7,936 research outputs found
Extremal polynomials in stratified groups
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials tre related to a new algebraic characterization of abnormal sub-Riemannian extremals in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations, in both normal and abnormal case
Force sensor for chameleon and Casimir force experiments with parallel-plate configuration
The search for non-Newtonian forces has been pursued following many different
paths. Recently it was suggested that hypothetical chameleon interactions,
which might explain the mechanisms behind dark energy, could be detected in a
high-precision force measurement. In such an experiment, interactions between
parallel plates kept at constant separation could be measured as a function of
the pressure of an ambient gas, thereby identifying chameleon interactions by
their unique inverse dependence on the local mass density. During the past
years we have been developing a new kind of setup complying with the high
requirements of the proposed experiment. In this article we present the first
and most important part of this setup -- the force sensor. We discuss its
design, fabrication, and characterization. From the results of the latter we
derive limits on chameleon interaction parameters that could be set by the
forthcoming experiment. Finally, we describe the opportunity to use the same
setup to measure Casimir forces at large surface separations with unprecedented
accuracy, thereby potentially giving unambiguous answers to long standing open
questions
Effective thermal dynamics following a quantum quench in a spin chain
We study the nonequilibrium dynamics of the Quantum Ising Model following an
abrupt quench of the transverse field. We focus on the on-site autocorrelation
function of the order parameter, and extract the phase coherence time
from its asymptotic behavior. We show that the initial state
determines only through an effective temperature set by its
energy and the final Hamiltonian. Moreover, we observe that the dependence of
on the effective temperature fairly agrees with that obtained
in thermal equilibrium as a function of the equilibrium temperature.Comment: 4 pages, 4 figures. Published versio
Hypercompact stellar clusters: morphological renditions and spectro-photometric models
Numerical relativity predicts that the coalescence of a black hole-binary
causes the newly formed black hole to recoil, and evidence for such recoils has
been found in the gravitational waves observed during the merger of
stellar-mass black holes. Recoiling (super)massive black holes are expected to
reside in hypercompact stellar clusters (HCSCs). Simulations of galaxy assembly
predict that hundreds of HCSCs should be present in the halo of a Milky
Way-type galaxy, and a fraction of those around the Milky Way should have
magnitudes within the sensitivity limit of existing surveys. However, recoiling
black holes and their HCSCs are still waiting to be securely identified. With
the goal of enabling searches through recent and forthcoming databases, we
improve over existing literature to produce realistic renditions of HCSCs bound
to black holes with a mass of 10 M. Including the effects of a
population of blue stragglers, we simulate their appearance in Pan-STARRS and
in forthcoming images. We also derive broad-band spectra and the
corresponding multi-wavelength colours, finding that the great majority of the
simulated HCSCs fall on the colour-colour loci defined by stars and galaxies,
with their spectra resembling those of giant K-type stars. We discuss the
clusters properties, search strategies, and possible interlopers.Comment: Accepted for publication on MNRAS, 17 pages, 7 figure
A Simple Generative Model of Collective Online Behaviour
Human activities increasingly take place in online environments, providing
novel opportunities for relating individual behaviours to population-level
outcomes. In this paper, we introduce a simple generative model for the
collective behaviour of millions of social networking site users who are
deciding between different software applications. Our model incorporates two
distinct components: one is associated with recent decisions of users, and the
other reflects the cumulative popularity of each application. Importantly,
although various combinations of the two mechanisms yield long-time behaviour
that is consistent with data, the only models that reproduce the observed
temporal dynamics are those that strongly emphasize the recent popularity of
applications over their cumulative popularity. This demonstrates---even when
using purely observational data without experimental design---that temporal
data-driven modelling can effectively distinguish between competing microscopic
mechanisms, allowing us to uncover new aspects of collective online behaviour.Comment: Updated, with new figures and Supplementary Informatio
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