Optimizing for minimum weight when two different finite element models and analyses are required

The Finite Element Structural Optimization Program's (FESOP) ability to perform minimum weight optimization using two different finite element analyses and models is discussed. FESOP uses the ADS optimizer developed by Dr. Garret Vanderplaats to solve the nonlinear constrained optimization problem. The design optimization problem requires a response spectrum analysis and model to evaluate the stress and displacement constraints. However, the problem needs a frequency analysis and model to calculate the natural frequencies used to evaluate the frequency range constraints. The results of both the successful and unsuccessful approaches used to solve this difficult weight minimization problem are summarized. The results show that no one ADS optimization algorithm worked in all cases. However, the Sequential Convex Programming and Modified Method of Feasible Directions algorithms were the most successful

The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

Sun-Like Magnetic Cycles in the Rapidly-Rotating Young Solar Analog HD 30495

A growing body of evidence suggests that multiple dynamo mechanisms can drive magnetic variability on different timescales, not only in the Sun but also in other stars. Many solar activity proxies exhibit a quasi-biennial ($\sim$2 year) variation, which is superimposed upon the dominant 11 year cycle. A well-characterized stellar sample suggests at least two different relationships between rotation period and cycle period, with some stars exhibiting long and short cycles simultaneously. Within this sample, the solar cycle periods are typical of a more rapidly rotating star, implying that the Sun might be in a transitional state or that it has an unusual evolutionary history. In this work, we present new and archival observations of dual magnetic cycles in the young solar analog HD 30495, an $\sim$1 Gyr-old G1.5V star with a rotation period near 11 days. This star falls squarely on the relationships established by the broader stellar sample, with short-period variations at $\sim$1.7 years and a long cycle of $\sim$12 years. We measure three individual long-period cycles and find durations ranging from 9.6-15.5 years. We find the short-term variability to be intermittent, but present throughout the majority of the time series, though its occurrence and amplitude are uncorrelated with the longer cycle. These essentially solar-like variations occur in a Sun-like star with more rapid rotation, though surface differential rotation measurements leave open the possibility of a solar equivalence.Comment: 12 pages, 6 figures. Submitted to Ap

Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type

We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.Comment: Final version. To appear in Journal of Functional Analysis. Minor revision

Mindfulness meditation targets transdiagnostic symptoms implicated in stress-related disorders: Understanding relationships between changes in mindfulness, sleep quality, and physical symptoms

Mindfulness-Based Stress Reduction (MBSR) is an 8-week meditation program known to improve anxiety, depression, and psychological well-being. Other health-related effects, such as sleep quality, are less well established, as are the psychological processes associated with therapeutic change. This prospective, observational study (n=213) aimed to determine whether perseverative cognition, indicated by rumination and intrusive thoughts, and emotion regulation, measured by avoidance, thought suppression, emotion suppression, and cognitive reappraisal, partly accounted for the hypothesized relationship between changes in mindfulness and two health-related outcomes: sleep quality and stress-related physical symptoms. As expected, increased mindfulness following the MBSR program was directly correlated with decreased sleep disturbance (r=-0.21, p=0.004) and decreased stress-related physical symptoms (r=-0.38, p<0.001). Partial correlations revealed that pre-post changes in rumination, unwanted intrusive thoughts, thought suppression, experiential avoidance, emotion suppression, and cognitive reappraisal each uniquely accounted for up to 32% of the correlation between the change in mindfulness and change in sleep disturbance and up to 30% of the correlation between the change in mindfulness and change in stress-related physical symptoms. Results suggest that the stress-reducing effects of MBSR are due, in part, to improvements in perseverative cognition and emotion regulation, two “transdiagnostic” mental processes that cut across stress-related disorders