Zonal flows and long-distance correlations during the formation of the edge shear layer in the TJ-II stellarator

A theoretical interpretation is given for the observed long-distance correlations in potential fluctuations in TJ-II. The value of the correlation increases above the critical point of the transition for the emergence of the plasma edge shear flow layer. Mean (i.e. surface averaged, zero-frequency) sheared flows cannot account for the experimental results. A model consisting of four envelope equations for the fluctuation level, the mean flow shear, the zonal flow amplitude shear, and the averaged pressure gradient is proposed. It is shown that the presence of zonal flows is essential to reproduce the main features of the experimental observations.Comment: 19 pages, 7 figure

Parabolic stable surfaces with constant mean curvature

We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrodinger operator $-L=-(\Delta +q)$ on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $H\in\mathbb{R}$ in homogeneous spaces $\mathbb{E}(\kappa,\tau)$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $\mathbb{H}^2\times\mathbb{R}$, then $|H|\leq 1/2$ and if equality holds, then M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange finite capacity by parabolicity, and simplify the proof of Theorem 1)

Managing affect in learners' questions in undergraduate science

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Society for Research into Higher Education.This article aims to position students' classroom questioning within the literature surrounding affect and its impact on learning. The article consists of two main sections. First, the act of questioning is discussed in order to highlight how affect shapes the process of questioning, and a four-part genesis to question-asking that we call CARE is described: the construction, asking, reception and evaluation of a learner's question. This work is contextualised through studies in science education and through our work with university students in undergraduate chemistry, although conducted in the firm belief that it has more general application. The second section focuses on teaching strategies to encourage and manage learners' questions, based here upon the conviction that university students in this case learn through questioning, and that an inquiry-based environment promotes better learning than a simple ‘transmission’ setting. Seven teaching strategies developed from the authors' work are described, where university teachers ‘scaffold’ learning through supporting learners' questions, and working with these to structure and organise the content and the shape of their teaching. The article concludes with a summary of the main issues, highlighting the impact of the affective dimension of learning through questioning, and a discussion of the implications for future research

Induced Pre-Saturation Tower: A Technological Innovation for Oily Water Treatment in Semi-Industrial Scale

In this work, an induced pre-saturation tower (IPST) for oil–water separation was built on a semi-industrial scale, based on experimental results obtained on a laboratory scale prototype. The main strategy for generating these criteria was to increase the efficiency of the bench scale prototype, which is limited by conditions of low levels of automation and control, with the use of a biosurfactant as an auxiliary collector. The validation of the developed criteria allowed the construction of an IPST with three stages, all fed with previously saturated effluents. The IPST was built in stainless steel, with multistage centrifugal pumps and adapted to generate microbubbles without the use of saturation tanks or compressors. The most relevant operational parameters were selected using a fractional factorial design, while a central composite rotatable design (CCRD) followed by the application of the desirability function allowed to optimize the conditions for partial and global variables, the latter with desirability of 95%. A nominal flow rate of approximately 1000 L·h−1, a recycle flow rate of 450 L·h−1, a scraper rotation speed of 80 rpm, an average pressure of the microbubble pumps of 11 bar, and an effluent temperature from IPST of about 38 °C ensured optimized operation for the proposed technological development

Algebraic approach in the study of time-dependent nonlinear integrable systems: Case of the singular oscillator

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map which may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator which we evaluate using a recent method of integrating the quantum Liouville-Bloch equations \cite{rau}. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the SU(1,1) algebra and that of simple dynamical systems.Comment: 17 pages, 4 figures, Accepted in PR

Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

We show that the ground state of the well-known pseudo-stationary states for the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty $\Delta q \Delta p = \hbar \sigma_0/2$, where $\sigma_0 (\geq 1)$ is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.Comment: RevTex4, 9 pages, no fingure; to be published in Journal of Physics