Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Decoupled trajectory planning for a submerged rigid body subject to dissipative and potential forces

This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Smoothly attaching bow flows with constant vorticity

The free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

meso-Porphyrinylphosphine Oxides: Mono- and Bidentate Ligands for Supramolecular Chemistry and the Crystal Structures of Monomeric [10,20-Diphenylporphyrinatonickel(II)-5,15-diyl]-bis-[P(O)Ph2] and Polymeric Self-Coordinated ([10,20-Diphenylporphyrinatozinc(II)-5,15-diyl]-bis-[P(O)Ph2])

A series of porphyrins substituted in one or two meso-positions by diphenylphosphine oxide groups has been prepared by the palladium catalysed reaction of diphenylphosphine or its oxide with the corresponding bromoporphyrins. Compounds {MDPP-[P(O)Ph2]n} (M = H2, Ni, Zn; H2DPP = 5,15-diphenylporphyrin; n = 1, 2) were isolated in yields of 60-95%. The reaction is believed to proceed via the conventional oxidative addition, phosphination and reductive elimination steps, as the stoichiometric reaction of η1-palladio(II) porphyrin [PdBr(H2DPP)(dppe)] (H2DPP = 5,15-diphenylporphyrin; dppe = 1,2-bis(diphenylphosphino)ethane) with diphenylphosphine oxide also results in the desired mono-porphyrinylphosphine oxide [H2DPP-P(O)Ph2]. Attempts to isolate the tertiary phosphines failed due to their extreme air-sensitivity. Variable temperature 1H NMR studies of [H2DPP-P(O)Ph2] revealed an intrinsic lack of symmetry, while fluorescence spectroscopy showed that the phosphine oxide group does not behave as a "heavy atom" quencher. The electron withdrawing effect of the phosphine oxide group was confirmed by voltammetry. The ligands were characterised by multinuclear NMR and UV-visible spectroscopy as well as mass spectrometry. Single crystal X-ray crystallography showed that the bis(phosphine oxide) nickel(II) complex {[NiDPP-[P(O)Ph2]2} is monomeric in the solid state, with a ruffled porphyrin core and the two P=O fragments on the same side of the average plane of the molecule. On the other hand, the corresponding zinc(II) complex formed infinite chains through coordination of one Ph2PO substituent to the neighbouring zinc porphyrin through an almost linear P=O---Zn unit, leaving the other Ph2PO group facing into a parallel channel filled with disordered water molecules. These new phosphine oxides are attractive ligands for supramolecular porphyrin chemistry.

Raman spectroscopy of selected borate minerals of the pinakiolite group

The Raman spectra of a series of related minerals of the pinakiolite group of minerals have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO33- ion. The site symmetry is reduced from D3h to C1. Intense Raman bands are observed for the minerals takeuchiite, pinakiolite, fredrikssonite and azoproite at 1084, 1086, 1086 and 1086 cm-1. These bands are assigned to the ν1 BO33- symmetric stretching mode. Low intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; 1436, 1749 cm-1. One probable assignment is to ν3 BO33- antisymmetric stretching mode. Intense Raman bands of takeuchiite, pinakiolite, fredrikssonite and azoproite at 712 cm-1 attributed to the ν2 out-of-plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill-defined structures can be obtained.

Distributed object tracking with robot and disjoint camera networks

We describe a novel two stage approach to object localization and tracking using a network of wireless cameras and a mobile robot. In the first stage, a robot travels through the camera network while updating its position in a global coordinate frame which it broadcasts to the cameras. The cameras use this information, along with image plane location of the robot, to compute a mapping from their image planes to the global coordinate frame. This is combined with an occupancy map generated by the robot during the mapping process to track the objects. We present results with a nine node indoor camera network to demonstrate that this approach is feasible and offers acceptable level of accuracy in terms of object locations.

Effect of spacing of reinforcement on the behaviour of partially grouted masonry shear walls

Partially Grouted Reinforced Masonry (PGRM) shear walls perform well in places where the cyclonic wind pressure dominates the design. Their out-of-plane flexural performance is better understood than their inplane shear behaviour; in particular, it is not clear whether the PGRM shear walls act as unreinforced masonry (URM) walls embedded with discrete reinforced grouted cores or as integral systems of reinforced masonry (RM) with wider spacing of reinforcement. With a view to understanding the inplane response of PGRM shear walls, ten full scale single leaf, clay block walls were constructed and tested under monotonic and cyclic inplane loading cases. It has been shown that where the spacing of the vertical reinforcement is less than 2000mm, the walls behave as an integral system of RM; for spacing greater than 2000mm, the walls behave similar to URM with no significant benefit from the reinforced cores based on the displacement ductility and stiffness degradation factors derived from the complete lateral load – lateral displacement curves.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.

English language study abroad program : an investigation of Hong Kong pre-service teachers’ experiences of a language immersion program

There has been minimal research focused on short-term study abroad language immersion programs, in particular, with home-stay families. The importance of authentic intercultural experience is increasingly clear and was acknowledged as central to the process of language learning (Liddicoat, 2004). In Hong Kong, education programs for pre-service language teachers have significantly emphasised language and intercultural training through short-term study abroad, and these short overseas language immersion courses have become a compulsory component for teacher training (Bodycott & Crew, 2001) in the last decade. This study aims to investigate eight Hong Kong pre-service teachers’ and their home-stay families’ experiences of a short-term (two months) language immersion program in Australia. The focus is on listening to commentaries concerning the development of communicative competence, intercultural competence and professional growth during the out-of-class study abroad experience. The conceptual framework adopted in this study views language and intercultural learning from social constructivist perspectives. Central to this framing is the notion that the internalisation of higher mental functions involves the transfer from the inter-psychological to the intra-psychological plane, that is, a progression process from the socially supported to individually controlled performance. From this perspective, language serves as a way to communicate about, and in relation to, actions and experience. Three research questions were addressed and studied through qualitative methodology. 1. How do the pre-service teachers and their home-stay families perceive the out-of-class component of the program in terms of opportunities for the development of language proficiency and communicative competence? 2. How do the pre-service teachers and their home-stay families perceive the out-of-class component of the program in terms of the development of intercultural competence? 3. How do the pre-service teachers and home-stay families perceive the outof- class component of the program in terms of teachers’ professional growth? Data were generated from multiple data collection methods and analysed through thematic analysis from both a “bottom up” and “top down” approach. The study showed that the pre-service teachers perceived that the immersion program influenced, to varying degrees, their language proficiency, communication and intercultural awareness, as well as their self-awareness and professional growth. These pre-service teachers believed that effective language learning centres on active engagement in the target language community. A mismatch between the views and evaluations of the two groups – the pre-service teachers and the home-stay family members – provides some evidence of misalignments in terms of expectations and perceptions of each other’s roles and responsibilities. The study has highlighted challenges encountered, and provided suggestions for ways of meeting these challenges. The inclusion in the study of the home-stay families’ perceptions and commentaries provided insights, which can inform program development. There is clearly further work to be done in terms of predeparture orientation and preparation, not only for the main participants themselves, the students, but also for the host families.

Bis(guanidinium) 4,5-dichlorophthalate monohydrate

In the structure of the title hydrate salt 2(CH6N3)+ C8H2Cl2O42- . H2O, the planes of the carboxylate groups of the dianion are rotated out of the plane of the benzene ring [dihedral angles 48.42(10) and 55.64(9)deg.]. A duplex-sheet structure is formed through guanidinium-carboxylate N-H...O, guanidinium-water N-H...O, and water-carboxylate O-H..O hydrogen-bonding associations.

The measurement of applied forces during anterior single rod surgical correction of adolescent idiopathic scoliosis

INTRODUCTION. Following anterior thoracoscopic instrumentation and fusion for the treatment of thoracic AIS, implant related complications have been reported as high as 20.8%. Currently the magnitudes of the forces applied to the spine during anterior scoliosis surgery are unknown. The aim of this study was to measure the segmental compressive forces applied during anterior single rod instrumentation in a series of adolescent idiopathic scoliosis patients. METHODS. A force transducer was designed, constructed and retrofitted to a surgical cable compression tool, routinely used to apply segmental compression during anterior scoliosis correction. Transducer output was continuously logged during the compression of each spinal joint, the output at completion converted to an applied compression force using calibration data. The angle between adjacent vertebral body screws was also measured on intra-operative frontal plane fluoroscope images taken both before and after each joint compression. The difference in angle between the two images was calculated as an estimate for the achieved correction at each spinal joint. RESULTS. Force measurements were obtained for 15 scoliosis patients (Aged 11-19 years) with single thoracic curves (Cobb angles 47˚- 67˚). In total, 95 spinal joints were instrumented. The average force applied for a single joint was 540 N (± 229 N)ranging between 88 N and 1018 N. Experimental error in the force measurement, determined from transducer calibration was ± 43 N. A trend for higher forces applied at joints close to the apex of the scoliosis was observed. The average joint correction angle measured by fluoroscope imaging was 4.8˚ (±2.6˚, range 0˚-12.6˚). CONCLUSION. This study has quantified in-vivo, the intra-operative correction forces applied by the surgeon during anterior single rod instrumentation. This data provides a useful contribution towards an improved understanding of the biomechanics of scoliosis correction. In particular, this data will be used as input for developing patient-specific finite element simulations of scoliosis correction surgery.