Changes in the phytoplankton

An article discussing changes observed in phytoplankton of the Lake District. An overview is given of previous phytoplankton studies undertaken in the area, detailing some changes found in various waterbodies. Water quality changes in Lake Windermere are mentioned, including the gradual increase of dissolved organic matter (DOM), believed to be caused by the increase of sewage to the lake. The lakes in the Alps are given as an example of a similar anthropogenic pollution scenario. The treatment of a Lake District tarn with bone meal is described. The article goes on to discuss the composition of plankton throughout the year under a variety of climatic conditions. A figure shows seasonal variation in the consistuents of phytoplankton in Windermere (north basin)

The culture of algae and its applications

An article explaining how the methods and results from the time spent by the author culturing algae can be applied to other algal investigations. The work by the author found that physiological requirements differ widely among algae belonging to different systematic groups. Details are given of the results of a series of experiments which were undertaken in solutions with similar proporties to some natural waters in the Lake District. Reference is made to a paper under preparation at that time containing data on phytoplankton studied in the field within the Lake District during 1937. Reference is also made to Loch Leven and the affects of bluegreen alga on the number of trout caught weekly during 1937

Photoheliograph alignment system, November 1967 - June 1968

Design and operation of photoheliograph alignment system for use with Apollo telescope moun

Witten effect in a crystalline topological insulator

It has been noted a long time ago that a term of the form theta (e^2/2\pi h) B dot E may be added to the standard Maxwell Lagrangian without modifying the familiar laws of electricity and magnetism. theta is known to particle physicists as the 'axion' field and whether or not it has a nonzero expectation value in vacuum remains a fundamental open question of the Standard Model. A key manifestation of the axion term is the Witten effect: a unit magnetic monopole placed inside a medium with non-zero theta is predicted to bind a (generally fractional) electric charge -e(theta/2 pi+n) with n integer. Here we conduct a first test of the Witten effect, based on the recently established fact that the axion term with theta=pi emerges naturally in the description of the electromagnetic response of a new class of crystalline solids called topological insulators - materials distinguished by strong spin-orbit coupling and non-trivial band structure. Using a simple physical model for a topological insulator, we demonstrate the existence of a fractional charge bound to a monopole by an explicit numerical calculation. We also propose a scheme for generating an 'artificial' magnetic monopole in a topological insulator film, that may be used to facilitate the first experimental test of Witten's prediction.Comment: 7 pages, 2 figures. Version to appear in PRB; minor changes, discussion of several issues expande

Complete Constant Mean Curvature surfaces and Bernstein type Theorems in M2×R\mathbb{M}^2\times \mathbb{R}

In this paper we study constant mean curvature surfaces $\Sigma$ in a product space, $\mathbb{M}^2\times \mathbb{R}$, where $\mathbb{M}^2$ is a complete Riemannian manifold. We assume the angle function \nu = \meta{N}{\partial_t} does not change sign on $\Sigma$. We classify these surfaces according to the infimum $c(\Sigma)$ of the Gaussian curvature of the projection of $\Sigma$. When $H \neq 0$ and $c(\Sigma)\geq 0$, then $\Sigma$ is a cylinder over a complete curve with curvature 2H. If H=0 and $c(\Sigma) \geq 0$, then $\Sigma$ must be a vertical plane or $\Sigma$ is a slice $\mathbb{M}^2 \times {t}$, or $\mathbb{M}^2 \equiv \mathbb{R}^2$ with the flat metric and $\Sigma$ is a tilted plane (after possibly passing to a covering space). When $c(\Sigma)\sqrt{-c(\Sigma)} /2$, then $\Sigma$ is a vertical cylinder over a complete curve of $\mathbb{M}^2$ of constant geodesic curvature $2H$. This result is optimal. We also prove a non-existence result concerning complete multi-graphs in $\mathbb{M}^2\times \mathbb{R}$, when $c(\mathbb{M}^2)<0$

Complete Constant Mean Curvature surfaces in homogeneous spaces

In this paper we classify complete surfaces of constant mean curvature whose Gaussian curvature does not change sign in a simply connected homogeneous manifold with a 4-dimensional isometry group.Comment: We have corrected a mistake in Theorem 2.

Fatou's Theorem and minimal graphs

In this paper we extend a recent result of Collin-Rosenberg ({\it a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere}) to a large class of differential operators in Divergence form. Moreover, we construct an example (in the spirit of \cite{CR2}) of a minimal graph in \mr, where \m is a Hadamard surface, over a geodesic disc which has finite radial limits in a mesure zero set.Comment: 13 figure