Model based experimental investigation on Powered Gait Orthosis (PGO)

Research on rehabilitation showed that appropriate and repetitive mechanical movements can help spinal cord injured individuals to restore their functional standing and walking. The objective of this paper was to achieve appropriate and repetitive joint movements and approximately normal gait through the PGO by replicating normal walking, and to minimize the energy consumption for both patients and the device. A model based experimental investigative approach is presented in this dissertation. First, a human model was created in Ideas and human walking was simulated in Adams. The main feature of this model was the foot ground contact model, which had distributed contact points along the foot and varied viscoelasticity. The model was validated by comparison of simulated results of normal walking and measured ones from the literature. It was used to simulate current PGO walking to investigate the real causes of poor function of the current PGO, even though it had joint movements close to normal walking. The direct cause was one leg moving at a time, which resulted in short step length and no clearance after toe off. It can not be solved by simply adding power on both hip joints. In order to find a better answer, a PGO mechanism model was used to investigate different walking mechanisms by locking or releasing some joints. A trade-off between energy consumption, control complexity and standing position was found. Finally a foot release PGO virtual model was created and simulated and only foot release mechanism was developed into a prototype. Both the release mechanism and the design of foot release were validated through the experiment by adding the foot release on the current PGO. This demonstrated an advancement in improving functional aspects of the current PGO even without a whole physical model of foot release PGO for comparison.

Análisis biomecánico zancada a zancada de la prueba "60 metros vallas" durante los campeonatos del mundo y de España de pista cubierta Valencia 2008

El principal objetivo del presente trabajo de investigación fue determinar las diferencias en distintas variables relacionadas con el rendimiento físico entre atletas de distinto nivel durante la prueba de los 60 metros vallas. Un total de 59 vallistas masculinos (los 31 participantes en el Campeonato del Mundo Absoluto de Pista Cubierta y los 28 participantes en el Campeonato de España Absoluto de Pista Cubierta, ambos celebrados en Valencia en el año 2008) formaron la muestra del estudio. El análisis biomecánico se realizó mediante un sistema fotogramétrico en dos dimensiones que permitió calcular, aplicando algoritmos basados en el procedimiento de la DLT (Abdel-Aziz y Karara, 1971), las coordenadas (x, y) de los sucesivos apoyos de los pies de los atletas sobre toda la superficie de competición. La filmación de las pruebas se llevó a cabo con seis cámaras de vídeo, ubicadas sobre la gradas, con una frecuencia de muestreo para el tratamiento de los datos de 50 Hz. En la fase de salida, los atletas de nivel superior mostraron una menor longitud (p<0,05) y tiempo de zancada (p<0,001), debido a un menor tiempo de vuelo (p<0,05). En la fase de vallas, los atletas de nivel más elevado presentaron mayores distancia de ataque a la valla (p<0,001), así como menores distancias de caída de la valla (p<0,001), tiempos de zancada (p<0,01-0,001) y de apoyo (p<0,01-0,001 ) en los cuatro pasos que conforman cada ciclo de vallas, así como un menor tiempo de vuelo en el paso de valla (p<0,001) y en el paso de transición (p<0,001). De manera adicional, se encontraron importantes diferencias en el reparto de los pasos entre vallas entre la primera y tercera valla y el resto de obstáculos. En la fase final, se observó una mayor longitud de zancada en los atletas de nivel superior (p<0,001), así como un menor tiempo de zancada (p<0,01) y de apoyo (p<0,01). Los resultados obtenidos en el presente estudio de investigación avalan la utilización de la fotogrametría en dos dimensiones para el análisis biomecánico de la prueba de 60 metros vallas en competición. Su aplicación en competiciones del máximo nivel internacional ha posibilitado conocer las características de los vallistas a lo largo de toda la prueba y determinar posibles implicaciones de cara al proceso de entrenamiento. ABSTRACT The aim of this research was to determine the differences in different variables related to physical performance among athletes of different levels during the race of 60 meter hurdles. A total of 59 male hurdlers (the 31 participants in the World Indoor Championship and the 28 participants in the Spanish Indoor Championship, both held in Valencia in 2008) formed the sample of the study. The biomechanical analysis of athletes was performed using a two-dimensional photogrammetric system which enabled calculation, applying algorithms based on the DLT method (Abdel -Aziz y Karara , 1971), the coordinates (x , y) of the successive supports of the feet on the entire competition surface. Filming test was conducted with six video cameras, located on the bleachers, with a sampling frequency for data processing of 50 Hz. In the approach run phase, the top-level athletes showed a smaller length step (p<0.05), and shorter step time (p<0.001), due to a shorter step flight time (p<0.05). In the hurdle unit phase, the higher level athletes had greater take-off distances (p<0.001), shorter landing distances (p<0.001), smaller step times (p<0.01-0.001), and support times (p<0.01- 0.001) in the four steps that comprised each hurdle unit, and smaller flight times in the hurdle step (p < 0.001), and the recovery step (p<0.001). Additionally, differences in the distribution of hurdle unit steps between the first and third hurdle, and other hurdles were found. In the run-in phase, a greater step length in top-level athletes (p<0.001), and a shorter step time (p<0.01) and contact time (p<0.01) was observed. The results obtained in this study support the use of photogrammetry in two dimensions for biomechanical analysis in 60 meter hurdles competition events. Its application at the highest international level competitions has allowed to know the characteristics of the hurdlers over the entire race and identify possible implications for the training process.

Optimización del método de ensayo del péndulo de fricción para la evaluación del riesgo de deslizamiento en pavimentos pulidos

El riesgo de caída por deslizamiento en los edificios es un riesgo muy importante ya que supone numerosas muertes, perdida de días laborales y secuelas, así como importantes costes económicos. Se trata de accidentes difíciles de predecir debido al número de factores que intervienen para que se produzcan, muchos de los cuales son difícilmente controlables, como el calzado del usuario o su comportamiento. Para evitar un resbalón es necesario que la fricción del conjunto pavimento/calzado/contaminante supere el coeficiente de fricción requerido para la estabilidad y que depende de la forma de caminar, la longitud del paso, etc. Por ello, es necesario medir la contribución del pavimento al riesgo de deslizamiento y limitarla adecuadamente. A lo largo de la historia reciente se han diseñado y desarrollado multitud de aparatos con la intención de medir esta contribución en la forma de coeficientes de fricción —dinámicos, estáticos, de transición— sin llegar a un acuerdo sobre cuál es el método más apropiado. La reglamentación española de edificación, que ha sufrido un importante cambio recientemente con la adopción de un nuevo código basado en prestaciones, ha sido innovadora en este campo introduciendo por primera vez una medida contrastable de la contribución del pavimento al riesgo de deslizamiento mediante el ensayo del péndulo de fricción en húmedo. Sin embargo, el desacuerdo a nivel europeo sobre un ensayo único y las limitaciones en las normas de ensayo existentes derivadas de esta falta de consenso, han sido la causa de que la solución aportada por el Código Técnico de la Edificación (CTE) se cimentara en normas que no contemplaban todas las modalidades de ensayo. Esto ha generado algunos problemas de aplicación que han afectado fundamentalmente a los pavimentos pulidos, que han visto prácticamente vetada su utilización en los edificios incluso en las zonas donde, por no existir presencia de agua, el riesgo es menor. El objetivo de esta tesis es analizar estos problemas de aplicación, ligados al ensayo del péndulo de fricción, y tratar de resolverlos optimizando el procedimiento de ensayo empleado, modificando sus condiciones, para representar de forma mucho más adecuada el riesgo que se pretende limitar. Para ello se ha estudiado de forma exhaustiva la literatura científica y las normas y reglamentaciones, tanto españolas como extranjeras. Se han detectado los posibles problemas que podría plantear la introducción del ensayo del péndulo de fricción en seco y se ha diseñado una campaña de ensayos, tanto de coeficiente de fricción con el péndulo, como de la rugosidad superficial, para confirmarlos o desecharlos. El análisis de los resultados de la campaña de ensayos ha permitido validar la modalidad de ensayo planteada y proponer una medida complementaria de la rugosidad superficial que resulte útil para facilitar la evaluación de este riesgo no poco importante. Los resultados de esta tesis han permitido desarrollar una modificación del CTE de próxima aparición y un documento de apoyo que ya la adelanta, y con ello, resolver el problema de aplicación del CTE a los pavimentos pulidos. ABSTRACT Slipping accidents in building environments are a serious problem involving numerous fatal accidents, loss of work days, incapacity and great costs. Prediction of such accidents is difficult due to the number of factors involved, many of which are not controllable, like footwear or users behavior. To prevent a slip the coefficient of friction provided by the combination floor-footwear-contaminant must be greater than the required coefficient of friction for stability, that depends on the step length and the walking speed among other factors. It is then necessary to measure the contribution of the floor to the slipping risk so it can be limited to an adequate extent. In the recent history many apparatuses have been developed in order to measure this contribution in the form of friction coefficients —dynamic, static or even transition COFs— but none of them seems to be internationally accepted as sufficiently valid. The Spanish Building Code, which has recently undergone a big change to a performance based code, has been innovative in this area, introducing for the first time a measurement of this contribution by means of the friction pendulum test. However, due to the European disagreement about an unique test for slip resistance, and to the limitations of the European standards derived from it, the Spanish Building Code relies on standards that do not take into account all possible methods. As a consequence, smooth floors have been seriously affected and cannot be installed in almost any place, not even in dry areas where the risk of slipping is much lower. The aim of this research is to analyze these problems associated with the pendulum test and resolve them proposing some changes to the test conditions in order to represent in a proper manner the real risk that is to be considered: the slip in dry conditions. Relevant scientific literature has been studied as well as Spanish and foreign codes and standards. Potential problems of the pendulum test in dry conditions have been detected and an experiment has been designed to confirm or discard them, testing both friction coefficient and surface roughness. The results of the experiment have permitted to validate the pendulum test in dry conditions and to suggest a complementary measurement of the surface roughness to help evaluate the slip resistance of a floor. These results have also permitted to develop an amendment to the building code that will appear soon. In the meanwhile it has been included in a support document issued by the administration to resolve this urgent problem.

Adequabilidade ambiental dos biomas brasileiros à ocorrência do lobo-guará (Chrysocyon brachyurus) e efeitos da composição da paisagem em sua ecologia espacial, atividade e movimentação

O lobo-guará é uma espécie de ampla distribuição na América do Sul, tendo no Brasil sua maior área de ocorrência. No entanto, as modificações das áreas naturais principalmente destinadas à agropecuária tornam a espécie vulnerável à extinção. A investigação objetivou conhecer em larga escala a área de distribuição potencial gerada por atributos ambientais favoráveis e áreas adequadas à sua ocorrência nos biomas brasileiros e investigar como a espécie responde à estrutura da paisagem, avaliando os efeitos de ambientes modificados pelo homem na sua ecologia espacial, nos padrões de atividade e na movimentação. Modelos de distribuição de espécie foram gerados pelo Maxent, utilizando uma base de pontos de localização de presença a partir de 2000 para o Cerrado (Ce), Pantanal (Pa), Mata Atlântica (MA) e Pampas (Pp) e um conjunto de onze variáveis ambientais não correlacionadas (topográficas, climáticas e paisagísticas). Para análises de ecologia espacial, das atividades e de movimentação, utilizou-se localizações de telemetria (GPS) de animais habitantes de áreas protegidas (AP), e indivíduos em paisagens modificados (AM). Análises de áreas de vida (AV) foram realizadas utilizando o estimador AKDE e associadas com classificação da paisagem local. Os modelos de distribuição do lobo-guará apresentaram uma área de distribuição potencial de 78% do total dos biomas. Apesar de possuírem grandes proporções de áreas adequadas (Ce, 90%; Pa, 93%; MA, 65% e Pp, 6%), somente um pequeno percentual (4,4% do Ce e 4,7% da MA) possui adequabilidade ambiental acima de 50%. Dos atributos que favorecem sua presença, a altitude (para todos os biomas), a precipitação (Ce e Pa), diferenças de temperatura e uso e cobertura do solo (Ma e Pp) foram os mais importantes. Em nível local, animais apresentaram média de AV de 90Km2 em AP e 41Km2 em AM, uma diferença significativa (p<0,01) com áreas diretamente proporcionais ao percentual de áreas naturais na paisagem. Ainda, apesar dos padrões regulares de atividade não mostrarem grandes mudanças, o período de repouso foi significativamente maior (p<0,01) entre os animais AM (46% do dia) que em animais AP (25% do dia). Lobos-guarás de AP e AM não apresentaram grandes diferenças no deslocamento diário com média geral de 14km caminhados por dia, com comprimentos de passos de 1Km. Diferenças no comprimento de passo foram relacionadas à composição da diversidade de contato de classes da paisagem com a proporção de ambientes naturais no passo (quanto maior as variáveis, maior o passo). Passos menores refletem menor persistência de movimento interferindo no deslocamento diário. Com os resultados desse estudo identificou-se a MA e Pa muito importantes, mas o Ce como bioma mais adequado à espécie. Foram encontrados indícios de que a estrutura de suas AV, o uso da paisagem, as atividades e movimentação são afetados pela paisagem modificada. Isso pode comprometer a viabilidade populacional, interferindo na presença em uma área e refletindo no seu potencial de distribuição. As estratégias de manejo de uso do solo, e a recuperação e conexão de áreas adequadas são urgentes e necessárias para que o lobo-guará permaneça presente e funcional nas paisagens dos biomas brasileiros.

Balance and gait in children with dyslexia

Tests of postural stability have provided some evidence of a link between deficits in gross motor skills and developmental dyslexia. The ordinal-level scales used previously, however, have limited measurement sensitivity, and no studies have investigated motor performance during walking in participants with dyslexia. The purpose of this study was to investigate if continuous-scaled measures of standing balance and gait could discriminate between groups of impaired and normal readers when investigators were blind to group membership during testing. Children with dyslexia (n=22) and controls (n=18), aged 10-12 years, performed walking tests at four different speeds (slow-preferred-fast-very fast) on an even and an uneven surface, and tests of unperturbed and perturbed body sway during standing. Body movements were registered by a triaxial accelerometer over the lower trunk, and measures of reaction time, body sway, walking speed, step length and cadence were calculated. Results were controlled for gender differences. Tests of standing balance with eyes closed did not discriminate between groups. All unperturbed standing tests with eyes open showed significant group differences (P<0.05) and classified correctly 70-77.5% of the subjects into their respective groups. Mean walking speed during very fast walking on both flat and uneven surface was ≥0.2 m/s (P≤0.01) faster for controls than for the group with dyslexia. This test classified 77.5% and 85% of the subjects correctly on flat and uneven surface, respectively Cadence at preferred or very fast speed did not differ statistically between groups, but revealed significant group differences when all subjects were compared at a normalised walking speed (P≤0.04). Very fast walking speed as well as cadence at a normalised speed discriminated better between groups when subjects were walking on an uneven surface compared to a flat floor. Continuous-scaled walking tests performed in field settings may be suitable for motor skill assessment as a component of a screening tool for developmental dyslexia.

On the convergence of the method of successive averages for calculating user equilibrium in traffic networks

Peer reviewed

Gait Regulation for Bipedal Locomotion

This work explores regulation of forward speed, step length, and slope walking for the passive-dynamic class of bipedal robots. Previously, an energy-shaping control for regulating forward speed has appeared in the literature; here we show that control to be a special case of a more general time-scaling control that allows for speed transitions in arbitrary time. As prior work has focused on potential energy shaping for fully actuated bipeds, we study in detail the shaping of kinetic energy for bipedal robots, giving special treatment to issues of underactuation. Drawing inspiration from features of human walking, an underactuated kinetic-shaping control is presented that provides efficient regulation of walking speed while adjusting step length. Previous results on energetic symmetries of bipedal walking are also extended, resulting in a control that allows regulation of speed and step length while walking on any slope. Finally we formalize the optimal gait regulation problem and propose a dynamic programming solution seeded with passive-dynamic limit cycles. Observations of the optimal solutions generated by this method reveal further similarities between passive dynamic walking and human locomotion and give insight into the structure of minimum-effort controls for walking.

Análise baropodométrica do apoio plantar em idosos e sua relação com as quedas

O presente estudo teve como principal objetivo a descrição, a análise e a comparação de parâmetros relacionados com o apoio plantar em idosos, através do método da baropodometria eletrónica, que oferece a avaliação das variáveis temporais e espaciais na postura estática e na marcha. Ademais, teve a finalidade de medir e comparar a distribuição da pressão plantar num grupo de idosos, institucionalizados e não institucionalizados, com e sem historial de quedas nos últimos 12 meses, para verificar se há um padrão comum ou divergente de apoio plantar, aspetos biomecânicos e diferenças significativas na marcha entre estes dois grupos e sua relação com a ocorrência de quedas. A amostra foi composta por 160 idosos, 80 institucionalizados e 80 não institucionalizados, onde foi realizado um levantamento das variáveis sociodemográficas como: idade, género, o índice de massa corporal (IMC), a ocorrência de quedas nos últimos 12 meses, a existência de patologias e a prática de atividade física. Foram analisadas, através da plataforma de pressão, a distribuição das pressões plantares, os picos de pressão plantar média e máxima, área de superfície plantar e a largura da base de sustentação na postura estática e, relativamente às variáveis temporais na postura dinâmica, foram avaliadas a duração do passo e o tempo de contato plantar, no momento da fase de apoio e propulsão da marcha. Foi analisada a correlação destas variáveis com a ocorrência de quedas. Foram identificados maiores valores de pressão média e máxima, na postura estática e dinâmica, nos idosos não institucionalizados. Na comparação entre os grupos, foram encontradas diferenças estatisticamente significativas em grande parte das variáveis na postura estática, especialmente aumento da largura da base (p=0,048) e, na postura dinâmica, a duração do passo e do tempo de contato do pé no solo (p=0,000) foram maiores nos idosos institucionalizados. O avançar da idade, o aumento na duração do passo e do tempo de contato do pé no solo, bem como a diminuição dos valores das pressões plantares apresentaram correlação com a ocorrência de quedas na amostra total de idosos, especialmente nos idosos institucionalizados. Entretanto, as variáveis índice de massa corporal e largura da base de sustentação não influenciaram na ocorrência de quedas na amostra total de idosos. Estes resultados demonstram a importância da análise do apoio plantar em idosos, pois alterações na distribuição das pressões plantares podem constituir um fator de risco para quedas.

Resin tag length of one-step and self-etching adhesives bonded to unground enamel

Length of resin tags yielded by utilization of an one-step conventional adhesive system and self-etching adhesive system on unground enamel was observed. In study Groups I and III, the enamel surface was etched for 60 seconds with 35% phosphoric acid gel and adhesive systems PQ1 (Ultradent Products, Inc) and Adper Prompt L Pop (3M/ESPE) were applied. Adper Prompt L Pop (3M/ESPE) was also applied in Group II in accordance with the manufacturer's recommendations. After application of these adhesive systems to dental enamel, specimens were prepared for light microscopy analysis to ascertain degree of penetration (x400). The results were submitted to an analysis of variance at the 5% level; whenever there was significance, the Tukey test was applied at the 5% level. It was found that acid etching prior to application of conventional and self-etching adhesive materials provided higher penetration of the adhesive into the unground enamel surface compared to that achieved solely by application of self-etching adhesive.

Correction of step artefact associated with MRI scanning of long bones

3D models of long bones are being utilised for a number of fields including orthopaedic implant design. Accurate reconstruction of 3D models is of utmost importance to design accurate implants to allow achieving a good alignment between two bone fragments. Thus for this purpose, CT scanners are employed to acquire accurate bone data exposing an individual to a high amount of ionising radiation. Magnetic resonance imaging (MRI) has been shown to be a potential alternative to computed tomography (CT) for scanning of volunteers for 3D reconstruction of long bones, essentially avoiding the high radiation dose from CT. In MRI imaging of long bones, the artefacts due to random movements of the skeletal system create challenges for researchers as they generate inaccuracies in the 3D models generated by using data sets containing such artefacts. One of the defects that have been observed during an initial study is the lateral shift artefact occurring in the reconstructed 3D models. This artefact is believed to result from volunteers moving the leg during two successive scanning stages (the lower limb has to be scanned in at least five stages due to the limited scanning length of the scanner). As this artefact creates inaccuracies in the implants designed using these models, it needs to be corrected before the application of 3D models to implant design. Therefore, this study aimed to correct the lateral shift artefact using 3D modelling techniques. The femora of five ovine hind limbs were scanned with a 3T MRI scanner using a 3D vibe based protocol. The scanning was conducted in two halves, while maintaining a good overlap between them. A lateral shift was generated by moving the limb several millimetres between two scanning stages. The 3D models were reconstructed using a multi threshold segmentation method. The correction of the artefact was achieved by aligning the two halves using the robust iterative closest point (ICP) algorithm, with the help of the overlapping region between the two. The models with the corrected artefact were compared with the reference model generated by CT scanning of the same sample. The results indicate that the correction of the artefact was achieved with an average deviation of 0.32 ± 0.02 mm between the corrected model and the reference model. In comparison, the model obtained from a single MRI scan generated an average error of 0.25 ± 0.02 mm when compared with the reference model. An average deviation of 0.34 ± 0.04 mm was seen when the models generated after the table was moved were compared to the reference models; thus, the movement of the table is also a contributing factor to the motion artefacts.

A strong quantitative trait locus for wing length on chromosome 2 in a wild population of great reed warblers

Wing length is a key character for essential behaviours related to bird flight such as migration and foraging. In the present study, we initiate the search for the genes underlying wing length in birds by studying a long-distance migrant, the great reed warbler (Acrocephalus arundinaceus). In this species wing length is an evolutionary interesting trait with pronounced latitudinal gradient and sex-specific selection regimes in local populations. We performed a quantitative trait locus (QTL) scan for wing length in great reed warblers using phenotypic, genotypic, pedigree and linkage map data from our long-term study population in Sweden. We applied the linkage analysis mapping method implemented in GRIDQTL (a new web-based software) and detected a genome-wide significant QTL for wing length on chromosome 2, to our knowledge, the first detected QTL in wild birds. The QTL extended over 25 cM and accounted for a substantial part (37%) of the phenotypic variance of the trait. A genome scan for tarsus length (a bodysize-related trait) did not show any signal, implying that the wing-length QTL on chromosome 2 was not associated with body size. Our results provide a first important step into understanding the genetic architecture of avian wing length, and give opportunities to study the evolutionary dynamics of wing length at the locus level. This journal is© 2010 The Royal Society.

Transfer pricing and multinational financial institutions : the case for replacing arm’s length price with a unitary approach

The international tax system, designed a century ago, has not kept pace with the modern multinational entity rendering it ineffective in taxing many modern businesses according to economic activity. One of those modern multinational entities is the multinational financial institution (MNFI). The recent global financial crisis provides a particularly relevant and significant example of the failure of the current system on a global scale. The modern MNFI is increasingly undertaking more globalised and complex trading operations. A primary reason for the globalisation of financial institutions is that they typically ‘follow-the-customer’ into jurisdictions where international capital and international investors are required. The International Monetary Fund (IMF) recently reported that from 1995-2009, foreign bank presence in developing countries grew by 122 per cent. The same study indicates that foreign banks have a 20 per cent market share in OECD countries and 50 per cent in emerging markets and developing countries. Hence, most significant is that fact that MNFIs are increasingly undertaking an intermediary role in developing economies where they are financing core business activities such as mining and tourism. IMF analysis also suggests that in the future, foreign bank expansion will be greatest in emerging economies. The difficulties for developing countries in applying current international tax rules, especially the current traditional transfer pricing regime, are particularly acute in relation to MNFIs, which are the biggest users of tax havens and offshore finance. This paper investigates whether a unitary taxation approach which reflects economic reality would more easily and effectively ensure that the profits of MNFIs are taxed in the jurisdictions which give rise to those profits. It has previously been argued that the uniqueness of MNFIs results in a failure of the current system to accurately allocate profits and that unitary tax as an alternative could provide a sounder allocation model for international tax purposes. This paper goes a step further, and examines the practicalities of the implementation of unitary taxation for MNFIs in terms of the key components of such a regime, along with their their implications. This paper adopts a two-step approach in considering the implications of unitary taxation as a means of improved corporate tax coordination which requires international acceptance and agreement. First, the definitional issues of the unitary MNFI are examined and second, an appropriate allocation formula for this sector is investigated. To achieve this, the paper asks first, how the financial sector should be defined for the purposes of unitary taxation and what should constitute a unitary business for that sector and second, what is the ‘best practice’ model of an allocation formula for the purposes of the apportionment of the profits of the unitary business of a financial institution.

Optimal control of arrivals to queues with delayed queue length information

We consider discrete-time versions of two classical problems in the optimal control of admission to a queueing system: i) optimal routing of arrivals to two parallel queues and ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as controlled Markov chains with expected total discounted cost as the minimization objective. For problem i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue). We also show that for this problem, for k greater than or equal to 2, JSEQ is not optimal. For problem ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds m(0) greater than or equal to m(1) > 0, such that mo is used when the previous action was to reject, and mi is used when the previous action was to accept.

Simulation of length-preserving motions of flexible one dimensional oObjects using optimization

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms-(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.