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

SCUBA polarisation observations of the magnetic fields in the prestellar cores L1498 and L1517B

We have mapped linearly polarized dust emission from the prestellar cores L1498 and L1517B with the James Clerk Maxwell Telescope (JCMT) using the Submillimetre Common User Bolometer Array (SCUBA) and its polarimeter SCUBAPOL at a wavelength of 850um. We use these measurements to determine the plane-of-sky magnetic field orientation in the cores. In L1498 we see a magnetic field across the peak of the core that lies at an offset of 19 degrees to the short axis of the core. This is similar to the offsets seen in previous observations of prestellar cores. To the southeast of the peak, in the filamentary tail of the core, we see that the magnetic field has rotated to lie almost parallel to the long axis of the filament. We hypothesise that the field in the core may have decoupled from the field in the filament that connects the core to the rest of the cloud. We use the Chandrasekhar-Fermi (CF) method to measure the plane-of-sky field strength in the core of L1498 to be 10 +/- 7 uG. In L1517B we see a more gradual turn in the field direction from the northern part of the core to the south. This appears to follow a twist in the filament in which the core is buried, with the field staying at a roughly constant 25 degree offset to the short axis of the filament, also consistent with previous observations of prestellar cores. We again use the CF method and calculate the magnetic field strength in L1517B also to be 30 +/- 10 uG. Both cores appear to be roughly virialised. Comparison with our previous work on somewhat denser cores shows that, for the denser cores, thermal and non-thermal (including magnetic) support are approximately equal, while for the lower density cores studied here, thermal support dominates.Comment: 6 pages, 2 figures; accepted for publication by MNRA

A search for debris disks in the Herschel-ATLAS

Aims. We aim to demonstrate that the Herschel-ATLAS (H-ATLAS) is suitable for a blind and unbiased survey for debris disks by identifying candidate debris disks associated with main sequence stars in the initial science demonstration field of the survey. We show that H-ATLAS reveals a population of far-infrared/sub-mm sources that are associated with stars or star-like objects on the SDSS main-sequence locus. We validate our approach by comparing the properties of the most likely candidate disks to those of the known population. Methods. We use a photometric selection technique to identify main sequence stars in the SDSS DR7 catalogue and a Bayesian Likelihood Ratio method to identify H-ATLAS catalogue sources associated with these main sequence stars. Following this photometric selection we apply distance cuts to identify the most likely candidate debris disks and rule out the presence of contaminating galaxies using UKIDSS LAS K-band images. Results. We identify 78 H-ATLAS sources associated with SDSS point sources on the main-sequence locus, of which two are the most likely debris disk candidates: H-ATLAS J090315.8 and H-ATLAS J090240.2. We show that they are plausible candidates by comparing their properties to the known population of debris disks. Our initial results indicate that bright debris disks are rare, with only 2 candidates identified in a search sample of 851 stars. We also show that H-ATLAS can derive useful upper limits for debris disks associated with Hipparcos stars in the field and outline the future prospects for our debris disk search programme

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

A modified R1 X R1 method for helioseismic rotation inversions

We present an efficient method for two dimensional inversions for the solar rotation rate using the Subtractive Optimally Localized Averages (SOLA) method and a modification of the R1 X R1 technique proposed by Sekii (1993). The SOLA method is based on explicit construction of averaging kernels similar to the Backus-Gilbert method. The versatility and reliability of the SOLA method in reproducing a target form for the averaging kernel, in combination with the idea of the R1 X R1 decomposition, results in a computationally very efficient inversion algorithm. This is particularly important for full 2-D inversions of helioseismic data in which the number of modes runs into at least tens of thousands.Comment: 12 pages, Plain TeX + epsf.tex + mn.te

Prospects for computational steering of evolutionary computation

Currently, evolutionary computation (EC) typically takes place in batch mode: algorithms are run autonomously, with the user providing little or no intervention or guidance. Although it is rarely possible to specify in advance, on the basis of EC theory, the optimal evolutionary algorithm for a particular problem, it seems likely that experienced EC practitioners possess considerable tacit knowledge of how evolutionary algorithms work. In situations such as this, computational steering (ongoing, informed user intervention in the execution of an otherwise autonomous computational process) has been profitably exploited to improve performance and generate insights into computational processes. In this short paper, prospects for the computational steering of evolutionary computation are assessed, and a prototype example of computational steering applied to a coevolutionary algorithm is presented