Browsing by Subject "Perturbations"
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Item Dynamic stability of human walking during perturbations and voluntary gait changes(2011-05) Young, Patricia Mary; Dingwell, Jonathan B.; Barr, Ronald; Grabiner, Mark; Markey, Mia; Neptune, RichardFalling during walking leads to millions of emergency room visits every year for all age groups and is a significant medical concern. While gait training has shown some promise for fall prevention, we know relatively little about how humans maintain stability, how we can quantify it and how we can use this knowledge to increase the success of fall prevention training. In this dissertation, I studied how human stability responds to continuous, small magnitude perturbations and to voluntary changes in gait characteristics by examining movement variability and long-term and instantaneous dynamic stability. In the first set of experiments, participants were exposed to continuous, pseudo-random external perturbations of the visual field and support surface in a Computer Assisted Rehabilitation ENvironment (CAREN). Participants exhibited increased step widths, shorter step lengths and increased step variability, orbital and short-term local instability. Despite this, mean instantaneous lateral stability remained approximately constant. In the second set of experiments, participants voluntarily adopted changes in their step widths and step lengths. Wider steps were associated with increased step width variability, decreased nonlinear stability, decreased anterior-posterior margins of stability and increased instantaneous lateral stability. Shorter steps were associated with decreased short-term and orbital stability but did not affect mean instantaneous stability. When instantaneous stability was examined between steps, as opposed to as an average over many steps, results from both studies indicated a relationship between each step’s stability and the stability of the immediately preceding step. From these studies, we now know that unpredictable, continuous perturbations during human walking applied in a given direction can be used to elicit predictable responses in motion variability and stability in that same direction. We know that the type of stability examined can influence the conclusions drawn about an individual’s stability during perturbed walking. For example, an individual’s variability may indicate increased risk of falling while he or she simultaneously demonstrates increased orbital stability and instantaneous lateral stability. A challenge faced in this area of research will be to understand how quantitative measures of stability relate to how we perceive our stability.Item Linear instability for incompressible inviscid fluid flows : two classes of perturbations(2009-08) Thoren, Elizabeth Erin; Vishik, MikhailOne approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations.