3 resultados para Stable And Unstable Manifolds

em Glasgow Theses Service


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Background: People with relapsing remitting MS (PwRRMS) suffer disproportionate decrements in gait under dual-task conditions, when walking and a cognitive task are combined. There has been much less investigation of the impact of cognitive demands on balance. This study investigated whether: (1) PwRRMS show disproportionate decrements in postural stability under dual-task conditions compared to healthy controls; (2) dual-task decrements are associated with everyday dual-tasking difficulties. In addition, the impact of mood, fatigue and disease severity on dual-tasking were also examined. Methods: 34 PwRRMS and 34 matched controls completed cognitive (digit span) and balance (movement of centre of pressure on a Biosway, on stable and unstable surfaces) tasks under single and dual-task conditions. Everyday dual-tasking was measured using the DTQ. Mood was measured by the HADS. Fatigue was measured via the MFIS. Results: No differences in age, gender, years of education, estimated pre-morbid IQ or baseline digit span between the groups. Compared to healthy controls, PwRRMS showed a significantly greater decrement in postural stability under dual-task conditions on an unstable surface (p=0.007), but not a stable surface (p=0.679). PwRRMS reported higher levels of everyday dual-tasking difficulties (p<0.001). Balance decrement scores were not correlated with everyday dual-tasking difficulties, or with fatigue. Stable surface balance decrement scores were significantly associated with levels of anxiety (rho=0.527, p=0.001) and depression (rho=0.451, p=0.007). Conclusion: RRMS causes difficulties with dual-tasking, impacting balance, particularly under challenging conditions, which may contribute to an increased risk of gait difficulties and falls. The striking relationship between anxiety/depression and dual-task decrement suggests that worry may be contributing to dual-task difficulties.

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George Keith, fourth Earl Marischal is a case study of long-term, quietly successful and stable lordship through the reign of James VI. Marischal’s life provides a wholly underrepresented perspective on this era, where the study of rebellious and notorious characters has dominated. He is also a counter-example to the notion of a general crisis among the European nobility, at least in the Scottish context, as well as to the notion of a ‘conservative’ or ‘Catholic’ north east. In 1580 George inherited the richest earldom in Scotland, with a geographical extent stretching along the east coast from Caithness to East Lothian. His family came to be this wealthy as a long term consequence of the Battle of Flodden (1513) where a branch of the family, the Inverugie Keiths had been killed. The heiress of this branch was married to the third earl and this had concentrated a large number of lands, and consequently wealth, in the hands of the earls. This had, however, also significantly decreased the number of members and hence power of the Keith kindred. The third earl’s conversion to Protestantism in 1544 and later his adherence to the King’s Party during the Marian Civil War forced the Keiths into direct confrontation with their neighbours in the north east, the Gordons (led by the Earls of Huntly), a Catholic family and supporters of the Queen’s Party. Although this feud was settled for a time at the end of the war, the political turmoil caused by a succession of short-lived factional regimes in the early part of the personal reign of James VI (c.1578-1585) led the new (fourth) Earl Marischal into direct confrontation with the new (sixth) Earl of Huntly. Marischal was outclassed, outmanoeuvred and outgunned at both court and in the locality in this feud, suffering considerably. However, Huntly’s over-ambition in wider court politics meant that Marischal was able to join various coalitions against his rival, until Huntly was exiled in 1595. Marischal also came into conflict briefly with Chancellor John Maitland of Thirlestane as a consequence of Marischal’s diplomatic mission to Denmark in 1589-1590, but was again outmatched politically and briefly imprisoned. Both of these feuds reveal Marischal to be relatively cautious and reactionary, and both reveal the limitations of his power. Elsewhere, the study of Marischal’s activities in the centre of Scottish politics reveal him to be unambitious. He was ready to serve King James, the two men having a healthy working relationship, but Marischal showed no ambition as a courtier, to woo the king’s favour or patronage, instead delegating interaction with the monarch to his kinsmen. Likewise, in government, Marischal rarely attended any of the committees he was entitled to attend, such as the Privy Council, although he did keep a keen eye on the land market and the business conducted under the Great Seal. Although personally devout and a committed Protestant, the study of Marischal’s interaction with the national Kirk and the parishes of which he was patron reveal that he was at times a negligent patron and exercised his right of ministerial presentation as lordly, not godly patronage. The notion of a ‘conservative North East’ is, however, rejected. Where Marischal was politically weak at court and weak in terms of force in the locality, we see him pursuing sideways approaches to dealing with this. Thus he was keen to build up his general influence in the north and in particular with the burgh of Aberdeen (one result of this being the creation of Marischal College in 1593), pursued disputes through increasing use of legal methods rather than bloodfeud (thus exploiting his wealth and compensating for his relative lack of force) and developed a sophisticated system of maritime infrastructure, ultimately expressed through the creating of the burghs of Peterhead and Stonehaven. Although his close family caused him a number of problems over his lifetime, he was able to pass on a stable and enlarged lordship to his son in 1623.

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A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.