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 $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ 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