135 research outputs found
Domain Walls in Two-Component Dynamical Lattices
We introduce domain-wall (DW) states in the bimodal discrete nonlinear
Schr{\"{o}}dinger equation, in which the modes are coupled by cross phase
modulation (XPM). By means of continuation from various initial patterns taken
in the anti-continuum (AC) limit, we find a number of different solutions of
the DW type, for which different stability scenarios are identified. In the
case of strong XPM coupling, DW configurations contain a single mode at each
end of the chain. The most fundamental solution of this type is found to be
always stable. Another solution, which is generated by a different AC pattern,
demonstrates behavior which is unusual for nonlinear dynamical lattices: it is
unstable for small values of the coupling constant (which measures the
ratio of the nonlinearity and coupling lengths), and becomes stable at larger
. Stable bound states of DWs are also found. DW configurations generated by
more sophisticated AC patterns are identified as well, but they are either
completely unstable, or are stable only at small values of . In the case of
weak XPM, a natural DW solution is the one which contains a combination of both
polarizations, with the phase difference between them 0 and at the
opposite ends of the lattice. This solution is unstable at all values of ,
but the instability is very weak for large , indicating stabilization as the
continuum limit is approached. The stability of DWs is also verified by direct
simulations, and the evolution of unstable DWs is simulated too; in particular,
it is found that, in the weak-XPM system, the instability may give rise to a
moving DW.Comment: 14 pages, 14 figures, Phys. Rev. E (in press
The Dynamics of Brane-World Cosmological Models
Brane-world cosmology is motivated by recent developments in string/M-theory
and offers a new perspective on the hierarchy problem. In the brane-world
scenario, our Universe is a four-dimensional subspace or {\em brane} embedded
in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are
confined to the brane while the gravitational field can also propagate in the
bulk, leading to modifications of Einstein's theory of general relativity at
high energies. In particular, the Randall-Sundrum-type models are
self-consistent and simple and allow for an investigation of the essential
non-linear gravitational dynamics. The governing field equations induced on the
brane differ from the general relativistic equations in that there are nonlocal
effects from the free gravitational field in the bulk, transmitted via the
projection of the bulk Weyl tensor, and the local quadratic energy-momentum
corrections, which are significant in the high-energy regime close to the
initial singularity. In this review we discuss the asymptotic dynamical
evolution of spatially homogeneous brane-world cosmological models containing
both a perfect fluid and a scalar field close to the initial singularity. Using
dynamical systems techniques it is found that, for models with a physically
relevant equation of state, an isotropic singularity is a past-attractor in all
orthogonal spatially homogeneous models (including Bianchi type IX models). In
addition, we describe the dynamics in a class of inhomogeneous brane-world
models, and show that these models also have an isotropic initial singularity.
These results provide support for the conjecture that typically the initial
cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ
ARIA 2016: Care pathways implementing emerging technologies for predictive medicine in rhinitis and asthma across the life cycle
The Allergic Rhinitis and its Impact on Asthma (ARIA) initiative commenced during a World Health Organization workshop in 1999. The initial goals were (1) to propose a new allergic rhinitis classification, (2) to promote the concept of multi-morbidity in asthma a
Age at first birth in women is genetically associated with increased risk of schizophrenia
Prof. Paunio on PGC:n jäsenPrevious studies have shown an increased risk for mental health problems in children born to both younger and older parents compared to children of average-aged parents. We previously used a novel design to reveal a latent mechanism of genetic association between schizophrenia and age at first birth in women (AFB). Here, we use independent data from the UK Biobank (N = 38,892) to replicate the finding of an association between predicted genetic risk of schizophrenia and AFB in women, and to estimate the genetic correlation between schizophrenia and AFB in women stratified into younger and older groups. We find evidence for an association between predicted genetic risk of schizophrenia and AFB in women (P-value = 1.12E-05), and we show genetic heterogeneity between younger and older AFB groups (P-value = 3.45E-03). The genetic correlation between schizophrenia and AFB in the younger AFB group is -0.16 (SE = 0.04) while that between schizophrenia and AFB in the older AFB group is 0.14 (SE = 0.08). Our results suggest that early, and perhaps also late, age at first birth in women is associated with increased genetic risk for schizophrenia in the UK Biobank sample. These findings contribute new insights into factors contributing to the complex bio-social risk architecture underpinning the association between parental age and offspring mental health.Peer reviewe
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