13,852 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
Equilibrium Temperature Structure in the Mesosphere and Lower Thermosphere
Radiative equilibrium temperature structure in earth mesosphere and lower thermospher
The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
We consider a non-autonomous dynamical system formed by coupling two
piecewise-smooth systems in \RR^2 through a non-autonomous periodic
perturbation. We study the dynamics around one of the heteroclinic orbits of
one of the piecewise-smooth systems. In the unperturbed case, the system
possesses two normally hyperbolic invariant manifolds of dimension two
with a couple of three dimensional heteroclinic manifolds between them. These
heteroclinic manifolds are foliated by heteroclinic connections between
tori located at the same energy levels. By means of the {\em impact map} we
prove the persistence of these objects under perturbation. In addition, we
provide sufficient conditions of the existence of transversal heteroclinic
intersections through the existence of simple zeros of Melnikov-like functions.
The heteroclinic manifolds allow us to define the {\em scattering map}, which
links asymptotic dynamics in the invariant manifolds through heteroclinic
connections. First order properties of this map provide sufficient conditions
for the asymptotic dynamics to be located in different energy levels in the
perturbed invariant manifolds. Hence we have an essential tool for the
construction of a heteroclinic skeleton which, when followed, can lead to the
existence of Arnol'd diffusion: trajectories that, on large time scales,
destabilize the system by further accumulating energy. We validate all the
theoretical results with detailed numerical computations of a mechanical system
with impacts, formed by the linkage of two rocking blocks with a spring
Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems
In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study
Time-delayed models of gene regulatory networks
We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems
Driving Rydberg-Rydberg transitions from a co-planar microwave waveguide
The coherent interaction between ensembles of helium Rydberg atoms and
microwave fields in the vicinity of a solid-state co-planar waveguide is
reported. Rydberg-Rydberg transitions, at frequencies between 25 GHz and 38
GHz, have been studied for states with principal quantum numbers in the range
30 - 35 by selective electric-field ionization. An experimental apparatus
cooled to 100 K was used to reduce effects of blackbody radiation.
Inhomogeneous, stray electric fields emanating from the surface of the
waveguide have been characterized in frequency- and time-resolved measurements
and coherence times of the Rydberg atoms on the order of 250 ns have been
determined.Comment: 5 pages, 5 figure
Gravity Waves from a Cosmological Phase Transition: Gauge Artifacts and Daisy Resummations
The finite-temperature effective potential customarily employed to describe
the physics of cosmological phase transitions often relies on specific gauge
choices, and is manifestly not gauge-invariant at finite order in its
perturbative expansion. As a result, quantities relevant for the calculation of
the spectrum of stochastic gravity waves resulting from bubble collisions in
first-order phase transitions are also not gauge-invariant. We assess the
quantitative impact of this gauge-dependence on key quantities entering
predictions for gravity waves from first order cosmological phase transitions.
We resort to a simple abelian Higgs model, and discuss the case of R_xi gauges.
By comparing with results obtained using a gauge-invariant Hamiltonian
formalism, we show that the choice of gauge can have a dramatic effect on
theoretical predictions for the normalization and shape of the expected gravity
wave spectrum. We also analyze the impact of resumming higher-order
contributions as needed to maintain the validity of the perturbative expansion,
and show that doing so can suppress the amplitude of the spectrum by an order
of magnitude or more. We comment on open issues and possible strategies for
carrying out "daisy resummed" gauge invariant computations in non-Abelian
models for which a gauge-invariant Hamiltonian formalism is not presently
available.Comment: 25 pages, 10 figure
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