Pattern forming pulled fronts: bounds and universal convergence

We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v^*. We discuss a method that allows to derive bounds on the front velocity, and which hence can be used to prove for, among others, the Swift-Hohenberg equation, the Extended Fisher-Kolmogorov equation and the cubic Complex Ginzburg-Landau equation, that the dynamically relevant fronts are of the pulled type. In addition, we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts. The analysis is based on a matching analysis of the dynamics in the leading edge of the front, to the behavior imposed by the nonlinear region behind it. Numerical simulations of fronts in the Swift-Hohenberg equation are in full accord with our analytical predictions.Comment: 27 pages, 9 figure

Tracking Streamer Blobs Into the Heliosphere

In this paper, we use coronal and heliospheric images from the STEREO spacecraft to track streamer blobs into the heliosphere and to observe them being swept up and compressed by the fast wind from low-latitude coronal holes. From an analysis of their elongation/time tracks, we discover a 'locus of enhanced visibility' where neighboring blobs pass each other along the line of sight and their corotating spiral is seen edge on. The detailed shape of this locus accounts for a variety of east-west asymmetries and allows us to recognize the spiral of blobs by its signatures in the STEREO images: In the eastern view from STEREO-A, the leading edge of the spiral is visible as a moving wavefront where foreground ejections overtake background ejections against the sky and then fade. In the western view from STEREO-B, the leading edge is only visible close to the Sun-spacecraft line where the radial path of ejections nearly coincides with the line of sight. In this case, we can track large-scale waves continuously back to the lower corona and see that they originate as face-on blobs.Comment: 15 pages plus 11 figures; figure 6 shows the 'locus of enhanced visibility', which we call 'the bean'. (accepted by ApJ 4/02/2010

Used-habitat calibration plots: a new procedure for validating species distribution, resource selection, and step-selection models

“Species distribution modeling” was recently ranked as one of the top five “research fronts” in ecology and the environmental sciences by ISI's Essential Science Indicators (Renner and Warton 2013), reflecting the importance of predicting how species distributions will respond to anthropogenic change. Unfortunately, species distribution models (SDMs) often perform poorly when applied to novel environments. Compounding on this problem is the shortage of methods for evaluating SDMs (hence, we may be getting our predictions wrong and not even know it). Traditional methods for validating SDMs quantify a model's ability to classify locations as used or unused. Instead, we propose to focus on how well SDMs can predict the characteristics of used locations. This subtle shift in viewpoint leads to a more natural and informative evaluation and validation of models across the entire spectrum of SDMs. Through a series of examples, we show how simple graphical methods can help with three fundamental challenges of habitat modeling: identifying missing covariates, non-linearity, and multicollinearity. Identifying habitat characteristics that are not well-predicted by the model can provide insights into variables affecting the distribution of species, suggest appropriate model modifications, and ultimately improve the reliability and generality of conservation and management recommendations