31,321 research outputs found
On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables
The distribution of the sum of independent identically distributed uniform
random variables is well-known. However, it is sometimes necessary to analyze
data which have been drawn from different uniform distributions. By inverting
the characteristic function, we derive explicit formulae for the distribution
of the sum of n non-identically distributed uniform random variables in both
the continuous and the discrete case. The results, though involved, have a
certain elegance. As examples, we derive from our general formulae some special
cases which have appeared in the literature.Comment: 20 page
MANAGING NUTRIENT LOSSES: SOME EMPIRICAL RESULTS ON THE POTENTIAL WATER QUALITY EFFECTS
Over-application of manure on cropland can cause water quality degradation. This paper reports a modeling approach for assessing tradeoffs among manure storage and handling systems as they relate to the nutrient loadings in cropland runoff, including nitrate losses to groundwater. The CREAMS simulation model provided estimates of nutrient losses. A linear optimization model was used to determine the income-nutrient loss tradeoffs. Six-month storage was profitable for farmers with average-size dairy herds, but compared to daily spreading caused increased nitrate leaching through the soil to groundwater resources. Twelve-month storage systems decreased farm profitability while decreasing the total nitrogen losses from farm fields.Environmental Economics and Policy,
A Gamma Ray Burst with a 220 Microsecond Rise Time and a Sharp Spectral Cutoff
The Gamma Ray Burst GRB920229 has four extreme and unprecedented properties;
a rise in brightness with an e-folding time scale of , a fall
in brightness with an e-folding time scale of , a large
change in spectral shape over a time of , and a sharp spectral
cutoff to high energies with . The rapid changes occur
during a spike in the light curve which was seen 0.164 s after the start of the
burst. The spectrum has a peak at 200 keV with no significant
flux above 239 keV, although the cutoff energy shifts to less than 100 keV
during the decay of the spike. These numbers can be used to place severe limits
on fireball models of bursts. The thickness of the energy production region
must be smaller than , ejected shells must have a dispersion of the
Lorentz factor of less than roughly 1% along a particular radius, and the
angular size of the radiation emission region is of order 1 arc-minute as
viewed from the burst center. The physical mechanism that caused the sharp
spectral cutoff has not been determined.Comment: 20 pages, 3 figures, Submitted to ApJ
Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models
The O(3) symmetric Anderson model is an example of a system which has a
stable low energy marginal Fermi liquid fixed point for a certain choice of
parameters. It is also exactly equivalent, in the large U limit, to a localized
model which describes the spin degrees of freedom of the linear dispersion two
channel Kondo model. We first use an argument based on conformal field theory
to establish this precise equivalence with the two channel model. We then use
the numerical renormalization group (NRG) approach to calculate both
one-electron and two-electron response functions for a range of values of the
interaction strength U. We compare the behaviours about the marginal Fermi
liquid and Fermi liquid fixed points and interpret the results in terms of a
renormalized Majorana fermion picture of the elementary excitations. In the
marginal Fermi liquid case the spectral densities of all the Majorana fermion
modes display a |omega| dependence on the lowest energy scale, and in addition
the zero Majorana mode has a delta function contribution. The weight of this
delta function is studied as a function of the interaction U and is found to
decrease exponentially with U for large U. Using the equivalence with the two
channel Kondo model in the large U limit, we deduce the dynamical spin
susceptibility of the two channel Kondo model over the full frequency range. We
use renormalized perturbation theory to interpret the results and to calculate
the coefficient of the ln omega divergence found in the low frequency behaviour
of the T=0 dynamic susceptibility.Comment: 26 pages, 18 figures, to be published in Eur. Phys. J.
Neutrino Capture and r-Process Nucleosynthesis
We explore neutrino capture during r-process nucleosynthesis in
neutrino-driven ejecta from nascent neutron stars. We focus on the interplay
between charged-current weak interactions and element synthesis, and we
delineate the important role of equilibrium nuclear dynamics. During the period
of coexistence of free nucleons and light and/or heavy nuclei, electron
neutrino capture inhibits the r-process. At all stages, capture on free
neutrons has a larger impact than capture on nuclei. However, neutrino capture
on heavey nuclei by itself, if it is very strong, is also detrimental to the
r-process until large nuclear equilibrium clusters break down and the classical
neutron-capture phase of the r-process begins. The sensitivity of the r-process
to neutrino irradiation means that neutrino-capture effects can strongly
constrain the r-process site, neutrino physics, or both. These results apply
also to r-process scenarios other than neutrino-heated winds.Comment: 20 pages, 17 figures, Submitted to Physical Review
Axistationary perfect fluids -- a tetrad approach
Stationary axisymmetric perfect fluid space-times are investigated using the
curvature description of geometries. Attention is focused on space-times with a
vanishing electric part of the Weyl tensor. It is shown that the only
incompressible axistationary magnetic perfect fluid is the interior
Schwarzschild solution. The existence of a rigidly rotating perfect fluid,
generalizing the interior Schwarzschild metric is proven. Theorems are stated
on Petrov types and electric/magnetic Weyl tensors.Comment: 12 page
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