4,910 research outputs found
Eguchi-Hanson Solitons in Odd Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added
feature of having Lorentzian signatures. They are asymptotic to
(A)dS. In the AdS case their energy is negative relative to that of
pure AdS. We present perturbative evidence in 5 dimensions that such metrics
are the states of lowest energy in their asymptotic class, and present a
conjecture that this is generally true for all such metrics. In the dS case
these solutions have a cosmological horizon. We show that their mass at future
infinity is less than that of pure dS.Comment: 26 pages, Late
A decade on where is the UK poultry industry for emergency on-farm killing?
Millions of poultry are farmed intensively every year across the United Kingdom (UK) to produce both meat and eggs. There are inevitable situations that require birds to be emergency killed on farm to alleviate pain and suffering. In Europe and the UK, emergency methods are regulated by the European Council Regulation (EC) No. 1099/2009 and The Welfare of Animals at the Time of Killing Regulations (England 2015; Scotland 2012; Wales and Northern Ireland 2014). Cervical dislocation has been reported to be the most widely used method prior to these legislative changes which took place from 1 January 2013. Based on limited scientific evidence and concern for bird welfare, these legislative changes incorporated restrictions based on bird weight for both manual (≤3 kg) and mechanical (≤5 kg) cervical dislocation, and introduced an upper limit in the number of applications for manual cervical dislocation (up to 70 birds per person per day). Furthermore, it removed methods which showed evidence of crushing injury to the neck. However, since legal reform new scientific evidence surrounding the welfare consequences of cervical dislocation and the development of novel methods for killing poultry in small numbers on farm have become available. Whether the UK poultry industry have adopted these novel methods, and whether legislative reform resulted in a change in the use of cervical dislocation in the UK remains unknown. Responses from 215 respondents working across the UK poultry industry were obtained. Despite legal reform, manual cervical dislocation remains the most prevalent method used across the UK for killing poultry on farm (used by 100% of farms) and remains the preferred method amongst respondents (81.9%). The use of alternative methods such as Livetec Nex® and captive bolt guns were available to less than half of individuals and were not frequently employed for broilers and laying hens. Our data suggests there is a lack of a clear alternative to manual cervical dislocation for individuals working with larger species and a lack of gold standard methodology. This risks bird welfare at killing and contributes to inconsistency across the industry. We suggest providing stakeholders with practical alternatives prior to imposing legislative changes and effective knowledge transfer between the scientific community and stakeholders to promote positive change and protect bird welfare
Hamiltonians separable in cartesian coordinates and third-order integrals of motion
We present in this article all Hamiltonian systems in E(2) that are separable
in cartesian coordinates and that admit a third-order integral, both in quantum
and in classical mechanics. Many of these superintegrable systems are new, and
it is seen that there exists a relation between quantum superintegrable
potentials, invariant solutions of the Korteweg-De Vries equation and the
Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy
Cosmic magnetic fields from velocity perturbations in the early Universe
We show, using a covariant and gauge-invariant charged multifluid
perturbation scheme, that velocity perturbations of the matter-dominated dust
Friedmann-Lemaitre-Robertson-Walker (FLRW) model can lead to the generation of
cosmic magnetic fields. Moreover, using cosmic microwave background (CMB)
constraints, it is argued that these fields can reach strengths of between
10^{-28} and 10^{-29} G at the time the dynamo mechanism sets in, making them
plausible seed field candidates.Comment: 11 pages, 1 figure, IOP style, minor changes and typos correcte
Symmetries of a class of nonlinear fourth order partial differential equations
In this paper we study symmetry reductions of a class of nonlinear fourth
order partial differential equations \be u_{tt} = \left(\kappa u + \gamma
u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2,
\ee where , , , and are constants. This
equation may be thought of as a fourth order analogue of a generalization of
the Camassa-Holm equation, about which there has been considerable recent
interest. Further equation (1) is a ``Boussinesq-type'' equation which arises
as a model of vibrations of an anharmonic mass-spring chain and admits both
``compacton'' and conventional solitons. A catalogue of symmetry reductions for
equation (1) is obtained using the classical Lie method and the nonclassical
method due to Bluman and Cole. In particular we obtain several reductions using
the nonclassical method which are no} obtainable through the classical method
Is backreaction really small within concordance cosmology?
Smoothing over structures in general relativity leads to a renormalisation of
the background, and potentially many other effects which are poorly understood.
Observables such as the distance-redshift relation when averaged on the sky do
not necessarily yield the same smooth model which arises when performing
spatial averages. These issues are thought to be of technical interest only in
the standard model of cosmology, giving only tiny corrections. However, when we
try to calculate observable quantities such as the all-sky average of the
distance-redshift relation, we find that perturbation theory delivers divergent
answers in the UV and corrections to the background of order unity. There are
further problems. Second-order perturbations are the same size as first-order,
and fourth-order at least the same as second, and possibly much larger, owing
to the divergences. Much hinges on a coincidental balance of 2 numbers: the
primordial power, and the ratio between the comoving Hubble scales at
matter-radiation equality and today. Consequently, it is far from obvious that
backreaction is irrelevant even in the concordance model, however natural it
intuitively seems.Comment: 28 pages. Invited contribution to Classical and Quantum Gravity
special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology
New insights on the Galactic Bulge Initial Mass Function
We have derived the Galactic bulge initial mass function of the SWEEPS field
in the mass range 0.15 1.0, using deep photometry collected
with the Advanced Camera for Surveys on the Hubble Space Telescope.
Observations at several epochs, spread over 9 years, allowed us to separate the
disk and bulge stars down to very faint magnitudes, F814W 26 mag, with a
proper-motion accuracy better than 0.5 mas/yr. This allowed us to determine the
initial mass function of the pure bulge component uncontaminated by disk stars
for this low-reddening field in the Sagittarius window. In deriving the mass
function, we took into account the presence of unresolved binaries, errors in
photometry, distance modulus and reddening, as well as the metallicity
dispersion and the uncertainties caused by adopting different theoretical
color-temperature relations. We found that the Galactic bulge initial mass
function can be fitted with two power laws with a break at M 0.56
, the slope being steeper ( = -2.410.50) for the higher
masses, and shallower ( = -1.250.20) for the lower masses. In the
high-mass range, our derived mass function agrees well with the mass function
derived for other regions of the bulge. In the low-mass range however, our mass
function is slightly shallower, which suggests that separating the disk and
bulge components is particularly important in the low-mass range. The slope of
the bulge mass function is also similar to the slope of the mass function
derived for the disk in the high-mass regime, but the bulge mass function is
slightly steeper in the low-mass regime. We used our new mass function to
derive stellar M/L values for the Galactic bulge and we obtained 2.1
2.4 and 3.1 3.6 according to different
assumptions on the slope of the IMF for masses larger than 1 .Comment: 13 pages, 8 figures, accepted for publication on Ap
New exact fronts for the nonlinear diffusion equation with quintic nonlinearities
We consider travelling wave solutions of the reaction diffusion equation with
quintic nonlinearities . If the parameters
and obey a special relation, then the criterion for the existence of a
strong heteroclinic connection can be expressed in terms of two of these
parameters. If an additional restriction is imposed, explicit front solutions
can be obtained. The approach used can be extended to polynomials whose highest
degree is odd.Comment: Revtex, 5 page
The Hamiltonian Structure of the Second Painleve Hierarchy
In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable depending on n
parameters denoted by and . We introduce new
canonical coordinates and obtain Hamiltonians for the and
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
- …