A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Triumph Of Freedom

https://digitalcommons.library.umaine.edu/mmb-vp/6630/thumbnail.jp

Defining correctness conditions for concurrent objects in multicore architectures

Correctness of concurrent objects is defined in terms of conditions that determine allowable relationships between histories of a concurrent object and those of the corresponding sequential object. Numerous correctness conditions have been proposed over the years, and more have been proposed recently as the algorithms implementing concurrent objects have been adapted to cope with multicore processors with relaxed memory architectures. We present a formal framework for defining correctness conditions for multicore architectures, covering both standard conditions for totally ordered memory and newer conditions for relaxed memory, which allows them to be expressed in uniform manner, simplifying comparison. Our framework distinguishes between order and commitment properties, which in turn enables a hierarchy of correctness conditions to be established. We consider the Total Store Order (TSO) memory model in detail, formalise known conditions for TSO using our framework, and develop sequentially consistent variations of these. We present a work-stealing deque for TSO memory that is not linearizable, but is correct with respect to these new conditions. Using our framework, we identify a new non-blocking compositional condition, fence consistency, which lies between known conditions for TSO, and aims to capture the intention of a programmer-specified fence

The Narrow Line Region: Current Models and Future Questions

I present a broad overview of modelling of the Narrow Line Region (NLR) of active galaxies, and discuss some of the more recent models we currently have for the emission from the NLR. I show why the emission line ratios from the NLR are constrained to certain observed values, and describe what physical parameters we can derive from observations using emission line models. Also presented are some examples of this, looking at the metallicity and excitation mechanism of active galaxies. As a final point, the limitations of the current models are discussed, and how how the combination of modelling and theory can help us solve some of the questions that still remain within the NLR

Arkansas Cotton Variety Test 2003

The primary aim of the Arkansas Cotton Variety Test is to provide unbiased data regarding the agronomic performance of cotton varieties and advanced breeding lines in the major cotton-growing areas of Arkansas. This information helps seed dealers establish marketing strategies and assists producers in choosing varieties to plant. In this way, the annual test facilitates the inclusion of new, improved genetic material in Arkansas cotton production

Characterizing spiral arm and interarm star formation

Interarm star formation contributes significantly to a galaxy's star formation budget, and provides an opportunity to study stellar birthplaces unperturbed by spiral arm dynamics. Using optical integral field spectroscopy of the nearby galaxy NGC 628 with VLT/MUSE, we construct Halpha maps including detailed corrections for dust extinction and stellar absorption to identify 391 HII regions at 35pc resolution over 12 kpc^2. Using tracers sensitive to the underlying gravitational potential, we associate HII regions with either arm (271) or interarm (120) environments. Using our full spectral coverage of each region, we find that most HII region physical properties (luminosity, size, metallicity, ionization parameter) are independent of environment. We calculate the fraction of Halpha luminosity due to the diffuse ionized gas (DIG) background contaminating each HII region, and find the DIG surface brightness to be higher within HII regions compared to the surroundings, and slightly higher within arm HII regions. Use of the temperature sensitive [SII]/Halpha line ratio map instead of the Halpha surface brightness to identify HII region boundaries does not change this result. Using the dust attenuation as a tracer of the gas, we find depletion times consistent with previous work (2 x 10^9 yr) with no differences between the arm and interarm, however this is very sensitive to the DIG correction. Unlike molecular clouds, which can be dynamically affected by the galactic environment, we see fairly consistent HII region properties in both arm and interarm environments. This suggests either a difference in arm star formation and feedback, or a decoupling of dense star forming clumps from the more extended surrounding molecular gas.Comment: 10 pages, 4 figures, 1 table, accepted for publication in Ap

Dust in dwarf galaxies: The case of NGC 4214

We have carried out a detailed modelling of the dust heating and emission in the nearby, starbursting dwarf galaxy NGC 4214. Due to its proximity and the great wealth of data from the UV to the millimeter range (from GALEX, HST, {\it Spitzer}, Herschel, Planck and IRAM) it is possible to separately model the emission from HII regions and their associated photodissociation regions (PDRs) and the emission from diffuse dust. Furthermore, most model parameters can be directly determined from the data leaving very few free parameters. We can fit both the emission from HII+PDR regions and the diffuse emission in NGC 4214 with these models with "normal" dust properties and realistic parameters.Comment: 4pages, 3 figures. To appear in 'The Spectral Energy Distribution of Galaxies' Proceedings IAU Symposium No 284, 201

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set of minimisers as a whole. `Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.Comment: 83 pages, 1 figur