Light capsules shaped by curvilinear meta-surfaces

We propose a simple yet efficient method for generating in-plane hollow beams with a nearly-full circular light shell without the contribution of backward propagating waves. The method relies on modulating the phase in the near field of a centro-symmetric optical wavefront, such as that from a high-numericalaperture focused wave field. We illustrate how beam acceleration may be carried out by using an ultranarrow non-flat meta-surface formed by engineered plasmonic nanoslits. A mirrorsymmetric, with respect to the optical axis, circular caustic surface is numerically demonstrated that can be used as an optical bottle

Stochastic theory of lineshape broadening in quasielastic He atom scattering with interacting adsorbates

The activated surface diffusion of interacting adsorbates is described in terms of the so-called interacting single adsorbate approximation, which is applied to the diffusion of Na atoms on Cu(001) for coverages up to 20% in quasielastic He atom scattering experiments. This approximation essentially consists of solving the standard Langevin equation with two noise sources and frictions: a Gaussian white noise accounting for the friction with the substrate, and a white shot noise characterized by a collisional friction simulating the adsorbate-adsorbate collisions. The broadenings undergone by the quasielastic peak are found to be in very good agreement with the experimental data reported at two surface temperatures 200 and 300 K.Comment: 6 pages, 3 figure

Quasi-elastic peak lineshapes in adsorbate diffusion on nearly flat surfaces at low coverages: the motional narrowing effect in Xe on Pt(111)

Quasi-elastic helium atom scattering measurements have provided clear evidence for a two-dimensional free gas of Xe atoms on Pt(111) at low coverages. Increasing the friction due to the surface, a gradual change of the shape of the quasi-elastic peak is predicted and analyzed for this system in terms of the so-called motional narrowing effect. The type of analysis presented here for the quasi-elastic peak should be prior to any deconvolution procedure carried out in order to better extract information from the process, e.g. diffusion coefficients and jump distributions. Moreover, this analysis also provides conditions for the free gas regime different than those reported earlier.Comment: 12 pages, 4 figures (revised version

Generalization of Vélu's formulae

Given an elliptic curve $E$ and a finite subgroup $G$, Vélu's formulae concern to a separable isogeny $\mathcal{I}_G\colon E\to E'$ with kernel $G$. In particular, for a point $P\in E$ these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set $P+G$ as the difference between the abscissa of $\mathcal{I}_G(P)$ and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel $G$. On the other hand, they express Weierstrass coefficients of $E'$ as polynomials in the coefficients of $E$ and two additional parameters: $w_0=t$ and $w_1=w$. We generalize this by defining parameters $w_n$ for all $n\ge 0$ and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in $P+G$. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when $G$ is a rational group

Sucrose homeostasis: Mechanisms and opportunity in crop yield improvement

Sugar homeostasis is a critical feature of biological systems. In humans, raised and dysregulated blood sugar is a serious health issue. In plants, directed changes in sucrose homeostasis and allocation represent opportunities in crop improvement. Plant tissue sucrose varies more than blood glucose and is found at higher concentrations (cytosol and phloem ca. 100 mM v 3.9–6.9 mM for blood glucose). Tissue sucrose varies with developmental stage and environment, but cytosol and phloem exhibit tight sucrose control. Sucrose homeostasis is a consequence of the integration of photosynthesis, synthesis of storage end products such as starch, transport of sucrose to sinks and sink metabolism. Trehalose 6-phosphate (T6P)-SnRK1 and TOR play central, still emerging roles in regulating and coordinating these processes. Overall, tissue sucrose levels are more strongly related to growth than to photosynthesis. As a key sucrose signal,T6P regulates sucrose levels, transport and metabolic pathways to coordinate source and sink at a whole plant level. Emerging evidence shows that T6P interacts with meristems. With careful targeting, T6P manipulation through exploiting natural variation, chemical intervention and genetic modification is delivering benefits for crop yields. Regulation of cereal grain set, filling and retention may be the most strategically important aspect of sucrose allocation and homeostasis for food security

Halving for the 2-Sylow subgroup of genus 2 curves over binary fields

AbstractWe give a deterministic polynomial time algorithm to find the structure of the 2-Sylow subgroup of the Jacobian of a genus 2 curve over a finite field of characteristic 2. Our procedure starts with the points of order 2 and then performs a chain of successive halvings while such an operation makes sense. The stopping condition is triggered when certain polynomials fail to have roots in the base field, as previously shown by I. Kitamura, M. Katagi and T. Takagi. The structure of our algorithm is similar to the already known case of genus 1 and odd characteristic