Trajectory structures and transport

The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.Comment: Latex file 19 pages, includes 12 EPS figures. Extended version of the invited talk at the ITCPP, Santorini, 200

Computational aspects of multilevel trajectory optimization

This paper presents new computational results in multilevel trajectory optimization. The original formulation of trajectory decomposition is extended and applied to a difficult multiple arc trajectory example, the low thrust interplanetary swingby problem. A numerical solution is obtained for this trajectory which is characterized by nonlinear, time variant differential equations and interior boundaries and discontinuities. The time domain decomposition of the trajectory is made at the boundaries between arc segments. A three level optimization hierarchy is employed to transform the first feasible trajectory iterate into a final solution trajectory. This example is characteristic of a large class of interplanetary swingby problems which defy solution by conventional computational methods because of multiple discontinuities, constraints, and severe numerical sensitivities. The multilevel approach appears to be effective in obtaining a solution to problems of this type when other more conventional methods are unsatisfactory

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

Trajectories of depressive symptoms after hip fracture

BACKGROUND: Hip fracture is often complicated by depressive symptoms in older adults. We sought to characterize trajectories of depressive symptoms arising after hip fracture and examine their relationship with functional outcomes and walking ability. We also investigated clinical and psychosocial predictors of these trajectories. METHOD: We enrolled 482 inpatients, aged ≥60 years, who were admitted for hip fracture repair at eight St Louis, MO area hospitals between 2008 and 2012. Participants with current depression diagnosis and/or notable cognitive impairment were excluded. Depressive symptoms and functional recovery were assessed with the Montgomery–Asberg Depression Rating Scale and Functional Recovery Score, respectively, for 52 weeks after fracture. Health, cognitive, and psychosocial variables were gathered at baseline. We modeled depressive symptoms using group-based trajectory analysis and subsequently identified correlates of trajectory group membership. RESULTS: Three trajectories emerged according to the course of depressive symptoms, which we termed ‘resilient’, ‘distressed’, and ‘depressed’. The depressed trajectory (10% of participants) experienced a persistently high level of depressive symptoms and a slower time to recover mobility than the other trajectory groups. Stressful life events prior to the fracture, current smoking, higher anxiety, less social support, antidepressant use, past depression, and type of implant predicted membership of the depressed trajectory. CONCLUSIONS: Depressive symptoms arising after hip fracture are associated with poorer functional status. Clinical and psychosocial variables predicted membership of the depression trajectory. Early identification and intervention of patients in a depressive trajectory may improve functional outcomes after hip fracture