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

Pattern formation in large domains

Pattern formation is a phenomenon that arises in a wide variety of physical, chemical and biological situations. A great deal of theoretical progress has been made in understanding the universal aspects of pattern formation in terms of amplitudes of the modes that make up the pattern. Much of the theory has sound mathematical justification, but experiments and numerical simulations over the last decade have revealed complex two-dimensional patterns that do not have a satisfactory theoretical explanation. This paper focuses on quasi-patterns, where the appearance of small divisors causes the standard theoretical method to fail, and ends with a discussion of other outstanding problems in the theory of two-dimensional pattern formation in large domains

Landform identification: Lunar radar images

Three sets of polarized radar-echo images of the Moon were examined to establish the relation between radar resolution and landform-identification resolution. After comparison with lunar maps and photographs, real and apparent landforms on the radar images were grouped into one of seven classes. Results show strong relations between radar resolution and diameter or relief of landforms that are clearly identified and those that would probably be correctly identified (class 1 and class 2). Landforms are not detected (class 5) at all diameters and reliefs, but the percentage of undetected landforms decreases with increasing mean diameter and mean relief. Landforms are simply detected (class 4) at most mean diameters and reliefs. Ambiguous arrays (class 6) portrayed by the radar constitute up to about 16, 22, and 15% of the landforms at various diameters and relief values for the 3.8 cm, 70 cm high resolution, and 70 cm low resolution images, respectively. Only a few percent of the landforms portrayed by the radar images at various diameters and relief values are fictitious (class 7)

A radar-echo model for Mars

Researchers developed a radar-echo model for Mars based on 12.6 cm continuous wave radio transmissions backscattered from the planet. The model broadly matches the variations in depolarized and polarized total radar cross sections with longitude observed by Goldstone in 1986 along 7 degrees S. and yields echo spectra that are generally similiar to the observed spectra. Radar map units in the model include an extensive cratered uplands unit with weak depolarized echo cross sections, average thermal inertias, moderate normal refelectivities, and moderate rms slopes; the volcanic units of Tharsis, Elysium, and Amazonis regions with strong depolarized echo cross sections, low thermal inertia, low normal reflectivities, and large rms slopes; and the northern planes units with moderate to strong depolarized echo cross sections, moderate to very high thermal inertias, moderate to large normal reflectivities, and moderate rms slopes. The relevance of the model to the interpretation of radar echoes from Mars is discussed

Planetary radar studies

Progress made in studying the evolution of Venusian craters and the evolution of infrared and radar signatures of lunar crater interiors is reported. Comparison of radar images of craters on Venus and the Moon present evidence for a steady state Venus crater population. Successful observations at the Arecibo Observatory yielded good data on five nights when data for a mix of inner and limb areas were acquired. Lunar craters with radar bright ejects are discussed. An overview of infrared radar crater catalogs in the data base is included