Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

A constraint and position identification (CPI) approach for the synthesis of decoupled spatial translational compliant parallel manipulators

This paper introduces a screw theory based method termed constraint and position identification (CPI) approach to synthesize decoupled spatial translational compliant parallel manipulators (XYZ CPMs) with consideration of actuation isolation. The proposed approach is based on a systematic arrangement of rigid stages and compliant modules in a three-legged XYZ CPM system using the constraint spaces and the position spaces of the compliant modules. The constraint spaces and the position spaces are firstly derived based on the screw theory instead of using the rigid-body mechanism design experience. Additionally, the constraint spaces are classified into different constraint combinations, with typical position spaces depicted via geometric entities. Furthermore, the systematic synthesis process based on the constraint combinations and the geometric entities is demonstrated via several examples. Finally, several novel decoupled XYZ CPMs with monolithic configurations are created and verified by finite elements analysis. The present CPI approach enables experts and beginners to synthesize a variety of decoupled XYZ CPMs with consideration of actuation isolation by selecting an appropriate constraint and an optimal position for each of the compliant modules according to a specific application.

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.

Novel smart modules for imaging, communications, and displays

This dissertation proposes and demonstrates novel smart modules to solve challenging problems in the areas of imaging, communications, and displays. The smartness of the modules is due to their ability to be able to adapt to changes in operating environment and application using programmable devices, specifically, electronically variable focus lenses (ECVFLs) and digital micromirror devices (DMD). The proposed modules include imagers for laser characterization and general purpose imaging which smartly adapt to changes in irradiance, optical wireless communication systems which can adapt to the number of users and to changes in link length, and a smart laser projection display that smartly adjust the pixel size to achieve a high resolution projected image at each screen distance. The first part of the dissertation starts with the proposal of using an ECVFL to create a novel multimode laser beam characterizer for coherent light. This laser beam characterizer uses the ECVFL and a DMD so that no mechanical motion of optical components along the optical axis is required. This reduces the mechanical motion overhead that traditional laser beam characterizers have, making this laser beam characterizer more accurate and reliable. The smart laser beam characterizer is able to account for irradiance fluctuations in the source. Using image processing, the important parameters that describe multimode laser beam propagation have been successfully extracted for a multi-mode laser test source. Specifically, the laser beam analysis parameters measured are the M2 parameter, w0 the minimum beam waist, and zR the Rayleigh range. Next a general purpose incoherent light imager that has a high dynamic range (>100 dB) and automatically adjusts for variations in irradiance in the scene is proposed. Then a data efficient image sensor is demonstrated. The idea of this smart image sensor is to reduce the bandwidth needed for transmitting data from the sensor by only sending the information which is required for the specific application while discarding the unnecessary data. In this case, the imager demonstrated sends only information regarding the boundaries of objects in the image so that after transmission to a remote image viewing location, these boundaries can be used to map out objects in the original image. The second part of the dissertation proposes and demonstrates smart optical communications systems using ECVFLs. This starts with the proposal and demonstration of a zero propagation loss optical wireless link using visible light with experiments covering a 1 to 4 m range. By adjusting the focal length of the ECVFLs for this directed line-of-sight link (LOS) the laser beam propagation parameters are adjusted such that the maximum amount of transmitted optical power is captured by the receiver for each link length. This power budget saving enables a longer achievable link range, a better SNR/BER, or higher power efficiency since more received power means the transmitted power can be reduced. Afterwards, a smart dual mode optical wireless link is proposed and demonstrated using a laser and LED coupled to the ECVFL to provide for the first time features of high bandwidths and wide beam coverage. This optical wireless link combines the capabilities of smart directed LOS link from the previous section with a diffuse optical wireless link, thus achieving high data rates and robustness to blocking. The proposed smart system can switch from LOS mode to Diffuse mode when blocking occurs or operate in both modes simultaneously to accommodate multiple users and operate a high speed link if one of the users requires extra bandwidth. The last part of this section presents the design of fibre optic and free-space optical switches which use ECVFLs to deflect the beams to achieve switching operation. These switching modules can be used in the proposed optical wireless indoor network. The final section of the thesis presents a novel smart laser scanning display. The ECVFL is used to create the smallest beam spot size possible for the system designed at the distance of the screen. The smart laser scanning display increases the spatial resoluti on of the display for any given distance. A basic smart display operation has been tested for red light and a 4X improvement in pixel resolution for the image has been demonstrated.

THAWS: automated wireless sensor network development and deployment

This research focuses on the design and implementation of a tool to speed-up the development and deployment of heterogeneous wireless sensor networks. The THAWS (Tyndall Heterogeneous Automated Wireless Sensors) tool can be used to quickly create and configure application-specific sensor networks. THAWS presents the user with a choice of options, in order to characterise the desired functionality of the network. With this information, THAWS generates the necessary code from pre-written templates and well-tested, optimized software modules. This is then automatically compiled to form binary files for each node in the network. Wireless programming of the network completes the task of targeting the wireless network towards a specific sensing application. THAWS is an adaptable tool that works with both homogeneous and heterogeneous networks built from wireless sensor nodes that have been developed in the Tyndall National Institute.

A study of silicon and germanium junctionless transistors

Technology boosters, such as strain, HKMG and FinFET, have been introduced into semiconductor industry to extend Moore’s law beyond 130 nm technology nodes. New device structures and channel materials are highly demanded to keep performance enhancement when the device scales beyond 22 nm. In this work, the properties and feasibility of the proposed Junctionless transistor (JNT) have been evaluated for both Silicon and Germanium channels. The performance of Silicon JNTs with 22 nm gate length have been characterized at elevated temperature and stressed conditions. Furthermore, steep Subthreshold Slopes (SS) in JNT and IM devices are compared. It is observed that the floating body in JNT is relatively dynamic comparing with that in IM devices and proper design of the device structure may further reduce the VD for a sub- 60 mV/dec subthreshold slope. Diode configuration of the JNT has also been evaluated, which demonstrates the first diode without junctions. In order to extend JNT structure into the high mobility material Germanium (Ge), a full process has been develop for Ge JNT. Germanium-on-Insulator (GeOI) wafers were fabricated using Smart-Cut with low temperature direct wafer bonding method. Regarding the lithography and pattern transfer, a top-down process of sub-50-nm width Ge nanowires is developed in this chapter and Ge nanowires with 35 nm width and 50 nm depth are obtained. The oxidation behaviour of Ge by RTO has been investigated and high-k passivation scheme using thermally grown GeO2 has been developed. With all developed modules, JNT with Ge channels have been fabricated by the CMOScompatible top-down process. The transistors exhibit the lowest subthreshold slope to date for Ge JNT. The devices with a gate length of 3 μm exhibit a SS of 216 mV/dec with an ION/IOFF current ratio of 1.2×103 at VD = -1 V and DIBL of 87 mV/V.

Simplified PRBMs of spatial compliant multi-beam modules for planar motion

PRBMs (pseudo-rigid-body models) have been becoming important engineering technologies/methods in the field of compliant mechanisms to simplify the design and analysis through the use of the knowledge body of rigid-body mechanisms coupling with springs. This article addresses the PRBMs of spatial multi-beam modules for planar motion, which are composed of three or more symmetrical wire/slender beams parallel to each other where the planar twisting DOF (degree of freedom) is assumed to be very small for specific applications/loading conditions. Simplified PRBMs are firstly proposed through replacing each beam in spatial multi-beam module with a rigid-body link plus two identical spherical joints at its two ends. The characteristics factor, bending stiffness and twisting stiffness for the spherical joint are determined. Load-displacement equations are then derived for a class of spatial multi-beam modules and general spatial multi-beam modules using the virtual work principle and kinematic relationships. Finally, nonlinear FEA (finite element analysis) is employed with comparisons with the PRBMs. The present PRBMs have shown the ability to predict the primary nonlinear constraint characteristics such as load-stiffening effect, cross-axis coupling in the two primary translational directions and buckling load.

CUBEs: decoupled, compact, and monolithic spatial translational compliant parallel manipulators

This paper deals with the conceptual design of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs): CUBEs. Position spaces of compliant P (P: prismatic) joints are first discussed, which are represented by circles about the translational directions. A design method of monolithic XYZ CPMs is then proposed in terms of both the kinematic substitution method and the position spaces. Three types of monolithic XYZ CPMs are finally designed using the proposed method with the help of three classes of kinematical decoupled 3-DOF (degree of freedom) translational parallel mechanisms (TPMs). These monolithic XYZ CPMs include a 3-PPP XYZ CPM composed of identical parallelogram modules (a previously reported design), a novel 3-PPPR (R: revolute) XYZ CPM composed of identical compliant four-beam modules, and a novel 3-PPPRR XYZ CPM. The latter two monolithic designs also have extended lives. It is shown that the proposed design method can be used to design other decoupled and compact XYZ CPMs by using the concept of position spaces, and the resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap.

National, inter-institutional, graduate modules – blended learning approaches for PhD education in Ireland

This paper is a case study that describes the design and delivery of national PhD lectures with 40 PhD candidates in Digital Arts and Humanities in Ireland simultaneously to four remote locations, in Trinity College Dublin, in University College Cork, in NUI Maynooth and NUI Galway. Blended learning approaches were utilized to augment traditional teaching practices combining: face-to-face engagement, video-conferencing to multiple sites, social media lecture delivery support – a live blog and micro blogging, shared, open student web presence online. Techniques for creating an effective, active learning environment were discerned via a range of learning options offered to students through student surveys after semester one. Students rejected the traditional lecture format, even through the novel delivery method via video link to a number of national academic institutions was employed. Students also rejected the use of a moderated forum as a means of creating engagement across the various institutions involved. Students preferred a mix of approaches for this online national engagement. The paper discusses successful methods used to promote interactive teaching and learning. These included Peer to peer learning, Workshop style delivery, Social media. The lecture became a national, synchronous workshop. The paper describes how allowing students to have a voice in the virtual classroom they become animated and engaged in an open culture of shared experience and scholarship, create networks beyond their institutions, and across disciplinary boundaries. We offer an analysis of our experiences to assist other educators in their course design, with a particular emphasis on social media engagement.

Examining current provision, practice and experience of initial teacher training providers in Ireland preparing pre service teachers for the inclusion of students with special education needs in physical education classes.

Research from an international perspective in relation to the preparation of pre service teachers in physical education and special educational needs indicates that initial teacher training providers are inconsistent in the amount of time spent addressing the issue and the nature of curricular content (Vickerman, 2007). In Ireland, research of Meegan and MacPhail (2005) and Crawford (2011) indicates that physical education teachers do not feel adequately prepared to accommodate students with Special Educational Needs (SEN) in physical education classes. This study examined initial teacher training provision in Ireland in the training of pre service physical education teachers in SEN. The methodology used was qualitative and included questionnaires and interviews (n=4). Findings indicated that time allocation (semester long modules), working with children with disabilities in mainstream settings (school or leisure centre based), lack of collaboration with other PETE providers (n=4) and a need for continued professional development were themes in need of address. Using a combined approach where the recently designed European Inclusive Physical Education Training (Kudlácěk, Jesina, & Flanagan, 2010) model is infused through the undergraduate degree programme is proposed. Further, the accommodation of hands on experience for undergraduates in mainstream settings and the establishment of inter institutional communities of practice, with a national disability research initiative, is essential to ensure quality adapted physical activity training can be accommodated throughout Ireland.