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.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Executive coaching : perspectives of effectiveness from executives and coaches

Over the past two decades there has been a remarkable expansion in the use of executive coaching as an executive development technique. The increasing prominence of executive coaching has been attributed to the emergence of new organisational cultures and the subtler competencies needed by executives in these faster moving organisations. The widespread popularity of executive coaching has been based largely on anecdotal feedback regarding its effectiveness. The small body of empirical research has been growing but conclusive outcomes are rare. The prominent question for those with the business imperative to implement executive coaching has been what are the ingredients of the process that engender an effective outcome? This investigation has focused on the factors of executive coaching that contribute to effectiveness. A qualitative methodology facilitated an in-depth study of the experiences of the participants of executive coaching with the perceptions of both executives and coaches being sought. Semi-structured interviews and a focus group provided rich, thick descriptions and together with a process of inductive analysis produced findings that confidently identify the key factors that contribute to coaching effectiveness. Six major themes were identified, each comprising a collection of meanings. These themes have been labelled Executive Engagement, Preliminary Assessment and Feedback, Coaching Process, Coach.s Contribution, Trusting Relationship and Support from the Organisation. One theme, Coaching Process, comprises three significant sub-themes, namely, Encouragement and Emotional Support, Challenge and Reflection and Enhancing Executive Performance. The findings of this study add value to the field by identifying factors contributing to coaching effectiveness, and providing for the coaching practitioner a basis for enhancing their practice of executive coaching to better meet the needs of executives and their organisations.

Diffracting the practices of research supervision

There are ever increasing demands and expectations in the research world, related to the quality of research supervision. It can be difficult for an individual research supervisor to recognize their own quality of research supervision. On top of this are the added challenges of trying to improve that quality of research supervision. Reflective practice is consistently identified as a way for developing professional practice in research supervision. This chapter offers a number of frameworks to facilitate reflective practice about research supervision. It does not propose to solve the problem of quality research supervision but to provide ways in which a research supervisor can reflect on this aspect of their professional academic practice and begin to plan ways in which their practice can improve.

Global Business Today 2nd edition

Global Business Today is focused on the fundamentals of international business. Not only does this text provide coverage of the strategic imperatives of operating IB out of a small, dependent economy but it also builds a thorough worldwide orientation. In this edition, international business Graduate Attributes have been integrated throughout and there is topical discussion of issues such as the Doha round of trade negotiation, climate change and the rise of China and India. The authors recognise that case studies reinforce relevance and have therefore included either entirely new or significantly revised cases in every chapter. With a concise treatment of the crucial elements of an IB course, Global Business Today is the ideal text for a first subject in international busines

Integrating a sustainable academic career around scholarly learning and teaching activities

To be scholarly in learning and teaching is rigorous academic work. It demands: currency and command of both discipline subject matter and educational theory; inquiring, methodical, and reflective approaches; the collection, evaluation and documentation of evidence of learning and teaching efficacy; and, optimally, entails participation in and communication among a community of teaching professionals. This chapter examines the author’s own practice in this regard to explicate the ‘how’ and ‘why’ of scholarly and scholarship approaches, as much as the ‘what’ and ‘where’ of that endeavour. In doing so, this meta‐analysis is made ‘community property’, in the same way that Shulman (1993: 6) exhorted we ‘change the status of teaching from private to community property’ so that teaching might be more greatly valued in the academy.

Commissioning of a Geant4 based treatment plan simulation tool : linac model and dicom-rt interface

A Geant4 based simulation tool has been developed to perform Monte Carlo modelling of a 6 MV VarianTM iX clinac. The computer aided design interface of Geant4 was used to accurately model the LINAC components, including the Millenium multi-leaf collimators (MLCs). The simulation tool was verified via simulation of standard commissioning dosimetry data acquired with an ionisation chamber in a water phantom. Verification of the MLC model was achieved by simulation of leaf leakage measurements performed using GafchromicTM film in a solid water phantom. An absolute dose calibration capability was added by including a virtual monitor chamber into the simulation. Furthermore, a DICOM-RT interface was integrated with the application to allow the simulation of treatment plans in radiotherapy. The ability of the simulation tool to accurately model leaf movements and doses at each control point was verified by simulation of a widely used intensity-modulated radiation therapy (IMRT) quality assurance (QA) technique, the chair test.

Pedagogy of feedback on student academic writing : research supervisor practices for the end of the research degree candidature

All academic writing is advanced with the benefit of feedback about the writing. In the case of the academic writing genres of the research proposal and the dissertation, feedback is usually provided by the research supervisor. Given that academic writing development is a process, and in the case of the research proposal and dissertation, writing which develops over time, it seems likely that the nature of feedback on drafts written early in the candidature may be different from feedback provided by the research supervisor later in a student’s candidature. ----- ----- When a research supervisor has been reading a student’s writing over a period of time, their own familiarity with the writing generates a risk to their ability to provide critical and objective feedback. Particularly by the end of a student’s candidature, the research supervisor’s familiarity with the work may cause them to miss elements of writing improvement. ----- ----- The author, as a research supervisor, has developed a feedback grid to facilitate feedback on the final drafts of a dissertation. This feedback grid is generated by the embedded promises in the early sections of the dissertation, which are then used to audit the content of the final sections of the dissertation to ascertain whether promises made have been fulfilled. This provides a strategy for the research supervisor to step back from the work and read the dissertation with the agenda of a dissertation examiner. ----- ----- The grid is one strategy within a broader pedagogy of providing feedback on writing samples.

All fours

A short stage play in the absurdist tradition. It was published by the Universidad Autónoma de Madrid, Universidad Nacional Autónoma de México and the University of North Carolina-Chapel Hill in "Movimiento Paroxista Revista Literatura" 1(1), 2011, pp. 17-25.