13,521 research outputs found
A dynamical systems model of unorganised segregation
We consider Schelling's bounded neighbourhood model (BNM) of unorganised
segregation of two populations from the perspective of modern dynamical systems
theory. We derive a Schelling dynamical system and carry out a complete
quantitative analysis of the system for the case of a linear tolerance schedule
in both populations. In doing so, we recover and generalise Schelling's
qualitative results. For the case of unlimited population movement, we derive
exact formulae for regions in parameter space where stable integrated
population mixes can occur. We show how neighbourhood tipping can be adequately
explained in terms of basins of attraction. For the case of limiting population
movement, we derive exact criteria for the occurrence of new population mixes
and identify the stable cases. We show how to apply our methodology to
nonlinear tolerance schedules, illustrating our approach with numerical
simulations. We associate each term in our Schelling dynamical system with a
social meaning. In particular we show that the dynamics of one population in
the presence of another can be summarised as follows
{rate of population change} = {intrinsic popularity of neighbourhood} -
{finite size of neighbourhood} - {presence of other population}
By approaching the dynamics from this perspective, we have a complementary
approach to that of the tolerance schedule.Comment: 17 pages (inc references), 9 figure
Experimental demonstration of a Rydberg-atom beam splitter
Inhomogeneous electric fields generated above two-dimensional electrode
structures have been used to transversely split beams of helium Rydberg atoms
into pairs of spatially separated components. The atomic beams had initial
longitudinal speeds of between 1700 and 2000 m/s and were prepared in Rydberg
states with principle quantum number and electric dipole moments of up
to 8700 D by resonance-enhanced two-color two-photon laser excitation from the
metastable 1s2s S level. Upon exiting the beam splitter the ensembles
of Rydberg atoms were separated by up to 15.6 mm and were detected by pulsed
electric field ionization. Effects of amplitude modulation of the electric
fields of the beam splitter were shown to cause particle losses through
transitions into unconfined Rydberg-Stark states.Comment: 6 pages, 5 figure
Recommended from our members
Estimating drizzle drop size and precipitation rate using two-colour lidar measurements
A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution.
The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions
SAO/NASA joint investigation of astronomical viewing quality at Mount Hopkins Observatory: 1969-1971
Quantitative measurements of the astronomical seeing conditions have been made with a stellar-image monitor system at the Mt. Hopkins Observatory in Arizona. The results of this joint SAO-NASA experiment indicate that for a 15-cm-diameter telescope, image motion is typically 1 arcsec or less and that intensity fluctuations due to scintillation have a coefficient of irradiance variance of less than 0.12 on the average. Correlations between seeing quality and local meteorological conditions were investigated. Local temperature fluctuations and temperature gradients were found to be indicators of image-motion conditions, while high-altitude-wind conditions were shown to be somewhat correlated with scintillation-spectrum bandwidth. The theoretical basis for the relationship of atmospheric turbulence to optical effects is discussed in some detail, along with a description of the equipment used in the experiment. General site-testing comments and applications of the seeing-test results are also included
Gravitational waves from the sound of a first order phase transition
We report on the first three-dimensional numerical simulations of first-order phase transitions in the early Universe to include the cosmic fluid as well as the scalar field order parameter. We calculate the gravitational wave (GW) spectrum resulting from the nucleation, expansion, and collision of bubbles of the low-temperature phase, for phase transition strengths and bubble wall velocities covering many cases of interest. We find that the compression waves in the fluid continue to be a source of GWs long after the bubbles have merged, a new effect not taken properly into account in previous modeling of the GW source. For a wide range of models, the main source of the GWs produced by a phase transition is, therefore, the sound the bubbles make
A dynamical systems model of unorganised segregation in two neighbourhoods
We present a complete analysis of the Schelling dynamical system [Haw2018] of
two connected neighbourhoods, with or without population reservoirs, for
different types of linear and nonlinear tolerance schedules. We show that
stable integration is only possible when the minority is small and combined
tolerance is large. Unlike the case of the single neighbourhood, limiting one
population does not necessarily produce stable integration and may destroy it.
We conclude that a growing minority can only remain integrated if the majority
increases its own tolerance. Our results show that an integrated single
neighbourhood may not remain so when a connecting neighbourhood is created.Comment: 26 pages, 13 figure
A Bayesian Estimate of the Primordial Helium Abundance
We introduce a new statistical method to estimate the primordial helium
abundance, Y_p from observed abundances in a sample of galaxies which have
experienced stellar helium enrichment. Rather than using linear regression on
metal abundance we construct a likelihood function using a Bayesian prior,
where the key assumption is that the true helium abundance must always exceed
the primordial value. Using a sample of measurements compiled from the
literature we find estimates of Y_p between 0.221 and 0.236, depending on the
specific subsample and prior adopted, consistent with previous estimates either
from a linear extrapolation of the helium abundance with respect to
metallicity, or from the helium abundance of the lowest metallicity HII region,
I Zw 18. We also find an upper limit which is insensitive to the specific
subsample or prior, and estimate a model-independent bound Y_p < 0.243 at 95%
confidence, favoring a low cosmic baryon density and a high primordial
deuterium abundance. The main uncertainty is not the model of stellar
enrichment but possible common systematic biases in the estimate of Y in each
individual HII region.Comment: 14 pages, latex, 3 ps figure
Collision of High Frequency Plane Gravitational and Electromagnetic Waves
We study the head-on collision of linearly polarized, high frequency plane
gravitational waves and their electromagnetic counterparts in the
Einstein-Maxwell theory. The post-collision space-times are obtained by solving
the vacuum Einstein-Maxwell field equations in the geometrical optics
approximation. The head-on collisions of all possible pairs of these systems of
waves is described and the results are then generalised to non-linearly
polarized waves which exhibit the maximum two degrees of freedom of
polarization.Comment: Latex file, 17 pages, accepted for publication in International
Journal of Modern Physics
Interferometers as Probes of Planckian Quantum Geometry
A theory of position of massive bodies is proposed that results in an
observable quantum behavior of geometry at the Planck scale, . Departures
from classical world lines in flat spacetime are described by Planckian
noncommuting operators for position in different directions, as defined by
interactions with null waves. The resulting evolution of position wavefunctions
in two dimensions displays a new kind of directionally-coherent quantum noise
of transverse position. The amplitude of the effect in physical units is
predicted with no parameters, by equating the number of degrees of freedom of
position wavefunctions on a 2D spacelike surface with the entropy density of a
black hole event horizon of the same area. In a region of size , the effect
resembles spatially and directionally coherent random transverse shear
deformations on timescale with typical amplitude . This quantum-geometrical "holographic noise" in position is not
describable as fluctuations of a quantized metric, or as any kind of
fluctuation, dispersion or propagation effect in quantum fields. In a Michelson
interferometer the effect appears as noise that resembles a random Planckian
walk of the beamsplitter for durations up to the light crossing time. Signal
spectra and correlation functions in interferometers are derived, and predicted
to be comparable with the sensitivities of current and planned experiments. It
is proposed that nearly co-located Michelson interferometers of laboratory
scale, cross-correlated at high frequency, can test the Planckian noise
prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review
- …