42,627 research outputs found
Stress Propagation and Arching in Static Sandpiles
We present a new approach to the modelling of stress propagation in static
granular media, focussing on the conical sandpile constructed from a point
source. We view the medium as consisting of cohesionless hard particles held up
by static frictional forces; these are subject to microscopic indeterminacy
which corresponds macroscopically to the fact that the equations of stress
continuity are incomplete -- no strain variable can be defined. We propose that
in general the continuity equations should be closed by means of a constitutive
relation (or relations) between different components of the (mesoscopically
averaged) stress tensor. The primary constitutive relation relates radial and
vertical shear and normal stresses (in two dimensions, this is all one needs).
We argue that the constitutive relation(s) should be local, and should encode
the construction history of the pile: this history determines the organization
of the grains at a mesoscopic scale, and thereby the local relationship between
stresses. To the accuracy of published experiments, the pattern of stresses
beneath a pile shows a scaling between piles of different heights (RSF scaling)
which severely limits the form the constitutive relation can take ...Comment: 38 pages, 24 Postscript figures, LATEX, minor misspellings corrected,
Journal de Physique I, Ref. Nr. 6.1125, accepte
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
Flatness of the setting Sun
Atmospheric refraction is responsible for the bending of light-rays in the
atmosphere. It is a result of the continuous decrease in the refractive index
of the air as a function of altitude. A well-known consequence of this
phenomenon is the apparently elliptic shape of the setting or rising Sun (or
full-Moon). In the present paper we systematically investigate this phenomenon
in a standard atmosphere. Theoretical and numerical calculations are compared
with experimental data. The asymmetric rim of the Sun is computed as a function
of its inclination angle, observational height and meteorological conditions
characterized by pressure, temperature and lapse-rate. We reveal and illustrate
some extreme and highly unusual situations.Comment: RevTex, 10 pages, 14 Figures. A web-page is accompanying this study:
http://www.fi.uib.no/~neda/sunset/index.htm
Stochastic cosmic ray sources and the TeV break in the all-electron spectrum
Despite significant progress over more than 100 years, no accelerator has
been unambiguously identified as the source of the locally measured flux of
cosmic rays. High-energy electrons and positrons are of particular importance
in the search for nearby sources as radiative energy losses constrain their
propagation to distances of about 1 kpc around 1 TeV. At the highest energies,
the spectrum is therefore dominated and shaped by only a few sources whose
properties can be inferred from the fine structure of the spectrum at energies
currently accessed by experiments like AMS-02, CALET, DAMPE, Fermi-LAT,
H.E.S.S. and ISS-CREAM. We present a stochastic model of the Galactic
all-electron flux and evaluate its compatibility with the measurement recently
presented by the H.E.S.S. collaboration. To this end, we have MC generated a
large sample of the all-electron flux from an ensemble of random distributions
of sources. We confirm the non-Gaussian nature of the probability density of
fluxes at individual energies previously reported in analytical computations.
For the first time, we also consider the correlations between the fluxes at
different energies, treating the binned spectrum as a random vector and
parametrising its joint distribution with the help of a pair-copula
construction. We show that the spectral break observed in the all-electron
spectrum by H.E.S.S. and DAMPE is statistically compatible with a distribution
of astrophysical sources like supernova remnants or pulsars, but requires a
rate smaller than the canonical supernova rate. This important result provides
an astrophysical interpretation of the spectrum at TeV energies and allows
differentiating astrophysical source models from exotic explanations, like dark
matter annihilation. We also critically assess the reliability of using
catalogues of known sources to model the electron-positron flux.Comment: 30 pages, 12 figures; extended discussion; accepted for publication
in JCA
DART-RAY: a 3D ray-tracing radiative transfer code for calculating the propagation of light in dusty galaxies
We present DART-Ray, a new ray-tracing 3D dust radiative transfer (RT) code designed specifically to calculate radiation field energy density (RFED) distributions within dusty galaxy models with arbitrary geometries. In this paper, we introduce the basic algorithm implemented in . DART-Ray which is based on a pre-calculation of a lower limit for the RFED distribution. This pre-calculation allows us to estimate the extent of regions around the radiation sources within which these sources contribute significantly to the RFED. In this way, ray-tracing calculations can be restricted to take place only within these regions, thus substantially reducing the computational time compared to a complete ray-tracing RT calculation. Anisotropic scattering is included in the code and handled in a similar fashion. Furthermore, the code utilizes a Cartesian adaptive spatial grid and an iterative method has been implemented to optimize the angular densities of the rays originated from each emitting cell. In order to verify the accuracy of the RT calculations performed by DART-Ray, we present results of comparisons with solutions obtained using the dusty 1D RT code for a dust shell illuminated by a central point source and existing 2D RT calculations of disc galaxies with diffusely distributed stellar emission and dust opacity. Finally, we show the application of the code on a spiral galaxy model with logarithmic spiral arms in order to measure the effect of the spiral pattern on the attenuation and RFED. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
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