Complex Modelling in the Primary and Middle School Years : An Interdisciplinary Approach

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual. With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to signifi cant changes in the forms of mathematical and scientifi c thinking required beyond the classroom. Modelling, in its various forms, can develop and broaden students’ mathematical and scientific thinking beyond the standard curriculum. This chapter first considers future competencies in the mathematical sciences within an increasingly complex world. Consideration is then given to interdisciplinary problem solving and models and modelling, as one means of addressing these competencies. Illustrative case studies involving complex, interdisciplinary modelling activities in Years 1 and 7 are presented.

Modelling of ellipsoidal nanowires : control and application

The properties of ellipsoidal nanowires are yet to be examined. They have likely applications in sensing, solar cells, microelectronics and cloaking devices. Little is known of the qualities that ellipse nanowires exhibit as we vary the aspect ratio with different dielectric materials and how varying these attributes affects plasmon coupling and propagation. It is known that the distance a plasmon can travel is further if it is supported by a thicker circular nanowire, while thinner nanowires are expected to be able to increase QD coupling. Ellipsoidal nanowires may be a good compromise due to their ability to have both thin and thick dimensions. Furthermore it has been shown that the plasmon resonances along the main axis of an ellipsoidal particle is governed by the relative aspect ratio of the ellipsoid, which may lead to further control of the plasmon. Research was done by the use of COMSOL Multiphysics by looking at the fundamental plasmon mode supported by an ellipsoidal nanowire and then studying this mode for various geometrical parameters, materials and illumination wavelength. Accordingly it was found that ellipsoidal nanowires exhibit a minimum for the wavenumber and a maximum for the propagation distance at roughly the same dimensions - Highlighting that there is an aspect ratio for which there is poor coupling but low loss. Here we investigate these and related attributes.

Reliability of spatiotemporal and kinetic gait parameters determined by a new instrumented treadmill system

Background Despite the emerging use of treadmills integrated with pressure platforms as outcome tools in both clinical and research settings, published evidence regarding the measurement properties of these new systems is limited. This study evaluated the within– and between–day repeatability of spatial, temporal and vertical ground reaction forces measured by a treadmill system instrumented with a capacitance–based pressure platform. Methods Thirty three healthy adults (mean age, 21.5 ± 2.8 years; height, 168.4 ± 9.9 cm; and mass, 67.8 ± 18.6 kg), walked barefoot on a treadmill system (FDM–THM–S, Zebris Medical GmbH) on three separate occasions. For each testing session, participants set their preferred pace but were blinded to treadmill speed. Spatial (foot rotation, step width, stride and step length), temporal (stride and step times, duration of stance, swing and single and double support) and peak vertical ground reaction force variables were collected over a 30–second capture period, equating to an average of 52 ± 5 steps of steady–state walking. Testing was repeated one week following the initial trial and again, for a third time, 20 minutes later. Repeated measures ANOVAs within a generalized linear modelling framework were used to assess between–session differences in gait parameters. Agreement between gait parameters measured within the same day (session 2 and 3) and between days (session 1 and 2; 1 and 3) were evaluated using the 95% repeatability coefficient. Results There were statistically significant differences in the majority (14/16) of temporal, spatial and kinetic gait parameters over the three test sessions (P < .01). The minimum change that could be detected with 95% confidence ranged between 3% and 17% for temporal parameters, 14% and 33% for spatial parameters, and 4% and 20% for kinetic parameters between days. Within–day repeatability was similar to that observed between days. Temporal and kinetic gait parameters were typically more consistent than spatial parameters. The 95% repeatability coefficient for vertical force peaks ranged between ± 53 and ± 63 N. Conclusions The limits of agreement in spatial parameters and ground reaction forces for the treadmill system encompass previously reported changes with neuromuscular pathology and footwear interventions. These findings provide clinicians and researchers with an indication of the repeatability and sensitivity of the Zebris treadmill system to detect changes in common spatiotemporal gait parameters and vertical ground reaction forces.

Temperature redistribution modelling during intermittent microwave convective heating

Microwave power is used for heating and drying processes because of its faster and volumetric heating capability. Non-uniform temperature distribution during microwave application is a major drawback of these processes. Intermittent application of microwave potentially reduces the impact of non-uniformity and improves energy efficiency by redistributing the temperature. However, temperature re-distribution during intermittent microwave heating has not been investigated adequately. Consequently, in this study, a coupled electromagnetic with heat and mass transfer model was developed using the finite element method embedded in COMSOL-Multyphysics software. Particularly, the temperature redistribution due to intermittent heating was investigated. A series of experiments were performed to validate the simulation. The test specimen was an apple and the temperature distribution was closely monitored by a TIC (Thermal Imaging Camera). The simulated temperature profile matched closely with thermal images obtained from experiments.

Modelling the salient factors influencing retired business professionals' participation in episodic skilled volunteering in rural settings

Retired business professionals represent an unexplored source of skill support for struggling rural communities. This research examined the feasibility of drawing on this valuable pool of knowledge and experience by engaging retirees in short term, project based volunteering roles in rural, not for profit agencies. Using the theory of planned behaviour and the functional approach to volunteering, the program of study generated a model comprising the key psychological and contextual factors determining the volunteers' decision to provide skill assistance in rural settings. The model provides a useful resource for creating suitable volunteering opportunities and for informing volunteer recruitment strategies.

A theory of process modelling impact

Process modelling – the design and use of graphical documentations of an organisation’s business processes – is a key method to document and use information about business processes. Still, despite current interest in process modelling, this research area faces essential challenges. Key unanswered questions concern the impact of process modelling in organisational practice, and the mechanisms through which impacts are developed. To answer these questions and to provide a better understanding of process modelling impact, I turn to the concept of affordances. Affordances describe the possibilities for goal-oriented action that technical objects offer to specified users. This notion has received growing attention from IS researchers. I report on my efforts to further develop the IS discipline’s understanding of affordances and impacts from informational objects, such as process models used by analysts for purposes of information systems analysis and design. Specifically, I seek to extend existing theory on the emergence and actualisation of affordances. I develop a research model that describes the process by which affordances are perceived and actualised and explain their dependence on available information and actualisation effort. I present my plans for operationalising and testing this research model empirically, and provide details about my design of a full-cycle, mixed methods study currently in progress.

Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

Deformation properties of single red blood cell in a stenosed microchannel

Red Blood Cells (RBCs) exhibit different types of motions and different deformed shapes, when they move through capillaries. RBCs can travel through capillaries having smaller diameters than RBCs’ diameter, due to the capacity of high deformability of the viscoelastic RBC membrane. The motion and the steady state shape of the RBCs depend on many factors, such as the geometrical parameters of the microvessel through which blood flows, the RBC membrane bending stiffness and the flow velocity. In this study, the effect of the RBC’s membrane stiffness on the deformation of a single RBC in a stenosed capillary is comprehensively examined. Smoothed Particle Hydrodynamics (SPH) in combination with the two-dimensional spring network membrane model is used to investigate the motion and the deformation property of the RBC. The simulation results demonstrate that the membrane bending stiffness of the RBC has a significant impact on the RBCs’ deformability.

Biomechanical characteristics of peripheral diabetic neuropathy : a systematic review and meta-analysis of findings from the gait cycle, muscle activity and dynamic barefoot plantar pressure

Background: Diabetic peripheral neuropathy is an important cause of foot ulceration and limb loss. This systematic review and meta-analysis investigated the effect of diabetic peripheral neuropathy on gait, dynamic electromyography and dynamic plantar pressures. Methods: Electronic databases were searched systematically for articles reporting the effect of diabetic peripheral neuropathy on gait, dynamic electromyography and plantar pressures. Searches were restricted to articles published between January 2000 and April 2012. Outcome measures assessed included spatiotemporal parameters, lower limb kinematics, kinetics, muscle activation and plantar pressure. Meta-analyses were carried out on all outcome measures reported by ≥3 studies. Findings: Sixteen studies were included consisting of 382 neuropathy participants, 216 diabetes controls without neuropathy and 207 healthy controls. Meta-analysis was performed on 11 gait variables. A high level of heterogeneity was noted between studies. Meta-analysis results suggested a longer stance time and moderately higher plantar pressures in diabetic peripheral neuropathy patients at the rearfoot, midfoot and forefoot compared to controls. Systematic review of studies suggested potential differences in the biomechanical characteristics (kinematics, kinetics, EMG) of diabetic neuropathy patients. However these findings were inconsistent and limited by small sample sizes.; Interpretation: Current evidence suggests that patients with diabetic peripheral neuropathy have elevated plantar pressures and occupy a longer duration of time in the stance-phase during gait. Firm conclusions are hampered by the heterogeneity and small sample sizes of available studies. Interpretation: Current evidence suggests that patients with diabetic peripheral neuropathy have elevated plantar pressures and occupy a longer duration of time in the stance-phase during gait. Firm conclusions are hampered by the heterogeneity and small sample sizes of available studies.

Correlating flow induced shear stress and chondrocytes activity in micro-porous scaffold using computational fluid dynamics and rapid prototyping

Flow induced shear stress plays an important role in regulating cell growth and distribution in scaffolds. This study sought to correlate wall shear stress and chondrocytes activity for engineering design of micro-porous osteochondral grafts based on the hypothesis that it is possible to capture and discriminate between the transmitted force and cell response at the inner irregularities. Unlike common tissue engineering therapies with perfusion bioreactors in which flow-mediated stress is the controlling parameter, this work assigned the associated stress as a function of porosity to influence in vitro proliferation of chondrocytes. D-optimality criterion was used to accommodate three pore characteristics for appraisal in a mixed level fractional design of experiment (DOE); namely, pore size (4 levels), distribution pattern (2 levels) and density (3 levels). Micro-porous scaffolds (n=12) were fabricated according to the DOE using rapid prototyping of an acrylic-based bio-photopolymer. Computational fluid dynamics (CFD) models were created correspondingly and used on an idealized boundary condition with a Newtonian fluid domain to simulate the dynamic microenvironment inside the pores. In vitro condition was reproduced for the 3D printed constructs seeded by high pellet densities of human chondrocytes and cultured for 72 hours. The results showed that cell proliferation was significantly different in the constructs (p<0.05). Inlet fluid velocity of 3×10-2mms-1 and average shear stress of 5.65×10-2 Pa corresponded with increased cell proliferation for scaffolds with smaller pores in hexagonal pattern and lower densities. Although the analytical solution of a Poiseuille flow inside the pores was found insufficient for the description of the flow profile probably due to the outside flow induced turbulence, it showed that the shear stress would increase with cell growth and decrease with pore size. This correlation demonstrated the basis for determining the relation between the induced stress and chondrocyte activity to optimize microfabrication of engineered cartilaginous constructs.

Mathematical modelling of counter flow v-grove solar air collector

Double-pass counter flow v-grove collector is considered one of the most efficient solar air-collectors. In this design of the collector, the inlet air initially flows at the top part of the collector and changes direction once it reaches the end of the collector and flows below the collector to the outlet. A mathematical model is developed for this type of collector and simulation is carried out using MATLAB programme. The simulation results were verified with three distinguished research results and it was found that the simulation has the ability to predict the performance of the air collector accurately as proven by the comparison of experimental data with simulation. The difference between the predicted and experimental results is, at maximum, approximately 7% which is within the acceptable limit considering some uncertainties in the input parameter values to allow comparison. A parametric study was performed and it was found that solar radiation, inlet air temperature, flow rate and length have a significant effect on the efficiency of the air collector. Additionally, the results are compared with single flow V-groove collector.

Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Exchanging data between Digital Human Modelling systems : a review of data formats

Digital human modeling (DHM) systems underwent significant development within the last years. They achieved constantly growing importance in the field of ergonomic workplace design, product development, product usability, ergonomic research, ergonomic education, audiovisual marketing and the entertainment industry. They help to design ergonomic products as well as healthy and safe socio-technical work systems. In the domain of scientific DHM systems, no industry specific standard interfaces are defined which could facilitate the exchange of 3D solid body data, anthropometric data or motion data. The focus of this article is to provide an overview of requirements for a reliable data exchange between different DHM systems in order to identify suitable file formats. Examples from the literature are discussed in detail. Methods: As a first step a literature review is conducted on existing studies and file formats for exchanging data between different DHM systems. The found file formats can be structured into different categories: static 3D solid body data exchange, anthropometric data exchange, motion data exchange and comprehensive data exchange. Each file format is discussed and advantages as well as disadvantages for the DHM context are pointed out. Case studies are furthermore presented, which show first approaches to exchange data between DHM systems. Lessons learnt are shortly summarized. Results: A selection of suitable file formats for data exchange between DHM systems is determined from the literature review.

A survey of user modelling in social media websites

With the widespread of social media websites in the internet, and the huge number of users participating and generating infinite number of contents in these websites, the need for personalisation increases dramatically to become a necessity. One of the major issues in personalisation is building users’ profiles, which depend on many elements; such as the used data, the application domain they aim to serve, the representation method and the construction methodology. Recently, this area of research has been a focus for many researchers, and hence, the proposed methods are increasing very quickly. This survey aims to discuss the available user modelling techniques for social media websites, and to highlight the weakness and strength of these methods and to provide a vision for future work in user modelling in social media websites.

Modelling survival data to account for model uncertainty: a single model or model averaging?

This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single “best” model, where “best” is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to account for model uncertainty. This was illustrated using a case study in which the aim was the description of lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample size was reduced, no single model was revealed as “best”, suggesting that a BMA approach would be appropriate. Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can provide robust predictions and facilitate more detailed investigation of the relationships between gene expression and patient survival. Keywords: Bayesian modelling; Bayesian model averaging; Cure model; Markov Chain Monte Carlo; Mixture model; Survival analysis; Weibull distribution