Conjugate quasilinear Dirichlet and Neumann problems and a posteriori error bounds

Quasilinear Dirichlet and Neumann problems on a rectangle D with boundary D prime are considered. Using these concepts, conjugate problems, that is, a pair of one Dirichlet and one Neumann problem, the minima of the energies of which add to zero, are introduced. From the concept of conjugate problems, two-sided bounds for the energy of the exact solution of any given Dirichlet or Neumann problem are constructed. These two-sided bounds for the energy at the exact solution are in turn used to obtain a posteriori error bounds for the norm of the difference of the approximate and exact solutions of the problem. These bounds do not involve the unknown exact solution and are easily constructed numerically

Robust interferometer for the routing of light beams carrying orbital angular momentum

We have developed an interferometer requiring only minimal angular alignment for the routing of beams carrying orbital angular momentum. The Mach–Zehnder interferometer contains a Dove prism in each arm where each has a mirror plane around which the transverse phase profile is inverted. One consequence of the inversions is that the interferometer needs no alignment. Instead the interferometer defines a unique axis about which the input beam must be coupled. Experimental results are presented for the fringe contrast, reaching a maximum value of 93±1%

A PI3K-mediated negative feedback regulates Drosophila motor neuron excitability

Negative feedback can act as a homeostatic mechanism to maintain neuronal activity at a particular specified value. At the Drosophila neuromuscular junction, a mutation in the type II metabotropic glutamate receptor gene (mGluRA) increased motor neuron excitability by disrupting an autocrine, glutamate-mediated negative feedback. We show that mGluRA mutations increase neuronal excitability by preventing PI3 kinase (PI3K) activation and consequently hyperactivating the transcription factor Foxo. Furthermore, glutamate application increases levels of phospho-Akt, a product of PI3K signaling, within motor nerve terminals in an mGluRA-dependent manner. In humans, PI3K and type II mGluRs are implicated in epilepsy, neurofibromatosis, autism, schizophrenia and other neurological disorders; however, neither the link between type II mGluRs and PI3K, nor the role of Foxo in the control of neuronal excitability, had been previously reported. Our work suggests that some of the deficits in these neurological disorders might result from disruption of glutamate-mediated homeostasis of neuronal excitability

Refractive elements for the measurement of the orbital angular momentum of a single photon

We have developed a mode transformer comprising two custom refractive optical elements which convert orbital angular momentum states into transverse momentum states. This transformation allows for an efficient measurement of the orbital angular momentum content of an input light beam. We characterise the channel capacity of the system for 50 input modes, giving a maximum value of 3.46 bits per photon. Using an electron multiplying CCD (EMCCD) camera with a laser source attenuated such that on average there is less than one photon present within the system per measurement period, we demonstrate that the elements are efficient for the use in single photon experiments

Measuring orbital angular momentum superpositions of light by mode transformation

We recently reported on a method for measuring orbital angular momentum (OAM) states of light based on the transformation of helically phased beams to tilted plane waves [Phys. Rev. Lett.105, 153601 (2010)]. Here we consider the performance of such a system for superpositions of OAM states by measuring the modal content of noninteger OAM states and beams produced by a Heaviside phase plate

Why compensating fibre nonlinearity will never meet capacity demands

Current research efforts are focussed on overcoming the apparent limits of communication in single mode optical fibre resulting from distortion due to fibre nonlinearity. It has been experimentally demonstrated that this Kerr nonlinearity limit is not a fundamental limit; thus it is pertinent to review where the fundamental limits of optical communications lie, and direct future research on this basis. This paper details recently presented results. The work herein briefly reviews the intrinsic limits of optical communication over standard single mode optical fibre (SMF), and shows that the empirical limits of silica fibre power handling and transceiver design both introduce a practical upper bound to the capacity of communication using SMF, on the order of 1 Pbit/s. Transmission rates exceeding 1 Pbit/s are shown to be possible, however, with currently available optical fibres, attempts to transmit beyond this rate by simply increasing optical power will lead to an asymptotically zero fractional increase in capacity.Comment: 4 pages, 2 figure

Divergence of an orbital-angular-momentum-carrying beam upon propagation

There is recent interest in the use of light beams carrying orbital angular momentum (OAM) for creating multiple channels within free-space optical communication systems. One limiting issue is that, for a given beam size at the transmitter, the beam divergence angle increases with increasing OAM, thus requiring a larger aperture at the receiving optical system if the efficiency of detection is to be maintained. Confusion exists as to whether this divergence scales linarly with, or with the square root of, the beam's OAM. We clarify how both these scaling laws are valid, depending upon whether it is the radius of the Gaussian beam waist or the rms intensity which is kept constant while varying the OAM.Comment: 4 pages, 2 figure

Twitter in the collaborative classroom: micro-blogging for in-class collaborative discussions

While small group discussion during undergraduate classes is an important pedagogic strategy, there are two primary concerns for instructors how to monitor the conversation that goes on within groups, and how to ensure that ideas that emerge within the groups become part of the classroom discourse. In this paper, we describe a design-experiment conducted in two sections of the same undergraduate education class, exploring the use of Twitter, and a shared display of the Twitter-chat, to address these issues. We describe three iterations of the use of Twitter in the classes, and our reflections on how it influenced the teaching experience. Data from student surveys indicates that students had minimal experience using Twitter for academic activities prior to participation in this class and that they felt Twitter was a valuable tool to support their in-class learning activities. The teaching team found that the use of Twitter kept students on task and focused on the activity, but expressed some concern about the depth of engagement with ideas during the task