Search

We present the results of an experimental and numerical investigation into the effects of noise on pitchfork and Hopf bifurcations. Good quantitative agreement is found between calculations and experiment. In the case of the pitchfork we find that natural imperfections override the effects of the noise. However, novel noise amplification effects have been uncovered in the study of the Hopf bifurcation. These destroy the critical event found in the noise‐free case and could be of considerable practical importance in systems containing dynamic bifurcations.

In this paper we describe three algorithms for estimating the spectrum of Liapunov exponents, which we have found to be robust and reasonably accurate when used in practical circumstances. Attention is focussed on least squares and total least squares methods for estimating tangent maps from time series data. The properties of the algorithms are demonstrated by application to a range of data sets: we consider numerical and experimental data, and discuss the effect of additive noise and system noise on the proposed methods.

We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number (Re) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re. This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

The High Resolution Dynamics Limb Sounder (HIRDLS) instrument is being built jointly by the UK and USA, and is scheduled for launch on the NASA EOS Chem satellite in 2002. HIRDLS will measure the concentration of trace species and aerosol, and temperature and pressure variations in the Earth's atmosphere between about 8 and 100 km altitude. It is an infrared limb emission sounder, and a primary aim is that it should measure to much finder spatial resolution than has previously been achieved, with simultaneous 1 km vertical and 500 km horizontal resolutions, globally, every 12 hours. Achieving these objectives will depend upon very precise pre-launch calibration. This will be undertaken at Oxford University in a test laboratory that is currently being constructed specifically for the task. The instrument will be surrounded by cryogenically cooled walls, and mounted together with the test equipment on an optical table contained in a vacuum chamber. The table will be mounted independently of the chamber, on an inertial mass supported on pneumatic isolators. Test equipment is being manufactured to measure (1) the radiometric response (with an absolute accuracy equivalent to 70 mK) using full aperture black body targets, (2) the spectral response of each of the filter channels using a grating monochromator, (3) the spatial response of the instrument field of view, including low level out-of-field contributions, to 10 (mu) rad accuracy using a monochromator. The methods and equipment used are described together with the principal requirements.

The reconstruction of a phase space using the method of delays and singular value decomposition is discussed. These procedures are applied to data from both experiments and numerical simulations. It is then shown how computer graphics techniques may be employed in the representation of phase portraits to clarify their topological structure.

Active current sheets or diamagnetic cavities in the solar wind have been observed both by the AMPTE-UKS spacecraft on a number of occasions, and independently from ISEE by Thomsen et al /1/. Preliminary results from one of these UKS observations have been discussed recently by Schwartz et al /2/. In this paper we consider these phenomena in more detail. Results are presented for the position of five events. High resolution plasma data and plasma wave activity associated with these current sheets are examined.

Selected events of plasma wave and electromagnetic emissions in the earth's electron fore-shock region have been studied. Strong emissions are observed in the plasma-wave band when the site of the satellite is magnetically connected to the bow shock. These emissions are generally highly fluctuating. Under certain conditions one observes electromagnetic radiation at the second harmonic produced locally. Electromagnetic emission generated at a position far away from the site of the spacecraft is occasionally detected giving rise to remote sensing of the bow shock. These emissions are related to energetic electron fluxes.

The plasma wave receiver on the AMPTE UKS has sensors for measuring magnetic (100 Hz < f < 60 kHz) and electric (100 Hz < f < 3 MHz) components of the wavefield. These are connected to a stepped-frequency analyzer and an autocorrelator. Additionally, the electric sensor is connected to four fixed-frequency filters. The signal processing elements are controlled by a microprocessor to give flexibility in operation.

The AMPTE barium ion release in the solar wind at 1232 UT on 27 December 1984 produced strong electric component plasma wave noise at frequencies below 3.9 kHz (amongst other emissions) which was detected at both the AMPTE-UKS and AMPTE-IRM spacecraft. In the region outside the magnetic cavity, this noise appears to be correlated with electron heating and changes sin the magnetic field. This paper compares data from the two spacecraft at high temporal resolution in order to identify the waves and the associated processes.

We present the results of an experimental investigation of intermittency in the flow between concentric cylinders where three of the four containing walls rotate. Intermittency of type 1 has been found together with a novel form which involves the interaction with another singularity.

The wave measurements from the Ion Release Module and the United Kingdom Satellite in the diamagnetic cavity, the transition region, and the upstream region are examined. Solar wind conditions during the releases on September 11 and 20, 1984 are described. The quasi-static electric field, wideband, high-frequency waves, and medium and VLF waves observations are analyzed. The data reveal that extremely low levels of wave activity are observed in the boundary between the diamagnetic cavity and external magnetic field, medium and VLF waves in the ion acoustic electrostatic cyclotron harmonic modes are detected in the transition region from the diamagnetic cavity to the solar wind, and decay in the magnetic field strength and density, and an increase in the quasi-static electric field is seen in the upstream edge of the transition region. The emissions observed are related to the different phases of the Li cloud development and different spatial regimes of the Li plasma-solar wind interaction.