Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as possible. We prove existence of solutions and investigate their qualitative properties. For example, we show that for some symmetric domains (thin annuli and dumbbells with narrow handle) optimal solutions must possess fewer symmetries than $\Omega$; on the other hand, for convex $\Omega$ reflection symmetries are preserved. Also, we present numerical results and formulate some conjectures suggested by them.Comment: 24 pages; 3 figures (as separate files); (shortened previous version); to appear in Comm. Math. Phy

The plasmonic eigenvalue problem

A plasmon of a bounded domain $\Omega\subset\mathbb{R}^n$ is a non-trivial bounded harmonic function on $\mathbb{R}^n\setminus\partial\Omega$ which is continuous at $\partial\Omega$ and whose exterior and interior normal derivatives at $\partial\Omega$ have a constant ratio. We call this ratio a plasmonic eigenvalue of $\Omega$. Plasmons arise in the description of electromagnetic waves hitting a metallic particle $\Omega$. We investigate these eigenvalues and prove that they form a sequence of numbers converging to one. Also, we prove regularity of plasmons, derive a variational characterization, and prove a second order perturbation formula. The problem can be reformulated in terms of Dirichlet-Neumann operators, and as a side result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in Review in Mathematical Physic

Noncontacting device to indicate deflection of turbopump internal rotating parts

Phase 2 (development) which was concluded for the ultrasonic Doppler device and the light-pipe-reflectance device is reported. An ultrasonic Doppler breadboard system was assembled which accurately measured runout in the J-2 LOX pump impeller during operation. The transducer was mounted on the outside of the pump volute using a C-clamp. Vibration was measured by conducting the ultrasonic wave through the volute housing and through the fluid in the volute to the impeller surface. The impeller vibration was also measured accurately using the light-pipe probe mounted in an elastomeric-gland fitting in the pump case. A special epoxy resin developed for cryogenic applications was forced into the end of the fiber-optic probe to retain the fibers. Subsequently, the probe suffered no damage after simultaneous exposure to 2150 psi and 77 F. Preliminary flash X-radiographs were taken of the turbine wheel and the shaft-bearing-seal assembly, using a 2-megavolt X-ray unit. Reasonable resolution and contrast was obtained. A fast-neutron detector was fabricated and sensitivity was measured. The results demonstrated that the technique is feasible for integrated-time measurements requiring, perhaps, 240 revolutions to obtain sufficient exposure at 35,000 rpm. The experimental verification plans are included

Noncontacting devices to indicate deflection and vibration of turbopump internal rotating parts

Published report discusses feasibility of ultrasonic techniques; neutron techniques; X-radiography; optical devices; gamma ray devices; and conventional displacement sensors. Use of signal transmitters in place of slip rings indicated possible improvement and will be subject of futher study

Storage-ring measurement of the hyperfine induced 47Ti18+(2s 2p 3P0 -> 2s2 1S0) transition rate

The hyperfine induced 2s 2p 3P0 > 2s2 1S0 transition rate AHFI in berylliumlike 47Ti18+ was measured. Resonant electron-ion recombination in a heavy-ion storage ring was employed to monitor the time dependent population of the 3P0 state. The experimental value AHFI=0.56(3)/s is almost 60% larger than theoretically predicted.Comment: 4 pages. 3 figures, 1 table, accepted for publication in Physical Review Letter

Determining Intensity Levels for Selected Wii Fit Activities in College Aged Individuals

Introduction: Physical activity is important to the proper growth, development, and overall health of an individual. Current physical activity trends show declines in activity level throughout aging. To counteract inactivity many physical activity interventions have been implemented in different age groups and yet very little change in activity level has been seen. The Nintendo Wii® offers a popular technological intervention tool with its movement oriented game play. The physiological costs and intensity of the Nintendo Wii Fit® game have not been thoroughly researched, yet the Wii is being used as a physical activity tool in many arenas. Purpose: The purpose of this study was to determine the intensity level of playing selected Nintendo Wii Fit® games using indirect calorimetry. Using the intensity information, it was determined if playing Wii Fit® (an exercise themed game) on the Nintendo Wii® video game console is an adequate activity for meeting the ACSM moderate physical activity guidelines threshold. Participants: Twenty-five participants, 5 males and 20 females, aged 22 ± 2 years (M ± SD) with little previous Wii experience (\u3c10 times played) were recruited for this study. Method: Participants randomly completed two different Wii Fit activity sessions with two difficulty levels within the strength, endurance, and yoga categories. A resting metabolic rate and exercise V(over dot)O2 were measured on each participant with a TrueMax 2400 metabolic cart. Oxygen consumption was then converted into metabolic equivalents to estimate activity intensity level. SPSS18.0 (Chicago, IL, USA) was used for statistical analysis. Results: Results indicated that V(over dot)O2 of the selected Wii Fit activities was significantly higher than resting V(over dot)O2 levels. For example, the least intense activity was the Yoga Warrior activity, which had a mean intensity of 2.30 ± 0.42 METs and was still significantly higher than resting V(over dot)O2 levels, t (24) = 15.5, p \u3c .001. The calculated MET values ranged from 3.28 ± 0.71 METs to 3.43 ± 0.60 METs for the strength activities, and ranged from 4.98 ± 1.22 METs to 5.73 ± 1.36 METs for the aerobic Basic Run exercises, indicating that the intensity levels of these activities met or exceeded the ACSM moderate intensity threshold of 3 METs. In contrast, the yoga exercises were significantly lower (from 2.30 ± 0.42 METs to 2.6749 ± .48 METs) than the recommended 3 METs, t (24) = -3.347, p= .003 for moderate intensity physical activity. Finally, the results showed that the medium difficulty level aerobic exercises (5.73 ± 1.36 METs) had significantly higher MET values than the easy aerobic exercises (4.98 ± 1.22 METs), t (24) = 5.00, p \u3c .001. Discussion: The findings of this study illustrate the potential of the Nintendo Wii Fit® game to be an adequate physical activity tool. Furthermore, these findings will allow for the further advancement of exercise themed video games to become satisfactory replacements for traditional physical activities in future interventions

Absolute rate coefficients for photorecombination and electron-impact ionization of magnesium-like iron ions from measurements at a heavy-ion storage ring

Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected to form in such plasmas the latest theoretical rate coefficients of Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron. Astrophys. 466, 771 (2007)] for EII agree with the experimental results to within the experimental uncertainties. Common features in the PR and EII resonance structures are identified and discussed.Comment: 12 pages, 6 figures, 3 tables, submitted for publication to Physical Review

Absolute rate coefficients for photorecombination of berylliumlike and boronlike silicon ions

We report measured rate coefficients for electron-ion recombination for Si10+ forming Si9+ and for Si9+ forming Si8+, respectively. The measurements were performed using the electron-ion merged-beams technique at a heavy-ion storage ring. Electron-ion collision energies ranged from 0 to 50 eV for Si9+ and from 0 to 2000 eV for Si10+, thus, extending previous measurements for Si10+ [Orban et al. 2010, Astrophys. J. 721, 1603] to much higher energies. Experimentally derived rate coefficients for the recombination of Si9+ and Si10+ ions in a plasma are presented along with simple parameterizations. These rate coefficients are useful for the modeling of the charge balance of silicon in photoionized plasmas (Si9+ and Si10+) and in collisionally ionized plasmas (Si10+ only). In the corresponding temperature ranges, the experimentally derived rate coefficients agree with the latest corresponding theoretical results within the experimental uncertainties.Comment: 17 pages, 7 figures, 3 tables, 66 references, submitted to the J. Phys. B special issue on atomic and molecular data for astrophysicist