3,291 research outputs found
Potential equivalence transformations for nonlinear diffusion-convection equations
Potential equivalence transformations (PETs) are effectively applied to a
class of nonlinear diffusion-convection equations. For this class all possible
potential symmetries are classified and a theorem on connection of them with
point ones via PETs is also proved. It is shown that the known non-local
transformations between equations under consideration are nothing but PETs.
Action of PETs on sets of exact solutions of a fast diffusion equation is
investigated.Comment: 10 page
Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation
The fast diffusion equation is investigated from the
symmetry point of view in development of the paper by Gandarias [Phys. Lett. A
286 (2001) 153-160]. After studying equivalence of nonclassical symmetries with
respect to a transformation group, we completely classify the nonclassical
symmetries of the corresponding potential equation. As a result, new wide
classes of potential nonclassical symmetries of the fast diffusion equation are
obtained. The set of known exact non-Lie solutions are supplemented with the
similar ones. It is shown that all known non-Lie solutions of the fast
diffusion equation are exhausted by ones which can be constructed in a regular
way with the above potential nonclassical symmetries. Connection between
classes of nonclassical and potential nonclassical symmetries of the fast
diffusion equation is found.Comment: 13 pages, section 3 is essentially revise
Formation of Millisecond Pulsars in Globular Clusters
In this contribution we discuss how neutron stars are produced and retained
in globular clusters, outlining the most important dynamical channels and
evolutionary events that affect thepopulation of mass-transferring binaries
with neutron stars and result in the formation of recycled pulsars. We confirm
the importance of electron-capture supernovae in globular clusters as the major
supplier of retained neutron stars.By comparing the observed millisecond pulsar
population and the results obtained from simulations, we discuss several
constraints on the evolution of mass-transferring systems.In particular, we
find that in our cluster model the following mass-gaining events create
populations of MSPs that do not match the observations (with respect to binary
periods and companion masses or the number of produced systems) and therefore
likely do not lead to NSs spun up to millisecond periods: (i) accretion during
a common envelope event with a NS formed through accretion-induced collapse,
and (ii) mass transfer from a WD donor. By restricting ourselves to the
evolutionary and dynamical paths that most likely lead to neutron star
recycling, we obtain good agreement between our models and the numbers and
characteristics of observed millisecond pulsars in the clusters Terzan 5 and 47
Tuc.Comment: 6 pages, 3 figures, to appear in the proceedings of the 40 Years of
Pulsars conference held at McGill University in August 200
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