate size, affecting the percolation rate were studied. For the plow layer, two types of plow soils, sieved and un-sieved soils were compared. The sieved soil plow layer was produced by mixing air-dried soils of different aggregate sizes of D > 9.50, 9.50 ≥ D > 4.75, 4.75 ≥ D > 2.0 mm and D ≤ 2.0 mm at 47.1, 19.5, 20.6, and 12.8%, respectively. The un-sieved plow layer soil was directly used after collecting from the field. Inert tracer was applied to ponding water with controlled boundary conditions to evaluate the reproducibility of the soil hydraulic characteristics. HYDRUS-1D was used to evaluate the movement of bromide tracer in the MPL. The proposed conditions of the MPL were that the hardpan layer can be made from soil aggregates smaller than 0.425 mm with 2 cm thickness and that the plow layer can be prepared with sieved or un-sieved soils. With these conditions, the obtained results proved that MPLs can be a useful tool to simulate solute transport in paddy environment.

Modelling of the evaporation of a droplet suspended in a binary atmosphere

The process of spray drying is applied in a number of contexts. One such application is the production of a synthetic rock used for storage of nuclear waste. To establish a framework for a model of the spray drying process for this application, we here develop a model describing evaporation from droplets of pure water, such that the model may be extended to account for the presence of colloid within the droplet. We develop a spherically-symmetric model and formulate continuum equations describing mass, momentum, and energy balance in both the liquid and gas phases from first principles. We establish appropriate boundary conditions at the surface of the droplet, including a generalised Clapeyron equation that accurately describes the temperature at the surface of the droplet. To account for experiment design, we introduce a simplified platinum ball and wire model into the system using a thin wire problem. The resulting system of equations is transformed in order to simplify a finite volume solution scheme. The results from numerical simulation are compared with data collected for validation, and the sensitivity of the model to variations in key parameters, and to the use of Clausius–Clapeyron and generalised Clapeyron equations, is investigated. Good agreement is found between the model and experimental data, despite the simplicity of the platinum phase model.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

Career adaptability and career entrenchment

Career adaptability constitutes a resource that can help employees to effectively manage career changes and challenges. The goal of this study was to investigate the relationship between the two higher-order constructs of career adaptability and career entrenchment (i.e., the perceived inability and/or unwillingness to pursue new career opportunities), as well as relationships among the dimensions of career adaptability and career entrenchment. We hypothesized a negative relationship between overall career adaptability and career entrenchment, and more differentiated associations among their dimensions. Data for this study came from 404 employees in Brazil. Results of structural equation modeling showed that overall career adaptability weakly negatively predicted overall career entrenchment (standardized effect = − .13), after controlling for age, gender, education, and job tenure. More differentiated findings emerged at the dimension level. Future research should examine the mechanisms and boundary conditions of the relationship between career adaptability and career entrenchment.

A lifespan perspective on leadership

In this chapter, we present a lifespan model of leadership that outlines how leader and follower age as well as age-related changes in leader traits and characteristics, leader behaviors, and follower attribution and identification processes may influence leadership effectiveness. First, we describe how leader traits and characteristics change with age and how these developmental changes may impact on leader behaviors and, subsequently, leadership effectiveness. Specifically, we discuss age-related changes in leaders’ task competence, interpersonal attributes, and motivation to lead. We particularly focus on how generativity – a set of interconnected motives pertaining to establishing and guiding future generations – may emerge as an important concern among older leaders. Second, we review theoretical approaches that help explain how and why leader age and age-related traits and characteristics, follower age, as well as leader-follower age differences may influence follower attribution and identification processes. Third, we outline a number of boundary conditions of the effects proposed by our lifespan model of leadership, including leader-follower relationship duration, situational characteristics, as well as the cultural, social, and historical context. We conclude the chapter by discussing our model’s implications for future research and organizational practice.

Numerical study on the surface depression of the concrete runway pavement under impact load

Airport runway pavement always subjected to huge impact loading due to the hard landing of aircraft on the pavement surface. Therefore runway pavements should have sufficient impact resistance capability to avoid damage causing by hard impact like surface deflection in downward or penetration since the repair works is cumbersome within the operating condition of airport and also increases the service life cost of the pavement structure. Several research works have been carried out on airport runway pavement to measure the present condition of pavement and also to predict future performance of it. However, most of the works are confined by pavement response under moving aircraft loading. Nevertheless, no comprehensive research work is yet conducted to identify the controlling factors which might have significant effect in changing the common pavements damage like surface penetration depth under impact of aircraft. Therefore, a 3D FE study is conducted to determine some effective factors in controlling the top surface penetration depth of runway pavement. Among the exterior factors, mass of the impactor, velocity of the impactor, impact angle and boundary conditions are selected and as interior factors, thickness of the runway pavement, compressive strength and density of materials used in the runway pavement are selected.

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.