Four bugs on a rectangle

The problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10^427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth’s double-arrow notation and level-index arithmetic are discussed

Asymptotic analysis of a system of algebraic equations arising in dislocation theory

The system of algebraic equations given by\ud \ud $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$\ud \ud appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole.\ud \ud We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n -> ∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment but, up to corrections of logarithmic order, it also leads to a differential equation.\ud \ud The continuum approximation is only valid for i not too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem

Transformation of scientists and engineers into managers

The purposes of this research were to determine the principal problems and obstacles faced by specialists during the transition period when they are becoming managers, and to discover ways by which their difficulties might be avoided or overcome. It was found that senior management officials are unaware--or tend to ignore the importance--of the transition process and its problems, that little attention has been given to developing management training to overcome transition problems, and that much of the training which is offered is largely irrelevant to these problems

Experimental performance of an ablative material as an external insulator for a hypersonic research aircraft

An ablative material composed of silica-filled elastomeric silicone was tested to evaluate its thermal and structural performance as an external insulator, or heat shield, for a hypersonic research aircraft. The material was also tested to determine whether it would form a durable char layer when initially heated and thereafter function primarily as an insulator with little further pyrolysis or char removal. Aerothermal tests were representative of nominal Mach 6 cruise conditions of the aircraft, and additional tests were representative of Mach 8 cruise and interference heating conditions. Radiant heating tests were used to simulate the complete nominal Mach 6 surface-temperature history. The silica char that formed during aerothermal tests was not durable. The char experienced a general and preferential surface recession, with the primary mechanism for char removal being erosion. Tests revealed that radiant heating is not a valid technique for simulating aerodynamic heating of the material

Propagation of a laser beam in a plasma

This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Application of shock tubes to transonic airfoil testing at high Reynolds numbers

Performance analysis of a gas-driven shock tube shows that transonic airfoil flows with chord Reynolds numbers of the order of 100 million can be produced, with limitations being imposed by the structural integrity of the facility or the model. A study of flow development over a simple circular arc airfoil at zero angle of attack was carried out in a shock tube at low and intermediate Reynolds numbers to assess the testing technique. Results obtained from schlieren photography and airfoil pressure measurements show that steady transonic flows similar to those produced for the same airfoil in a wind tunnel can be generated within the available testing time in a shock tube with properly contoured test section walls

Investigating the Martian atmosphere using the ExoMars 2016 lander

Accurate modelling of the Martian atmosphere is essential both for planning and completing future missions to the Martian surface, and for accurate analysis and interpretation of the data that they return. Large dust storms and local wind patterns can affect spacecraft landing profiles, and the level of dust present in the atmosphere may impact lander performance. The ExoMars 2016 Mission will carry an Entry, Descent and Landing Demonstrator Module (EDM), primarily designed to test the ability of ESA’s lander technology to carry a science package to the surface [1]. The Atmospheric Mars Entry and Landing Investigations and Analysis (AMELIA) team [2] will use the module’s entry and descent trajectory to characterise the structure of the atmosphere along the travelled landing profile, and to determine properties of the atmosphere, such as density and wind speed, over a wide altitude range from the upper atmosphere to the surface. Aerosol abundances, including atmospheric dust, will also be characterised. These combined datasets will enable more accurate predictions of the atmospheric environment that future landers will encounter. EDM’s surface science package, DREAMS (Dust characterisation, Risk assessment, and Environment Analyser on the Martian Surface), includes sensors to measure wind speed and direction, surface temperature, pressure, and the amount of atmospheric dust present near the surface [3]. We will use the descent and surface profile data collected by EDM to verify and improve current Martian atmospheric modelling completed at The Open University, using both the global circulation and mesoscale models. [1] Forget et al. (2011) Fourth International Workshop on the Mars Atmosphere: Modeling and Observations, Paris. [2] Ferri et al. (2012) 9th International Planetary Probe Workshop (IPPW9), Toulouse. [3] Esposito et al. (2013) EPSC Abstracts Vol. 8, EPSC2013-815