Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Integrated control system for a gas turbine engine

A control system for a turbofan engine receives signals from a number of engine sensors and from the engine operator, and generates control signals. One control signal regulates the fan exhaust nozzle area in order to control inlet throat Mach number to maintain a low level of engine noise. Additional control signals regulate fuel flow to control engine thrust and fan pitch to control fan speed. A number of schedules are utilized to maintain a predetermined relationship between the controlled parameters and a number of fixed and calculated limits can override the control signals to prevent unsatisfactory engine performance

Spin Freezing in Geometrically Frustrated Antiferromagnets with Weak Disorder

We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbour exchange on the pyrochlore lattice, we examine low-temperature behaviour. We show that random exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random strains in the presence of magnetoelastic coupling, may account for the spin freezing observed in many geometrically frustrated magnets.Comment: 4 pages, 5 figure

Immune cells and preterm labour:do invariant NKT cells hold the key?

We have developed our original made-to-measure (M2M) algorithm, PRIMAL, with the aim of modelling the Galactic disc from upcoming Gaia data. From a Milky Way like N-body disc galaxy simulation, we have created mock Gaia data using M0III stars as tracers, taking into account extinction and the expected Gaia errors. In PRIMAL, observables calculated from the N-body model are compared with the target stars, at the position of the target stars. Using PRIMAL, the masses of the N-body model particles are changed to reproduce the target mock data, and the gravitational potential is automatically adjusted by the changing mass of the model particles. We have also adopted a new resampling scheme for the model particles to keep the mass resolution of the N-body model relatively constant. We have applied PRIMAL to this mock Gaia data and we show that PRIMAL can recover the structure and kinematics of a Milky Way like barred spiral disc, along with the apparent bar structure and pattern speed of the bar despite the galactic extinction and the observational errors

The energy efficient engine project

The Energy Efficient Engine Project is directed at providing, by 1984, the advanced technologies which could be used for a generation of fuel conservative turbofan engines. The project is conducted through contracts with the General Electric Company and Pratt and Whitney Aircraft. The scope of the entire project and the current status of these efforts are summarized. A description of the preliminary designs of the fully developed engines is included and the potential benefits of these advanced engines, as well as highlights of some of the component technology efforts conducted to date, are discussed

The average magnetic field draping and consistent plasma properties of the Venus magnetotail

A new technique has been developed to determine the average structure of the Venus magnetotail (in the range from −8 Rv to −12 Rv) from the Pioneer Venus magnetometer observations. The spacecraft position with respect to the cross-tail current sheet is determined from an observed relationship between the field-draping angle and the magnitude of the field referenced to its value in the nearby magnetosheath. This allows us statistically to remove the effects of tail flapping and variability of draping for the first time and thus to map the average field configuration in the Venus tail. From this average configuration we calculate the cross-tail current density distribution and J × B forces. Continuity of the tangential electric field is utilized to determine the average variations of the X-directed velocity which is shown to vary from −250 km/s at −8 Rv to −470 km/s at −12 Rv. From the calculated J × B forces, plasma velocity, and MHD momentum equation the approximate plasma acceleration, density, and temperature in the Venus tail are determined. The derived ion density is approximately ∼0.07 p+/cm³ (0.005 O+/cm³) in the lobes and ∼0.9 p+/cm³ (0.06 O+/cm³) in the current sheet, while the derived approximate average plasma temperature for the tail is ∼6×106 K for a hydrogen plasma or ∼9×107 K for an oxygen plasma

Experimental radio frequency link for Ka-band communications applications

An experimental radio frequency link has been demonstrated to provide two-way communication between a remote user ground terminal and a ground-based Ka-band transponder. Bit-error-rate performance and radio frequency characteristics of the communication link were investigated

Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabling more accurate, efficient data capture. The complex nature of these data streams in combination with challenge of deriving meaning from missing data mean pose a significant analytic challenge. The signature method is derived from stochastic analysis and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.Comment: 12 pages, 3 tables, 10 figure

A physics-based life prediction methodology for thermal barrier coating systems

A novel mechanistic approach is proposed for the prediction of the life of thermal barrier coating (TBC) systems. The life prediction methodology is based on a criterion linked directly to the dominant failure mechanism. It relies on a statistical treatment of the TBC's morphological characteristics, non-destructive stress measurements and on a continuum mechanics framework to quantify the stresses that promote the nucleation and growth of microcracks within the TBC. The last of these accounts for the effects of TBC constituents' elasto-visco-plastic properties, the stiffening of the ceramic due to sintering and the oxidation at the interface between the thermally insulating yttria stabilized zirconia (YSZ) layer and the metallic bond coat. The mechanistic approach is used to investigate the effects on TBC life of the properties and morphology of the top YSZ coating, metallic low-pressure plasma sprayed bond coat and the thermally grown oxide. Its calibration is based on TBC damage inferred from non-destructive fluorescence measurements using piezo-spectroscopy and on the numerically predicted local TBC stresses responsible for the initiation of such damage. The potential applicability of the methodology to other types of TBC coatings and thermal loading conditions is also discussed