19,408 research outputs found
Some symmetry classifications of hyperbolic vector evolution equations
Motivated by recent work on integrable flows of curves and 1+1 dimensional
sigma models, several O(N)-invariant classes of hyperbolic equations for an -component vector are considered. In each
class we find all scaling-homogeneous equations admitting a higher symmetry of
least possible scaling weight. Sigma model interpretations of these equations
are presented.Comment: Revision of published version, incorporating errata on geometric
aspects of the sigma model interpretations in the case of homogeneous space
Investigating the cores of fossil systems with Chandra
We investigate the cores of fossil galaxy groups and clusters (`fossil
systems') using archival Chandra data for a sample of 17 fossil systems. We
determined the cool-core fraction for fossils via three observable diagnostics,
the central cooling time, cuspiness, and concentration parameter. We quantified
the dynamical state of the fossils by the X-ray peak/brightest cluster galaxy
(BCG), and the X-ray peak/emission weighted centre separations. We studied the
X-ray emission coincident with the BCG to detect the presence of potential
thermal coronae. A deprojection analysis was performed for z < 0.05 fossils to
obtain cooling time and entropy profiles, and to resolve subtle temperature
structures. We investigated the Lx-T relation for fossils from the 400d
catalogue to see if the scaling relation deviates from that of other groups.
Most fossils are identified as cool-core objects via at least two cool-core
diagnostics. All fossils have their dominant elliptical galaxy within 50 kpc of
the X-ray peak, and most also have the emission weighted centre within that
distance. We do not see clear indications of a X-ray corona associated with the
BCG unlike that has been observed for some other objects. Fossils do not have
universal temperature profiles, with some low-temperature objects lacking
features that are expected for ostensibly relaxed objects with a cool-core. The
entropy profiles of the z < 0.05 fossil systems can be well-described by a
power law model, albeit with indices smaller than 1. The 400d fossils Lx-T
relation shows indications of an elevated normalisation with respect to other
groups, which seems to persist even after factoring in selection effects.Comment: Accepted for publication in Astronomy and Astrophysic
Three-dimensional Binary Superlattices of Oppositely-charged Colloids
We report the equilibrium self-assembly of binary crystals of
oppositely-charged colloidal microspheres at high density. By varying the
magnitude of the charge on near equal-sized spheres we show that the structure
of the binary crystal may be switched between face-centered cubic, cesium
chloride and sodium chloride. We interpret these transformations in terms of a
competition between entropic and Coulombic forces
Reductions of integrable equations on A.III-type symmetric spaces
We study a class of integrable non-linear differential equations related to
the A.III-type symmetric spaces. These spaces are realized as factor groups of
the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to
this symmetric space as an element of the reduction group and restrict generic
Lax operators to this symmetric space. The symmetries of the Lax operator are
inherited by the fundamental analytic solutions and give a characterization of
the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl
Representations of sl(2,?) in category O and master symmetries
We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries
Radiation-induced nucleic acid synthesis in L cells under energy deprivation
Radiation induced nucleic acid synthesis in energy deprived L cell
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