Gerbes, simplicial forms and invariants for families of foliated bundles

The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to `characteristic gerbes' associated to families of bundles and connections. In turn this gives invariants for families of foliated bundles. A special case is the Quillen line bundle associated to families of flat SU(2)-bundlesComment: 28 page

Can managed grasslands enhance pollinators in intensively farmed areas?

Wild flower strips is a common agri-environmental scheme used by farmers and land managers in order to improve biodiversity of pollinators. However, managed grasslands may also provide flower resources for flower visiting insects in agricultural landscapes. Botanically diverse grasslands on arable farms may support a range of wild pollinators, enhancing pollination services of crops. Intensively managed leys, on the other hand, typically contain only a few high-yielding, competitively strong species. One of the aims of the Multiplant project (2014-2018) was to test perennial seed mixtures targeted for bio-energy, feed protein and biodiversity, in order to develop multi-functional seed mixtures for grasslands. In the current study, we specifically investigated if yield (biomass production) and floral resources for pollinators could be simultaneously optimized by varying botanical composition of mixtures and cutting frequency. We tested four different perennial seed mixtures (3-, 5-, 11- and 13-species mixtures) at three sites varying in surrounding environment using three cutting strategies (no cutting, two cuts per year, four cuts per year). We measured flower production during the season, composition of flower-visitors (in functional groups), and biomass production of all plant species in the seed mixtures. The 11- and 13-species mixtures, which were designed to enhance pollinators, produced similar or higher yield than the 3- and 5- species mixtures under certain cutting regimes. The 3- and 5- species mixtures had a high accumulated flower abundance due to excessive flowering of lucerne under the two-cut strategy and white clover under the four-cut strategy. However, the 11- and 13 species mixtures presented a higher diversity of flowers during the flowering season. Interestingly, accumulated flower abundance was not significantly reduced under the two-cut strategy compared to no cut. Pollinator profiles (visits by different functional groups of insects) were plant-species specific, i.e. at all sites, plant species attracted similar types of insects. Legume species mainly attracted large bees (honey bees and bumblebees), while herbs attracted other insect groups, in particular syrphids and other flies. Our results suggest that multi-species grassland mixtures can be designed to support a higher diversity of pollinators without compromising herbage yield. In particular, adding forbs to the grass-legume mixtures and using a two-cut strategy rather than four cuts per year, may increase flower resources available for a larger range of wild pollinators

NMR relaxation in the spin-1 Heisenberg chain

We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $\Delta$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to $q\approx 0$ and $q\approx \pi$ as a function of temperature. At high-temperature, we observe spin diffusion with a non-trivial exponent. At low-temperature, we argue that a simple activated behavior $1/T_1 \propto\exp(-\Delta/T)$ can only be observed at temperatures much smaller than the gap $\Delta$.Comment: published versio

Density Distribution Sunflower Plots

Density distribution sunflower plots are used to display high-density bivariate data. They are useful for data where a conventional scatter plot is difficult to read due to overstriking of the plot symbol. The x-y plane is subdivided into a lattice of regular hexagonal bins of width w specified by the user. The user also specifies the values of l, d, and k that affect the plot as follows. Individual observations are plotted when there are less than l observations per bin as in a conventional scatter plot. Each bin with from l to d observations contains a light sunflower. Other bins contain a dark sunflower. In a light sunflower each petal represents one observation. In a dark sunflower, each petal represents k observations. (A dark sunflower with p petals represents between /2-pk k and /2+pk k observations.) The user can control the sizes and colors of the sunflowers. By selecting appropriate colors and sizes for the light and dark sunflowers, plots can be obtained that give both the overall sense of the data density distribution as well as the number of data points in any given region. The use of this graphic is illustrated with data from the Framingham Heart Study. A documented Stata program, called sunflower, is available to draw these graphs. It can be downloaded from the Statistical Software Components archive at http://ideas.repec.org/c/boc/bocode/s430201.html . (Journal of Statistical Software 2003; 8 (3): 1-5. Posted at http://www.jstatsoft.org/index.php?vol=8 .)

Dynamical properties of the S=12S=\frac{1}{2} random Heisenberg chain

We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,\omega)$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $\omega$, in nuclear magnetic resonance (NMR) experiments through the spin-lattice relaxation rate $1/T_1$. Our work combines three complementary methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Unlike the uniform system, whose low-energy excitations at low $T$ are restricted to $q$ close to $0$ and $\pi$, our study reveals a continuous narrow band of low-energy excitations in $S(q,\omega)$, extending throughout the Brillouin zone. Close to $q=\pi$, the scaling properties of these excitations are well captured by the RS theory, but we also see disagreements with some aspects of the predicted $q$-dependence further away from $q=\pi$. Furthermore we find spin diffusion effects close to $q=0$ that are not contained within the RS theory but give non-negligible contributions to the mean $1/T_1$. To compare with NMR experiments, we consider the distribution of the local $1/T_1$ values, which is broad, approximately described by a stretched exponential. The mean value first decreases with $T$, but starts to increase and diverge below a crossover temperature. Although a similar divergent behavior has been found for the static uniform susceptibility, this divergent behavior of $1/T_1$ has never been seen in experiments. Our results show that the divergence of the mean $1/T_1$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/T_1$ value is accessed.Comment: 19 pages, 14 figure

Electromagnetic analysis of arbitrarily shaped pinched carpets

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.Comment: 6 pages, 6 figures, Current Status of Manuscript: 19Apr10 26May10-Sent on appeal;report rcvd 29Dec09 13Apr10-Ed. decision and/or ref. comments to author;response rcvd 04Dec09 21Dec09-Ed. decision and/or ref. comments to author;response rcvd 01Dec09-Transferred from PRL to PRA 18Aug09 30Nov09-Ed.decision and/or ref. comments to author;response rcvd 14Aug09 - Correspondence sent to autho

A Mesoscopic Resonating Valence Bond system on a triple dot

We introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly-occupied dot (spin qubit). Two other strongly capacitively islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1); this embodies the weight of the pendulum. The triple dot is placed between two superconducting leads as shown in Fig. 1. Under well-defined conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent. Consequences in a SQUID-geometry are carefully investigated.Comment: final version to appear in PR

Primary and secondary prophylaxis of gastric variceal bleeding

Gastric variceal bleeding is a common problem in patients with cirrhosis and is associated with increased morbidity and mortality. Management is complex and includes pharmacotherapy, endoscopic therapy, and shunt placement. Recent studies indicate that endoscopic therapy with tissue adhesives has similar hemostasis rates and outcomes in terms of mortality as shunt placement but has a lower complication rate and therefore could be considered the first line therapy for acute bleeding and secondary prophylaxis of gastric varices