Technological and pedagogical convergence between work-based and campus-based learning

There is a strong technological and economic push for higher education providers to adopt online learning strategies. This is driven, in part, by the requirement of industry for lifelong learning on a flexible, just-in-time basis. Simultaneously, there is a rising awareness amongst engineering faculty of the pedagogical issues that underpin good teaching and learning practice, stimulated by revised accreditation approaches and related reviews. These significant drivers of change are often experienced as discordant if not competing issues. This paper presents a case study of work-integrated learning that parallels traditional on-campus learning. Technology and pedagogy begin to converge when: (1) pedagogical assumptions are identified early; (2) flexible learning is not confused with on-line learning; (3) intrinsic and external motivations of stakeholders are aligned; (4) there is broad ownership; and (5) a sustainable development strategy is adopted

Multi-source self-calibration: Unveiling the microJy population of compact radio sources

Context. Very Long Baseline Interferometry (VLBI) data are extremely sensitive to the phase stability of the VLBI array. This is especially important when we reach {\mu}Jy r.m.s. sensitivities. Calibration using standard phase referencing techniques is often used to improve the phase stability of VLBI data but the results are often not optimal. This is evident in blank fields that do not have in-beam calibrators. Aims. We present a calibration algorithm termed Multi-Source Self-Calibration (MSSC) which can be used after standard phase referencing on wide-field VLBI observations. This is tested on a 1.6 GHz wide-field VLBI data set of the Hubble Deep Field-North and the Hubble Flanking Fields. Methods. MSSC uses multiple target sources detected in the field via standard phase referencing techniques and modifies the visibili- ties so that each data set approximates to a point source. These are combined to increase the signal to noise and permit self-calibration. In principle, this should allow residual phase changes caused by the troposphere and ionosphere to be corrected. By means of faceting, the technique can also be used for direction dependent calibration. Results. Phase corrections, derived using MSSC, were applied to a wide-field VLBI data set of the HDF-N comprising of 699 phase centres. MSSC was found to perform considerably better than standard phase referencing and single source self-calibration. All detected sources exhibited dramatic improvements in dynamic range. Using MSSC, one source reached the detection threshold taking the total detected sources to twenty. 60% of these sources can now be imaged with uniform weighting compared to just 45% with standard phase referencing. The Parseltongue code which implements MSSC has been released and made publicly available to the astronomical community (https://github.com/jradcliffe5/multi_self_cal).Comment: 7 pages, 4 figures, accepted to A&

Generalising some results about right-angled Artin groups to graph products of groups

We prove three results about the graph product G=\G(\Gamma;G_v, v \in V(\Gamma)) of groups $G_v$ over a graph $\Gamma$. The first result generalises a result of Servatius, Droms and Servatius, proved by them for right-angled Artin groups; we prove a necessary and sufficient condition on a finite graph $\Gamma$ for the kernel of the map from $G$ to the associated direct product to be free (one part of this result already follows from a result in S. Kim's Ph.D. thesis). The second result generalises a result of Hermiller and Sunic, again from right-angled Artin groups; we prove that for a graph $\Gamma$ with finite chromatic number, $G$ has a series in which every factor is a free product of vertex groups. The third result provides an alternative proof of a theorem due to Meier, which provides necessary and sufficient conditions on a finite graph $\Gamma$ for $G$ to be hyperbolic

Spin squeezing in nonlinear spin coherent states

We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and y directions.Comment: 4 pages, 2 figs, revised version submitted to J. Opt.

Nowhere to Hide: Radio-faint AGN in the GOODS-N field. I. Initial catalogue and radio properties

(Abridged) Conventional radio surveys of deep fields ordinarily have arc-second scale resolutions often insufficient to reliably separate radio emission in distant galaxies originating from star-formation and AGN-related activity. Very long baseline interferometry (VLBI) can offer a solution by identifying only the most compact radio emitting regions in galaxies at cosmological distances where the high brightness temperatures (in excess of $10^5$ K) can only be reliably attributed to AGN activity. We present the first in a series of papers exploring the faint compact radio population using a new wide-field VLBI survey of the GOODS-N field. The unparalleled sensitivity of the European VLBI Network (EVN) will probe a luminosity range rarely seen in deep wide-field VLBI observations, thus providing insights into the role of AGN to radio luminosities of the order $10^{22}~\mathrm{W\,Hz^{-1}}$ across cosmic time. The newest VLBI techniques are used to completely cover an entire 7'.5 radius area to milliarcsecond resolutions, while bright radio sources ($S > 0.1$ mJy) are targeted up to 25 arcmin from the pointing centre. Multi-source self-calibration, and a primary beam model for the EVN array are used to correct for residual phase errors and primary beam attenuation respectively. This paper presents the largest catalogue of VLBI detected sources in GOODS-N comprising of 31 compact radio sources across a redshift range of 0.11-3.44, almost three times more than previous VLBI surveys in this field. We provide a machine-readable catalogue and introduce the radio properties of the detected sources using complementary data from the e-MERLIN Galaxy Evolution survey (eMERGE).Comment: 15 pages, 8 figures, accepted in A&A. Machine-readable table available upon reques

Two-photon excitation and relaxation of the 3d-4d resonance in atomic Kr

Two-photon excitation of a single-photon forbidden Auger resonance has been observed and investigated using the intense extreme ultraviolet radiation from the free electron laser in Hamburg. At the wavelength 26.9 nm (46 eV) two photons promoted a 3d core electron to the outer 4d shell. The subsequent Auger decay, as well as several nonlinear above threshold ionization processes, were studied by electron spectroscopy. The experimental data are in excellent agreement with theoretical predictions and analysis of the underlying multiphoton processes

Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum $J$. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1, ...$, with $K=\infty$ corresponding to the Wehrl map to classical densities. For each $J$ and $J<K\leq \infty$ we show that the minimal output entropy for these channels occurs for a $J$ coherent state. We also show that coherent states both Glauber and Bloch minimize any concave functional, not just entropy.Comment: Version 2 only minor change

On the semiclassical treatment of anharmonic quantum oscillators via coherent states - The Toda chain revisited

We use coherent states as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators. In this approach the square variance of the Hamiltonian within coherent states is of particular interest. This quantity turns out to have natural interpretation with respect to time-dependent solutions of the semiclassical equations of motion. Moreover, our approach allows for an estimate of the decoherence time of a classical object due to quantum fluctuations. We illustrate our findings at the example of the Toda chain.Comment: 12 pages, some remarks added. Version to be published in J. Phys. A: Math. Ge