Propagation of the First Flames in Type Ia Supernovae

We consider the competition of the different physical processes that can affect the evolution of a flame bubble in a Type Ia supernovae -- burning, turbulence and buoyancy. Even in the vigorously turbulent conditions of a convecting white dwarf, thermonuclear burning that begins at a point near the center (within 100 km) of the star is dominated by the spherical laminar expansion of the flame, until the burning region reaches kilometers in size. Consequently flames that ignite in the inner ~20 km promptly burn through the center, and flame bubbles anywhere must grow quite large--indeed, resolvable by large-scale simulations of the global system--for significant motion or deformation occur. As a result, any hot-spot that successfully ignites into a flame can burn a significant amount of white dwarf material. This potentially increases the stochastic nature of the explosion compared to a scenario where a simmering progenitor can have small early hot-spots float harmlessly away. Further, the size where the laminar flame speed dominates other relevant velocities sets a characteristic scale for fragmentation of larger flame structures, as nothing--by definition--can easily break the burning region into smaller volumes. This makes possible the development of semi-analytic descriptions of the earliest phase of the propagation of burning in a Type Ia supernovae, which we present here. Our analysis is supported by fully resolved numerical simulations of flame bubbles.Comment: 33 pages, 14 figures, accepted for publication in Ap

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case

Feeling good about being hungry: food-related thoughts in eating disorder

Objectives: This study explores the relationships to food and hunger in women living with anorexic type eating difficulties and asks how imagery-based elaborations of food and eating thoughts are involved in their eating restraint, and recovery. Design: The qualitative idiographic approach of Interpretative Phenomenological Analysis (IPA) was used. Four in-depth semi-structured interviews were conducted with women self-selected as having experienced anorexia or anorexic like behaviour. Methods: The data was analysed using IPA and an audit of the analysis was conducted to ensure that the process followed had been systematic and rigorous and appropriately considered reflexivity. Results: Hunger was perceived positively by participants as confirmation that they were achieving their goal of losing weight, or avoiding weight gain. Hunger conferred a sense of being in control for the participants. Intrusive thoughts about food were reported as being quickly followed by elaborative mental imagery of the positive aspects of weight loss, and the negative consequences of eating. Imagery appeared to serve to maintain anorexic behaviours rather than to motivate food seeking. However, negative imagery of the consequences of anorexia were also described as supporting recovery. Conclusions: The finding that physiological sensations of hunger were experienced as positive confirmation of maintaining control has potentially important clinical and theoretical implications. It suggests further attention needs to be focused upon how changes in cognitive elaboration, involving mental imagery, are components of the psychological changes in the development of, maintenance of, and recovery from, anorexia

Effects of Electron Correlations on Hofstadter Spectrum

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.Comment: 13 pages, 5 Postscript figure

In-line and cascaded DWDM transmission using a 15dB net-gain polarization-insensitive fiber optical parametric amplifier

We demonstrate and characterize polarization-division multiplexed (PDM) DWDM data transmission for the first time in a range of systems incorporating a net-gain polarization-insensitive fiber optical parametric amplifier (PI-FOPA) for loss compensation. The PI-FOPA comprises a modified diversity-loop architecture to achieve 15dB net-gain, and up to 2.3THz (~18nm) bandwidth. Three representative systems are characterized using a 100Gb/s PDM-QPSK signal in conjunction with emulated DWDM neighbouring channels: (a) a 4x75km in-line fiber transmission system incorporating multiple EDFAs and a single PI-FOPA (b) N cascaded PI-FOPA amplification stages in an unlevelled Nx25km recirculating loop arrangement, with no EDFAs used within the loop signal path, and (c) M cascaded PI-FOPA amplification stages as part of an Mx75.6km gain-flattened recirculating loop system with the FOPA compensating for the transmission fiber loss, and EDFA compensation for loop switching and levelling loss. For the 4x75km in-line system (a), we transmit 45x50GHz-spaced signals (‘equivalent’ data-rate of 4.5Tb/s) with average OSNR penalty of 1.3dB over the band at 10−3 BER. For the unlevelled ‘FOPA-only’ 25.2km cascaded system (b), we report a maximum of eight recirculations for all 10x100GHz-spaced signals, and five recirculations for 20x50GHz-spaced signals. For the 75.6km levelled system (c), we achieve eight recirculations for all 20x50GHz signals resulting in a total transmission distance of 604.8km

Dealing with mobility: Understanding access anytime, anywhere

The rapid and accelerating move towards the adoption and use of mobile technologies has increasingly provided people and organisations with the ability to work away from the office and on the move. The new ways of working afforded by these technologies are often characterised in terms of access to information and people ‘anytime, anywhere’. This paper presents a study of mobile workers that highlights different facets of access to remote people and information, and different facets of anytime, anywhere. Four key factors in mobile work are identified from the study: the role of planning, working in ‘dead time’, accessing remote technological and informational resources, and monitoring the activities of remote colleagues. By reflecting on these issues, we can better understand the role of technology and artefact use in mobile work and identify the opportunities for the development of appropriate technological solutions to support mobile workers

Boundedness, compactness and Schatten-class membership of weighted composition operators

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces $\mathcal{A}^2 \alpha(\mathbb{D})$ are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.Comment: 12 page

Thermal boundary conditions on western Greenland: Observational constraints and impacts on the modeled thermomechanical state

The surface and basal boundary conditions exert an important control on the thermodynamic state of the Greenland Ice Sheet, but their representation in numerical ice sheet models is poorly constrained due to the lack of observations. Here we investigate a land-terminating sector of western Greenland and (1) quantify differences between new observations and commonly used boundary condition data sets and (2) demonstrate the impact of improved boundary conditions on simulated thermodynamics in a higher-order numerical flow model. We constrain near-surface temperature with measurements from two 20mboreholes in the ablation zone and 10m firn temperature from the percolation zone. We constrain basal heat flux using in situ measurement in a deep bedrock hole at the study area margin and other existing assessments. To assess boundary condition influences on simulated thermal-mechanical processes, we compare model output to multiple full-thickness temperature profiles collected in the ablation zone.Our observation-constrained basal heat flux is 30mW m2 less than commonly used representations. In contract, measured near-surface temperatures are warmed than common surface warmer than common surface temperature data sets by up to 15 degrees C. Application of lower basal heat flux increases a model cold bias compared to the measured temperature profiles and causes frozen basal conditions across the ablation zone. Temperate basal conditions are reestablished by our warmer surface boundary. Warmer surface ice and firn can introduce several times more energy to the modeled ice mass than what is lost at the bed from reduced basal heat flux, indicating that the thermomechanical state of the ice sheet is highly sensitive to near-surface effects

On semiclassical dispersion relations of Harper-like operators

We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied for the case of integer flux. We derive asymptotic formula for the dispersion relations, the width of bands and gaps, and show how geometric characteristics and the absence of symmetries of the Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004

Semiclassical theory for small displacements

Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However, knowledge of a finite number of moments does not allow for accurate determination of the chord function. For pure states this provides the overlap of the state with all its possible rigid translations (or displacements). We here present a semiclassical approximation of the chord function for large Bohr-quantized states, which is accurate right up to a caustic, beyond which the chord function becomes evanescent. It is verified to pick out blind spots, which are displacements for zero overlaps. These occur even for translations within a Planck area of the origin. We derive a simple approximation for the closest blind spots, depending on the Schroedinger covariance matrix, which is verified for Bohr-quantized states.Comment: 16 pages, 4 figures