2,738 research outputs found
Applications of the Gauss-Bonnet theorem to gravitational lensing
In this geometrical approach to gravitational lensing theory, we apply the
Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static,
spherically symmetric, perfect non-relativistic fluid, in the weak deflection
limit. We find that the focusing of the light rays emerges here as a
topological effect, and we introduce a new method to calculate the deflection
angle from the Gaussian curvature of the optical metric. As examples, the
Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are
discussed within this framework.Comment: 10 pages, 1 figure, IoP styl
Quantum Statistics and Slow Neutron Scattering by Gases
A surprisingly simple expression in ``closed form'' for the cross section d2Ï/dΩdÏ” for the scattering of thermal neutrons (including polarized neutrons) from an ideal quantum gas is derived. This result extends the work of Van Hove on the quantum gas. An expansion is obtained for dÏ/dÏ”. The case of elastic scattering is treated separately. From these expressions is obtained a criterion for ignoring the statistics of the scatterer in favor of classical (Boltzmann) statistics. This criterion should have some validity for weakly interacting systems. It is shown that the effects of statistics on the neutron cross section for a heliumâ4 gas range from 5% or less for the noninteracting gas up to as much as 40% for the interacting system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70882/2/JCPSA6-47-12-4923-1.pd
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Contributions to twentieth century total column ozone change from halocarbons, tropospheric ozone precursors, and climate change
We investigate ozone changes from preindustrial times
to the present using a chemistry-climate model. The
influence of changes in physical climate, ozone-depleting
substances, N2O, and tropospheric ozone precursors is estimated using equilibrium simulations with these different factors set at either preindustrial or present-day values. When these effects are combined, the entire decrease in total column ozone from preindustrial to present day is very small (â1.8 DU) in the global annual average, though with significant decreases in total column ozone over large parts of the Southern Hemisphere during austral spring and widespread increases in column ozone over the Northern Hemisphere during boreal summer. A significant contribution to the total ozone column change is the increase in lower stratospheric ozone associated with the increase in ozone precursors (5.9 DU). Also noteworthy is the near cancellation of the global average climate change effect on ozone (3.5 DU) by the increase in N2O (â3.9 DU)
Modelling the dynamical evolution of the Bootes dwarf spheroidal galaxy
We investigate a wide range of possible evolutionary histories for the
recently discovered Bootes dwarf spheroidal galaxy, a Milky Way satellite. By
means of N-body simulations we follow the evolution of possible progenitor
galaxies of Bootes for a variety of orbits in the gravitational potential of
the Milky Way. The progenitors considered cover the range from dark-matter-free
star clusters to massive, dark-matter dominated outcomes of cosmological
simulations. For each type of progenitor and orbit we compare the observable
properties of the remnant after 10 Gyr with those of Bootes observed today. Our
study suggests that the progenitor of Bootes must have been, and remains now,
dark matter dominated. In general our models are unable to reproduce the
observed high velocity dispersion in Bootes without dark matter. Our models do
not support time-dependent tidal effects as a mechanism able to inflate
significantly the internal velocity dispersion. As none of our initially
spherical models is able to reproduce the elongation of Bootes, our results
suggest that the progenitor of Bootes may have had some intrinsic flattening.
Although the focus of the present paper is the Bootes dwarf spheroidal, these
models may be of general relevance to understanding the structure, stability
and dark matter content of all dwarf spheroidal galaxies.Comment: 10 pages, 7 figures, accepted by MNRA
Orientational Defects in Ice Ih: An Interpretation of Electrical Conductivity Measurements
We present a first-principles study of the structure and energetics of
Bjerrum defects in ice Ih and compare the results to experimental electrical
conductivity data. While the DFT result for the activation energy is in good
agreement with experiment, we find that its two components have quite different
values. Aside from providing new insight into the fundamental parameters of the
microscopic electrical theory of ice, our results suggest the activity of traps
in doped ice in the temperature regime typically assumed to be controlled by
the free migration of L defects.Comment: 4 pages, 4 Figures, 1 Tabl
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Quantifying the contributions to stratospheric ozone changes from ozone depleting substances and greenhouse gases
A state-of-the-art chemistry climate model coupled to a three-dimensional ocean model is used to produce three experiments, all seamlessly covering the period 1950â2100, forced by different combinations of long-lived Greenhouse Gases (GHGs) and Ozone Depleting Substances (ODSs). The experiments are designed to quantify the separate effects of GHGs and ODSs on the evolution of ozone, as well as the extent to which these effects are independent of each other, by alternately holding one set of these two forcings constant in combination with a third experiment where both ODSs and GHGs vary. We estimate that up to the year 2000 the net decrease in the column amount of ozone above 20 hPa is approximately 75% of the decrease that can be attributed to ODSs due to the offsetting effects of cooling by increased CO2. Over the 21st century, as ODSs decrease, continued cooling from CO2 is projected to account for more than 50% of the projected increase in ozone above 20 hPa. Changes in ozone below 20 hPa show a redistribution of ozone from tropical to extra-tropical latitudes with an increase in the Brewer-Dobson circulation. In addition to a latitudinal redistribution of ozone, we find that the globally averaged column amount of ozone below 20 hPa decreases over the 21st century, which significantly mitigates the effect of upper stratospheric cooling on total column ozone. Analysis by linear regression shows that the recovery of ozone from the effects of ODSs generally follows the decline in reactive chlorine and bromine levels, with the exception of the lower polar stratosphere where recovery of ozone in the second half of the 21st century is slower than would be indicated by the decline in reactive chlorine and bromine concentrations. These results also reveal the degree to which GHGrelated effects mute the chemical effects of N2O on ozone in the standard future scenario used for the WMO Ozone Assessment. Increases in the residual circulation of the atmosphere and chemical effects from CO2 cooling more than halve the increase in reactive nitrogen in the mid to upper stratosphere that results from the specified increase in N2O between 1950 and 2100
Stable manifolds and homoclinic points near resonances in the restricted three-body problem
The restricted three-body problem describes the motion of a massless particle
under the influence of two primaries of masses and that circle
each other with period equal to . For small , a resonant periodic
motion of the massless particle in the rotating frame can be described by
relatively prime integers and , if its period around the heavier primary
is approximately , and by its approximate eccentricity . We give a
method for the formal development of the stable and unstable manifolds
associated with these resonant motions. We prove the validity of this formal
development and the existence of homoclinic points in the resonant region.
In the study of the Kirkwood gaps in the asteroid belt, the separatrices of
the averaged equations of the restricted three-body problem are commonly used
to derive analytical approximations to the boundaries of the resonances. We use
the unaveraged equations to find values of asteroid eccentricity below which
these approximations will not hold for the Kirkwood gaps with equal to
2/1, 7/3, 5/2, 3/1, and 4/1.
Another application is to the existence of asymmetric librations in the
exterior resonances. We give values of asteroid eccentricity below which
asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2
resonances for any however small. But if the eccentricity exceeds these
thresholds, asymmetric librations will exist for small enough in the
unaveraged restricted three-body problem
The construction of identities in narratives about serious leisure occupations
Engagement in occupation contributes to the shaping of identity throughout the human life. The act of telling about such engagement involves interaction based on symbolic meaning; the speaker constructing an identity by conveying how the occupation is personally meaningful. This study explored meaning in narratives told by people who engage in serious leisure occupations. A total of 78 narratives were extracted from interviews with 17 people who invest considerable time and other resources into their leisure. Analysis focused on the content, structure and performance of each narrative in order to explore meaning. The meanings were organised into a framework based around three dimensions: the located self, the active self and the changing self. Each dimension has facets that the individual might emphasise, constructing a unique identity. The framework offers a structured basis for conceptualising how occupation contributes to the shaping of the internalised self and the socially situated identity
Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction
We consider dissipative one-dimensional systems subject to a periodic force
and study numerically how a time-varying friction affects the dynamics. As a
model system, particularly suited for numerical analysis, we investigate the
driven cubic oscillator in the presence of friction. We find that, if the
damping coefficient increases in time up to a final constant value, then the
basins of attraction of the leading resonances are larger than they would have
been if the coefficient had been fixed at that value since the beginning. From
a quantitative point of view, the scenario depends both on the final value and
the growth rate of the damping coefficient. The relevance of the results for
the spin-orbit model are discussed in some detail.Comment: 30 pages, 6 figure
Understanding uncertainty in temperature effects on vector-borne disease: A Bayesian approach
Extrinsic environmental factors influence the distribution and population
dynamics of many organisms, including insects that are of concern for human
health and agriculture. This is particularly true for vector-borne infectious
diseases, like malaria, which is a major source of morbidity and mortality in
humans. Understanding the mechanistic links between environment and population
processes for these diseases is key to predicting the consequences of climate
change on transmission and for developing effective interventions. An important
measure of the intensity of disease transmission is the reproductive number
. However, understanding the mechanisms linking and temperature, an
environmental factor driving disease risk, can be challenging because the data
available for parameterization are often poor. To address this we show how a
Bayesian approach can help identify critical uncertainties in components of
and how this uncertainty is propagated into the estimate of . Most
notably, we find that different parameters dominate the uncertainty at
different temperature regimes: bite rate from 15-25 C; fecundity across
all temperatures, but especially 25-32 C; mortality from
20-30 C; parasite development rate at 15-16C and again at
33-35C. Focusing empirical studies on these parameters and
corresponding temperature ranges would be the most efficient way to improve
estimates of . While we focus on malaria, our methods apply to improving
process-based models more generally, including epidemiological, physiological
niche, and species distribution models.Comment: 27 pages, including 1 table and 3 figure
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