Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Evaluating effects of eco-driving at traffic intersections based on traffic micro-simulation

Eco-driving is an initiative driving behavior which aims to reduce fuel consumption and emissions from automobiles. Recently, it has attracted increasing interests and has been adopted by many drivers in Australia. Although many of the studies have revealed considerable benefits in terms of fuel consumption and emissions after utilising eco-driving, most of the literature investigated eco-driving effects on individual driver but not traffic flow. The driving behavior of eco-drivers will potentially affect other drivers and thereby affects the entire traffic flow. To comprehensively assess and understand how effectively eco-driving can perform, therefore, measurement on traffic flow is necessary. In this paper, we proposed and demonstrated an evaluation method based on a microscopic traffic simulator (Aimsun). We focus on one particular eco-driving style which involves moderate and smooth acceleration. We evaluated both traffic performance (travel time) and environmental performance (fuel consumption and CO2 emission) at traffic intersection level in a simple simulation model. The before-and-after comparisons indicated potentially negative impacts when using eco-driving, which highlighted the necessity to carefully evaluate and improve eco-driving before wide promotion and implementation.

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Optical waveguide and cavity effects on whispering-gallery mode resonances in a ZnO nanonail

Spatially resolved cathodoluminescence (CL) study of a ZnO nanonail, having thin shank, tapered neck, and hexagonal head sections, is reported. Monochromatic imaging and line scan profiling indicate that the wave guiding and leaking from growth imperfections in addition to the oxygen deficiency variation determine the spatial contrast of CL emissions. Occurrence of resonance peaks at identical wavelengths regardless of CL-excitation spots is inconsistent with the whispering-gallery mode (WGM) resonances of a two-dimensional cavity in the finite difference time domain simulation. However, three dimensioanl cavity simulation produced WGM peaks that are consistent with the experimental spectra, including transverse-electric resonances that are comparable to transverse-magnetic ones.

Characteristics of modal sound radiation of finite cylindrical shells

Characteristics of modal sound radiation of finite cylindrical shells are studied using finite element and boundary element methods in this paper. In the low frequency range, modal radiation efficiencies of finite cylindrical shells are found to asymptotically approach those of the corresponding infinite cylindrical shell when structural trace wavelengths of the cylindrical shells are greater than the acoustic wavelength. Modal radiation efficiencies for each group of modes having the same circumferential modal index decrease as the axial modal index increases. They converge to each other when the axial trace wavelength is much greater than the circumferential trace wavelength. The mechanism leading to lower radiation efficiency of modes with higher circumferential modal index of short cylinders is explained. Similar to those of flat plate panels, change in slope or waviness is observed in modal radiation efficiency curves of modes with higher order axial modal index at medium frequencies. This is attributed to the interference of sound radiated by neighbouring vibrating cells when the distance between nodal lines of a vibrating mode is in the same order or smaller than the acoustic wavelength. Effects of the internal sound field on modal radiation efficiencies of a finite open-end cylinder are discussed.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

A traffic simulation standard based on data marts

Traffic Simulation models tend to have their own data input and output formats. In an effort to standardise the input for traffic simulations, we introduce in this paper a set of data marts that aim to serve as a common interface between the necessaary data, stored in dedicated databases, and the swoftware packages, that require the input in a certain format. The data marts are developed based on real world objects (e.g. roads, traffic lights, controllers) rather than abstract models and hence contain all necessary information that can be transformed by the importing software package to their needs. The paper contains a full description of the data marts for network coding, simulation results, and scenario management, which have been discussed with industry partners to ensure sustainability.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

A study of abrasive water jet characteristics by CFD simulation

Computational fluid dynamics (CFD) models for ultrahigh velocity waterjets and abrasive waterjets (AWJs) are established using the Fluent 6 flow solver. Jet dynamic characteristics for the flow downstream from a very fine nozzle are then simulated under steady state, turbulent, two-phase and three-phase flow conditions. Water and particle velocities in a jet are obtained under different input and boundary conditions to provide an insight into the jet characteristics and a fundamental understanding of the kerf formation process in AWJ cutting. For the range of downstream distances considered, the results indicate that a jet is characterised by an initial rapid decay of the axial velocity at the jet centre while the cross-sectional flow evolves towards a top-hat profile downstream.

High fidelity simulation; challenges encountered in developing and implementing student learning experiences, staff education and researching approaches to learning

High fidelity simulation as a teaching and learning approach is being embraced by many schools of nursing. Our school embarked on integrating high fidelity (HF) simulation into the undergraduate clinical education program in 2011. Low and medium fidelity simulation has been used for many years, but this did not simplify the integration of HF simulation. Alongside considerations of how and where HF simulation would be integrated, issues arose with: student consent and participation for observed activities; data management of video files; staff development, and conceptualising how methods for student learning could be researched. Simulation for undergraduate student nurses commenced as a formative learning activity, undertaken in groups of eight, where four students undertake the ‘doing’ role and four are structured observers, who then take a formal role in the simulation debrief. Challenges for integrating simulation into student learning included conceptualising and developing scenarios to trigger students’ decision making and application of skills, knowledge and attitudes explicit to solving clinical ‘problems’. Developing and planning scenarios for students to ‘try out’ skills and make decisions for problem solving lay beyond choosing pre-existing scenarios inbuilt with the software. The supplied scenarios were not concept based but rather knowledge, skills and technology (of the manikin) focussed. Challenges lay in using the technology for the purpose of building conceptual mastery rather than using technology simply because it was available. As we integrated use of HF simulation into the final year of the program, focus was on building skills, knowledge and attitudes that went beyond technical skill, and provided an opportunity to bridge the gap with theory-based knowledge that students often found difficult to link to clinical reality. We wished to provide opportunities to develop experiential knowledge based on application and clinical reasoning processes in team environments where problems are encountered, and to solve them, the nurse must show leadership and direction. Other challenges included students consenting for simulations to be videotaped and ethical considerations of this. For example if one student in a group of eight did not consent, did this mean they missed the opportunity to undertake simulation, or that others in the group may be disadvantaged by being unable to review their performance. This has implications for freely given consent but also for equity of access to learning opportunities for students who wished to be taped and those who did not. Alongside this issue were the details behind data management, storage and access. Developing staff with varying levels of computer skills to use software and undertake a different approach to being the ‘teacher’ required innovation where we took an experiential approach. Considering explicit learning approaches to be trialled for learning was not a difficult proposition, but considering how to enact this as research with issues of blinding, timetabling of blinded groups, and reducing bias for testing results of different learning approaches along with gaining ethical approval was problematic. This presentation presents examples of these challenges and how we overcame them.

Using ‘think aloud’ as a strategy for learning clinical reasoning in high fidelity case-based simulation for undergraduate nursing students

AIMS This paper reports on the implementation of a research project that trials an educational strategy implemented over six months of an undergraduate third year nursing curriculum. This project aims to explore the effectiveness of ‘think aloud’ as a strategy for learning clinical reasoning for students in simulated clinical settings. BACKGROUND Nurses are required to apply and utilise critical thinking skills to enable clinical reasoning and problem solving in the clinical setting [1]. Nursing students are expected to develop and display clinical reasoning skills in practice, but may struggle articulating reasons behind decisions about patient care. For students learning to manage complex clinical situations, teaching approaches are required that make these instinctive cognitive processes explicit and clear [2-5]. In line with professional expectations, nursing students in third year at Queensland University of Technology (QUT) are expected to display clinical reasoning skills in practice. This can be a complex proposition for students in practice situations, particularly as the degree of uncertainty or decision complexity increases [6-7]. The ‘think aloud’ approach is an innovative learning/teaching method which can create an environment suitable for developing clinical reasoning skills in students [4, 8]. This project aims to use the ‘think aloud’ strategy within a simulation context to provide a safe learning environment in which third year students are assisted to uncover cognitive approaches that best assist them to make effective patient care decisions, and improve their confidence, clinical reasoning and active critical reflection on their practice. MEHODS In semester 2 2011 at QUT, third year nursing students will undertake high fidelity simulation, some for the first time commencing in September of 2011. There will be two cohorts for strategy implementation (group 1= use think aloud as a strategy within the simulation, group 2= not given a specific strategy outside of nursing assessment frameworks) in relation to problem solving patient needs. Students will be briefed about the scenario, given a nursing handover, placed into a simulation group and an observer group, and the facilitator/teacher will run the simulation from a control room, and not have contact (as a ‘teacher’) with students during the simulation. Then debriefing will occur as a whole group outside of the simulation room where the session can be reviewed on screen. The think aloud strategy will be described to students in their pre-simulation briefing and allow for clarification of this strategy at this time. All other aspects of the simulations remain the same, (resources, suggested nursing assessment frameworks, simulation session duration, size of simulation teams, preparatory materials). RESULTS Methodology of the project and the challenges of implementation will be the focus of this presentation. This will include ethical considerations in designing the project, recruitment of students and implementation of a voluntary research project within a busy educational curriculum which in third year targets 669 students over two campuses. CONCLUSIONS In an environment of increasingly constrained clinical placement opportunities, exploration of alternate strategies to improve critical thinking skills and develop clinical reasoning and problem solving for nursing students is imperative in preparing nurses to respond to changing patient needs. References 1. Lasater, K., High-fidelity simulation and the development of clinical judgement: students' experiences. Journal of Nursing Education, 2007. 46(6): p. 269-276. 2. Lapkin, S., et al., Effectiveness of patient simulation manikins in teaching clinical reasoning skills to undergraduate nursing students: a systematic review. Clinical Simulation in Nursing, 2010. 6(6): p. e207-22. 3. Kaddoura, M.P.C.M.S.N.R.N., New Graduate Nurses' Perceptions of the Effects of Clinical Simulation on Their Critical Thinking, Learning, and Confidence. The Journal of Continuing Education in Nursing, 2010. 41(11): p. 506. 4. Banning, M., The think aloud approach as an educational tool to develop and assess clinical reasoning in undergraduate students. Nurse Education Today, 2008. 28: p. 8-14. 5. Porter-O'Grady, T., Profound change:21st century nursing. Nursing Outlook, 2001. 49(4): p. 182-186. 6. Andersson, A.K., M. Omberg, and M. Svedlund, Triage in the emergency department-a qualitative study of the factors which nurses consider when making decisions. Nursing in Critical Care, 2006. 11(3): p. 136-145. 7. O'Neill, E.S., N.M. Dluhy, and C. Chin, Modelling novice clinical reasoning for a computerized decision support system. Journal of Advanced Nursing, 2005. 49(1): p. 68-77. 8. Lee, J.E. and N. Ryan-Wenger, The "Think Aloud" seminar for teaching clinical reasoning: a case study of a child with pharyngitis. J Pediatr Health Care, 1997. 11(3): p. 101-10.