An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

A stochastic model for natural feature representation

This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning scheme. The representation is computed offline and results in a non-linear, non-Gaussian likelihood model relating visual observations such as color and texture to the underlying visual states. The likelihood model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The likelihoods are expressed as a Gaussian Mixture Model so as to permit convenient integration within existing nonlinear filtering algorithms. The resulting compactness of the representation is especially suitable to decentralized sensor networks. Real visual data consisting of natural imagery acquired from an Unmanned Aerial Vehicle is used to demonstrate the versatility of the feature representation.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Discovering characteristics of stochastic collections of process models

Process models in organizational collections are typically modeled by the same team and using the same conventions. As such, these models share many characteristic features like size range, type and frequency of errors. In most cases merely small samples of these collections are available due to e.g. the sensitive information they contain. Because of their sizes, these samples may not provide an accurate representation of the characteristics of the originating collection. This paper deals with the problem of constructing collections of process models, in the form of Petri nets, from small samples of a collection for accurate estimations of the characteristics of this collection. Given a small sample of process models drawn from a real-life collection, we mine a set of generation parameters that we use to generate arbitrary-large collections that feature the same characteristics of the original collection. In this way we can estimate the characteristics of the original collection on the generated collections.We extensively evaluate the quality of our technique on various sample datasets drawn from both research and industry.

Brisbane floods : a traffic and transport perspective

Flood-besieged Brisbane residents were forced to watch the monster river consume their homes and livelihoods then see the receding water leave behind a putrid, tar-like sludge. The rains formed by multiple low pressure systems over Central Queensland caused chaos over the Christmas and New Year break for many parts of Queensland.

Development of a software model of a heavy vehicle suspension for research

A Simulink Matlab control system of a heavy vehicle suspension has been developed. The aim of the exercise presented in this paper was to develop a Simulink Matlab control system of a heavy vehicle suspension. The objective facilitated by this outcome was the use of a working model of a heavy vehicle (HV) suspension that could be used for future research. A working computer model is easier and cheaper to re-configure than a HV axle group installed on a truck; it presents less risk should something go wrong and allows more scope for variation and sensitivity analysis before embarking on further "real-world" testing. Empirical data recorded as the input and output signals of a heavy vehicle (HV) suspension were used to develop the parameters for computer simulation of a linear time invariant system described by a second-order differential equation of the form: (i.e. a "2nd-order" system). Using the empirical data as an input to the computer model allowed validation of its output compared with the empirical data. The errors ranged from less than 1% to approximately 3% for any parameter, when comparing like-for-like inputs and outputs. The model is presented along with the results of the validation. This model will be used in future research in the QUT/Main Roads project Heavy vehicle suspensions – testing and analysis, particularly so for a theoretical model of a multi-axle HV suspension with varying values of dynamic load sharing. Allowance will need to be made for the errors noted when using the computer models in this future work.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Participation index : a measure to identify rural transport disadvantage?

This paper develops a composite participation index (PI) to identify patterns of transport disadvantage in space and time. It is operationalised using 157 weekly activity-travel diaries data collected from three case study areas in rural Northern Ireland. A review of activity space and travel behaviour research found that six dimensional indicators of activity spaces were typically used including the number of unique locations visited, distance travelled, area of activity spaces, frequency of activity participation, types of activity participated in, and duration of participation in order to identify transport disadvantage. A combined measure using six individual indices were developed based on the six dimensional indicators of activity spaces, by taking into account the relativity of the measures for weekdays, weekends, and for a week. Factor analyses were conducted to derive weights of these indices to form the PI measure. Multivariate analysis using general linear models of the different indicators/indices identified new patterns of transport disadvantage. The research found that: indicator based measures and index based measures are complement each other; interactions between different factors generated new patterns of transport disadvantage; and that these patterns vary in space and time. The analysis also indicates that the transport needs of different disadvantaged groups are varied.

Participation index : improved measure of transport related social exclusion?

Although transport related social exclusion has been identified through zonal accessibility measures in the recent past, the debate has shifted from zonal to individual level measures. One way to identify disadvantaged individuals is to measure their size of participation in society (activity spaces). After reviewing existing literature, this paper has found two approaches to measure the activity spaces. One approach is based on the time-geographic potential path area (PPA) concept. The size of the PPA has largely been used as an indicator to the size of potential activity spaces and consequently individual accessibility. The limitations of the PPA concept have been identified in this paper and it is argued cannot be applied as a measure of social exclusion. The other approach is based on individuals’ actual travel activity participation called actual activity spaces. The size of actual activity spaces possesses a good potential measure of social exclusion. However, the indicators to measure the size of actual activity spaces are multidimensional representing the different aspects of social exclusion. The development of a unified approach has therefore been found to be important. This paper has developed a participation index (PI) using the different dimensions of actual activity spaces encountered. A framework has also been developed to operationalise the concept in GIS. The framework, on the one hand, will visualize individuals’ actual travel behaviour in real geographic space; on the other hand, it will calculate the size of their participation in society.

Mobility, accessibility and activity participation : a comparative assessment of methods to identify rural transport disadvantage

Traditionally, transport disadvantage has been identified using accessibility analysis although the effectiveness of the accessibility planning approach to improving access to goods and services is not known. This paper undertakes a comparative assessment of measures of mobility, accessibility, and participation used to identify transport disadvantage using the concept of activity spaces. A 7 day activity-travel diary data for 89 individuals was collected from two case study areas located in rural Northern Ireland. A spatial analysis was conducted to select the case study areas using criteria derived from the literature. The criteria are related to the levels of area accessibility and area mobility which are known to influence the nature of transport disadvantage. Using the activity-travel diary data individuals weekly as well as day to day variations in activity-travel patterns were visualised. A model was developed using the ArcGIS ModelBuilder tool and was run to derive scores related to individual levels of mobility, accessibility, and participation in activities from the geovisualisation. Using these scores a multiple regression analysis was conducted to identify patterns of transport disadvantage. This study found a positive association between mobility and accessibility, between mobility and participation, and between accessibility and participation in activities. However, area accessibility and area mobility were found to have little impact on individual mobility, accessibility, and participation in activities. Income vis-àvis ´ car-ownership was found to have a significant impact on individual levels of mobility, and accessibility; whereas participation in activities were found to be a function of individual levels of income and their occupational status.

Rural activity spaces and transport disadvantage : qualitative analysis of quantitative models integrating time and space

Current knowledge about the relationship between transport disadvantage and activity space size is limited to urban areas, and as a result, very little is known to date about this link in a rural context. In addition, although research has identified transport disadvantaged groups based on their size of activity spaces, these studies have, however, not empirically explained such differences and the result is often a poor identification of the problems facing disadvantaged groups. Research has shown that transport disadvantage varies over time. The static nature of analysis using the activity space concept in previous research studies has lacked the ability to identify transport disadvantage in time. Activity space is a dynamic concept; and therefore possesses a great potential in capturing temporal variations in behaviour and access opportunities. This research derives measures of the size and fullness of activity spaces for 157 individuals for weekdays, weekends, and for a week using weekly activity-travel diary data from three case study areas located in rural Northern Ireland. Four focus groups were also conducted in order to triangulate the quantitative findings and to explain the differences between different socio-spatial groups. The findings of this research show that despite having a smaller sized activity space, individuals were not disadvantaged because they were able to access their required activities locally. Car-ownership was found to be an important life line in rural areas. Temporal disaggregation of the data reveals that this is true only on weekends due to a lack of public transport services. In addition, despite activity spaces being at a similar size, the fullness of activity spaces of low-income individuals was found to be significantly lower compared to their high-income counterparts. Focus group data shows that financial constraint, poor connections both between public transport services and between transport routes and opportunities forced individuals to participate in activities located along the main transport corridors.

The impact of school connectedness on violent behavior, transport risk taking behavior and associated injuries in adolescence

Adolescents engage in many risk-taking behaviors that have the potential to lead to injury. The school environment has a significant role in shaping adolescent behavior, and this study aimed to provide additional information about the benefits associated with connectedness to school. Early adolescents aged 13 to 15 years (N = 509, 49% boys) were surveyed about school connectedness, engagement in transport and violence risk-taking, and injury experiences. Significant relations were found between school connectedness and reduced engagement in both transport and violence risk-taking, as well as fewer associated injuries. This study has implications for the area of risk-taking and injury prevention, as it suggests the potential for reducing adolescents' injury through school based interventions targeting school connectedness.

Shrinking neighborhood evolution : a novel stochastic algorithm for numerical optimization

Focusing on the conditions that an optimization problem may comply with, the so-called convergence conditions have been proposed and sequentially a stochastic optimization algorithm named as DSZ algorithm is presented in order to deal with both unconstrained and constrained optimizations. The principle is discussed in the theoretical model of DSZ algorithm, from which we present the practical model of DSZ algorithm. Practical model efficiency is demonstrated by the comparison with the similar algorithms such as Enhanced simulated annealing (ESA), Monte Carlo simulated annealing (MCS), Sniffer Global Optimization (SGO), Directed Tabu Search (DTS), and Genetic Algorithm (GA), using a set of well-known unconstrained and constrained optimization test cases. Meanwhile, further attention goes to the strategies how to optimize the high-dimensional unconstrained problem using DSZ algorithm.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin