74 research outputs found
Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general
investigations on transformational properties of classes of differential
equations is proposed. It is based on mappings between classes of differential
equations, generated by families of point transformations. A class of variable
coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the
general form () is studied from the
symmetry point of view in the framework of the approach proposed. The singular
subclass of the equations with is singled out. The group classifications
of the entire class, the singular subclass and their images are performed with
respect to both the corresponding (generalized extended) equivalence groups and
all point transformations. The set of admissible transformations of the imaged
class is exhaustively described in the general case . The procedure of
classification of nonclassical symmetries, which involves mappings between
classes of differential equations, is discussed. Wide families of new exact
solutions are also constructed for equations from the classes under
consideration by the classical method of Lie reductions and by generation of
new solutions from known ones for other equations with point transformations of
different kinds (such as additional equivalence transformations and mappings
between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica
The Planetary Nebula Luminosity Function at the Dawn of Gaia
The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent
extragalactic standard candle. In theory, the PNLF method should not work at
all, since the luminosities of the brightest planetary nebulae (PNe) should be
highly sensitive to the age of their host stellar population. Yet the method
appears robust, as it consistently produces < 10% distances to galaxies of all
Hubble types, from the earliest ellipticals to the latest-type spirals and
irregulars. It is therefore uniquely suited for cross-checking the results of
other techniques and finding small offsets between the Population I and
Population II distance ladders. We review the calibration of the method and
show that the zero points provided by Cepheids and the Tip of the Red Giant
Branch are in excellent agreement. We then compare the results of the PNLF with
those from Surface Brightness Fluctuation measurements, and show that, although
both techniques agree in a relative sense, the latter method yields distances
that are ~15% larger than those from the PNLF. We trace this discrepancy back
to the calibration galaxies and argue that, due to a small systematic error
associated with internal reddening, the true distance scale likely falls
between the extremes of the two methods. We also demonstrate how PNLF
measurements in the early-type galaxies that have hosted Type Ia supernovae can
help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally,
we discuss how the results from space missions such as Kepler and Gaia can help
our understanding of the PNLF phenomenon and improve our knowledge of the
physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic
Distance Scale: State of the Art and Gaia Perspective", to appear in
Astrophysics and Space Scienc
Stability of the Einstein static universe in IR modified Ho\v{r}ava gravity
Recently, Horava proposed a power counting renormalizable theory for
(3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a
non-vanishing cosmological constant in IR, but possesses improved UV behaviors.
In this work, we analyze the stability of the Einstein static universe by
considering linear homogeneous perturbations in the context of an IR
modification of Horava gravity, which implies a `soft' breaking of the
`detailed balance' condition. The stability regions of the Einstein static
universe are parameterized by the linear equation of state parameter w=p/\rho
and the parameters appearing in the Horava theory, and it is shown that a large
class of stable solutions exists in the respective parameter space.Comment: 9 pages, 5 figures; references adde
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
The Physics of Star Cluster Formation and Evolution
© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe
Catching Element Formation In The Act ; The Case for a New MeV Gamma-Ray Mission: Radionuclide Astronomy in the 2020s
High Energy Astrophysic
Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures
Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo
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