On the stability of travelling waves with vorticity obtained by minimisation

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimisation of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimisation appears in Burton and Toland after a first maximisation). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea

Evidence for view-invariant Face Recognition Units in unfamiliar face learning

Many models of face recognition incorporate the idea of a face recognition unit (FRU). This is an abstracted representation formed from each experience of a face. Longmore et al. (2008) devised a face learning experiment to investigate such a construct (i.e., view-invariance) but failed to find evidence of its existence. Three experiments developed Longmore et al.’s study further by using a different learning task, by employing more stimuli. One or two views of previously unfamiliar faces were shown to participants in a serial matching task (learning). Later, participants attempted to recognise both seen and novel views of the learned faces. Experiment one tested participants’ recognition of a novel view, a day after learning. Experiment two was identical, but tested participants on the same day as learning. And experiment three repeated experiment one, but tested participants on a novel view that was outside the rotation of those views learned. Results revealed a significant advantage for recognising a novel view when two views had been learned, rather than a single learned view – for all experiments. The effect of view-invariance found when both views were learned is discussed

Doppler lidar observations of sensible heat flux and intercomparisons with a ground-based energy balance station and WRF model output

This is an open access article - Copyright @ 2009 E. Schweizerbart'sche VerlagsbuchhandlungDuring the Convective and Orographically induced Precipitation Study (COPS), a scanning Doppler lidar was deployed at Achern, Baden-Wüttemberg, Germany from 13th June to 16th August 2007. Vertical velocity profiles ('rays') through the boundary layer were measured every 3 seconds with vertical profiles of horizontal wind velocity being derived from performing azimuth scans every 30 minutes. During Intense Observation Periods radiosondes were launched from the site. In this paper, a case study of convective boundary layer development on 15th July 2007 is investigated. Estimates of eddy dissipation rate are made from the vertically pointing lidar data and used as one input to the velocity-temperature co-variance equation to estimate sensible heat flux. The sensible heat flux values calculated from Doppler lidar data are compared with a surface based energy balance station and output from the Weather Research and Forecasting (WRF) model.Funding is obtained from NER

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

We grew SrTiO3 on SrTiO3 (001) by pulsed laser deposition, using x-ray scattering to monitor the growth in real time. The time-resolved small angle scattering exhibits a well-defined length scale associated with the spacing between unit cell high surface features. This length scale imposes a discrete spectrum of Fourier components and rate constants upon the diffusion equation solution, evident in multiple exponential relaxation of the "anti-Bragg" diffracted intensity. An Arrhenius analysis of measured rate constants confirms that they originate from a single activation energy.Comment: 4 pages, 3 figure

Statistics of Ku-band microwave response of the United States with a satellite borne radiometer/scatterometer

The author has identified the following significant results. The Skylab S-193 radiometer/scatterometer collected thousands of measurements of scattering coefficient and brightness temperature over various parts of the United States during the summer of 1973 at angles of incidence between vertical and about 45 deg. These measurements have been combined to produce histograms of the response at each of several angles within this range, and to establish average scattering coefficient vs angle curves with 10% and 90% exceedance levels as well. The variation of the radiometric measurements is primarily in the region from 255 K to 285 K, with very few measurements giving higher values, but a significant, though small, number giving values down to and even below 200 K. The scattering coefficient varies, for the mean, from about 0 db at 1 deg off vertical to a low in the neighborhood of -10 db at 45 deg. The variability of the scattering coefficient measurements with this coarse resolution sensor is surprisingly small. The number of distinguishable levels is slightly more for the scatterometer than for the radiometer, but the amount of variation in brightness temperature caused by the physical temperature of the ground is enough so that the scatterometer can be used to distinguish significantly more meaningful levels than the radiometer

Percolation and number of phases in the 2D Ising model

We reconsider the percolation approach of Russo, Aizenman and Higuchi for showing that there exist only two phases in the Ising model on the square lattice. We give a fairly short alternative proof which is only based on FKG monotonicity and avoids the use of GKS-type inequalities originally needed for some background results. Our proof extends to the Ising model on other planar lattices such as the triangular and honeycomb lattice. We can also treat the Ising antiferromagnet in an external field and the hard-core lattice gas model on $Z^2$.Comment: 22 pages. Further details on extensions. To appear in J.Math.Phys., special issue on `Probabilistic Methods in Statistical Physics', March 200

The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a crossover region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram

Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin