25,139 research outputs found
Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice
In first-passage percolation on the integer lattice, the Shape Theorem
provides precise conditions for convergence of the set of sites reachable
within a given time from the origin, once rescaled, to a compact and convex
limiting shape. Here, we address convergence towards an asymptotic shape for
cone-like subgraphs of the lattice, where . In particular, we
identify the asymptotic shapes associated to these graphs as restrictions of
the asymptotic shape of the lattice. Apart from providing necessary and
sufficient conditions for - and almost sure convergence towards this
shape, we investigate also stronger notions such as complete convergence and
stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the
old. The main results have been strengthened and an earlier error in the
statement corrected. To appear in J. Theoret. Proba
Backpack VLBI terminal with subscentimeter capability
Backpack portable equipment was developed to measure vector baseline from approximately 1 km to 100 km in length with subcentimeter to few centimeter accuracy. The equipment design features as well as the instrumentation specifications are discussed. It is shown that the unit has the following advantages: it is simple in concept; it is reliable in unattended operation; and it is inexpensive (less than $15,000 per unit)
Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling
We propose simple, explicit, analytical approximations for the kinematics of
an adiabatic blast wave propagating in an exponentially stratified ambient
medium, and for the onset of radiative cooling, which ends the adiabatic era.
Our method, based on the Kompaneets implicit solution and the Kahn
approximation for the radiative cooling coefficient, gives straightforward
estimates for the size, expansion velocity, and progression of cooling times
over the surface, when applied to supernova remnants (SNRs). The remnant shape
is remarkably close to spherical for moderate density gradients, but even a
small gradient in ambient density causes the cooling time to vary substantially
over the remnant's surface, so that for a considerable period there will be a
cold dense expanding shell covering only a part of the remnant. Our
approximation provides an effective tool for identifying the approximate
parameters when planning 2-dimensional numerical models of SNRs, the example of
W44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with
ecmatex.sty and lscape.sty package
3D Simulations of MHD Jet Propagation Through Uniform and Stratified External Environments
We present a set of high-resolution 3D MHD simulations of steady light,
supersonic jets, exploring the influence of jet Mach number and the ambient
medium on jet propagation and energy deposition over long distances. The
results are compared to simple self-similar scaling relations for the
morphological evolution of jet-driven structures and to previously published 2D
simulations. For this study we simulated the propagation of light jets with
internal Mach numbers 3 and 12 to lengths exceeding 100 initial jet radii in
both uniform and stratified atmospheres.
The propagating jets asymptotically deposit approximately half of their
energy flux as thermal energy in the ambient atmosphere, almost independent of
jet Mach number or the external density gradient. Nearly one-quarter of the jet
total energy flux goes directly into dissipative heating of the ICM, supporting
arguments for effective feedback from AGNs to cluster media. The remaining
energy resides primarily in the jet and cocoon structures. Despite having
different shock distributions and magnetic field features, global trends in
energy flow are similar among the different models.
As expected the jets advance more rapidly through stratified atmospheres than
uniform environments. The asymptotic head velocity in King-type atmospheres
shows little or no deceleration. This contrasts with jets in uniform media with
heads that are slowed as they propagate. This suggests that the energy
deposited by jets of a given length and power depends strongly on the structure
of the ambient medium. While our low-Mach jets are more easily disrupted, their
cocoons obey evolutionary scaling relations similar to the high-Mach jets.Comment: Accepted in ApJ, 32 pages, 18 figures, animations available from:
http://www.msi.umn.edu/Projects/twj/newsite/projects/radiojets/movies
Closed form solution for a double quantum well using Gr\"obner basis
Analytical expressions for spectrum, eigenfunctions and dipole matrix
elements of a square double quantum well (DQW) are presented for a general case
when the potential in different regions of the DQW has different heights and
effective masses are different. This was achieved by Gr\"obner basis algorithm
which allows to disentangle the resulting coupled polynomials without
explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo
Development and Testing of Relative Risk-based Health Messages for Electronic Cigarette Products
Background: Health messages on e-cigarette packs emphasise nicotine addiction or harms using similar wording to warnings on cigarette packs. These may not be appropriate for e-cigarettes which constitute a reduced risk alternative for smokers. This research aimed to i) develop and test a selection of relative risk messages for e-cigarette products; ii) compare these to the two current EU Tobacco Products Directive (TPD) nicotine addiction messages; and iii) explore differences between smokers, non-smokers and dual users.
Method: Twenty-six messages focusing on either harm-reduction or cessation were developed and rated by multidisciplinary experts for accuracy, persuasiveness and clarity. The eight highest ranking messages were compared alongside the TPD messages in a sample of 983 European residents (316 smokers, 327 non-smokers, 340 dual users) on understandability, believability and convincingness.
Results: On all three constructs combined, the two TPD messages rated the highest, closely followed by four relative risk messages âCompletely switching to e-cigarettes lowers your risk of smoking related diseasesâ, âUse of this product is much less harmful than smokingâ, âCompletely switching to e-cigarettes is a healthier alternative to smokingâ, and âThis product presents substantially lower risks to health than cigarettesâ which did not differ statistically from the TPD messages. Non-smokers rated TPD1 significantly higher overall than dual users. Dual users rated âThis product is a safer alternative to smokingâ significantly higher than non-smokers. Messages did not differ on understandability.
Conclusions: These alternative messages provide a useful resource for future research and for policy makers considering updating e-cigarette product labelling
Consistency of the Shannon entropy in quantum experiments
The consistency of the Shannon entropy, when applied to outcomes of quantum
experiments, is analysed. It is shown that the Shannon entropy is fully
consistent and its properties are never violated in quantum settings, but
attention must be paid to logical and experimental contexts. This last remark
is shown to apply regardless of the quantum or classical nature of the
experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published
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