Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Information for regulating action in sport : metastability and emergence of tactical solutions under ecological constraints

The aims of this chapter are twofold. First, we show how experiments related to nonlinear dynamical systems theory can bring about insights on the interconnectedness of different information sources for action. These include the amount of information as emphasised in conventional models of cognition and action in sport and the nature of perceptual information typically emphasised in the ecological approach. The second aim was to show how, through examining the interconnectedness of these information sources, one can study the emergence of novel tactical solutions in sport; and design experiments where tactical/decisional creativity can be observed. Within this approach it is proposed that perceptual and affective information can be manipulated during practice so that the athlete's cognitive and action systems can be transposed to a meta-stable dynamical performance region where the creation of novel action information may reside.

Integrity determination of RTK solutions in precision farming applications

Integrity of Real Time Kinematic (RTK) positioning solutions relates to the confidential level that can be placed in the information provided by the RTK system. It includes the ability of the RTK system to provide timely valid warnings to users when the system must not be used for the intended operation. For instance, in the controlled traffic farming (CTF) system that controls traffic separates wheel beds and root beds, RTK positioning error causes overlap and increases the amount of soil compaction. The RTK system’s integrity capacity can inform users when the actual positional errors of the RTK solutions have exceeded Horizontal Protection Levels (HPL) within a certain Time-To-Alert (TTA) at a given Integrity Risk (IR). The later is defined as the probability that the system claims its normal operational status while actually being in an abnormal status, e.g., the ambiguities being incorrectly fixed and positional errors having exceeded the HPL. The paper studies the required positioning performance (RPP) of GPS positioning system for PA applications such as a CTF system, according to literature review and survey conducted among a number of farming companies. The HPL and IR are derived from these RPP parameters. A RTK-specific rover autonomous integrity monitoring (RAIM) algorithm is developed to determine the system integrity according to real time outputs, such as residual square sum (RSS), HDOP values. A two-station baseline data set is analyzed to demonstrate the concept of RTK integrity and assess the RTK solution continuity, missed detection probability and false alarm probability.

Determination of vertical hydraulic conductivity of aquitards in a multilayered leaky system using water-level signals in adjacent aquifers

This paper presents a methodology for determining the vertical hydraulic conductivity (Kv) of an aquitard, in a multilayered leaky system, based on the harmonic analysis of arbitrary water-level fluctuations in aquifers. As a result, Kv of the aquitard is expressed as a function of the phase-shift of water-level signals measured in the two adjacent aquifers. Based on this expression, we propose a robust method to calculate Kv by employing linear regression analysis of logarithm transformed frequencies and phases. The frequencies, where the Kv are calculated, are identified by coherence analysis. The proposed methods are validated by a synthetic case study and are then applied to the Westbourne and Birkhead aquitards, which form part of a five-layered leaky system in the Eromanga Basin, Australia.

Thermal conductivity of Si nanowires with faulted stacking layers

Faulted stacking layers are ubiquitously observed during the crystal growth of semiconducting nanowires (NWs). In this paper, we employ the reverse non-equilibrium molecular dynamics simulation to elucidate the effect of various faulted stacking layers on the thermal conductivity (TC) of silicon (Si) NWs. We find that the stacking faults can greatly reduce the TC of the Si NW. Among the different stacking faults that are parallel to the NW's axis, the 9R polytype structure, the intrinsic and extrinsic stacking faults (iSFs and eSFs) exert more pronounced effects in the reduction of TC than the twin boundary (TB). However, for the perpendicularly aligned faulted stacking layers, the eSFs and 9R polytype structures are observed to induce a larger reduction to the TC of the NW than the TB and iSFs. For all considered NWs, the TC does not show a strong relation with the increasing number of faulted stacking layers. Our studies suggest the possibility of tuning the thermal properties of Si NWs by altering the crystal structure via the different faulted stacking layers.

Surface functionalization on the thermal conductivity of graphene–polymer nanocomposites

Exploring thermal transport in graphene-polymer nanocomposite is significant to its applications with better thermal properties. Interfacial thermal conductance between graphene and polymer matrix plays a critical role in the improvement of thermal conductivity of graphene-polymer nanocomposite. Unfortunately, it is still challenging to understand the interfacial thermal transport between graphene nanofiller and polymer matrix at small material length scale. To this end, using non-equilibrium molecular dynamics simulations, we investigate the interfacial thermal conductance of graphene-polyethylene (PE) nanocomposite. The influence of functionalization with hydrocarbon chains on the interfacial thermal conductance of graphene-polymer nanocomposites was studied, taking into account of the effects of model size and thermal conductivity of graphene. An analytical model is also used to calculate the thermal conductivity of nanocomposite. The results are considered to contribute to development of new graphene-polymer nanocomposites with tailored thermal properties.

Investigation on Temperature-Dependent Electrical Conductivity of Carbon Nanotube/Epoxy Composites for Sustainable Energy Applications

Composites with carbon nanotubes are becoming increasingly used in energy storage and electronic devices, due to incorporated excellent properties from carbon nanotubes and polymers. Although their properties make them more attractive than conventional smart materials, their electrical properties are found to be temperature-dependent which is important to consider for the design of devices. To study the effects of temperature in electrically conductive multi-wall carbon nanotube/epoxy composites, thin films were prepared and the effect of temperature on the resistivity, thermal properties and Raman spectral characteristics of the composite films was evaluated. Resistivity-temperature profiles showed three distinct regions in as-cured samples and only two regions in samples whose thermal histories had been erased. In the vicinity of the glass transition temperature, the as-cured composites exhibited pronounced resistivity and enthalpic relaxation peaks, which both disappeared after erasing the composites’ thermal histories by temperature cycling. Combined DSC, Raman spectroscopy, and resistivity-temperature analyses indicated that this phenomenon can be attributed to the physical aging of the epoxy matrix and that, in the region of the observed thermal history-dependent resistivity peaks, structural rearrangement of the conductive carbon nanotube network occurs through a volume expansion/relaxation process. These results have led to an overall greater understanding of the temperature-dependent behaviour of conductive carbon nanotube/epoxy composites, including the positive temperature coefficient effect.

Thermal conductivity of configurable two-dimensional carbon nanotube architecture and strain modulation

We reported the thermal conductivity of the two-dimensional carbon nanotube (CNT)-based architecture, which can be constructed through welding of single-wall CNTs by electron beam. Using large-scale nonequilibrium molecular dynamics simulations, the thermal conductivity is found to vary with different junction types due to their different phonon scatterings at the junction. The strong length and strain dependence of the thermal conductivity suggests an effective avenue to tune the thermal transport properties of the CNT-based architecture, benefiting the design of nanoscale thermal rectifiers or phonon engineering.

Suppressed thermal conductivity of bilayer graphene with vacancy-initiated linkages

Through larger-scale molecular dynamics simulations, we investigated the impacts from vacancy-initiated linkages on the thermal conductivity of bilayer graphene sheets (of size L × W = 24.5 nm × 3.7 nm). Three different interlayer linkages, including divacancy bridging, “spiro” interstitial bridging and Frenkel pair defects, are considered. It is found that the presence of interlayer linkages induces a significant degradation in the thermal conductivity of the bilayer graphene sheet. The degradation is strongly dependent on the interlayer linkage type, concentration and location. More importantly, the linkages that contain vacancies lead to more severe suppression of the thermal conductivity, in agreement with theoretical predictions that vacancies induce strong phonon scattering. Our finding provides useful guidelines for the application of multilayer graphene sheets in practical thermal management.

Ion exchange treatment of saline solutions using lanxess S108H strong acid cation resin

Common to many types of water and wastewater is the presence of sodium ions which can be removed by desalination technologies, such as reverse osmosis and ion exchange. The focus of this investigation was ion exchange as it potentially offered several advantages compared to competing methods. The equilibrium and column behaviour of a strong acid cation (SAC) resin was examined for the removal of sodium ions from aqueous sodium chloride solutions of varying normality as well as a coal seam gas water sample. The influence of the bottle-point method to generate the sorption isotherms was evaluated and data interpreted with the Langmuir Vageler, Competitive Langmuir, Freundlich, and Dubinin-Astakhov models. With the constant concentration bottle point method, the predicted maximum exchange levels of sodium ions on the resin ranged from 61.7 to 67.5 g Na/kg resin. The general trend was that the lower the initial concentration of sodium ions in the solution, the lower the maximum capacity of the resin for sodium ions. In contrast, the constant mass bottle point method was found to be problematic in that the isotherm profiles may not be complete, if experimental parameters were not chosen carefully. Column studies supported the observations of the equilibrium studies, with maximum sodium loading of ca. 62.9 g Na/kg resin measured, which was in excellent agreement with the predictions of the data from the constant concentration bottle point method. Equilibria involving coal seam gas water were more complex due to the presence of sodium bicarbonate in solution, albeit the maximum loading capacity for sodium ions was in agreement with the results from the more simple sodium chloride solutions.

Thermal conductivity of a new carbon nanotube analog: The diamond nanothread

Based on the non-equilibrium molecular dynamics simulations, we have studied the thermal conductivities of a novel ultra-thin one-dimensional carbon nanomaterial - diamond nanothread (DNT). Unlike single-wall carbon nanotube (CNT), the existence of the Stone-Wales transformations in DNT endows it with richer thermal transport characteristics. There is a transition from wave-dominated to particle-dominated transport region, which depends on the length of poly-benzene rings. However, independent of the transport region, strong length dependence in thermal conductivity is observed in DNTs with different lengths of poly-benzene ring. The distinctive SW characteristic in DNT provides more degrees of freedom to tune the thermal conductivity not found in the homogeneous structure of CNT. Therefore, DNT is an ideal platform to investigate various thermal transport mechanisms at the nanoscale. Its high tunability raises the potential to design DNTs for different applications, such as thermal connection and temperature management.