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

Canonical and Grand Canonical Ensemble Expectation Values from Quantum Monte Carlo Simulations

We show how canonical ensemble expectation values can be extracted from quantum Monte Carlo simulations in the grand canonical ensemble. In order to obtain results for all particle sectors, a modest number of grand canonical simulations must be performed, each at a different chemical potential. From the canonical ensemble results, grand canonical expectation values can be extracted as a continuous function of the chemical potential. Results are presented from the application of this method to the two-dimensional Hubbard model.Comment: 5 pages, 5 figure

Nonlinear lifting-line model using a vector formulation of the unsteady Kutta-Joukowski theorem

In this paper, a vector form of the unsteady Kutta-Joukowski theorem is derived and then used in the formulation of a general Lifting-Line Model capable of analysing a wide range of engineering problems of interest. The model is applicable to investigating lifting surfaces having low to moderate sweep, dihedral, out-of-plane features such as winglets, in both steady-state and unsteady cases. It features corrections of the span-wise circulation distribution based on available two-dimensional aerofoil experimental data, and stable wake relaxation through fictitious time marching. Potential applications include the conceptual and initial design of low-speed Unmanned Aerial Vehicles, the study of flapping flight or Wind Turbine blade design and analysis. Several verification and validation cases are presented, showing good agreement with experimental data and widely-used computational methods

A randomized clinical trial comparing family-focused treatment and individual supportive therapy for depression in childhood and early adolescence

OBJECTIVE: Despite the morbidity and negative outcomes associated with early-onset depression, few studies have examined the efficacy of psychosocial treatment for depressive disorders during childhood. Integrating family in treatment could have particularly salutary effects during this developmental period. This trial compared immediate posttreatment effects of family-focused treatment for childhood depression (FFT-CD) with those of individual supportive psychotherapy (IP) for children 7 to 14 years old with depressive disorders. METHOD: Children were randomized to 15 sessions of FFT-CD (n = 67) or IP (n = 67) over 4 months. The primary treatment outcome was adequate clinical depression response, defined as at least a 50% decrease in score on the Children's Depression Rating Scale-Revised (CDRS-R). Additional outcomes included patient-centered outcomes (parent- and child-reported treatment satisfaction), remission (defined as CDRS-R score ≤28), change in continuous CDRS-R score, and change in child and parent reports of depressive and non-depressive symptoms and social adjustment. RESULTS: Significant improvement was evident across groups for depressive and non-depressive symptoms, global response, and functioning and social adjustment. Compared with children randomized to IP, children randomized to FFT-CD showed higher rates of adequate clinical depression response (77.7% versus 59.9%; number needed to treat = 5.72; odds ratio 2.29; 95% CI 1.001-5.247; t = 1.97, p = .0498). Across treatments, families reported high satisfaction; compared with IP families, FFT-CD families reported greater knowledge and skills for managing depression. There were no significant differences between treatment arms on secondary outcomes. CONCLUSION: Results support the value of psychosocial intervention, emphasize the important role that families play, and highlight the potential for FFT-CD for supporting recovery in children with depression. Clinical trial registration information-Systems of Support Study for Childhood Depression; http://clinicaltrials.gov; NCT01159041.R01 MH082856 - NIMH NIH HHS; R01 MH082861 - NIMH NIH HH

Discrete adjoint-based simultaneous analysis and design approach for conceptual aerodynamic optimization

In this paper, a simultaneous analysis and design method is derived and applied for a non-linear constrained aerodynamic optimization problem. The method is based on the approach of defining a Lagrange functional based on the objective function and the aerodynamic model’s equations, using two sets of multipliers. A fully-coupled, non-linear system of equations is derived by requiring that the Gateaux variation of the Lagrange functional vanishes for arbitrary variations of the aerodynamic model’s dependent variables and design parameters. The optimization problem is approached using a one-shot technique, by solving the non-linear system in which all sensitivities and problem constraints are included. The computational efficiency of the method is compared against a gradient-based optimization algorithm using adjoint-provided gradient. A conceptual-stage aerodynamic optimization problem is solved, based on a non-linear numerical lifting-line method with viscous corrections