Azimuthal Modulational Instability of Vortices in the Nonlinear Schr\"odinger Equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize solutions.Comment: 8 pages, 6 figures, in press for Optics Communication

The UK HeartSpare study: randomised evaluation of voluntary deep-inspiratory breath-hold in women undergoing breast radiotherapy

Purpose: to determine whether voluntary deep-inspiratory breath-hold (v_DIBH) and deep-inspiratory breath-hold with the active breathing coordinator™ (ABC_DIBH) in patients undergoing left breast radiotherapy are comparable in terms of normal-tissue sparing, positional reproducibility and feasibility of delivery.Methods: following surgery for early breast cancer, patients underwent planning-CT scans in v_DIBH and ABC_DIBH. Patients were randomised to receive one technique for fractions 1–7 and the second technique for fractions 8–15 (40?Gy/15 fractions total). Daily electronic portal imaging (EPI) was performed and matched to digitally-reconstructed radiographs. Cone-beam CT (CBCT) images were acquired for 6/15 fractions and matched to planning-CT data. Population systematic (?) and random errors (?) were estimated. Heart, left-anterior-descending coronary artery, and lung doses were calculated. Patient comfort, radiographer satisfaction and scanning/treatment times were recorded. Within-patient comparisons between the two techniques used the paired t-test or Wilcoxon signed-rank test.Results: twenty-three patients were recruited. All completed treatment with both techniques. EPI-derived ? were ?1.8?mm (v_DIBH) and ?2.0?mm (ABC_DIBH) and ? ?2.5?mm (v_DIBH) and ?2.2?mm (ABC_DIBH) (all p non-significant). CBCT-derived ? were ?3.9?mm (v_DIBH) and ?4.9?mm (ABC_DIBH) and ? ??4.1?mm (v_DIBH) and ??3.8?mm (ABC_DIBH). There was no significant difference between techniques in terms of normal-tissue doses (all p non-significant). Patients and radiographers preferred v_DIBH (p?=?0.007, p?=?0.03, respectively). Scanning/treatment setup times were shorter for v_DIBH (p?=?0.02, p?=?0.04, respectively).Conclusions: v_DIBH and ABC_DIBH are comparable in terms of positional reproducibility and normal tissue sparing. v_DIBH is preferred by patients and radiographers, takes less time to deliver, and is cheaper than ABC_DIB

Accessing elite nurses for research: reflections on the theoretical and practical issues of telephone interviewing

Elite groups are interesting as they frequently are powerful (in terms of position, knowledge and influence) and enjoy considerable authority. It is important, therefore, to involve them in research concerned with understanding social contexts and processes. This is particularly pertinent in healthcare, where considerable strategic development and change are features of everyday practice that may be guided or perceived as being guided, by elites. This paper evolved from a study investigating the availability and role of nurses whose remit involved leading nursing research and development within acute NHS Trusts in two health regions in Southern England. The study design included telephone interviews with Directors of Nursing Services during which time the researchers engaged in a reflective analysis of their experiences of conducting research with an `elite' group. Important issues identified were the role of gatekeepers, engagement with elites and the use of the telephone interview method in this context. The paper examines these issues and makes a case for involving executive nurses in further research. The paper also offers strategies to help researchers design and implement telephone interview studies successfully to maximise access to the views and experiences of `hard to reach groups', such as elites, while minimising the associated disruption

Experiences of postpartum mothers and a significant other in a dyadic physical activity programme

Dyadic interventions may promote physical activity (PA) amongst postpartum mothers. However, such interventions may not always be effective, and research is needed to explore the factors influencing engagement. Amongst this population, this study explores the perceived benefits, barriers to, and facilitators of a) PA participation, and b) engagement with two dyadic PA interventions. We conducted interviews with 17 postpartum mothers and 10 significant others (aged 26–61 years old). Data were analysed with reflexive thematic analysis. Barriers to PA engagement were that it was easy to set plans, but hard to carry them out due to childcare, work, studying/chores. Setting PA plans and receiving practical support from their partner were important ways to overcome barriers to being active, e.g., some participants looked after the children, so their partner could engage in PA, as a part of their plan. Feeling motivated to exercise as a family was also a facilitator of PA. Barriers to programme participation were a lack of motivation and a preference for exercise prescription. Perceived benefits of programme participation included increased PA commitment and accountability to the plans. Amongst other techniques, participants used prompts (e.g. spouse getting their children breakfast/coming home from work/their partner ‘checking in’), as a cue to start their PA plans. Findings show that tailored interventions to address the challenges of being a postpartum mother are needed; “one-size” fits all approach does not work

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio

String Cosmology: The Pre-Big Bang Scenario

A review is attempted of physical motivations, theoretical and phenomenological aspects, as well as outstanding problems, of the pre-big bang scenario in string cosmology.Comment: 46 pages, 8 Figures, Latex, Lectures delivered in Les Houches, July 199

Massive stars as thermonuclear reactors and their explosions following core collapse

Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiescent conditions are discussed next. In the subsequent core-collapse phase, neutronization due to electron capture from the top of the Fermi sea in a degenerate core takes place. The expected signal of neutrinos from a nearby supernova is calculated. The supernova often explodes inside a dense circumstellar medium, which is established due to the progenitor star losing its outermost envelope in a stellar wind or mass transfer in a binary system. The nature of the circumstellar medium and the ejecta of the supernova and their dynamics are revealed by observations in the optical, IR, radio, and X-ray bands, and I discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry" Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure

Thermogalvanic effects on the corrosion of copper in heavy brine LiBr solutions

Thermogalvanic corrosion of copper in heavy brine LiBr solutions has been investigated using a zero-resistance ammeter (ZRA). The temperature gradients between copper electrodes immersed in the same LiBr solution result in the formation of thermogalvanic cells with hot anodes, leading to high and sustained thermogalvanic currents. Copper loss rates, calculated using Faraday's law, substantially exceed 0.025 mm year−1, a value regarded as the threshold of low corrosion rates. The effects of thermogalvanic coupling on the surface properties of the anode and the cathode have been analysed by means of electrochemical impedance spectroscopy (EIS). The results obtained in this analysis have been related to the process of copper electrodissolution in bromide media