Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.Comment: 10 pages, RevTex4, 4 color eps figure

The effect of autonomy, training opportunities, age and salaries on job satisfaction in the South East Asian retail petroleum industry

South East Asian petroleum retailers are under considerable pressure to improve service quality by reducing turnover. An empirical methodology from this industry determined the extent to which job characteristics, training opportunities, age and salary influenced the level of job satisfaction, an indicator of turnover. Responses are reported on a random sample of 165 site employees (a 68% response rate) of a Singaporean retail petroleum firm. A restricted multivariate regression model of autonomy and training opportunities explained the majority (35.4%) of the variability of job satisfaction. Age did not moderate these relationships, except for employees >21 years of age, who reported enhanced job satisfaction with additional salary. Human Capital theory, Life Cycle theory and Job Enrichment theory are invoked and explored in the context of these findings in the South East Asian retail petroleum industry. In the South East Asian retail petroleum industry, jobs providing employees with the opportunity to undertake a variety of tasks that enhanced the experienced meaningfulness of work are likely to promote job satisfaction, reduce turnover and increase the quality of service

A Neptune-mass exoplanet in close orbit around a very low-mass star challenges formation models

Stars and planetary system

Measurement in the study of menstrual health and hygiene: A systematic review and audit

Please note that the peer-reviewed version of this paper has now been published. Please view and cite that final version: Hennegan, J., Brooks, D.J., Schwab, K.J., & Melendez-Torres, G.J. (2020). Measurement in the study of menstrual health and hygiene: A systematic review and audit. PLOS One, 15(6), e0232935. https://doi.org/10.1371/journal.pone.023293

The individual time trial as an optimal control problem

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial andinvolves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.Applied ProbabilityOptimizationBiomechatronics & Human-Machine Contro

A variational approach to determine the optimal power distribution for cycling in a time trial

The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclists endurance capacity. Previous experimental and theoretical studies have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a mathematical optimal control problem which we solve using Pontryagin's maximum principle. Our solution of the pacing problem is partly numerical and partly analytical. It applies to a straight course without bends. It turns out that the optimal pacing problem is a singular control problem. Intricate mathematical arguments are required to prove that the singular control times form a single interval: optimal pacing starts with maximum power and decays through a singular control, which may be degenerate, to minimum power.Applied ProbabilityOptimizationBiomechatronics & Human-Machine Contro

A variational approach to determine the optimal power distribution for cycling in a time trial

The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclists endurance capacity. Previous experimental and theoretical studies have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a mathematical optimal control problem which we solve using Pontryagin's maximum principle. Our solution of the pacing problem is partly numerical and partly analytical. It applies to a straight course without bends. It turns out that the optimal pacing problem is a singular control problem. Intricate mathematical arguments are required to prove that the singular control times form a single interval: optimal pacing starts with maximum power and decays through a singular control, which may be degenerate, to minimum power.</p

Combination technique based second moment analysis for elliptic PDEs on random domains

In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin’s method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique if the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method