Remarks on a Paper of Leighton

Counterexamples to theorems for zeros of solutions of second order linear differential equation

Wettability-independent droplet transport by \emph{Bendotaxis}

We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful means of transporting droplets in technological applications, for example in developing self-cleaning surfaces, and discuss the implications of our results for such applications.Comment: 5 pages, 4 figures. Supplementary Information available on reques

Reports of injury risks and reasons for choice of sleep environments for infants and toddlers

OBJECTIVE: Compare mothers\u27 reports of injuries for infants and toddlers sleeping with crib-bumpers/mesh-liners/no-barriers and reasons for these sleep environment choices. METHODS: A cross-sectional survey of mothers subscribing to a parenting magazine and using crib bumpers (n = 224), mesh liners (n = 262), and no barriers (n = 842). Analyses of four possible injuries (face-covered, climb-out/fall, slat-entrapment, hit-head) including multivariate logistic regression adjusted for missing data/demographics and Chi squared analyses of reasons for mothers\u27 choices. RESULTS: Maternal reports of finding infants/toddlers with face covered had 3.5 times higher adjusted odds (aOR) for crib bumper versus mesh liner use. Breathing difficulties and wedgings were reported for infants/toddlers using crib bumpers but not mesh liners. Climb-outs/falls showed no significant difference in aORs for crib bumpers versus no-barriers and mesh liners versus no barriers. Reports of slat-entrapment were less likely for mothers using crib bumpers and mesh liners than using no barrier (aOR = .28 and .32). Reports of hit-heads were less likely for crib bumpers vs no barrier (aOR = .38) with no significant difference between mesh liners versus no barrier use. Mothers using crib bumpers and mesh liners felt their choice prevented slat-entrapment (89%, 91%); 93.5% of crib bumper users felt their choice prevented hit-heads. Significantly more mesh liner than crib bumper users chose them because There is no suffocation risk (64.1% vs. 40.6%), while 83.6% of no-barrier users chose them because I was concerned about suffocation risk. CONCLUSIONS FOR PRACTICE: Mothers appeared to be more concerned about preventing minor risks than suffocation. Understanding reasons for mothers\u27 use of barriers/no-barriers is important in tailoring counseling for mothers with infants/toddlers

Non-destructive spatial heterodyne imaging of cold atoms

We demonstrate a new method for non-destructive imaging of laser-cooled atoms. This spatial heterodyne technique forms a phase image by interfering a strong carrier laser beam with a weak probe beam that passes through the cold atom cloud. The figure of merit equals or exceeds that of phase-contrast imaging, and the technique can be used over a wider range of spatial scales. We show images of a dark spot MOT taken with imaging fluences as low as 61 pJ/cm^2 at a detuning of 11 linewidths, resulting in 0.0004 photons scattered per atom.Comment: text+3 figures, submitted to Optics Letter

Nonlocal Landau theory of the magnetic phase diagram of highly frustrated magnetoelectric CuFeO2_2

A nonlocal Landau-type free energy functional of the spin density is developed to model the large variety of magnetic states which occur in the magnetic field-temperature phase diagram of magnetoelectric CuFeO$_2$. Competition among long-range quadratic exchange, biquadratic anti-symmetric exchange, and trigonal anisotropy terms, consistent with the high-temperature rhombohedral R$\bar{3}$m crystal symmetry, are shown to all play important roles in stabilizing the unusual combination of commensurate and incommensurate spin structures in this highly frustrated triangular antiferromagnet. It is argued that strong magnetoelastic coupling is largely responsible for the nonlocal nature of the free energy. A key feature of the analysis is that an electric polarization is induced by a canting of the non-collinear incommensurate spin structure. Application of the model to ordered spin states in the triangular antiferromagnets MnBr$_2$ and NaFeO$_2$ is also discussed.Comment: 20 pages, 2 figure

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Out With the Old, In With the New: Are Western Commodity Producers Ready for Buyouts?

Agricultural and Food Policy,