Nonlinear dynamic Interactions between flow-induced galloping and shell-like buckling

Acknowledgement The research of J.S. is supported by EPSRC Grant EP/J010820/1.Peer reviewedPublisher PD

Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

3D Reconstruction of a Rotating Erupting Prominence

A bright prominence associated with a coronal mass ejection (CME) was seen erupting from the Sun on 9 April 2008. This prominence was tracked by both the Solar Terrestrial Relations Observatory (STEREO) EUVI and COR1 telescopes, and was seen to rotate about the line of sight as it erupted; therefore, the event has been nicknamed the "Cartwheel CME." The threads of the prominence in the core of the CME quite clearly indicate the structure of a weakly to moderately twisted flux rope throughout the field of view, up to heliocentric heights of 4 solar radii. Although the STEREO separation was 48 degrees, it was possible to match some sharp features in the later part of the eruption as seen in the 304 {\AA} line in EUVI and in the H\alpha-sensitive bandpass of COR1 by both STEREO Ahead and Behind. These features could then be traced out in three-dimensional space, and reprojected into a view in which the eruption is directed towards the observer. The reconstructed view shows that the alignment of the prominence to the vertical axis rotates as it rises up to a leading-edge height of \approx 2.5 solar radii, and then remains approximately constant. The alignment at 2.5 solar radii differs by about 115 degrees from the original filament orientation inferred from H{\alpha} and EUV data, and the height profile of the rotation, obtained here for the first time, shows that two thirds of the total rotation is reached within \approx 0.5 solar radii above the photosphere. These features are well reproduced by numerical simulations of an unstable moderately twisted flux rope embedded in external flux with a relatively strong shear field component.Comment: published in Solar Physics (Online First

Goldstone radar observations of Mars: The 1986 opposition

Radar echoes from the planet Mars were obtained on 27 S-band (wavelength = 12.5 cm) and 2 X-band (wavelength = 3.5 cm) tracks using the Goldstone Solar System Radar. These observations took advantage of the favorable 1986 opposition since the Earth-Mars distance was 0.40 AU at opposition and radar echo strength is proportional to inverse-fourth-power of the distance to the target. The coverages of the Goldstone observations are summarized. The observations were conducted via the CW-spectra techniques described by Harmon et al. A continuous tone was transmitted at Mars and the radar echo was sampled to obtain a Doppler spread spectrum. Each received event was separated into polarized (opposite sense circular) and depolarized (same sense circular) periods. There was one successful ranging run which had a resolution of 2 microseconds. This should yield surface heights accurate to 300 meters

High resolution radar map of the Moon

Previous radar mappings of the Moon at 70 cm wavelength in the late 1960's by Thompson have been replaced with a new set of observations using the 430 MHz radar at the Arecibo Observatory, Puerto Rico. Radar resolution was reduced to 2 to 5 km radar cell size and a beam-sweep, limb-to-limb calibration was conducted. Advances in computer technology provided the principle means of improving lunar radar mapping at this wavelength. Observation techniques and data processing are described and scattering differences found in the orthographic projection of the radar data are discussed