Potential for broad range multiplexing of fibre Bragg gratings in polymer optical fibres and operation in the 700-nm wavelength range

Refractive index and structural characteristics of optical polymers are strongly influenced by the thermal history of the material. Polymer optical fibres (POF) are drawn under tension, resulting in axial orientation of the polymer molecular chains due to their susceptibility to align in the fibre direction. This change in orientation from the drawing process results in residual strain in the fibre and also affects the transparency and birefringence of the material (1-3). PMMA POF has failure strain as high as over 100%. POF has to be drawn under low tension to achieve this value. The drawing tension affects the magnitude of molecular alignment along the fibre axis, thus affecting the failure strain. The higher the tension the lower the failure stain will be. However, the properties of fibre drawn under high tension can approach that of fibre drawn under low tension by means of an annealing process. Annealing the fibre can generally optimise the performance of POF while keeping most advantages intact. Annealing procedures can reduce index difference throughout the bulk and also reduce residual stress that may cause fracture or distortion. POF can be annealed at temperatures approaching the glass transition temperature (Tg) of the polymer to produce FBG with a permanent blue Bragg wave-length shift at room temperature. At this elevated temperature segmental motion in the structure results in a lower viscosity. The material softens and the molecular chains relax from the axial orientation causing shrinking of the fibre. The large attenuation of typically 1dB/cm in the 1550nm spectral region of PMMA POF has limited FBG lengths to less than 10cm. The more expensive fluorinated polymers with lower absorption have had no success as FBG waveguides. Bragg grating have been inscribed onto various POF in the 800nm spectral region using a 30mW continuous wave 325nm helium cadmium laser, with a much reduced attenuation coefficient of 10dB/m (5). Fabricating multiplexed FBGs in the 800nm spectral region in TOPAS and PMMA POF consistently has lead to fabrication of multiplexed FBG in the 700nm spectral region by a method of prolonged annealing. The Bragg wavelength shift of gratings fabricated in PMMA fibre at 833nm and 867nm was monitored whilst the POF was thermally annealed at 80°C. Permanent shifts exceeding 80nm into the 700nm spectral region was attained by both gratings on the fibre. The large permanent shift creates the possibility of multiplexed Bragg sensors operating over a broad range. -------------------------------------------------------------------------------------------------------------------- 1. Pellerin C, Prud'homme RE, Pézolet M. Effect of thermal history on the molecular orientation in polystyrene/poly (vinyl methyl ether) blends. Polymer. 2003;44(11):3291-7. 2. Dvoránek L, Machová L, Šorm M, Pelzbauer Z, Švantner J, Kubánek V. Effects of drawing conditions on the properties of optical fibers made from polystyrene and poly (methyl methacrylate). Die Angewandte Makromolekulare Chemie. 1990;174(1):25-39. 3. Dugas J, Pierrejean I, Farenc J, Peichot JP. Birefringence and internal stress in polystyrene optical fibers. Applied optics. 1994;33(16):3545-8. 4. Jiang C, Kuzyk MG, Ding JL, Johns WE, Welker DJ. Fabrication and mechanical behavior of dye-doped polymer optical fiber. Journal of applied physics. 2002;92(1):4-12. 5. Johnson IP, Webb DJ, Kalli K, Yuan W, Stefani A, Nielsen K, et al., editors. Polymer PCF Bragg grating sensors based on poly (methyl methacrylate) and TOPAS cyclic olefin copolymer2011: SPIE.

Stochastically forced dislocation density distribution in plastic deformation

The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem but all nonlinear processes, both Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time τ. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples.

Cyberbullying: estudo da prevalência de comportamentos de cyberbullying e sua relação com vivências de vergonha e estados emocionais negativos

Objectivos: O presente estudo tem como principal objectivo avaliar a prevalência dos comportamentos de cyberbullying, analisando a influência de variáveis sóciodemográficas, e, compreender a sua relação com as vivências de vergonha interna e externa e com os estados emocionais negativos, particularmente a depressão, a ansiedade e o stress. Método: Para a recolha de dados recorreu-se a uma mostra de adolescentes (N=131) a frequentar o 3º ciclo do ensino básico, com idades compreendidas entre os 12 e os 18 anos (M= 13,76; DP= 1,25). O protocolo de avaliação foi constituído por um questionário psicossocial desenvolvido especificamente para este estudo e por um conjunto de medidas fidedignas para avaliar o cyberbullying (CBQ e CBQ-V), a vergonha interna (ISS), vergonha externa (OAS) e os estados emocionais negativos (DASS-21). Resultados: Os nossos dados revelaram que 76 adolescentes (58%) exerceram um qualquer comportamento de cyberbullying (com um predomínio dos rapazes), enquanto 50 adolescentes (38,2%) já foram vítimas de um qualquer comportamento de cyberbullying (com igual proporção entre rapazes e raparigas). Manter lutas e discussões online, usando insultos mediante mensagens electrónicas foi o comportamento praticado mais frequente (30,5%), enquanto o ser removido intencionalmente de um grupo online foi o comportamento sofrido mais frequente (16,1%). A idade e os anos de reprovações mostraram uma associação positiva com os comportamentos de agressão por cyberbullying. Foi ainda analisada a sobreposição entre a execução e a vitimização de comportamentos de cyberbullying, tendo sido discriminados quatro grupos de adolescentes: só agressores (adolescentes que apenas exerceram comportamentos de agressão), só vítimas (apenas sofreram comportamentos de cyberbulling), vítimas e agressores (adolescentes que são simultaneamente agressores e vítimas), e nem vítimas nem agressores (adolescentes que não exerceram nem sofreram qualquer comportamento de cyberbullying). Os resultados evidenciaram que quanto maior a frequência de comportamentos de agressão por cyberbullying, maior a vergonha interna e maior os níveis de stress demonstrados. Por sua vez, quanto maior a frequência de vitimização por cyberbullying, maior a vergonha interna e externa, bem como maior os níveis de ansiedade e stress. Conclusão: Devido a complexidade do fenómeno cyberbullying e seu recente surgimento, serão necessários mais estudos, particularmente longitudinais, para compreender a relação antecedente e/ou consequentes aos comportamentos de cyberbullying entre estados emocionais negativos e as experiências de vergonha. / Objectives: The present study has as main objective to assess the prevalence of cyberbullying behaviours, analyzing the influence of socio demographic variables, and, understand its relationship to the experiences of internal and external shame and negative emotional states, particularly depression, anxiety and stress. Method: For data collection we used a sample of adolescents (N=131) attending the 3rd cycle of basic education, aged between 12 and 18 years (M=13,76; SD=1,25). The evaluation protocol consisted of a psychosocial questionnaire developed specifically for this study and a set of reliable measure to assess cyberbullying (CBQ and CBQ-V), internal shame (ISS), external shame (OAS) and the emotional states negative (DASS-21). Results: Our data indicate that 76 adolescents (58%) exerted any conduct of a cyberbullying (with a predominance of boys), while 50 adolescents (38,2%) had been victims of cyberbullying behaviour of any one (with an equal ratio of boys and girls). Keep fighting and discussions online, through e-mails using insults behaviour was practiced more often (30,5%), while being intentionally removed a group of online behaviour is seen more frequently (16,1%). The age and years of failures were positively associated with the behaviours of aggression by cyberbullying. Was further examined the overlap between enforcement and victimization of cyberbullying behaviours, having been discriminated four groups of adolescents: only aggressors (adolescents who have had only aggressive behaviour), only victims (only suffered cyberbullying behaviours), victims and aggressors (adolescents who are both perpetrators and victims), and neither victims nor aggressors (adolescents who did not exercise any behaviour or suffered cyberbullying). Results showed that the higher the frequency of aggression by cyberbullying behaviour, the greater shame and internal stress levels demonstrated. In turn, the higher the frequency of cyberbullying victimization, the greater the shame internal and external, as well as higher levels of anxiety and stress. Conclusion: Due to the complexity of the phenomenon cyberbullying and its recent emergence, further studies are needed, particularly longitudinal, to understand the relationship between antecedent and/or consequential to cyberbullying behaviours between negative emotional states and experiences of shame.

From the inside to the outside. Architecture Venice Biennales 2014 and 2016

The comparison between the Position Statements of the latest two Venice Biennale of Architecture, Fundamentals, directed by Rem Koolhaas in 2014 and Reporting from the front that Alejandro Aravena prepares for 2016, is an evident sign of the internal stress that architectural practice has been suffering during the last decade. Koolhaas intensively focused on the immediate past whilst Aravena presents a Biennalle strongly decided to explore possible alternatives for the future of Architecture. The first one tried to define the core, theessence, the most elemental particles that utterly compose Architecture. The second looks at the boundaries, the periphery, the outskirts, the limits of the discipline. Fundamentals was theoretical, personal, abstract, compact and aesthetic. Reporting from the front will be practical, collective, concrete, permeable and ethical. This fertile antagonism or counterpoint between both approaches is too frequently understood as incompatible. However, as a matter of fact the coexistence of these two different perspectives within architectural practice is the mostdistinctive feature of the complex contemporary architectural landscape. The insertion of the analysis of both position statements within the historical evolution of the Venice Bienale since 1980, allows a reinterpretation of the antagonism between the two exhibitions and evidences some lines of thought and action in the architectural world. Following the war industry terminology that Report from the front has chosen, Aravena identifies with precision the theatre of operations; the space and time that is requesting an urgent response from architecture.Previously Koolhaas had defined the armament that Architecture has available to undertake this crucial mission: to define the role and relevance of Architecture in the immediate future. Until now, battles in the front have been a guerrilla warfare. More reactive than proactive. Battles for survival more than for experience. Necessary but, at the same time, insufficient. Valuable actions in radical contexts; heroic acts in extreme situations; occasional infiltrations that find their final reason for being in their own audacity. Time has come for these counterattackarchitectures to evolve from protests to proposals.

Exploring the internal dimensions of work stress : evidence from construction cost estimators in China

A recurring feature of modern practice is the stress placed on project professionals, with both debilitating effects on the people concerned and indirectly affecting project success. Cost estimation, for example, is an essential task for successful project management involving a high level of uncertainty. It is not surprising, therefore, that young cost estimators especially can become stressful at work due to a lack of experience and the heavy responsibilities involved. However, the concept of work stress and the associated underlying dimensions has not been clearly defined in extant studies in the construction management field. To redress this situation, an updated psychology perceived stress questionnaire (PSQ) , first developed by Levenstein et al (1993) and revised by Fliege et al (2005), is used to explore the dimensions of work stress with empirical evidence from the construction industry in China. With 145 reliable responses from young (less than 5 years’ experience) Chinese cost estimators, this study explores the internal dimensions of work stress, identifying four dimensions of tension, demands, lack of joy and worries. It is suggested that this four-dimensional structure may also be applicable in a more general context.

Exploring and validating the internal dimensions of occupational stress: Evidence from construction cost estimators in China

A recurring feature of modern practice is occupational stress of project professionals, with both debilitating effects on the people concerned and indirectly affecting project success. Previous research outside the construction industry has involved the use of a psychology perceived stress questionnaire (PSQ) to measure occupational stress, resulting in the identification of one stressor – demand - and three sub-dimensional emotional reactions in terms of worry, tension and joy. The PSQ is translated into Chinese with a back translation technique and used in a survey of young construction cost professionals in China. Principal component analysis and confirmatory factor analysis are used to test the divisibility of occupational stress - little mentioned in previous research on stress in the construction context. In addition, structural equation modelling is used to assess nomological validity by testing the effects of the three dimensions on organizational commitment, the main finding of which is that lack of joy has the sole significant effect. The three-dimensional measurement framework facilitates the standardizing measurement of occupational stress. Further research will establish if the findings are also applicable in other settings and explore the relations between stress dimensions and other managerial concepts.

Internal Residual Stress Measurements in a Bioactive Glass-Ceramic Using Vickers Indentation

The residual stress distribution that arises in the glass matrix during cooling of a partially crystallized 17.2Na(2)O-32.1CaO-48.1SiO(2)-2.5P(2)O(5) (mol%) bioactive glass-ceramic was measured using the Vickers indentation method proposed by Zeng and Rowcliffe (ZR). The magnitude of the determined residual stress at the crystal/glass boundary was 1/4-1/3 of the values measured using X-ray diffraction (within the crystals) and calculated using Selsing`s model. A correction for the crack geometry factor, assuming a semi-elliptical shape, is proposed and then good agreement between experimental and theoretical values is found. Thus, if the actual crack geometry is taken into account, the indentation technique of ZR can be successfully used. In addition, a numerical model for the calculation of residual stresses that takes into account the hemispherical shape of the crystalline precipitates at a free surface was developed. The result is that near the sample surface, the radial component of the residual stress is increased by 70% in comparison with the residual stress calculated by Selsing`s model.

Stress distribution in implant-supported prosthesis with external and internal implant-abutment connections

Objective. This study aimed to investigate the stress distribution in screwed implant-supported prostheses with different implant-abutment connections by using a photoelastic analysis. Materials and methods. Four photoelastic models were fabricated in PL-2 resin and divided according to the implant-abutment connection (external hexagon (EH) and Morse taper (MT) implants (3.75 × 11.5 mm)) and the number crowns (single and 3-unit piece). Models were positioned in a circular polariscope and 100-N axial and oblique (45) loading were applied in the occlusal surface of the crowns by using a universal testing machine. The stresses were photographically recorded and qualitatively analyzed using software (Adobe Photoshop). Results. Under axial loading, the MT implants exhibited a lower number of fringes for single-unit crowns than EH implants, whereas for a 3-unit piece the MT implants showed a higher number of fringes vs EH implants. The oblique loading increased the number of fringes for all groups. Conclusion. In conclusion, the MT implant-abutment connection reduced the amount of stress in single-unit crowns, for 3-unit piece crowns the amount of stress was lower using an external hexagon connection. The stress pattern was similar for all groups. Oblique loading promoted a higher stress concentration than axial loading. © Informa Healthcare.

Biomechanical influence of crown-to-implant ratio on stress distribution over internal hexagon short implant: 3-D finite element analysis with statistical test

The study of short implants is relevant to the biomechanics of dental implants, and research on crown increase has implications for the daily clinic. The aim of this study was to analyze the biomechanical interactions of a singular implant-supported prosthesis of different crown heights under vertical and oblique force, using the 3-D finite element method. Six 3-D models were designed with Invesalius 3.0, Rhinoceros 3D 4.0, and Solidworks 2010 software. Each model was constructed with a mandibular segment of bone block, including an implant supporting a screwed metal-ceramic crown. The crown height was set at 10, 12.5, and 15 mm. The applied force was 200 N (axial) and 100 N (oblique). We performed an ANOVA statistical test and Tukey tests; p < 0.05 was considered statistically significant. The increase of crown height did not influence the stress distribution on screw prosthetic (p > 0.05) under axial load. However, crown heights of 12.5 and 15 mm caused statistically significant damage to the stress distribution of screws and to the cortical bone (p <0.001) under oblique load. High crown to implant (C/I) ratio harmed microstrain distribution on bone tissue under axial and oblique loads (p < 0.001). Crown increase was a possible deleterious factor to the screws and to the different regions of bone tissue. (C) 2014 Elsevier Ltd. All rights reserved.

Stress distribution around osseointegrated implants with different internal-cone connections: photoelastic and finite element analysis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Coral communities exposed to differential large amplitude internal waves cooling and a severe heat stress in 2010 in the Andaman Sea

Tropical scleractinian corals are particularly vulnerable to global warming as elevated sea surface temperatures (SST) disrupt the delicate balance between the coral host and their algal endosymbionts, leading to symbiont expulsion, mass bleaching and mortality. While satellite sensing of SST has proven a good predictor of coral bleaching at the regional scale, there are large deviations in bleaching severity and mortality on the local scale, which are only poorly understood. Here, we show that internal waves play a major role in explaining local coral bleaching and mortality patterns in the Andaman Sea. In spite of a severe region-wide SST anomaly in May 2010, frequent upslope intrusions of cold sub-pycnocline waters due to breaking large amplitude internal waves (LAIW) alleviated heating and mitigated coral bleaching and mortality in shallow LAIW-exposed waters. In LAIW-sheltered waters, by contrast, bleaching susceptible species suffered severe bleaching and total mortality. These findings suggest that LAIW, which are ubiquitous in tropical stratified waters, benefit coral reefs during thermal stress and provide local refugia for bleaching susceptible corals. The swash zones of LAIW may thus be important, so far overlooked, conservation areas for the maintainance of coral diversity in a warming climate. The consideration of LAIW can significantly improve coral bleaching predictions and can provide a valuable tool for coral reef conservation and management.

The manipulation of apoptosis-related genes to generate resistance to Fusarium wilt and water stress in banana

Bananas are susceptible to a diverse range of biotic and abiotic stresses, many of which cause serious production constraints worldwide. One of the most destructive banana diseases is Fusarium wilt caused by the soil-borne fungus, Fusarium oxysporum f. sp. cubense (Foc). No effective control strategy currently exists for this disease which threatens global banana production. Although disease resistance exists in some wild bananas, attempts to introduce resistance into commercially acceptable bananas by conventional breeding have been hampered by low fertility, long generation times and association of poor agronomical traits with resistance genes. With the advent of reliable banana transformation protocols, molecular breeding is now regarded as a viable alternative strategy to generate disease-resistant banana plants. Recently, a novel strategy involving the expression of anti-apoptosis genes in plants was shown to result in resistance against several necrotrophic fungi. Further, the transgenic plants showed increased resistance to a range of abiotic stresses. In this thesis, the use of anti-apoptosis genes to generate transgenic banana plants with resistance to Fusarium wilt was investigated. Since water stress is an important abiotic constraint to banana production, the resistance of the transgenic plants to water stress was also examined. Embryogenic cell suspensions (ECS) of two commercially important banana cultivars, Grand Naine (GN) and Lady Finger (LF), were transformed using Agrobacterium with the anti-apoptosis genes, Bcl-xL, Bcl-xL G138A, Ced-9 and Bcl- 2 3’ UTR. An interesting, and potentially important, outcome was that the use of anti-apoptosis genes resulted in up to a 50-fold increase in Agrobacterium-mediated transformation efficiency of both LF and GN cells over vector controls. Regenerated plants were subjected to a complete molecular characterisation in order to detect the presence of the transgene (PCR), transcript (RT-PCR) and gene product (Western blot) and to determine the gene copy number (Southern blot). A total of 36 independently-transformed GN lines (8 x Bcl-xL, 5 x Bcl-xL G138A, 15 x Ced-9 and 8 x Bcl-2 3’ UTR) and 41 independently-transformed LF lines (8 x Bcl-xL, 7 x BclxL G138A, 13 x Ced-9 and 13 x Bcl-2 3’ UTR) were identified. The 41 transgenic LF lines were multiplied and clones from each line were acclimatised and grown under glasshouse conditions for 8 weeks to allow monitoring for phenotypic abnormalities. Plants derived from 3 x Bcl-xL, 2 x Ced-9 and 5 x Bcl-2 3’ UTR lines displayed a variety of aberrant phenotypes. However, all but one of these abnormalities were off-types commonly observed in tissue-cultured, non-transgenic banana plants and were therefore unlikely to be transgene-related. Prior to determining the resistance of the transgenic plants to Foc race 1, the apoptotic effects of the fungus on both wild-type and Bcl-2 3’ UTR-transgenic LF banana cells were investigated using rapid in vitro root assays. The results from these assays showed that apoptotic-like cell death was elicited in wild-type banana root cells as early as 6 hours post-exposure to fungal spores. In contrast, these effects were attenuated in the root cells of Bcl-2 3’ UTR-transgenic lines that were exposed to fungal spores. Thirty eight of the 41 transgenic LF lines were subsequently assessed for resistance to Foc race 1 in small-plant glasshouse bioassays. To overcome inconsistencies in rating the internal (vascular discolouration) disease symptoms, a MatLab-based computer program was developed to accurately and reliably assess the level of vascular discolouration in banana corms. Of the transgenic LF banana lines challenged with Foc race 1, 2 x Bcl-xL, 3 x Ced-9, 2 x Bcl-2 3’ UTR and 1 x Bcl-xL G138A-transgenic line were found to show significantly less external and internal symptoms than wild-type LF banana plants used as susceptible controls at 12 weeks post-inoculation. Of these lines, Bcl-2 3’ UTR-transgenic line #6 appeared most resistant, displaying very mild symptoms similar to the wild-type Cavendish banana plants that were included as resistant controls. This line remained resistant for up to 23 weeks post-inoculation. Since anti-apoptosis genes have been shown to confer resistance to various abiotic stresses in other crops, the ability of these genes to confer resistance against water stress in banana was also investigated. Clonal plants derived from each of the 38 transgenic LF banana plants were subjected to water stress for a total of 32 days. Several different lines of transgenic plants transformed with either Bcl-xL, Bcl-xL G138A, Ced-9 or Bcl-2 3’ UTR showed a delay in visual water stress symptoms compared with the wild-type control plants. These plants all began producing new growth from the pseudostem following daily rewatering for one month. In an attempt to determine whether the protective effect of anti-apoptosis genes in transgenic banana plants was linked with reactive oxygen species (ROS)-associated programmed cell death (PCD), the effect of the chloroplast-targeting, ROS-inducing herbicide, Paraquat, on wild-type and transgenic LF was investigated. When leaf discs from wild-type LF banana plants were exposed to 10 ìM Paraquat, complete decolourisation occurred after 48 hours which was confirmed to be associated with cell death and ROS production by trypan blue and 3,3-diaminobenzidine (DAB) staining, respectively. When leaf discs from the transgenic lines were exposed to Paraquat, those derived from some lines showed a delay in decolourisation, suggesting only a weak protective effect from the transgenes. Finally, the protective effect of anti-apoptosis genes against juglone, a ROS-inducing phytotoxin produced by the causal agent of black Sigatoka, Mycosphaerella fijiensis, was investigated. When leaf discs from wild-type LF banana plants were exposed to 25 ppm juglone, complete decolourisation occurred after 48 hours which was again confirmed to be associated with cell death and ROS production by trypan blue and DAB staining, respectively. Further, TdT-mediated dUTP nick-end labelling (TUNEL) assays on these discs suggested that the cell death was apoptotic. When leaf discs from the transgenic lines were exposed to juglone, discs from some lines showed a clear delay in decolourisation, suggesting a protective effect. Whether these plants are resistant to black Sigatoka is unknown and will require future glasshouse and field trials. The work presented in this thesis provides the first report of the use of anti-apoptosis genes as a strategy to confer resistance to Fusarium wilt and water stress in a nongraminaceous monocot, banana. Such a strategy may be exploited to generate resistance to necrotrophic pathogens and abiotic stresses in other economically important crop plants.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

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.