3,884 research outputs found
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 (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 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 1.7 years
and a long cycle of 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
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