Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Online estimation of distorted power system signal parameters

An algorithm based on the concept of Kalman filtering is proposed in this paper for the estimation of power system signal attributes, like amplitude, frequency and phase angle. This technique can be used in protection relays, digital AVRs, DSTATCOMs, FACTS and other power electronics applications. Furthermore this algorithm is particularly suitable for the integration of distributed generation sources to power grids when fast and accurate detection of small variations of signal attributes are needed. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations are presented to highlight the usefulness of the proposed approach. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Simulation and enhancement of a cardiovascular device test rig

Cardiovascular assist devices are tested in mock circulation loops (MCLs) prior to animal and clinical testing. These MCLs rely on characteristics such as pneumatic parameters to create pressure and flow, and pipe dimensions to replicate the resistance, compliance and fluid inertia of the natural cardiovascular system. A mathematical simulation was developed in SIMULINK to simulate an existing MCL. Model validation was achieved by applying the physical MCL characteristics to the simulation and comparing the resulting pressure traces. These characteristics were subsequently altered to improve and thus predict the performance of a more accurate physical system. The simulation was successful in simulating the physical mock circulation loop, and proved to be a useful tool in the development of improved cardiovascular device test rigs.

Changing musical emotion : a computational rule system for modifying score and performance

When communicating emotion in music, composers and performers encode their expressive intentions through the control of basic musical features such as: pitch, loudness, timbre, mode, and articulation. The extent to which emotion can be controlled through the systematic manipulation of these features has not been fully examined. In this paper we present CMERS, a Computational Music Emotion Rule System for the control of perceived musical emotion that modifies features at the levels of score and performance in real-time. CMERS performance was evaluated in two rounds of perceptual testing. In experiment I, 20 participants continuously rated the perceived emotion of 15 music samples generated by CMERS. Three music works, each with five emotional variations were used (normal, happy, sad, angry, and tender). The intended emotion by CMERS was correctly identified 78% of the time, with significant shifts in valence and arousal also recorded, regardless of the works’ original emotion.

Communication of business process models via virtual environment simulations

Games and related virtual environments have been a much-hyped area of the entertainment industry. The classic quote is that games are now approaching the size of Hollywood box office sales [1]. Books are now appearing that talk up the influence of games on business [2], and it is one of the key drivers of present hardware development. Some of this 3D technology is now embedded right down at the operating system level via the Windows Presentation Foundations – hit Windows/Tab on your Vista box to find out... In addition to this continued growth in the area of games, there are a number of factors that impact its development in the business community. Firstly, the average age of gamers is approaching the mid thirties. Therefore, a number of people who are in management positions in large enterprises are experienced in using 3D entertainment environments. Secondly, due to the pressure of demand for more computational power in both CPU and Graphical Processing Units (GPUs), your average desktop, any decent laptop, can run a game or virtual environment. In fact, the demonstrations at the end of this paper were developed at the Queensland University of Technology (QUT) on a standard Software Operating Environment, with an Intel Dual Core CPU and basic Intel graphics option. What this means is that the potential exists for the easy uptake of such technology due to 1. a broad range of workers being regularly exposed to 3D virtual environment software via games; 2. present desktop computing power now strong enough to potentially roll out a virtual environment solution across an entire enterprise. We believe such visual simulation environments can have a great impact in the area of business process modeling. Accordingly, in this article we will outline the communication capabilities of such environments, giving fantastic possibilities for business process modeling applications, where enterprises need to create, manage, and improve their business processes, and then communicate their processes to stakeholders, both process and non-process cognizant. The article then concludes with a demonstration of the work we are doing in this area at QUT.

SCAPE sustainable urban design simulation

SCAPE is an interactive simulation that allows teachers and students to experiment with sustainable urban design. The project is based on the Kelvin Grove Urban Village, Brisbane. Groups of students role play as political, retail, elderly, student, council and builder characters to negotiate on game decisions around land use, density, housing types and transport in order to design a sustainable urban community. As they do so, the 3D simulation reacts in real time to illustrate what the village would look like as well as provide statistical information about the community they are creating. SCAPE brings together education, urban professional and technology expertise, helping it achieve educational outcomes, reflect real-world scenarios and include sophisticated logic and decision making processes and effects.---------- The research methodology was primarily practice led underpinned by action research methods resulting in innovative approaches and techniques in adapting digital games and simulation technologies to create dynamic and engaging experiences in pedagogical contexts. It also illustrates the possibilities for urban designers to engage a variety of communities in the processes, complexities and possibilities of urban development and sustainability.

Farm it right : the sustainable farming simulation

Farm It Right is an innovative creative work that simulates sustainable farming techniques using ecological models prepared by academics at Bradford University (School of Life Sciences). This interactive work simulates the farming conditions and options of our ancestors and demonstrates the direct impact their actions had on their environment and on the ’future of their cultures’ (Schmidt 2008). Specifically, the simulation allows users to explore and experiment with the complex relationships between environmental factors and human decision making within the harsh conditions of an early (9th century) Nordic farm. The simulation interface displays both statistical and graphical feedback in response to the users selections regarding animal reproduction rates, shelter provisions, food supplies etc. as well as demonstrating resulting impacts to soil erosion, water supply, animal population sizes etc.---------- 'Farm It Right' is now used at Bradford University (School of Life Sciences) as a dynamic e-Learning resource for incorporating environmental archaeology with sustainable development education, improving the engagement with complex data and the appreciation of human impacts on the environment and the future of their cultures. 'Farm It Right' is also demonstrated as an exemplar case study for interaction design students at Queensland University of Technology.

Automated symbolic and numeric procedure for manipulator rigid-body dynamic significance analysis and simplification

This paper describes an automated procedure for analysing the significance of each of the many terms in the equations of motion for a serial-link robot manipulator. Significance analysis provides insight into the rigid-body dynamic effects that are significant locally or globally in the manipulator's state space. Deleting those terms that do not contribute significantly to the total joint torque can greatly reduce the computational burden for online control, and a Monte-Carlo style simulation is used to investigate the errors thus introduced. The procedures described are a hybrid of symbolic and numeric techniques, and can be readily implemented using standard computer algebra packages.

Bayesian hybrid algorithms and models : implementation and associated issues

This thesis addresses computational challenges arising from Bayesian analysis of complex real-world problems. Many of the models and algorithms designed for such analysis are ‘hybrid’ in nature, in that they are a composition of components for which their individual properties may be easily described but the performance of the model or algorithm as a whole is less well understood. The aim of this research project is to after a better understanding of the performance of hybrid models and algorithms. The goal of this thesis is to analyse the computational aspects of hybrid models and hybrid algorithms in the Bayesian context. The first objective of the research focuses on computational aspects of hybrid models, notably a continuous finite mixture of t-distributions. In the mixture model, an inference of interest is the number of components, as this may relate to both the quality of model fit to data and the computational workload. The analysis of t-mixtures using Markov chain Monte Carlo (MCMC) is described and the model is compared to the Normal case based on the goodness of fit. Through simulation studies, it is demonstrated that the t-mixture model can be more flexible and more parsimonious in terms of number of components, particularly for skewed and heavytailed data. The study also reveals important computational issues associated with the use of t-mixtures, which have not been adequately considered in the literature. The second objective of the research focuses on computational aspects of hybrid algorithms for Bayesian analysis. Two approaches will be considered: a formal comparison of the performance of a range of hybrid algorithms and a theoretical investigation of the performance of one of these algorithms in high dimensions. For the first approach, the delayed rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin algorithm, and the hybrid version of the population Monte Carlo (PMC) algorithm are selected as a set of examples of hybrid algorithms. Statistical literature shows how statistical efficiency is often the only criteria for an efficient algorithm. In this thesis the algorithms are also considered and compared from a more practical perspective. This extends to the study of how individual algorithms contribute to the overall efficiency of hybrid algorithms, and highlights weaknesses that may be introduced by the combination process of these components in a single algorithm. The second approach to considering computational aspects of hybrid algorithms involves an investigation of the performance of the PMC in high dimensions. It is well known that as a model becomes more complex, computation may become increasingly difficult in real time. In particular the importance sampling based algorithms, including the PMC, are known to be unstable in high dimensions. This thesis examines the PMC algorithm in a simplified setting, a single step of the general sampling, and explores a fundamental problem that occurs in applying importance sampling to a high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of the estimate under conditions on the importance function. Additionally, the exponential growth of the asymptotic variance with the dimension is demonstrated and we illustrates that the optimal covariance matrix for the importance function can be estimated in a special case.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

A cable-array robot for air vehicle simulation

The development of autonomous air vehicles can be an expensive research pursuit. To alleviate some of the financial burden of this process, we have constructed a system consisting of four winches each attached to a central pod (the simulated air vehicle) via cables - a cable-array robot. The system is capable of precisely controlling the three dimensional position of the pod allowing effective testing of sensing and control strategies before experimentation on a free-flying vehicle. In this paper, we present a brief overview of the system and provide a practical control strategy for such a system.

Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment

With a view to assessing the vulnerability of columns to low elevation vehicular impacts, a non-linear explicit numerical model has been developed and validated using existing experimental results. The numerical model accounts for the effects of strain rate and confinement of the reinforced concrete, which are fundamental to the successful prediction of the impact response. The sensitivity of the material model parameters used for the validation is also scrutinised and numerical tests are performed to examine their suitability to simulate the shear failure conditions. Conflicting views on the strain gradient effects are discussed and the validation process is extended to investigate the ability of the equations developed under concentric loading conditions to simulate flexural failure events. Experimental data on impact force–time histories, mid span and residual deflections and support reactions have been verified against corresponding numerical results. A universal technique which can be applied to determine the vulnerability of the impacted columns against collisions with new generation vehicles under the most common impact modes is proposed. Additionally, the observed failure characteristics of the impacted columns are explained using extended outcomes. Based on the overall results, an analytical method is suggested to quantify the vulnerability of the columns.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is 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 the non-linear ASDE. The discrete system of equations is obtained by using the 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 formulations 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 modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.