Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

A Note on Tachyons in the D3+D3ˉD3+{\bar {D3}} System

The periodic bounce of Born-Infeld theory of $D3$-branes is derived, and the BPS limit of infinite period is discussed as an example of tachyon condensation. The explicit bounce solution to the Born--Infeld action is interpreted as an unstable fundamental string stretched between the brane and its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3: explanations and references added. Final version to appear in Mod. Phys. Lett.

Low-Cost, Open-Source, and Low-Power: But What to Do With the Data?

There are now many ongoing efforts to develop low-cost, open-source, low-power sensors and datalogging solutions for environmental monitoring applications. Many of these have advanced to the point that high quality scientific measurements can be made using relatively inexpensive and increasingly off-the-shelf components. With the development of these innovative systems, however, comes the ability to generate large volumes of high-frequency monitoring data and the challenge of how to log, transmit, store, and share the resulting data. This paper describes a new web application that was designed to enable citizen scientists to stream sensor data from a network of Arduino-based dataloggers to a web-based Data Sharing Portal. This system enables registration of new sensor nodes through a Data Sharing Portal website. Once registered, any Internet connected data-logging device (e.g., connected via cellular or Wi-Fi) can then post data to the portal through a web service application programming interface (API). Data are stored in a back-end data store that implements Version 2 of the Observations Data Model (ODM2). Live data can then be viewed using multiple visualization tools, downloaded from the Data Sharing Portal in a simple text format, or accessed via WaterOneFlow web services for machine-to-machine data exchange. This system was built to support an emerging network of open-source, wireless water quality monitoring stations developed and deployed by the EnviroDIY community for do-it-yourself environmental science and monitoring, initially within the Delaware River Watershed. However, the architecture and components of the ODM2 Data Sharing Portal are generic, open-source, and could be deployed for use with any Internet connected device capable of making measurements and formulating an HTTP POST request

Nano-probing station incorporating MEMS probes for 1D device RF on-wafer characterization

International audienc

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Fifth-year medical students’ perspectives on rural training in Botswana: A qualitative approach

Background. The curriculum of the Faculty of Medicine at the University of Botswana includes rural community exposure for students throughout their 5 years of training. In addition to community exposure during the first 2 years, students complete 16 weeks of family medicine and 8 weeks of public health medicine. However, as a new faculty, students’ experiences and perceptions regarding rural clinical training are not yet known.Objective. To describe the experiences and perceptions of the 5th-year medical students during their rural training and solicit their recommendations for improvement.Methods. This qualitative study used face-to-face interviews with 5th-year undergraduate medical students (N=36) at the end of their family medicine rotation in Mahalapye and Maun villages. We used a phenomenological paradigm to underpin the study. Voice-recorded interviews were transcribed and analysed using Atlas TI version 7 software (USA).Results. Three main themes were identified: (i) experiences and perceptions of the rural training environment; (ii) perceptions of the staff at rural sites; and (iii) perceptions of clinical benefits and relevance during rural training. While the majority of students perceived rural training as beneficial and valuable, a few felt that learning was compromised by limited resources and processes, such as medical equipment, internet connectivity and inadequate supervision.Conclusion. While the majority of students perceived rural training as beneficial, students identified limitations in both resources and supervision that need to be improved. Understanding students’ rural training experiences and perceptions can help the Faculty of Medicine, stakeholders and site facilitators to guide future rural training implementation

Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions

Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical box of radius R. With the aid of the asymptotic iteration method, the exact analytic solutions under certain constraints, and general approximate solutions, are obtained. These exhibit the parametric dependence of the eigenenergies on a, b, and R. The wave functions have the simple form of a product of a power function, an exponential function, and a polynomial. In order to achieve our results the question of determining the polynomial solutions of the second-order differential equation (\sum_{i=0}^{k+2}a_{k+2,i}r^{k+2-i})y"+(\sum_{i=0}^{k+1}a_{k+1,i}r^{k+1-i})y'-(\sum_{i=0}^{k}\tau_{k,i}r^{k-i})y=0 for k=0,1,2 is solved.Comment: 16 pages, 1 figur

Extended parametric resonances in nonlinear Schrodinger systems

We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in Nonlinear Optics.Comment: 1 figur

Quantum mass correction for the twisted kink

We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted \phi^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral representation of the spectral zeta function. By solving the Bethe ansatz equations for the n=2 Lame equation we obtain an analytic expression for the corresponding spectral discriminant. We discuss the renormalization issues of this model. An energetically preferred size for the compact space is finally obtained.Comment: 18 pages, 2 figures;v2:references and discussion added, typos correcte