Quantum lattice solitons in ultracold bosons near Feshbach resonance

Quantum lattice solitons in a system of two ultracold bosons near Feshbach resonance are investigated. It is shown that their binding energy, effective mass, and spatial width, can be manipulated varying the detuning from the Feshbach resonance. In the case of attractive atomic interactions, the molecule creation stabilizes the solitons. In the case of repulsive interactions, the molecule creation leads to the possibility of existence of bright solitons in some interval of detunings. Due to quantum fluctuations the soliton width is a random quantity. Its standard deviation is larger than the mean value for such a small number of particles

Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence

We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar $\theta=(-\Delta)^{\alpha/2}\psi$ is advected by the incompressible flow $\u=(-\psi_y,\psi_x)$. The dynamics of this family are characterized by the material conservation of $\theta$, whose variance is preferentially transferred to high wave numbers. As this transfer proceeds to ever-smaller scales, the gradient $\nabla\theta$ grows without bound. This growth is due to the stretching term $(\nabla\theta\cdot\nabla)\u$ whose ``effective degree of nonlinearity'' differs from one member of the family to another. This degree depends on the relation between the advecting flow $\u$ and the active scalar $\theta$ and is wide ranging, from approximately linear to highly superlinear. Linear dynamics are realized when $\nabla\u$ is a quantity of no smaller scales than $\theta$, so that it is insensitive to the direct transfer of the variance of $\theta$, which is nearly passively advected. This case corresponds to $\alpha\ge2$, for which the growth of $\nabla\theta$ is approximately exponential in time and non-accelerated. For $\alpha<2$, superlinear dynamics are realized as the direct transfer of entails a growth in \nabla\u, thereby enhancing the production of $\nabla\theta$. This superlinearity reaches the familiar quadratic nonlinearity of three-dimensional turbulence at $\alpha=1$ and surpasses that for $\alpha<1$. The usual vorticity equation ($\alpha=2$) is the border line, where \nabla\u and $\theta$ are of the same scale, separating the linear and nonlinear regimes of the small-scale dynamics. We discuss these regimes in detail, with an emphasis on the locality of the direct transfer.Comment: 6 journal pages, to appear in Physical Review

An Electron‐Rich Calix[4]arene‐Based Receptor with Unprecedented Binding Affinity for Nitric Oxide

Calixarenes have found widespread application as building blocks for the design and synthesis of functional materials in host–guest chemistry. The ongoing desire to develop a detailed understanding of the nature of NO bonding to multichromophoric π‐stacked assemblies led us to develop an electron‐rich methoxy derivative of calix[4]arene (3), which we show exists as a single conformer in solution at ambient temperature. Here, we examine the redox properties of this derivative, generate its cation radical (3+.) using robust chemical oxidants, and determine the relative efficacy of its NO binding in comparison with model calixarenes. We find that 3/3+. is a remarkable receptor for NO+/NO, with unprecedented binding efficacy. The availability of precise experimental structures of this calixarene derivative and its NO complex, obtained by X‐ray crystallography, is critically important both for developing novel functional NO biosensors, and understanding the role of stacked aromatic donors in efficient NO binding, which may have relevance to biological NO transport

Investigations of meltwater refreezing and density variations in the snowpack and firn within the percolation zone of the Greenland Ice Sheet

The mass balance of polythermal ice masses is critically dependent on the proportion of surface-generated meltwater that subsequently refreezes in the snowpack and firn. In order to quantify this effect and to characterize its spatial variability, we measured near-surface (26%, resulting in a 32% increase in net accumulation. This 'seasonal densification' increased at lower elevations, rising to 47% 10 km closer to the ice-sheet margin at 1860 m a. s. l. Density/depth profiles from nine sites within 1 km2 at ∼1945 m a.s.l. reveal complex stratigraphies that change over short spatial scales and seasonally. We conclude that estimates of mass-balance change cannot be calculated solely from observed changes in surface elevation, but that near-surface densification must also be considered. However, predicting spatial and temporal variations in densification may not be straightforward. Further, the development of complex firn-density profiles both masks discernible annual layers in the near-surface firn and ice stratigraphy and is likely to introduce error into radar-derived estimates of surface elevation

A Characteristic Planetary Feature in Double-Peaked, High-Magnification Microlensing Events

A significant fraction of microlensing planets have been discovered in high-magnification events, and a significant fraction of these events exhibit a double-peak structure at their peak. However, very wide or very close binaries can also produce double-peaked high-magnification events, with the same gross properties as those produced by planets. Traditionally, distinguishing between these two interpretations has relied upon detailed modeling, which is both time-consuming and generally does not provide insight into the observable properties that allow discrimination between these two classes of models. We study the morphologies of these two classes of double-peaked high-magnification events, and identify a simple diagnostic that can be used to immediately distinguish between perturbations caused by planetary and binary companions, without detailed modeling. This diagnostic is based on the difference in the shape of the intra-peak region of the light curves. The shape is smooth and concave for binary lensing, while it tends to be either boxy or convex for planetary lensing. In planetary lensing this intra-peak morphology is due to the small, weak cusp of the planetary central caustic located between the two stronger cusps. We apply this diagnostic to five observed double-peaked high-magnification events to infer their underlying nature. A corollary of our study is that good coverage of the intra-peak region of double-peaked high-magnification events is likely to be important for their unique interpretation.Comment: 6 pages, 3 figure

Development of low cost packaged fibre optic sensors for use in reinforced concrete structures

There is an ongoing need to measure strains in reinforced concrete structures more reliably and under a range of circumstances e.g. long term durability (such as effects of cracking and reinforcement corrosion), response to normal working loads and response under abnormal load conditions. Fibre optic sensors have considerable potential for this purpose and have the additional advantages, including of immunity to electromagnetic interference and light weight (Grattan et al., 2000). This is important in railway scenarios and particularly so when the lines are electrified. Their small size allows for easy installation. However, their use as commercial ‘packaged’ devices (traditionally seen as necessary to achieve adequate robustness) is limited by their high cost relative to other sensor devices such as encapsulated electric resistance strain gauges. This paper describes preliminary work to produce a cost-effective and easy-to-use technique for encapsulating fibre optic sensors in resin using 3D printing techniques to produce a robust, inexpensive ‘packaged’ sensor system suitable for use with concrete structures. The work done to date has shown this to be a convenient and economical way of producing multiple sensors which were suitable for both surface mounting and embedment in reinforced concrete structures. The proof-of-concept testing to which the trial packages were subjected is described in the paper and the results indicate that 3D printed packages have considerable potential for further development and use in a variety of civil engineering applications, competing well with more conventional sensor systems