21,371 research outputs found
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
A kinetic model of radiating electrons
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of phase space. The pathological solutions of the 1-particle theory may be removed by expanding the latter equation in powers of τ ≔ q 2/6πm. The radiation-induced change in entropy is explored and its physical origin is discussed. As a simple demonstration of the theory, the radiative damping rate of longitudinal plasma waves is calculated
Mapping warm molecular hydrogen with Spitzer's Infrared Array Camera (IRAC)
Photometric maps, obtained with Spitzer's Infrared Array Camera (IRAC), can
provide a valuable probe of warm molecular hydrogen within the interstellar
medium. IRAC maps of the supernova remnant IC443, extracted from the Spitzer
archive, are strikingly similar to spectral line maps of the H2 pure rotational
transitions that we obtained with the Infrared Spectrograph (IRS) instrument on
Spitzer. IRS spectroscopy indicates that IRAC Bands 3 and 4 are indeed
dominated by the H2 v=0-0 S(5) and S(7) transitions, respectively. Modeling of
the H2 excitation suggests that Bands 1 and 2 are dominated by H2 v=1-0 O(5)
and v=0-0 S(9). Large maps of the H2 emission in IC433, obtained with IRAC,
show band ratios that are inconsistent with the presence of gas at a single
temperature. The relative strengths of IRAC Bands 2, 3, and 4 are consistent
with pure H2 emission from shocked material with a power-law distribution of
gas temperatures. CO vibrational emissions do not contribute significantly to
the observed Band 2 intensity. Assuming that the column density of H2 at
temperatures T to T+dT is proportional to T raised to the power -b for
temperatures up to 4000 K, we obtained a typical estimate of 4.5 for b. The
power-law index, b, shows variations over the range 3 to 6 within the set of
different sight-lines probed by the maps, with the majority of sight-lines
showing b in the range 4 to 5. The observed power-law index is consistent with
the predictions of simple models for paraboloidal bow shocks.Comment: 27 pages, including 11 figures. Accepted for publication in Ap
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
Missing covariate data within cancer prognostic studies: a review of current reporting and proposed guidelines
Prognostic models play a crucial role in the clinical decision-making process. Unfortunately, missing covariate data impede the construction of valid and reliable models, potentially introducing bias, if handled inappropriately. The extent of missing covariate data within reported cancer prognostic studies, the current handling and the quality of reporting this missing covariate data are unknown. Therefore, a review was conducted of 100 articles reporting multivariate survival analyses to assess potential prognostic factors, published within seven cancer journals in 2002. Missing covariate data is a common occurrence in studies performing multivariate survival analyses, being apparent in 81 of the 100 articles reviewed. The percentage of eligible cases with complete data was obtainable in 39 articles, and was <90% in 17 of these articles. The methods used to handle incomplete covariates were obtainable in 32 of the 81 articles with known missing data and the most commonly reported approaches were complete case and available case analysis. This review has highlighted deficiencies in the reporting of missing covariate data. Guidelines for presenting prognostic studies with missing covariate data are proposed, which if followed should clarify and standardise the reporting in future articles
Quadrilateral-octagon coordinates for almost normal surfaces
Normal and almost normal surfaces are essential tools for algorithmic
3-manifold topology, but to use them requires exponentially slow enumeration
algorithms in a high-dimensional vector space. The quadrilateral coordinates of
Tollefson alleviate this problem considerably for normal surfaces, by reducing
the dimension of this vector space from 7n to 3n (where n is the complexity of
the underlying triangulation). Here we develop an analogous theory for
octagonal almost normal surfaces, using quadrilateral and octagon coordinates
to reduce this dimension from 10n to 6n. As an application, we show that
quadrilateral-octagon coordinates can be used exclusively in the streamlined
3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing
experimental running times by factors of thousands. We also introduce joint
coordinates, a system with only 3n dimensions for octagonal almost normal
surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using
cohomology, plus other minor changes; v3: Minor housekeepin
Design comparison of cesium and potassium vapor turbine-generator units for space power
Design comparison of cesium and potassium vapor turbogenerator units for space power plant
Estimating the Impacts of Storage Dry Matter Losses on Switchgrass Production
This poster estimates dry matter losses as a function of harvest method, storage treatment, and time in storage. We then calculate the cost to store switchgrass bales under alternate harvest method and storage treatment scenarios; and determine the breakeven harvest method and storage treatment as a function of biomass price and time in storage.Biomass, bioenergy crops, function form, sustainable systems, Farm Management, Production Economics, Q10, Q42,
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