Nonlinear heave-roll coupling and ship rolling

A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincaré mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.     

Warped products of Hadamard spaces

In the Riemannian case, our approach to warped products illuminates curvature formulas that previously seemed formal and somewhat mysterious. Moreover, the geometric approach allows us to study warped products in a much more general class of spaces. For complete metric spaces, it is known that nonpositive curvature in the Alexandrov sense is preserved by gluing on isometric closed convex subsets and by Gromov–Hausdorff limits with strictly positive convexity radius; we show it is also preserved by warped products with convex warping functions. Received: 9 January 1998/ Revised version: 12 March 1998     

Supersonic velocimetry in a shock tube using laser enhanced ionisation and planar laser induced fluorescence

 A novel flow-tagging technique is presented which was employed to measure gas velocities in the free stream of a shock tube. This method is based on the laser spectroscopic techniques of Laser-Enhanced Ionisation (LEI) and Laser-Induced Fluorescence (LIF). The flow in the shock tube is seeded with small amounts of sodium, and LEI is used to produce a substantial depletion of neutral sodium atom concentration in a well-defined region of the flow, by using two wavelength-resonance excitation and subsequent collisional ionisation. At a specific time delay, single-laser-pulse planar LIF is utilised to produce a two-dimensional (2-D) inverse image of the depleted tagged region downstream of the flow. By measuring the displacement of the tagged region, free stream velocities in a shock tube were determined. Large variations in the concentration of sodium seeded into the flow were observed and even in the presence of these large variations accurate free-stream velocity measurements were obtained. The experimentally determined value for velocity compares very well with the predicted velocity. Received: 25 March 1996/Revised version: 8 July 1996     

Gauss Equation And Injectivity Radii For Subspaces in Spaces of Curvature Bounded Above

A Gauss Equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature ⩽ A, defined by a cubic inequality on the difference of arc and chord, has intrinsic curvature ⩽ K+A². Sharp bounds on injectivity radii of subspaces, new even in the Riemannian case, are derived.     

Thermal contact between Na3[Ce(C7H3NO4)3] · 15H2O and liquid 3He at millikelvin temperatures

Very short thermal equilibrium times have been observed at millikelvin temperatures between powdered Na₃[Ce(C₇H₃NO₄)₃] · 15 H₂O, and pure ³He. Both a large increase in these times and a change in their temperature dependence occurs when 1% ⁴He. Both a large increase in these times and a change in their temperature dependence occurs when 1% ⁴He is added.     

The event horizons of two Schwarzschild black holes

The problem of two Schwarzschild black holes, one much smaller than the other, is investigated by an approximate analytic method. The critical separation between the black holes at which their event horizons join is found for two cases, (a) time-symmetric initial data, and (b) the small black hole falls from rest at infinity.     

Infrared properties of AsχTe1−χ glasses

Infrared reflection and transmission measurements in As_χTe_1?χ glasses (45?×?55) show well-defined Gaussian vibrational absorption peaks. Comparisons with spectra observed in crystalline and glassy As₂S₃ and As₂Se₃ indicate that the local order in As_χTe_1?χ glasses is not like that found in crystalline As₂Te₃, but rather it consists primarily of AsTe₃ pyramids which are probably linked together in a fashion similar to that found in As₂S₃ and As₂Se₃.     

Nuclear gamma-ray emission from antiproton annihilation at rest in uranium

We have observed low energy nuclear gamma-rays, which we interpret as coming from fission fragments, from antiproton annihilation at rest in a uranium target. The high gamma-ray and previously reported fission neutron temperatures, as well as large relative neutron-to-gamma ray yields, suggest a high level of excitation of the fission fragments.     

A determination of the mass and some energy levels of the nuclide 44Ar

The mass and some energy levels of the nuclide ⁴⁴Ar have been determined from the ⁴⁸Ca(³He, ⁷Be)⁴⁴Ar reaction. A comparison with theoretical values of the mass is made.